Finite Group Databasebeta

← #33972209

Subgroups — #33972209

Order 18688.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624249C211yesmaximal, characteristic, complemented
2#22623593C211yesmaximal, characteristic, complemented
3#22622088C211yesmaximal, characteristic, complemented
4#22621953C211yesmaximal, characteristic, complemented
5#22621930C211yesmaximal, characteristic, complemented
6#22621915C211yesmaximal, characteristic, complemented
7#22621877C211yesmaximal, characteristic, complemented
8#22621819C211yesmaximal, characteristic, complemented
9#22621785C211yesmaximal, characteristic, complemented
10#22621737C211yesmaximal, characteristic, complemented
11#22621684C211yesmaximal, characteristic, complemented
12#22621641C211yesmaximal, characteristic, complemented
13#22621616C211yesmaximal, characteristic, complemented
14D8×C22⋊D73C211yesmaximal, characteristic, complemented
15#22621469C211yesmaximal, characteristic, complemented
16#22621465C211yesmaximal, characteristic, complemented
17#22621420C211yesmaximal, characteristic, complemented
18#22621409C211yesmaximal, characteristic, complemented
19#22621021C211yesmaximal, characteristic, complemented
20#22620977C211yesmaximal, characteristic, complemented
21#22620833C211yesmaximal, characteristic, complemented
22#22620783C211yesmaximal, characteristic, complemented
23#22620693C211yesmaximal, characteristic, complemented
24#22620680C211yesmaximal, characteristic, complemented
25#22620186C211yesmaximal, characteristic, complemented
26#22620123C211yesmaximal, characteristic, complemented
27#22619235C211yesmaximal, characteristic, complemented
28#22619146C211yesmaximal, characteristic, complemented
29#449×D73C211yesmaximal, characteristic, complemented
30#22618983C211yesmaximal, characteristic, complemented
31C73×#3008C211yesmaximal, characteristic, complemented
32C2×#41×D73C2211yescharacteristic, complemented
33C2×#14556617C2211yescharacteristic, complemented
34C2×#14556612C2211yescharacteristic, complemented
35C2×#14556611C2211yescharacteristic, complemented
36C2×#14556610C2211yescharacteristic, complemented
37C2×SD16×D73C2211yescharacteristic, complemented
38C2×D8×D73C2211yescharacteristic, complemented
39#17989331—21no—
40#17989326—21no—
41#17989300C2211yescharacteristic, complemented
42#17989289C2211yescharacteristic, complemented
43#17989276C2211yescharacteristic, complemented
44#17989267—21no—
45#17989256C2211yescharacteristic, complemented
46#17989256C2211yescharacteristic, complemented
47#17989255C2211yescharacteristic, complemented
48#17989244C2211yescharacteristic
49#17989244C2211yescharacteristic, complemented
50#17989237C2211yescharacteristic, complemented
51#17989234C2211yescharacteristic, complemented
52#17989231—21no—
53#17989231—21no—
54#17989231C2211yescharacteristic, complemented
55#17989231C2211yescharacteristic, complemented
56#17989231C2211yescharacteristic, complemented
57#17989224—21no—
58D4×C22⋊D73—21no—
59D4×C22⋊D73—21no—
60D4×C22⋊D73C2211yescharacteristic
61D4×C22⋊D73C2211yescharacteristic, complemented
62D4×C22⋊D73C2211yescharacteristic, complemented
63#17989204C2211yescharacteristic, complemented
64#17989191—21no—
65#17989190C2211yescharacteristic, complemented
66#17989172—21no—
67#17989165—21no—
68#17989165C2211yescharacteristic, complemented
69#17989165C2211yescharacteristic, complemented
70#17989154—21no—
71#17989154C2211yescharacteristic, complemented
72#17989150—21no—
73#17989147—21no—
74#17989097C2211yescharacteristic, complemented
75#17989094—21no—
76#17989094C2211yescharacteristic
77C2×#14556562—21no—
78C2×#14556562C2211yescharacteristic, complemented
79#121×D73C2211yescharacteristic, complemented
80#17989070C2211yescharacteristic, complemented
81#17988975C2211yescharacteristic, complemented
82#17988975C2211yescharacteristic, complemented
83#17988970C2211yescharacteristic, complemented
84#17988962C2211yescharacteristic, complemented
85#17988950C2211yescharacteristic, complemented
86#17988945C2211yescharacteristic, complemented
87#17988940C2211yescharacteristic, complemented
88#17988932C2211yescharacteristic, complemented
89#17988928C2211yescharacteristic, complemented
90#17988923C2211yescharacteristic, complemented
91#17988923C2211yescharacteristic, complemented
92#17988911C2211yescharacteristic, complemented
93#17988909C2211yescharacteristic, complemented
94#17988909C2211yescharacteristic, complemented
95#17988903C2211yescharacteristic, complemented
96#17988901C2211yescharacteristic, complemented
97#17988901C2211yescharacteristic, complemented
98#17988899C2211yescharacteristic, complemented
99#17988899C2211yescharacteristic, complemented
100#17988898C2211yescharacteristic, complemented
101#17988896C2211yescharacteristic, complemented
102#17988885C2211yescharacteristic, complemented
103#17988880C2211yescharacteristic, complemented
104#17988865C2211yescharacteristic, complemented
105#17988838C2211yescharacteristic, complemented
106#17988833C2211yescharacteristic, complemented
107#17988833C2211yescharacteristic, complemented
108#17988831C2211yescharacteristic, complemented
109#17988828C2211yescharacteristic, complemented
110#17988823C2211yescharacteristic, complemented
111#17988822C2211yescharacteristic, complemented
112#17988822C2211yescharacteristic, complemented
113#17988821C2211yescharacteristic, complemented
114#17988820C2211yescharacteristic, complemented
115#17988820C2211yescharacteristic, complemented
116#17988820C2211yescharacteristic, complemented
117#17988820C2211yescharacteristic, complemented
118#17988815C2211yescharacteristic, complemented
119#17988815C2211yescharacteristic, complemented
120#17988814C2211yescharacteristic, complemented
121#17988808C2211yescharacteristic, complemented
122#17988807C2211yescharacteristic, complemented
123#17988801C2211yescharacteristic, complemented
124#17988800C2211yescharacteristic, complemented
125#17988800C2211yescharacteristic, complemented
126#17988800C2211yescharacteristic, complemented
127#17988786C2211yescharacteristic, complemented
128#17988785C2211yescharacteristic, complemented
129#17988781C2211yescharacteristic, complemented
130#17988780C2211yescharacteristic, complemented
131#17988780C2211yescharacteristic, complemented
132#17988780C2211yescharacteristic, complemented
133#17988751C2211yescharacteristic, complemented
134#17988751C2211yescharacteristic, complemented
135#17988749C2211yescharacteristic, complemented
136#17988749C2211yescharacteristic, complemented
