Finite Group Databasebeta

← #33964239

Subgroups — #33964239

Order 18688.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623845C211yesmaximal, characteristic, complemented
2#22623722C211yesmaximal, characteristic, complemented
3#22622204C211yesmaximal, characteristic, complemented
4#22622185C211yesmaximal, characteristic, complemented
5#22622180C211yesmaximal, characteristic, complemented
6#22622153C211yesmaximal, characteristic, complemented
7#22622142C211yesmaximal, characteristic, complemented
8#22622134C211yesmaximal, characteristic, complemented
9#22622131C211yesmaximal, characteristic, complemented
10#22621833C211yesmaximal, characteristic, complemented
11#22621830C211yesmaximal, characteristic, complemented
12#22621822C211yesmaximal, characteristic, complemented
13#22621811C211yesmaximal, characteristic, complemented
14#22621784C211yesmaximal, characteristic, complemented
15#22621779C211yesmaximal, characteristic, complemented
16#22621773C211yesmaximal, characteristic, complemented
17#22621760C211yesmaximal, characteristic, complemented
18#488×D73C211yesmaximal, characteristic, complemented
19#22619899C211yesmaximal, characteristic, complemented
20#22619886C211yesmaximal, characteristic, complemented
21#22619750C211yesmaximal, characteristic, complemented
22#22619619C211yesmaximal, characteristic, complemented
23#22619606C211yesmaximal, characteristic, complemented
24#22619422C211yesmaximal, characteristic, complemented
25#22619247C211yesmaximal, characteristic, complemented
26#22619239C211yesmaximal, characteristic, complemented
27C4×#14556614C211yesmaximal, characteristic, complemented
28#22618640C211yesmaximal, characteristic, complemented
29#22618463C211yesmaximal, characteristic, complemented
30#22618455C211yesmaximal, characteristic, complemented
31C73×#3327C211yesmaximal, characteristic, complemented
32C2×#14556639C2211yescharacteristic
33C2×#14556637C2211yescharacteristic
34C2×#14556623C2211yescharacteristic, complemented
35C2×#14556618C2211yescharacteristic
36C2×#14556614C2211yescharacteristic
37C2×#14556599C2211yescharacteristic
38C2×#14556599C2211yescharacteristic, complemented
39#17989290—21no—
40#17989290C2211yescharacteristic, complemented
41#17989288—21no—
42#17989285C2211yescharacteristic, complemented
43#17989283C2211yescharacteristic, complemented
44#17989282—21no—
45#17989281—21no—
46#17989281C2211yescharacteristic, complemented
47#17989279C2211yescharacteristic, complemented
48#17989278C2211yescharacteristic, complemented
49#17989271C2211yescharacteristic, complemented
50#17989249C2211yescharacteristic
51#17989248C2211yescharacteristic
52#17989244C2211yescharacteristic
53#17989234—21no—
54#17989234C2211yescharacteristic
55#17989233—21no—
56#17989233C2211yescharacteristic
57#17989230—21no—
58#17989230C2211yescharacteristic
59#17989228—21no—
60#17989228C2211yescharacteristic
61#17989196—21no—
62#17989189—21no—
63#17989167C2211yescharacteristic
64#17989167C2211yescharacteristic, complemented
65#17989160—21no—
66#17989160C2211yescharacteristic
67#17989153—21no—
68#17989153C2211yescharacteristic
69#17989134—21no—
70#17989134C2211yescharacteristic
71#17989120—21no—
72#17989115—21no—
73#125×D73C2211yescharacteristic, complemented
74#124×D73—21no—
75#124×D73C2211yescharacteristic
76#17989068C2211yescharacteristic
77#17989067C2211yescharacteristic, complemented
78C4×#11924029C2211yescharacteristic
79C4×#11924029C2211yescharacteristic, complemented
80#17988944C2211yescharacteristic, complemented
81#17988943C2211yescharacteristic, complemented
82#17988943C2211yescharacteristic, complemented
83#17988942C2211yescharacteristic, complemented
84#17988941C2211yescharacteristic, complemented
85#17988940C2211yescharacteristic, complemented
86#17988940C2211yescharacteristic, complemented