137#17988744C2211yescharacteristic, complemented
138#17988739C2211yescharacteristic, complemented
139#17988738C2211yescharacteristic, complemented
140#17988738C2211yescharacteristic, complemented
141#17988738C2211yescharacteristic, complemented
142#17988735C2211yescharacteristic, complemented
143#17988734C2211yescharacteristic, complemented
144#17988734C2211yescharacteristic, complemented
145#17988733C2211yescharacteristic, complemented
146#17988732C2211yescharacteristic, complemented
147#17988732C2211yescharacteristic, complemented
148#17988731C2211yescharacteristic, complemented
149#17988730C2211yescharacteristic, complemented
150#17988730C2211yescharacteristic, complemented
151#17988729C2211yescharacteristic, complemented
152#17988729C2211yescharacteristic, complemented
153#17988729C2211yescharacteristic, complemented
154#17988724C2211yescharacteristic, complemented
155#17988721C2211yescharacteristic, complemented
156#17988721C2211yescharacteristic, complemented
157#17988721C2211yescharacteristic, complemented
158#17988719C2211yescharacteristic, complemented
159#17988719C2211yescharacteristic, complemented
160#17988719C2211yescharacteristic, complemented
161#17988696C2211yescharacteristic, complemented
162#17988688C2211yescharacteristic, complemented
163#17988688C2211yescharacteristic, complemented
164#17988684C2211yescharacteristic, complemented
165#17988679C2211yescharacteristic, complemented
166#17988672C2211yescharacteristic, complemented
167D8×Dic73C2211yescharacteristic, complemented
168D8×Dic73C2211yescharacteristic, complemented
169#17988661C2211yescharacteristic, complemented
170#17988661C2211yescharacteristic, complemented
171#17988656C2211yescharacteristic, complemented
172#17988656C2211yescharacteristic, complemented
173C8×C22⋊D73C2211yescharacteristic, complemented
174C8×C22⋊D73C2211yescharacteristic, complemented
175#17988650C2211yescharacteristic, complemented
176#17988650C2211yescharacteristic, complemented
177#17988645C2211yescharacteristic, complemented
178#17988645C2211yescharacteristic, complemented
179#17988588C2211yescharacteristic, complemented
180#17988582C2211yescharacteristic, complemented
181#17988580C2211yescharacteristic, complemented
182#103×D73C2211yescharacteristic, complemented
183C2×#14556512C2211yescharacteristic, complemented
184#102×D73C2211yescharacteristic, complemented
185#17988554C2211yescharacteristic, complemented
186C22⋊C8×D73C2211yescharacteristic, complemented
187C22⋊C8×D73C2211yescharacteristic, complemented
188C2×H(5,𝔽2)×C73C2211yescharacteristic, complemented
189C2×AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
190C22×D8×C73C2211yescharacteristic, complemented
191#535×C73C2211yescharacteristic, complemented
192#449×C73C2211yescharacteristic
193#449×C73C2211yescharacteristic, complemented
194#449×C73C2211yescharacteristic, complemented
195#449×C73C2211yescharacteristic, complemented
196#447×C73C2211yescharacteristic, complemented
197#447×C73C2211yescharacteristic, complemented
198#447×C73C2211yescharacteristic, complemented
199#447×C73C2211yescharacteristic, complemented
200#418×C73C2211yescharacteristic, complemented
201#416×C73C2211yescharacteristic, complemented
202#408×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924028—21no—
205C2×#11924028C2311yescharacteristic
206C2×#11924028C2311yescharacteristic
207C2×#11924027—21no—
208C2×#11924027—21no—
209C2×#11924027C2311yescharacteristic
210C2×#11924027C2311yescharacteristic
211#41×D73—42no—
212#41×D73—42no—
213C2×Q8×D73C2311yescharacteristic
214C22×C22⋊D73—21no—
215C22×C22⋊D73—21no—
216C22×C22⋊D73—21no—
217C22×C22⋊D73—21no—
218C2×D4×D73—21no—
219C2×D4×D73—21no—
220C2×D4×D73C2311yescharacteristic
221C2×D4×D73C2311yescharacteristic
222C22×C4×D73—21no—
223C22×C4×D73C2311yescharacteristic
224#14556617—42no—
225#14556612—42no—
226#14556611—42no—
227#14556610—42no—
228C2×Dic292C2311yescharacteristic
229C2×#11924018C2311yescharacteristic
230C2×#11924017C2311yescharacteristic
231C2×#11924017C2311yescharacteristic
232C2×#11924016C2311yescharacteristic
233C2×#11924016C2311yescharacteristic
234C2×#11924016C2311yescharacteristic
235C2×#11924016C2311yescharacteristic
236C2×#11924016C2311yescharacteristic
237C2×#11924015C2311yescharacteristic
238SD16×D73—42no—
239C2×D584C2311yescharacteristic
240C2×#11924013C2311yescharacteristic
241C2×#11924013C2311yescharacteristic
242C2×#11924013C2311yescharacteristic
243C2×#11924013C2311yescharacteristic
244C2×#11924013C2311yescharacteristic
245D8×D73—42no—
246C2×#11924012C2311yescharacteristic
247C22×#10596831C2311yescharacteristic
248C2×C8×D73C2311yescharacteristic
249C2×C8×D73C2311yescharacteristic
250C2×C8×D73C2311yescharacteristic
251C2×C8×D73C2311yescharacteristic
252#14556590C2311yescharacteristic
253#14556587—21no—
254#14556587—21no—
255#14556587—21no—
256#14556587C2311yescharacteristic
257#14556587C2311yescharacteristic
258#14556587C2311yescharacteristic
259#14556584—21no—
260#14556584—21no—
261#14556584—21no—
262#14556583—21no—
263#14556582C2311yescharacteristic
264#14556579—21no—
265#14556578—21no—
266#14556578—21no—
267#14556578—21no—
268#14556578C2311yescharacteristic
269#14556578C2311yescharacteristic
270#14556578C2311yescharacteristic
271#14556577—21no—
272#14556575—21no—
273#14556575—21no—
274#14556573—21no—
275#14556573—21no—
276#14556573—21no—
277#14556573—21no—
278#14556573—21no—
279#14556572—21no—
280#14556572—21no—
281#14556572—21no—
282#14556572—21no—
283#14556572—21no—
284#14556572D411yescharacteristic
285#14556572D411yescharacteristic
286#14556571C2311yescharacteristic
287#14556570—21no—
288#14556570—21no—
289#14556570C2311yescharacteristic
290#14556570C2311yescharacteristic
291#14556570C2311yescharacteristic
292#14556570C2311yescharacteristic
293#14556568—21no—
294#14556568—21no—
295#14556567—21no—
296#14556567—21no—
297#14556567D411yescharacteristic
298#14556567D411yescharacteristic
299#14556566C2311yescharacteristic
300#14556565—21no—
301#14556565—21no—
302#14556565C2311yescharacteristic
303#14556565C2311yescharacteristic
304#14556565C2311yescharacteristic
305#14556565C2311yescharacteristic
306#14556564—21no—
307#14556564—21no—
308#14556564—21no—
309#14556563—21no—
310#14556563—21no—
311#14556563—21no—
312#14556563—21no—
313#14556563—21no—
314#14556563—21no—
315#14556563—21no—
316#14556563—21no—
317#14556563—21no—
318#14556563—21no—
319#14556563—21no—
320#14556563—21no—
321#14556563—21no—
322#14556563—21no—
323#14556562—21no—
324#14556562—21no—
325#14556562—21no—
326#14556562—21no—
327#14556562—21no—
328#14556562—21no—
329#14556562—21no—
330#14556562—21no—
331#14556562—21no—
332#14556562—21no—
333#14556562—21no—
334#14556562—21no—
335#14556562D411yescharacteristic
336#14556562D411yescharacteristic
337#14556562C2311yescharacteristic
338#14556562C2311yescharacteristic
339#14556562C2311yescharacteristic
340#14556562C2311yescharacteristic
341#14556562C2311yescharacteristic
342#14556562C2311yescharacteristic
343#14556560—21no—
344#14556560—21no—
345#14556560—21no—
346#14556560—21no—
347#14556560—21no—
348#14556560—21no—
349#14556560—21no—
350#14556560—21no—
351#14556559—21no—
352#14556559—21no—
353#14556559—21no—
354#14556559—21no—
355#14556559—21no—
356#14556559D411yescharacteristic
357#14556559D411yescharacteristic
358Q8×Dic73C2311yescharacteristic
359Q8×Dic73C2311yescharacteristic
360#14556556C2311yescharacteristic
361D4×Dic73—21no—
362D4×Dic73—21no—
363D4×Dic73—21no—
364D4×Dic73—21no—
365D4×Dic73C2311yescharacteristic
366D4×Dic73C2311yescharacteristic
367D4×Dic73C2311yescharacteristic
368D4×Dic73C2311yescharacteristic
369#14556553C2311yescharacteristic
370C4×C22⋊D73—21no—
371C4×C22⋊D73—21no—
372C4×C22⋊D73—21no—
373C4×C22⋊D73—21no—
374C4×C22⋊D73C2311yescharacteristic
375C4×C22⋊D73C2311yescharacteristic
376C4×C22⋊D73C2311yescharacteristic
377C4×C22⋊D73C2311yescharacteristic
378#14556551—21no—
379#14556551—21no—
380#14556550—21no—
381#14556550C2311yescharacteristic
382#14556549C2311yescharacteristic
383#14556548—21no—
384#14556548—21no—
385C2×C4⋊Dic73—21no—
386C2×C4⋊Dic73C2311yescharacteristic
387C2×C4⋊Dic73C2311yescharacteristic
388C4⋊C4×D73C2311yescharacteristic
389C2×C22⋊Dic73—21no—
390C2×C22⋊Dic73—21no—
391C2×C22⋊Dic73—21no—
392C2×C22⋊Dic73—21no—
393C22⋊C4×D73—21no—
394C22⋊C4×D73—21no—
395#14556525C2311yescharacteristic
396#14556525C2311yescharacteristic
397#14556525C2311yescharacteristic
398#14556525C2311yescharacteristic
399#14556524C2311yescharacteristic
400#14556524C2311yescharacteristic
401#14556522C2311yescharacteristic
402#14556522C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556520C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556516C2311yescharacteristic
409#14556516C2311yescharacteristic
410#14556516C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556514C2311yescharacteristic
414#14556514C2311yescharacteristic
415#14556513C2311yescharacteristic
416#14556513C2311yescharacteristic
417#14556513C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556512C2311yescharacteristic
420#14556512C2311yescharacteristic
421#14556512C2311yescharacteristic
422#14556512C2311yescharacteristic
423#14556512C2311yescharacteristic
424#14556512C2311yescharacteristic
425#14556512C2311yescharacteristic
426#14556512C2311yescharacteristic
427#14556512C2311yescharacteristic
428#14556512C2311yescharacteristic
429#14556511C2311yescharacteristic
430#14556511C2311yescharacteristic
431C22⋊#10596831C2311yescharacteristic
432C22⋊#10596831C2311yescharacteristic
433C22⋊#10596831C2311yescharacteristic
434C22⋊#10596831C2311yescharacteristic
435#14556503C2311yescharacteristic
436#14556503C2311yescharacteristic
437#14556503C2311yescharacteristic
438#14556503C2311yescharacteristic
439#14556501C2311yescharacteristic
440#14556501C2311yescharacteristic
441C8×Dic73C2311yescharacteristic
442C8×Dic73C2311yescharacteristic
443H(5,𝔽2)×C73—42no—
444H(5,𝔽2)×C73—42no—
445C2×#41×C73—21no—
446C2×#41×C73C2311yescharacteristic
447C2×#41×C73C2311yescharacteristic
448C2×#41×C73C2311yescharacteristic
449C2×#41×C73C2311yescharacteristic
450C22×D4×C73—21no—
451C22×D4×C73—21no—
452C22×D4×C73—21no—
453C22×D4×C73C2311yescharacteristic
454C22×D4×C73C2311yescharacteristic
455C22×D4×C73C2311yescharacteristic
456C22×D4×C73C2311yescharacteristic
457AGL(1,ℤ/8)×C73—42no—
458C2×SD16×C73C2311yescharacteristic
459C2×SD16×C73C2311yescharacteristic
460C2×D8×C73—42no—
461C2×D8×C73C2311yescharacteristic
462C2×D8×C73C2311yescharacteristic
463C2×D8×C73C2311yescharacteristic
464C2×D8×C73C2311yescharacteristic
465C2×D8×C73C2311yescharacteristic
466C2×D8×C73C2311yescharacteristic
467C2×M16×C73C2311yescharacteristic
468C22×C8×C73C2311yescharacteristic
469#127×C73—21no—
470#124×C73—21no—
471#121×C73C2311yescharacteristic
472#121×C73C2311yescharacteristic
473#121×C73C2311yescharacteristic
474#121×C73C2311yescharacteristic
475#120×C73—21no—
476#120×C73—21no—
477#117×C73C2311yescharacteristic
478#103×C73C2311yescharacteristic
479#103×C73C2311yescharacteristic
480#102×C73C2311yescharacteristic
481#102×C73C2311yescharacteristic
482#102×C73C2311yescharacteristic
483#102×C73C2311yescharacteristic
484#102×C73C2311yescharacteristic
485#102×C73C2311yescharacteristic
486C22⋊C8×C73C2311yescharacteristic
487C22⋊C8×C73C2311yescharacteristic
488C22⋊C8×C73C2311yescharacteristic
489C22⋊C8×C73C2311yescharacteristic
490C23×D73—21no—
491C23×D73—21no—
492C23×D73C2×D411yescharacteristic
493#11924029—22no—
494#11924029—41no—
495#11924028—41no—
496#11924028—41no—
497#11924028—41no—
498#11924028—41no—
499#11924028—44no—
500#11924027—22no—
501#11924027—41no—
502#11924027—41no—
503#11924027—41no—
504#11924027—44no—
505#11924027—82no—
506C2×Dic146—21no—
507C2×Dic146—21no—
508C2×Dic146C2411yescharacteristic
509C2×Dic146C2411yescharacteristic
510Q8×D73—22no—
511Q8×D73—41no—
512C2×D292—21no—
513C2×D292—21no—
514C2×D292C2411yescharacteristic
515C2×D292C2411yescharacteristic
516C2×C22⋊D73—21no—
517C2×C22⋊D73—21no—
518C2×C22⋊D73—21no—
519C2×C22⋊D73—21no—
520C2×C22⋊D73—21no—
521C2×C22⋊D73—21no—
522C2×C22⋊D73—21no—
523C2×C22⋊D73—21no—
524C2×C22⋊D73—21no—
525C2×C22⋊D73—21no—
526C2×C22⋊D73—21no—
527C2×C22⋊D73—21no—
528C2×C22⋊D73—21no—
529C2×C22⋊D73—21no—
530C2×C22⋊D73—21no—
531C2×C22⋊D73—21no—
532C2×C22⋊D73—21no—
533C2×C22⋊D73—21no—
534C2×C22⋊D73—21no—
535C2×C22⋊D73—21no—
536C2×C22⋊D73—21no—
537C2×C22⋊D73—21no—
538C2×C22⋊D73—82no—
539C2×C22⋊D73—82no—
540C2×C22⋊D73—82no—
541C2×C22⋊D73—82no—
542C2×C22⋊D73C2×D411yescharacteristic
543C2×C22⋊D73C2×D411yescharacteristic
544C2×C22⋊D73C2×D411yescharacteristic
545C2×C22⋊D73C2×D411yescharacteristic
546D4×D73—22no—
547D4×D73—41no—
548D4×D73—41no—
549D4×D73—41no—
550D4×D73—44no—
551D4×D73—82no—
552C22×Dic73—21no—
553C22×Dic73—21no—
554C22×Dic73—21no—
555C22×Dic73—21no—
556C22×Dic73—21no—
557C22×Dic73—21no—
558C22×Dic73—21no—
559C22×Dic73—21no—
560C22×Dic73C2×D411yescharacteristic
561C2×C4×D73—21no—
562C2×C4×D73—21no—
563C2×C4×D73—21no—
564C2×C4×D73—21no—
565C2×C4×D73—21no—
566C2×C4×D73—21no—
567C2×C4×D73—41no—
568C2×C4×D73—41no—
569C2×C4×D73—44no—
570C2×C4×D73C2×D411yescharacteristic