87#17988930C2211yescharacteristic, complemented
88#17988929C2211yescharacteristic, complemented
89#17988927C2211yescharacteristic, complemented
90#17988925C2211yescharacteristic, complemented
91#17988924C2211yescharacteristic, complemented
92#17988917C2211yescharacteristic, complemented
93#17988916C2211yescharacteristic, complemented
94#17988914C2211yescharacteristic, complemented
95#17988911C2211yescharacteristic, complemented
96#17988909C2211yescharacteristic, complemented
97#17988907C2211yescharacteristic, complemented
98#17988903C2211yescharacteristic, complemented
99#17988901C2211yescharacteristic, complemented
100#17988899C2211yescharacteristic, complemented
101#17988896C2211yescharacteristic, complemented
102#17988894C2211yescharacteristic, complemented
103#17988892C2211yescharacteristic, complemented
104#17988890C2211yescharacteristic, complemented
105#17988888C2211yescharacteristic, complemented
106#17988886C2211yescharacteristic, complemented
107#17988884C2211yescharacteristic, complemented
108#17988844C2211yescharacteristic, complemented
109#17988840C2211yescharacteristic, complemented
110#17988839C2211yescharacteristic, complemented
111#17988836C2211yescharacteristic, complemented
112#17988836C2211yescharacteristic, complemented
113#17988833C2211yescharacteristic, complemented
114#17988826C2211yescharacteristic, complemented
115#17988825C2211yescharacteristic, complemented
116#17988824C2211yescharacteristic, complemented
117#17988821C2211yescharacteristic, complemented
118#17988818C2211yescharacteristic, complemented
119#17988818C2211yescharacteristic, complemented
120#17988817C2211yescharacteristic, complemented
121#17988813C2211yescharacteristic, complemented
122#17988811C2211yescharacteristic, complemented
123#17988809C2211yescharacteristic, complemented
124#17988807C2211yescharacteristic, complemented
125#17988805C2211yescharacteristic, complemented
126#17988803C2211yescharacteristic, complemented
127#17988801C2211yescharacteristic, complemented
128#17988799C2211yescharacteristic, complemented
129#17988748C2211yescharacteristic
130#17988748C2211yescharacteristic, complemented
131#17988747C2211yescharacteristic, complemented
132#17988741C2211yescharacteristic, complemented
133#17988737C2211yescharacteristic
134#17988736C2211yescharacteristic
135#17988735C2211yescharacteristic
136#17988735C2211yescharacteristic, complemented
137#17988734C2211yescharacteristic, complemented
138#17988732C2211yescharacteristic
139#17988727C2211yescharacteristic, complemented
140#17988726C2211yescharacteristic, complemented
141#17988723C2211yescharacteristic
142#17988722C2211yescharacteristic
143Q16×Dic73C2211yescharacteristic, complemented
144C4×#11924015C2211yescharacteristic, complemented
145C4×#11924015C2211yescharacteristic, complemented
146#17988672C2211yescharacteristic, complemented
147#17988672C2211yescharacteristic, complemented
148C4×D584C2211yescharacteristic, complemented
149#17988669C2211yescharacteristic, complemented
150#17988666C2211yescharacteristic, complemented
151#17988663C2211yescharacteristic, complemented
152#17988663C2211yescharacteristic, complemented
153D4×#10596831C2211yescharacteristic, complemented
154#17988652C2211yescharacteristic, complemented
155#17988650C2211yescharacteristic, complemented
156#17988650C2211yescharacteristic, complemented
157#17988628C2211yescharacteristic, complemented
158#17988626C2211yescharacteristic, complemented
159#17988624C2211yescharacteristic, complemented
160#17988609C2211yescharacteristic, complemented
161#17988594C2211yescharacteristic, complemented
162#17988594C2211yescharacteristic, complemented
163#17988593C2211yescharacteristic
164#17988590C2211yescharacteristic
165#17988590C2211yescharacteristic
166#17988589C2211yescharacteristic, complemented
167#17988587C2211yescharacteristic