571C2×C4×D73C2×D411yescharacteristic
572C2×C4×D73C2411yescharacteristic
573C2×C4×D73C2411yescharacteristic
574Dic292—41no—
575#11924018—22no—
576#11924017—41no—
577#11924017—41no—
578#11924016—22no—
579#11924016—41no—
580#11924016—41no—
581#11924016—41no—
582#11924016—41no—
583#11924015—22no—
584D584—41no—
585#11924013—22no—
586#11924013—41no—
587#11924013—41no—
588#11924013—41no—
589#11924013—41no—
590#11924012—41no—
591C2×#10596831—41no—
592C2×#10596831C2411yescharacteristic
593C2×#10596831C2411yescharacteristic
594C2×#10596831C2411yescharacteristic
595C2×#10596831C2411yescharacteristic
596C8×D73—41no—
597C8×D73—41no—
598C8×D73—41no—
599C8×D73—41no—
600C4⋊Dic73—21no—
601C4⋊Dic73—21no—
602C4⋊Dic73—21no—
603C4⋊Dic73—21no—
604C4⋊Dic73—21no—
605C4⋊Dic73—21no—
606C4⋊Dic73C2×D411yescharacteristic
607C4⋊Dic73C2×D411yescharacteristic
608C4⋊Dic73C2411yescharacteristic
609C4⋊Dic73C2411yescharacteristic
610C4⋊Dic73C2411yescharacteristic
611C4⋊Dic73C2411yescharacteristic
612#11924007—21no—
613#11924007—21no—
614#11924007—21no—
615#11924007—21no—
616#11924007—21no—
617#11924007—21no—
618#11924007—21no—
619#11924007—21no—
620#11924007C2×D411yescharacteristic
621#11924007C2×D411yescharacteristic
622#11924007C2×D411yescharacteristic
623#11924007C2×D411yescharacteristic
624C22⋊Dic73—21no—
625C22⋊Dic73—21no—
626C22⋊Dic73—21no—
627C22⋊Dic73—21no—
628C22⋊Dic73—21no—
629C22⋊Dic73—21no—
630C22⋊Dic73—21no—
631C22⋊Dic73—21no—
632C22⋊Dic73—21no—
633C22⋊Dic73—21no—
634C22⋊Dic73—21no—
635C22⋊Dic73—21no—
636C22⋊Dic73—21no—
637C22⋊Dic73—21no—
638C22⋊Dic73—21no—
639C22⋊Dic73—21no—
640C22⋊Dic73—21no—
641C22⋊Dic73—21no—
642C22⋊Dic73—21no—
643C22⋊Dic73—21no—
644C22⋊Dic73C2×D411yescharacteristic
645C22⋊Dic73C2×D411yescharacteristic
646C22⋊Dic73C2×D411yescharacteristic
647C22⋊Dic73C2×D411yescharacteristic
648C22⋊Dic73C2×D411yescharacteristic
649C22⋊Dic73C2×D411yescharacteristic
650#11924005—21no—
651#11924005—21no—
652#11924005—21no—
653#11924005—21no—
654#11924005—21no—
655#11924005—21no—
656#11924005—21no—
657#11924005—21no—
658#11924005C2×D411yescharacteristic
659#11924005C2×D411yescharacteristic
660#11924005C2×D411yescharacteristic
661#11924005C2×D411yescharacteristic
662C4×Dic73—21no—
663C4×Dic73—21no—
664C4×Dic73—21no—
665C4×Dic73—21no—
666C4×Dic73C2411yescharacteristic
667C4×Dic73C2411yescharacteristic
668C24×C73—21no—
669C24×C73—21no—
670C24×C73—21no—
671C24×C73—21no—
672#41×C73—22no—
673#41×C73—22no—
674#41×C73—22no—
675#41×C73—22no—
676#41×C73—41no—
677#41×C73—41no—
678#41×C73—41no—
679#41×C73—41no—
680#41×C73—44no—
681C2×Q8×C73C2×D411yescharacteristic
682C2×Q8×C73C2411yescharacteristic
683C2×D4×C73—21no—
684C2×D4×C73—22no—
685C2×D4×C73—22no—
686C2×D4×C73—21no—
687C2×D4×C73—21no—
688C2×D4×C73—21no—
689C2×D4×C73—21no—
690C2×D4×C73—21no—
691C2×D4×C73—21no—
692C2×D4×C73—21no—
693C2×D4×C73—21no—
694C2×D4×C73—21no—
695C2×D4×C73—21no—
696C2×D4×C73—41no—
697C2×D4×C73—41no—
698C2×D4×C73—41no—
699C2×D4×C73—41no—
700C2×D4×C73—41no—
701C2×D4×C73—41no—
702C2×D4×C73—44no—
703C2×D4×C73—44no—
704C2×D4×C73—44no—
705C2×D4×C73C2×D411yescharacteristic
706C2×D4×C73C2×D411yescharacteristic
707C2×D4×C73C2×D411yescharacteristic
708C2×D4×C73C2411yescharacteristic
709C2×D4×C73C2411yescharacteristic
710C2×D4×C73C2411yescharacteristic
711C2×D4×C73C2411yescharacteristic
712C2×D4×C73C2411yescharacteristic
713C22×C4×C73—21no—
714C22×C4×C73—21no—
715C22×C4×C73—21no—
716C22×C4×C73C2411yescharacteristic
717C22×C4×C73C2411yescharacteristic
718C22×C4×C73C2411yescharacteristic
719SD16×C73—22no—
720SD16×C73—22no—
721D8×C73—22no—
722D8×C73—22no—
723D8×C73—41no—
724D8×C73—41no—
725D8×C73—41no—
726D8×C73—41no—
727M16×C73—41no—
728C2×C8×C73—41no—
729C2×C8×C73C2411yescharacteristic
730C2×C8×C73C2411yescharacteristic
731C2×C8×C73C2411yescharacteristic
732C2×C8×C73C2411yescharacteristic
733C4⋊C4×C73C2411yescharacteristic
734C4⋊C4×C73C2411yescharacteristic
735C22⋊C4×C73—21no—
736C22⋊C4×C73—21no—
737C22⋊C4×C73—21no—
738C22⋊C4×C73—21no—
739C22⋊C4×C73—21no—
740C42×C73—21no—
741C23×C73—21no—
742C23×C73—21no—
743C23×C73—21no—
744C23×C73—21no—
745C23×C73—21no—
746C23×C73—42no—
747C23×C73—42no—
748C23×C73—42no—
749C23×C73—81no—
750C23×C73—81no—
751C23×C73—81no—
752C23×C73—81no—
753C23×C73—81no—
754C23×C73—81no—
755C23×C73—81no—
756C23×C73—81no—
757C23×C73—81no—
758C23×C73C22×D411yescharacteristic
759C23×C73C22×D411yescharacteristic
760C23×C73C22×D411yescharacteristic
761C22×D73—22no—
762C22×D73—21no—
763C22×D73—21no—
764C22×D73—41no—
765C22×D73—41no—
766C22×D73—42no—
767C22×D73—42no—
768C22×D73—42no—
769C22×D73—81no—
770C22×D73—81no—
771C22×D73—81no—
772C22×D73C22×D411yescharacteristic
773C22×D73C22×D411yescharacteristic
774Q8×C73—21no—
775Q8×C73—41no—
776Q8×C73H(5,𝔽2)12yes—
777D4×C73—24no—
778D4×C73—21no—
779D4×C73—21no—
780D4×C73—21no—
781D4×C73—21no—
782D4×C73—21no—
783D4×C73—21no—
784D4×C73—21no—
785D4×C73—21no—
786D4×C73—21no—
787D4×C73—41no—
788D4×C73—41no—
789D4×C73—41no—
790D4×C73—42no—
791D4×C73—42no—
792D4×C73—42no—
793D4×C73—42no—
794D4×C73—42no—
795D4×C73—81no—
796D4×C73—81no—
797D4×C73—81no—
798D4×C73—81no—
799D4×C73—81no—
800D4×C73H(5,𝔽2)12yes—
801C2×C4×C73—24no—
802C2×C4×C73—21no—
803C2×C4×C73—21no—
804C2×C4×C73—21no—
805C2×C4×C73—21no—
806C2×C4×C73—21no—
807C2×C4×C73—21no—
808C2×C4×C73—21no—
809C2×C4×C73—21no—
810C2×C4×C73—21no—
811C2×C4×C73—42no—
812C2×C4×C73—42no—
813C2×C4×C73C22×D411yescharacteristic
814C2×C4×C73C22×D411yescharacteristic
815C2×C4×C73C22×D411yescharacteristic
816C2×C4×C73C2511yescharacteristic
817C22⋊D73—22no—
818C22⋊D73—22no—
819C22⋊D73—41no—
820C22⋊D73—41no—
821C22⋊D73—42no—
822C22⋊D73—42no—
823C22⋊D73—42no—
824C22⋊D73—42no—
825C22⋊D73—42no—
826C22⋊D73—42no—
827C22⋊D73—81no—
828C22⋊D73—81no—
829C22⋊D73—81no—
830C22⋊D73—81no—
831C22⋊D73—81no—
832C22⋊D73—81no—
833C22⋊D73—81no—
834C22⋊D73—81no—
835C22⋊D73—81no—
836C22⋊D73—81no—
837C22⋊D73—81no—
838C22⋊D73—81no—
839C22⋊D73—81no—
840C22⋊D73—81no—
841C22⋊D73—81no—
842C22⋊D73—81no—
843C2×Dic73—21no—
844C2×Dic73—21no—
845C2×Dic73—21no—
846C2×Dic73—21no—
847C2×Dic73—21no—
848C2×Dic73—21no—
849C2×Dic73—41no—
850C2×Dic73—42no—
851C2×Dic73—81no—
852C2×Dic73—81no—
853C2×Dic73—81no—
854C2×Dic73—81no—
855C2×Dic73—81no—
856C2×Dic73—81no—
857C2×Dic73—81no—
858C2×Dic73C22×D411yescharacteristic
859C2×Dic73C22×D411yescharacteristic
860C2×Dic73C22×D411yescharacteristic
861C2×Dic73C22×D411yescharacteristic
862C2×Dic73C22×D411yescharacteristic
863C2×Dic73C22×D411yescharacteristic
864D292—21no—
865D292—21no—
866D292—21no—
867D292—21no—
868D292—42no—
869D292—81no—
870C4×D73—21no—
871C4×D73—21no—
872C4×D73—21no—
873C4×D73—21no—
874C4×D73—41no—
875C4×D73—41no—
876C4×D73—42no—
877C4×D73—42no—
878C4×D73—42no—
879C4×D73—42no—
880C4×D73—81no—
881C4×D73—81no—
882Dic146—21no—
883Dic146—21no—
884Dic146—21no—
885Dic146—21no—
886Dic146—42no—
887Dic146—81no—
888C8×C73—21no—
889C8×C73—21no—
890C8×C73—21no—
891C8×C73—21no—
892#10596831—21no—
893#10596831—21no—
894#10596831—21no—
895#10596831—21no—
896C22×C73—21no—
897C22×C73—21no—
898C22×C73—21no—
899C22×C73—21no—
900C22×C73—22no—
901C22×C73—21no—
902C22×C73—21no—
903C22×C73—21no—
904C22×C73—21no—
905C22×C73—21no—
906C22×C73—41no—
907C22×C73—41no—
908C22×C73—41no—
909C22×C73—41no—
910C22×C73—41no—
911C22×C73—41no—
912C22×C73—41no—
913C22×C73—41no—
914C22×C73—41no—
915C22×C73—41no—
916C22×C73—41no—
917C22×C73—41no—
918C22×C73—41no—
919C22×C73—41no—
920C22×C73—162no—
921C22×C73—162no—
922C22×C73—162no—
923C22×C73—162no—
924C22×C73C23×D411yescharacteristic
925C2×D73—21no—
926C2×D73—21no—
927C2×D73—21no—
928C2×D73—21no—
929C2×D73—21no—
930C2×D73—41no—
931C2×D73—41no—
932C2×D73—41no—
933C2×D73—41no—
934C2×D73—41no—
935C2×D73—41no—
936C2×D73—82no—
937C2×D73—84no—
938C2×D73—162no—
939C2×D73#57612yes—
940C4×C73—22no—
941C4×C73—21no—
942C4×C73—21no—
943C4×C73—21no—
944C4×C73—41no—
945C4×C73—41no—
946C4×C73C2×H(5,𝔽2)11yescharacteristic
947C4×C73C2×H(5,𝔽2)11yescharacteristic
948Dic73—21no—
949Dic73—21no—
950Dic73—21no—
951Dic73—21no—
952Dic73—21no—
953Dic73—21no—
954Dic73—41no—
955Dic73—41no—
956Dic73—41no—
957Dic73—41no—
958Dic73—41no—
959Dic73—41no—
960#61639—731nomaximal, Sylow
961C2×C73—41no—
962C2×C73—42no—
963C2×C73—41no—
964C2×C73—41no—
965C2×C73—81no—
966C2×C73—81no—
967C2×C73—81no—
968C2×C73—81no—
969C2×C73#348411yescharacteristic
970C2×C73C2×#57611yescharacteristic
971C2×C73#358411yescharacteristic
972D73—22no—
973D73—41no—
974D73—81no—
975D73—81no—
976#3542—731no—
977#3488—731no—
978#3319—731no—
979#3310—731no—
980#3309—731no—
981#3308—731no—
982#3305—731no—
983#3300—731no—
984#3297—731no—
985#3294—731no—
986#3287—731no—
987#3282—731no—
988#3280—731no—
989D4×D8—731no—
990#3268—731no—
991#3268—731no—
992#3265—731no—
993#3264—731no—
994#3224—731no—
995#3220—731no—
996#3203—731no—
997#3198—731no—
998#3188—731no—
999#3186—731no—
1000#3124—731no—
1001#3119—731no—
1002#3012—731no—
1003#3008D7311yescharacteristic, complemented
1004#3002—731no—
1005C2×#449—731no—
1006#2977—731no—
1007C73#6163911yescharacteristic, complemented, Sylow
1008C2×H(5,𝔽2)C2×D7311yescharacteristic, complemented
1009C22×#41—731no—
1010C2×AGL(1,ℤ/8)—731no—
1011C2×AGL(1,ℤ/8)C2×D7311yescharacteristic, complemented
1012C2×#135—731no—
1013C2×#135—731no—
1014C2×#135—731no—
1015C22×SD16—731no—
1016C22×D8—731no—
1017C22×D8C2×D7311yescharacteristic, complemented
1018#562—1461no—
1019#560—1461no—
1020#555—731no—
1021#553—731no—
1022#552—731no—
1023#551—1461no—
1024#550—731no—
1025#550—731no—
1026#550—731no—
1027#548—731no—
1028#548—731no—
1029#547—731no—
1030#546—731no—
1031#546—731no—
1032#546—731no—
1033#546—731no—
1034#546—1461no—
1035#546—1461no—
1036#546—1461no—
1037D42—731no—
1038D42—731no—
1039D42—731no—
1040D42—1461no—
1041D42—1461no—
1042#542—731no—
1043#540—731no—
1044#540—1461no—
1045#538—1461no—
1046#537—731no—
1047#537—731no—
1048#537—1461no—
1049#535—731no—
1050#535—1461no—
1051#535—1461no—
1052#535C2×D7311yescharacteristic, complemented
1053#534—1461no—
1054#525—731no—
1055#525—731no—
1056#525—1461no—
1057C2×#121—731no—
1058C2×#121—731no—
1059C2×#121—1461no—
1060#520—731no—
1061#496—731no—
1062#496—731no—
1063#495—731no—
1064#493—731no—
1065#490—731no—
1066#489—731no—
1067#488—731no—
1068#486—731no—
1069#485—731no—
1070#484—731no—
1071#484—731no—
1072#482—731no—
1073#482—731no—
1074#482—731no—
1075#481—731no—
1076#480—731no—
1077#480—731no—
1078#480—731no—
1079#480—731no—
1080#480—731no—
1081#479—731no—
1082#478—731no—
1083#477—731no—
1084#474—731no—
1085#469—731no—
1086#468—731no—
1087#468—731no—
1088#468—731no—
1089#467—731no—
1090#466—731no—
1091#466—731no—
1092#466—731no—
1093#466—731no—
1094#466—731no—
1095#466—731no—
1096#466—731no—
1097#466—731no—
1098#465—731no—
1099#465—731no—
1100#465—731no—
1101#464—731no—
1102#464—731no—
1103#463—731no—
1104#463—731no—
1105#463—731no—
1106#463—731no—
1107#460—731no—
1108#460—731no—
1109#459—731no—
1110#459—731no—
1111#459—731no—
1112#459—731no—
1113#452—731no—
1114#452—731no—
1115#452—731no—
1116#452—731no—
1117#451—731no—
1118#450—731no—
1119#450—731no—
1120#450—731no—
1121#450—731no—
1122#449—731no—
1123#449—731no—
1124#449—731no—
1125#449—731no—
1126#449—731no—
1127#449—731no—
1128#449—731no—
1129#449—731no—
1130#449—731no—
1131#449—731no—
1132#449—731no—
1133#449—731no—
1134#449C2×D7311yescharacteristic
1135#449C2×D7311yescharacteristic, complemented
1136#449C2×D7311yescharacteristic, complemented
1137#449C2×D7311yescharacteristic, complemented
1138#448—731no—
1139#447—731no—
1140#447—731no—
1141#447—731no—
1142#447—731no—
1143#447—731no—
1144#447—731no—
1145#447C2×D7311yescharacteristic, complemented
1146#447C2×D7311yescharacteristic, complemented
1147#447C2×D7311yescharacteristic, complemented
1148#447C2×D7311yescharacteristic, complemented
1149#442—731no—
1150#440—731no—
1151#440—731no—
1152#440—731no—
1153C4×Q16—731no—
1154C4×SD16—731no—
1155C4×D8—731no—
1156C4×D8—731no—
1157#435—731no—
1158#435—731no—
1159#435—731no—
1160#435—731no—
1161C8×D4—731no—
1162C8×D4—731no—
1163C8×D4—731no—
1164C8×D4—731no—
1165#433—731no—
1166#433—731no—
1167#418C2×D7311yescharacteristic, complemented
1168#417—731no—
1169#416—731no—
1170#416—731no—
1171#416C2×D7311yescharacteristic, complemented
1172C2×#103—731no—
1173C2×#102—731no—
1174C2×#102—731no—
1175#408—731no—
1176#408C2×D7311yescharacteristic, complemented
1177C2×C22⋊C8—731no—
1178C2×C22⋊C8—731no—
1179H(5,𝔽2)—42no—
1180H(5,𝔽2)—42no—
1181C2×#41—21no—
1182C2×#41—2922no—
1183C2×#41—2922no—
1184C2×#41—731no—
1185C2×#41—731no—
1186C2×#41—731no—
1187C2×#41—731no—
1188C2×#41—731no—
1189C2×#41—1461no—
1190C2×#41—1461no—
1191C2×#41—1461no—
1192C2×#41C22×D7311yescharacteristic
1193C2×#41C22×D7311yescharacteristic
1194C2×#41C22×D7311yescharacteristic
1195C2×#41C22×D7311yescharacteristic
1196C22×Q8—731no—
1197C22×D4—21no—
1198C22×D4—21no—
1199C22×D4—21no—
1200C22×D4—731no—
1201C22×D4—731no—
1202C22×D4—1461no—
1203C22×D4—1461no—
1204C22×D4—1461no—
1205C22×D4—1461no—
1206C22×D4—1461no—
1207C22×D4—1461no—
1208C22×D4C22×D7311yescharacteristic
1209C22×D4C22×D7311yescharacteristic
1210C22×D4C22×D7311yescharacteristic
1211C22×D4C22×D7311yescharacteristic
1212C23×C4—731no—
1213C23×C4—1461no—
1214AGL(1,ℤ/8)—42no—
1215AGL(1,ℤ/8)—2922no—
1216#135—2922no—
1217#135—2922no—
1218#135—2922no—
1219C2×Q16—731no—
1220C2×Q16—731no—
1221C2×SD16—2922no—
1222C2×SD16—731no—
1223C2×SD16—731no—
1224C2×SD16—731no—
1225C2×SD16—731no—
1226C2×SD16—731no—
1227C2×SD16—731no—
1228C2×SD16—731no—
1229C2×SD16—731no—
1230C2×SD16C22×D7311yescharacteristic
1231C2×SD16C22×D7311yescharacteristic
1232C2×D8—42no—
1233C2×D8—2922no—
1234C2×D8—731no—
1235C2×D8—731no—
1236C2×D8—731no—
1237C2×D8—731no—
1238C2×D8—731no—
1239C2×D8—731no—
1240C2×D8C22×D7311yescharacteristic
1241C2×D8C22×D7311yescharacteristic
1242C2×D8C22×D7311yescharacteristic
1243C2×D8C22×D7311yescharacteristic
1244C2×D8C22×D7311yescharacteristic
1245C2×D8C22×D7311yescharacteristic
1246C2×M16—731no—
1247C2×M16C22×D7311yescharacteristic
1248C22×C8—731no—
1249C22×C8—731no—
1250C22×C8—731no—
1251C22×C8—731no—
1252C22×C8—731no—
1253C22×C8C22×D7311yescharacteristic
1254C4⋊Q8—731no—
1255#127—21no—
1256#127—731no—
1257#127—731no—
1258#127—731no—
1259#127—1461no—
1260#127—1461no—
1261#127—1461no—
1262#126—1461no—
1263#126—1461no—
1264#126—1461no—
1265#125—731no—
1266#125—1461no—
1267#124—21no—
1268#124—731no—
1269#124—731no—
1270#124—731no—
1271#124—1461no—
1272#124—1461no—
1273#124—1461no—
1274#124—1461no—
1275#124—1461no—
1276#123—731no—
1277#123—731no—
1278#123—1461no—
1279#123—1461no—
1280#123—1461no—
1281#123—1461no—
1282#123—1461no—
1283#123—1461no—
1284#123—1461no—
1285#123—1461no—
1286#123—1461no—
1287#123—1461no—
1288#123—1461no—
1289#123—1461no—
1290C22⋊Q8—731no—
1291C22⋊Q8—731no—
1292C22⋊Q8—731no—
1293C22⋊Q8—731no—
1294C22⋊Q8—731no—
1295C22⋊Q8—731no—
1296C22⋊Q8—731no—
1297C22⋊Q8—1461no—
1298C22⋊Q8—1461no—
1299C22⋊Q8—1461no—
1300C22⋊Q8—1461no—
1301C22⋊Q8—1461no—
1302C22⋊Q8—1461no—
1303#121—731no—
1304#121—731no—
1305#121—731no—
1306#121—731no—
1307#121—731no—
1308#121—731no—
1309#121—731no—
1310#121—731no—
1311#121—731no—
1312#121—731no—
1313#121—731no—
1314#121—731no—
1315#121—731no—
1316#121—1461no—
1317#121—1461no—
1318#121—1461no—
1319#121—1461no—
1320#121—1461no—
1321#121—1461no—
1322#121—1461no—
1323#121—1461no—
1324#121—1461no—
1325#121—1461no—
1326#121—1461no—
1327#121—1461no—
1328#121—1461no—
1329#121—1461no—
1330#121—1461no—
1331#121—1461no—
1332#121—1461no—
1333#121—1461no—
1334#121—1461no—
1335#121—1461no—
1336#121—1461no—
1337#121—1461no—
1338#121—1461no—
1339#121—1461no—
1340#121—1461no—
1341#121—1461no—
1342#121—1461no—
1343#121—1461no—
1344#121—1461no—
1345#121—1461no—
1346#121—1461no—
1347#121C22×D7311yescharacteristic
1348#121C22×D7311yescharacteristic
1349#121C22×D7311yescharacteristic
1350#121C22×D7311yescharacteristic
1351#120—21no—
1352#120—21no—
1353#120—731no—
1354#120—731no—
1355#120—1461no—
1356#120—1461no—
1357#120—1461no—
1358#120—1461no—
1359#120—1461no—
1360#120—1461no—
1361#120—1461no—
1362#120—1461no—
1363#120—1461no—
1364#120—1461no—
1365#120—1461no—
1366#120—1461no—
1367#120—1461no—
1368C4×Q8—731no—
1369C4×Q8—731no—
1370C4×Q8—731no—
1371C4×D4—731no—
1372C4×D4—731no—
1373C4×D4—731no—
1374C4×D4—731no—
1375C4×D4—731no—
1376C4×D4—731no—
1377C4×D4—731no—
1378C4×D4—731no—
1379C4×D4—731no—
1380C4×D4—1461no—
1381C4×D4—1461no—
1382C4×D4—1461no—
1383C4×D4—1461no—
1384C4×D4—1461no—
1385C4×D4—1461no—
1386C4×D4—1461no—
1387C4×D4—1461no—
1388C4×D4—1461no—
1389C4×D4—1461no—
1390#117—731no—
1391#117—731no—
1392#117—1461no—
1393#117—1461no—
1394#117—1461no—
1395#117C22×D7311yescharacteristic
1396C2×C4⋊C4—731no—
1397C2×C4⋊C4—731no—
1398C2×C4⋊C4—731no—
1399C2×C4⋊C4—1461no—
1400C2×C22⋊C4—1461no—
1401C2×C22⋊C4—1461no—
1402C2×C22⋊C4—1461no—
1403C2×C22⋊C4—1461no—
1404C2×C22⋊C4—1461no—
1405C2×C22⋊C4—1461no—
1406#107—731no—
1407#107—731no—
1408#107—731no—
1409#107—731no—
1410#107—731no—
1411#107—731no—
1412#106—731no—
1413#106—731no—
1414C4⋊C8—731no—
1415C4⋊C8—731no—
1416C4⋊C8—731no—
1417C4⋊C8—731no—
1418#103—731no—
1419#103—731no—
1420#103—731no—
1421#103—731no—
1422#103—731no—
1423#103—731no—
1424#103—731no—
1425#103—731no—
1426#103C22×D7311yescharacteristic
1427#103C22×D7311yescharacteristic
1428#102—731no—
1429#102—731no—
1430#102—731no—
1431#102—731no—
1432#102—731no—
1433#102—731no—
1434#102—731no—
1435#102—731no—
1436#102—731no—
1437#102—731no—
1438#102—731no—
1439#102—731no—
1440#102—731no—
1441#102—731no—
1442#102—731no—
1443#102—731no—
1444#102C22×D7311yescharacteristic
1445#102C22×D7311yescharacteristic
1446#102C22×D7311yescharacteristic
1447#102C22×D7311yescharacteristic
1448#102C22×D7311yescharacteristic
1449#102C22×D7311yescharacteristic
1450C22⋊C8—731no—
1451C22⋊C8—731no—
1452C22⋊C8—731no—
1453C22⋊C8—731no—
1454C22⋊C8—731no—
1455C22⋊C8—731no—
1456C22⋊C8—731no—
1457C22⋊C8—731no—
1458C22⋊C8C22×D7311yescharacteristic
1459C22⋊C8C22×D7311yescharacteristic
1460C22⋊C8C22×D7311yescharacteristic
1461C22⋊C8C22×D7311yescharacteristic
1462#97—731no—
1463#97—731no—
1464C4×C8—731no—
1465C4×C8—731no—
1466C24—21no—
1467C24—21no—
1468C24—21no—
1469C24—21no—
1470C24—731no—
1471C24—1461no—
1472C24—1461no—
1473#41—22no—
1474#41—22no—
1475#41—22no—
1476#41—22no—
1477#41—41no—
1478#41—41no—
1479#41—41no—
1480#41—41no—
1481#41—44no—
1482#41—2924no—
1483#41—2921no—
1484#41—2921no—
1485#41—2921no—
1486#41—2921no—
1487#41—2924no—
1488#41—2921no—
1489#41—2921no—
1490#41—2921no—
1491#41—2921no—
1492#41—5842no—
1493#41—1462no—
1494#41—1462no—
1495C2×Q8—2921no—
1496C2×Q8—731no—
1497C2×Q8—731no—
1498C2×Q8—1461no—
1499C2×Q8—1461no—
1500C2×Q8—1462no—
1501C2×Q8D4×D7311yescharacteristic
1502C2×Q8C23×D7311yescharacteristic
1503C2×D4—21no—
1504C2×D4—22no—
1505C2×D4—22no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—21no—
1511C2×D4—21no—
1512C2×D4—21no—
1513C2×D4—21no—
1514C2×D4—21no—
1515C2×D4—21no—
1516C2×D4—41no—
1517C2×D4—41no—
1518C2×D4—41no—
1519C2×D4—41no—
1520C2×D4—41no—
1521C2×D4—41no—
1522C2×D4—44no—
1523C2×D4—44no—
1524C2×D4—44no—
1525C2×D4—2924no—
1526C2×D4—2921no—
1527C2×D4—2921no—
1528C2×D4—2921no—
1529C2×D4—5842no—
1530C2×D4—5842no—
1531C2×D4—5842no—
1532C2×D4—5842no—
1533C2×D4—5842no—
1534C2×D4—731no—
1535C2×D4—731no—
1536C2×D4—731no—
1537C2×D4—731no—
1538C2×D4—731no—
1539C2×D4—731no—
1540C2×D4—1461no—
1541C2×D4—1461no—
1542C2×D4—1461no—
1543C2×D4—1461no—
1544C2×D4—1461no—
1545C2×D4—1461no—
1546C2×D4—1461no—
1547C2×D4—1461no—
1548C2×D4—1461no—
1549C2×D4—1461no—
1550C2×D4—1461no—
1551C2×D4—1461no—
1552C2×D4—1461no—
1553C2×D4—1461no—
1554C2×D4—1461no—
1555C2×D4—1462no—
1556C2×D4—1461no—
1557C2×D4—1461no—
1558C2×D4—1461no—
1559C2×D4—1461no—
1560C2×D4—1461no—
1561C2×D4—1461no—
1562C2×D4—1461no—
1563C2×D4—1461no—
1564C2×D4—1461no—
1565C2×D4D4×D7311yescharacteristic
1566C2×D4D4×D7311yescharacteristic
1567C2×D4D4×D7311yescharacteristic
1568C2×D4C23×D7311yescharacteristic
1569C2×D4C23×D7311yescharacteristic
1570C2×D4C23×D7311yescharacteristic
1571C2×D4C23×D7311yescharacteristic
1572C2×D4C23×D7311yescharacteristic
1573C22×C4—21no—
1574C22×C4—21no—
1575C22×C4—21no—
1576C22×C4—2924no—
1577C22×C4—2921no—
1578C22×C4—2921no—
1579C22×C4—731no—
1580C22×C4—731no—
1581C22×C4—731no—
1582C22×C4—731no—
1583C22×C4—731no—
1584C22×C4—1461no—
1585C22×C4—1461no—
1586C22×C4—1461no—
1587C22×C4—1461no—
1588C22×C4—1461no—
1589C22×C4—1461no—
1590C22×C4—1461no—
1591C22×C4—1461no—
1592C22×C4—1461no—
1593C22×C4—1461no—
1594C22×C4—1461no—
1595C22×C4—1461no—
1596C22×C4—1461no—
1597C22×C4—1461no—
1598C22×C4C23×D7311yescharacteristic
1599C22×C4C23×D7311yescharacteristic
1600C22×C4C23×D7311yescharacteristic
1601Q16—2921no—
1602Q16—1462no—
1603SD16—22no—
1604SD16—22no—
1605SD16—2921no—
1606SD16—2921no—
1607SD16—2921no—
1608SD16—2921no—
1609SD16—2921no—
1610SD16—2921no—
1611SD16—1462no—
1612SD16—1462no—
1613D8—22no—
1614D8—22no—
1615D8—41no—
1616D8—41no—
1617D8—41no—
1618D8—41no—
1619D8—2921no—
1620D8—2921no—
1621D8—2921no—
1622D8—2921no—
1623D8—2921no—
1624D8—1462no—
1625M16—41no—
1626M16—2921no—
1627C2×C8—41no—
1628C2×C8—2921no—
1629C2×C8—2921no—
1630C2×C8—2921no—
1631C2×C8—2921no—
1632C2×C8—2921no—
1633C2×C8—731no—
1634C2×C8—731no—
1635C2×C8—731no—
1636C2×C8—731no—
1637C2×C8C23×D7311yescharacteristic
1638C2×C8C23×D7311yescharacteristic
1639C2×C8C23×D7311yescharacteristic
1640C2×C8C23×D7311yescharacteristic
1641C4⋊C4—731no—
1642C4⋊C4—731no—
1643C4⋊C4—731no—
1644C4⋊C4—731no—
1645C4⋊C4—731no—
1646C4⋊C4—731no—
1647C4⋊C4—731no—
1648C4⋊C4—731no—
1649C4⋊C4—731no—
1650C4⋊C4—731no—
1651C4⋊C4—1461no—
1652C4⋊C4—1461no—
1653C4⋊C4—1461no—
1654C4⋊C4—1461no—
1655C4⋊C4—1461no—
1656C4⋊C4—1461no—
1657C4⋊C4—1461no—
1658C4⋊C4—1461no—
1659C4⋊C4—1461no—
1660C4⋊C4—1461no—
1661C4⋊C4—1461no—
1662C4⋊C4—1461no—
1663C4⋊C4—1461no—
1664C4⋊C4—1461no—
1665C4⋊C4C23×D7311yescharacteristic
1666C4⋊C4C23×D7311yescharacteristic
1667C22⋊C4—21no—
1668C22⋊C4—21no—
1669C22⋊C4—21no—
1670C22⋊C4—21no—
1671C22⋊C4—21no—
1672C22⋊C4—731no—
1673C22⋊C4—731no—
1674C22⋊C4—731no—
1675C22⋊C4—731no—
1676C22⋊C4—731no—
1677C22⋊C4—731no—
1678C22⋊C4—731no—
1679C22⋊C4—731no—
1680C22⋊C4—731no—
1681C22⋊C4—731no—
1682C22⋊C4—1461no—
1683C22⋊C4—1461no—
1684C22⋊C4—1461no—
1685C22⋊C4—1461no—
1686C22⋊C4—1461no—
1687C22⋊C4—1461no—
1688C22⋊C4—1461no—
1689C22⋊C4—1461no—
1690C22⋊C4—1461no—
1691C22⋊C4—1461no—
1692C22⋊C4—1461no—
1693C22⋊C4—1461no—
1694C22⋊C4—1461no—
1695C22⋊C4—1461no—
1696C22⋊C4—1461no—
1697C22⋊C4—1461no—
1698C22⋊C4—1461no—
1699C22⋊C4—1461no—
1700C22⋊C4—1461no—
1701C22⋊C4—1461no—
1702C22⋊C4—1461no—
1703C22⋊C4—1461no—
1704C22⋊C4—1461no—
1705C22⋊C4—1461no—
1706C22⋊C4—1461no—
1707C22⋊C4—1461no—
1708C22⋊C4—1461no—
1709C22⋊C4—1461no—
1710C42—21no—
1711C42—731no—
1712C42—731no—
1713C42—1461no—
1714C42—1461no—
1715C42—1461no—
1716C42—1461no—
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—21no—
1722C23—42no—
1723C23—42no—
1724C23—42no—
1725C23—81no—
1726C23—81no—
1727C23—81no—
1728C23—81no—
1729C23—81no—
1730C23—81no—
1731C23—81no—
1732C23—81no—
1733C23—81no—
1734C23—2922no—
1735C23—2921no—
1736C23—2921no—
1737C23—2922no—
1738C23—2922no—
1739C23—5841no—
1740C23—5841no—
1741C23—5841no—
1742C23—731no—
1743C23—731no—
1744C23—1462no—
1745C23—1461no—
1746C23—1461no—
1747C23C2×D4×D7311yescharacteristic
1748C23C2×D4×D7311yescharacteristic
1749C23C2×D4×D7311yescharacteristic
1750Q8—21no—
1751Q8—41no—
1752Q8—2922no—
1753Q8—5841no—
1754Q8—1461no—
1755Q8—1461no—
1756Q8—1461no—
1757Q8—1461no—
1758Q8#1455663612yes—
1759D4—24no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—21no—
1764D4—21no—
1765D4—21no—
1766D4—21no—
1767D4—21no—
1768D4—21no—
1769D4—41no—
1770D4—41no—
1771D4—41no—
1772D4—42no—
1773D4—42no—
1774D4—42no—
1775D4—42no—
1776D4—42no—
1777D4—81no—
1778D4—81no—
1779D4—81no—
1780D4—81no—
1781D4—81no—
1782D4—2922no—
1783D4—2922no—
1784D4—2922no—
1785D4—2922no—
1786D4—2922no—
1787D4—2922no—
1788D4—2922no—
1789D4—2921no—
1790D4—2921no—
1791D4—5841no—
1792D4—5841no—
1793D4—5841no—
1794D4—5841no—
1795D4—5841no—
1796D4—5841no—
1797D4—5841no—
1798D4—5841no—
1799D4—5841no—
1800D4—5841no—
1801D4—5841no—
1802D4—5841no—
1803D4—5841no—
1804D4—5841no—
1805D4—5841no—
1806D4—5841no—
1807D4—5841no—
1808D4—1462no—
1809D4—1462no—
1810D4—1461no—
1811D4—1461no—
1812D4—1461no—
1813D4—1461no—
1814D4#1455663612yes—
1815C2×C4—24no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—21no—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—21no—
1825C2×C4—42no—
1826C2×C4—42no—
1827C2×C4—2922no—
1828C2×C4—2922no—
1829C2×C4—2922no—
1830C2×C4—2921no—
1831C2×C4—2921no—
1832C2×C4—2922no—
1833C2×C4—2922no—
1834C2×C4—2921no—
1835C2×C4—5841no—
1836C2×C4—5841no—
1837C2×C4—5841no—
1838C2×C4—5841no—
1839C2×C4—5841no—
1840C2×C4—5841no—
1841C2×C4—5841no—
1842C2×C4—5841no—
1843C2×C4—5841no—
1844C2×C4—731no—
1845C2×C4—731no—
1846C2×C4—731no—
1847C2×C4—731no—
1848C2×C4—731no—
1849C2×C4—731no—
1850C2×C4—1461no—
1851C2×C4—1461no—
1852C2×C4—1461no—
1853C2×C4—1461no—
1854C2×C4—1461no—
1855C2×C4—1461no—
1856C2×C4—1461no—
1857C2×C4—1461no—
1858C2×C4—1461no—
1859C2×C4—1461no—
1860C2×C4C2×D4×D7311yescharacteristic
1861C2×C4C2×D4×D7311yescharacteristic
1862C2×C4C2×D4×D7311yescharacteristic
1863C2×C4C24×D7311yescharacteristic
1864C8—21no—
1865C8—21no—
1866C8—21no—
1867C8—21no—
1868C8—1461no—
1869C8—1461no—
1870C8—1461no—
1871C8—1461no—
1872C22—21no—
1873C22—22no—
1874C22—21no—
1875C22—21no—
1876C22—21no—
1877C22—21no—
1878C22—21no—
1879C22—21no—
1880C22—21no—
1881C22—21no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—41no—
1890C22—41no—
1891C22—41no—
1892C22—41no—
1893C22—41no—
1894C22—41no—
1895C22—41no—
1896C22—162no—
1897C22—162no—
1898C22—162no—
1899C22—162no—
1900C22—2921no—
1901C22—2921no—
1902C22—2921no—
1903C22—2921no—
1904C22—2921no—
1905C22—2921no—
1906C22—5842no—
1907C22—5844no—
1908C22—732no—
1909C22—11682no—
1910C22—1461no—
1911C22—1461no—
1912C22—1461no—
1913C22—1461no—
1914C22—1461no—
1915C22C22×D4×D7311yescharacteristic
1916C4—21no—
1917C4—22no—
1918C4—21no—
1919C4—21no—
1920C4—41no—
1921C4—41no—
1922C4—2921no—
1923C4—2921no—
1924C4—2921no—
1925C4—2921no—
1926C4—2921no—
1927C4—2921no—
1928C4—1461no—
1929C4—1461no—
1930C4—1461no—
1931C4—1461no—
1932C4—1461no—
1933C4—1461no—
1934C4C2×#1455663611yescharacteristic
1935C4C2×#1455663611yescharacteristic
1936C2—41no—
1937C2—41no—
1938C2—41no—
1939C2—42no—
1940C2—81no—
1941C2—81no—
1942C2—81no—
1943C2—81no—
1944C2—2921no—
1945C2—5841no—
1946C2—5841no—
1947C2—1462no—
1948C2#2262356011yescharacteristic
1949C2#576×D7311yescharacteristic
1950C2#2262469911yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3008C2
socleC22×C73C23×D4
hypercenter#3008D73
hypocenterC73#61639
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3008

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624249C2semidirect
2. #22623593C2semidirect
3. #22622088C2semidirect
4. #22621953C2semidirect
5. #22621930C2semidirect
6. #22621915C2semidirect
7. #22621877C2semidirect
8. #22621819C2semidirect
9. #22621785C2semidirect
10. #22621737C2semidirect
11. #22621684C2semidirect
12. #22621641C2semidirect
13. #22621616C2semidirect
14. D8×C22⋊D73C2semidirect
15. #22621469C2semidirect
16. #22621465C2semidirect
17. #22621420C2semidirect
18. #22621409C2semidirect
19. #22621021C2semidirect
20. #22620977C2semidirect
21. #22620833C2semidirect
22. #22620783C2semidirect
23. #22620693C2semidirect
24. #22620680C2semidirect
25. #22620186C2semidirect
26. #22620123C2semidirect
27. #22619235C2semidirect
28. #22619146C2semidirect
29. #449×D73C2semidirect
30. #22618983C2semidirect
31. C73×#3008C2semidirect
32. C2×#41×D73C22semidirect
33. C2×#14556617C22semidirect
34. C2×#14556612C22semidirect
35. C2×#14556611C22semidirect
36. C2×#14556610C22semidirect
37. C2×SD16×D73C22semidirect
38. C2×D8×D73C22semidirect
41. #17989300C22semidirect
42. #17989289C22semidirect
43. #17989276C22semidirect
45. #17989256C22semidirect
46. #17989256C22semidirect
47. #17989255C22semidirect
49. #17989244C22semidirect
50. #17989237C22semidirect
51. #17989234C22semidirect
54. #17989231C22semidirect
55. #17989231C22semidirect
56. #17989231C22semidirect
61. D4×C22⋊D73C22semidirect
62. D4×C22⋊D73C22semidirect
63. #17989204C22semidirect
65. #17989190C22semidirect
68. #17989165C22semidirect
69. #17989165C22semidirect
71. #17989154C22semidirect
74. #17989097C22semidirect
78. C2×#14556562C22semidirect
79. #121×D73C22semidirect
80. #17989070C22semidirect
81. #17988975C22semidirect
82. #17988975C22semidirect
83. #17988970C22semidirect
84. #17988962C22semidirect
85. #17988950C22semidirect
86. #17988945C22semidirect
87. #17988940C22semidirect
88. #17988932C22semidirect
89. #17988928C22semidirect
90. #17988923C22semidirect
91. #17988923C22semidirect
92. #17988911C22semidirect
93. #17988909C22semidirect
94. #17988909C22semidirect
95. #17988903C22semidirect
96. #17988901C22semidirect
97. #17988901C22semidirect
98. #17988899C22semidirect
99. #17988899C22semidirect
100. #17988898C22semidirect
101. #17988896C22semidirect
102. #17988885C22semidirect
103. #17988880C22semidirect
104. #17988865C22semidirect
105. #17988838C22semidirect
106. #17988833C22semidirect
107. #17988833C22semidirect
108. #17988831C22semidirect
109. #17988828C22semidirect
110. #17988823C22semidirect
111. #17988822C22semidirect
112. #17988822C22semidirect
113. #17988821C22semidirect
114. #17988820C22semidirect
115. #17988820C22semidirect
116. #17988820C22semidirect
117. #17988820C22semidirect
118. #17988815C22semidirect
119. #17988815C22semidirect
120. #17988814C22semidirect
121. #17988808C22semidirect
122. #17988807C22semidirect
123. #17988801C22semidirect
124. #17988800C22semidirect
125. #17988800C22semidirect
126. #17988800C22semidirect
127. #17988786C22semidirect
128. #17988785C22semidirect
129. #17988781C22semidirect
130. #17988780C22semidirect
131. #17988780C22semidirect
132. #17988780C22semidirect
133. #17988751C22semidirect
134. #17988751C22semidirect
135. #17988749C22semidirect
136. #17988749C22semidirect
137. #17988744C22semidirect
138. #17988739C22semidirect
139. #17988738C22semidirect
140. #17988738C22semidirect
141. #17988738C22semidirect
142. #17988735C22semidirect
143. #17988734C22semidirect
144. #17988734C22semidirect
145. #17988733C22semidirect
146. #17988732C22semidirect
147. #17988732C22semidirect
148. #17988731C22semidirect
149. #17988730C22semidirect
150. #17988730C22semidirect
151. #17988729C22semidirect
152. #17988729C22semidirect
153. #17988729C22semidirect
154. #17988724C22semidirect
155. #17988721C22semidirect
156. #17988721C22semidirect
157. #17988721C22semidirect
158. #17988719C22semidirect
159. #17988719C22semidirect
160. #17988719C22semidirect
161. #17988696C22semidirect
162. #17988688C22semidirect
163. #17988688C22semidirect
164. #17988684C22semidirect
165. #17988679C22semidirect
166. #17988672C22semidirect
167. D8×Dic73C22semidirect
168. D8×Dic73C22semidirect
169. #17988661C22semidirect
170. #17988661C22semidirect
171. #17988656C22semidirect
172. #17988656C22semidirect
173. C8×C22⋊D73C22semidirect
174. C8×C22⋊D73C22semidirect
175. #17988650C22semidirect
176. #17988650C22semidirect
177. #17988645C22semidirect
178. #17988645C22semidirect
179. #17988588C22semidirect
180. #17988582C22semidirect
181. #17988580C22semidirect
182. #103×D73C22semidirect
183. C2×#14556512C22semidirect
184. #102×D73C22semidirect
185. #17988554C22semidirect
186. C22⋊C8×D73C22semidirect
187. C22⋊C8×D73C22semidirect
188. C2×H(5,𝔽2)×C73C22semidirect
189. C2×AGL(1,ℤ/8)×C73C22semidirect
190. C22×D8×C73C22semidirect
191. #535×C73C22semidirect
193. #449×C73C22semidirect
194. #449×C73C22semidirect
195. #449×C73C22semidirect
196. #447×C73C22semidirect
197. #447×C73C22semidirect
198. #447×C73C22semidirect
199. #447×C73C22semidirect
200. #418×C73C22semidirect
201. #416×C73C22semidirect
202. #408×C73C22semidirect
1003. #3008D73semidirect
1007. C73#61639semidirect
1008. C2×H(5,𝔽2)C2×D73semidirect
1011. C2×AGL(1,ℤ/8)C2×D73semidirect
1017. C22×D8C2×D73semidirect
1052. #535C2×D73semidirect
1135. #449C2×D73semidirect
1136. #449C2×D73semidirect
1137. #449C2×D73semidirect
1145. #447C2×D73semidirect
1146. #447C2×D73semidirect
1147. #447C2×D73semidirect
1148. #447C2×D73semidirect
1167. #418C2×D73semidirect
1171. #416C2×D73semidirect
1176. #408C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226242492
#226235932
#226220882
#226219532
#226219302
#226219152
#226218772
#226218192
#226217852
#226217372
#226216842
#226216412
#226216162
D8×C22⋊D732
#226214692
#226214652
#226214202
#226214092
#226210212
#226209772
#226208332
#226207832
#226206932
#226206802
#226201862
#226201232
#226192352
#226191462
#449×D732
#226189832
C73×#30082
#6163973