168#17988587C2211yescharacteristic
169#17988587C2211yescharacteristic
170#17988587C2211yescharacteristic, complemented
171#17988583C2211yescharacteristic
172#17988582C2211yescharacteristic
173#17988582C2211yescharacteristic
174#17988582C2211yescharacteristic, complemented
175#17988582C2211yescharacteristic, complemented
176#17988581C2211yescharacteristic, complemented
177C2×#14556515C2211yescharacteristic, complemented
178#103×D73C2211yescharacteristic, complemented
179#103×D73C2211yescharacteristic, complemented
180#103×D73C2211yescharacteristic, complemented
181C2×#14556511C2211yescharacteristic
182#102×D73C2211yescharacteristic
183#102×D73C2211yescharacteristic
184#102×D73C2211yescharacteristic
185#17988552C2211yescharacteristic
186#17988552C2211yescharacteristic, complemented
187C4×C8×D73C2211yescharacteristic, complemented
188#552×C73C2211yescharacteristic, complemented
189#548×C73C2211yescharacteristic
190#488×C73C2211yescharacteristic, complemented
191#484×C73C2211yescharacteristic, complemented
192#482×C73C2211yescharacteristic, complemented
193#479×C73C2211yescharacteristic, complemented
194#470×C73C2211yescharacteristic, complemented
195#468×C73C2211yescharacteristic, complemented
196#464×C73C2211yescharacteristic, complemented
197#452×C73C2211yescharacteristic
198#451×C73C2211yescharacteristic, complemented
199C4×Q16×C73C2211yescharacteristic, complemented
200#436×C73C2211yescharacteristic, complemented
201#419×C73C2211yescharacteristic, complemented
202#417×C73C2211yescharacteristic
203#14556639—24no—
204#14556639—42no—
205#14556637—24no—
206#14556637—42no—
207C2×#11924029—21no—
208C2×#11924029C2311yescharacteristic
209C2×#11924029C2311yescharacteristic
210C2×#11924029C2311yescharacteristic
211C2×#11924029C2311yescharacteristic
212C2×#11924028—21no—
213C2×#11924028—21no—
214C2×#11924028—21no—
215C2×#11924028C2311yescharacteristic
216C2×#11924028C2311yescharacteristic
217C2×#11924028C2311yescharacteristic
218C2×Q8×D73—21no—
219C2×Q8×D73C2311yescharacteristic
220C2×Q8×D73C2311yescharacteristic
221C22×D292—21no—
222C22×D292C2311yescharacteristic
223C2×D4×D73—21no—
224C2×D4×D73—21no—
225C2×D4×D73C2311yescharacteristic
226C2×D4×D73C2311yescharacteristic
227#14556623—42no—
228#14556618—42no—
229#14556614—24no—
230C2×#11924018C2311yescharacteristic
231C2×#11924017C2311yescharacteristic
232C2×#11924015C2311yescharacteristic
233C2×#11924015C2311yescharacteristic
234C2×#11924015C2311yescharacteristic
235C2×#11924015C2311yescharacteristic
236C2×D584C2311yescharacteristic
237C2×D584C2311yescharacteristic
238C2×#11924013C2311yescharacteristic
239#14556599—42no—
240#14556599—42no—
241C2×#11924011C2311yescharacteristic
242C2×#11924011C2311yescharacteristic
243C2×#11924011C2311yescharacteristic
244C2×#11924011C2311yescharacteristic
245C22×#10596831C2311yescharacteristic
246C22×#10596831C2311yescharacteristic
247C2×C8×D73C2311yescharacteristic
248C2×C8×D73C2311yescharacteristic
249C2×C8×D73C2311yescharacteristic
250C2×C8×D73C2311yescharacteristic
251#14556590—21no—
252#14556590D411yescharacteristic
253#14556587—21no—
254#14556587D411yescharacteristic
255#14556586—21no—
256#14556586—21no—
257#14556586—21no—
258#14556586—21no—
259#14556585—21no—
260#14556585—21no—
261#14556584—21no—
262#14556583C2311yescharacteristic
263#14556582—21no—
264#14556582C2311yescharacteristic
265#14556582C2311yescharacteristic
266#14556581—21no—
267#14556581—21no—
268#14556581—21no—
269#14556581—21no—
270#14556580—21no—
271#14556580C2311yescharacteristic
272#14556579—21no—
273#14556579C2311yescharacteristic
274#14556578—21no—
275#14556578C2311yescharacteristic
276#14556577—21no—
277#14556577—21no—
278#14556577—21no—
279#14556577—21no—
280#14556577D411yescharacteristic
281#14556577D411yescharacteristic
282#14556576—21no—
283#14556576—21no—
284#14556576—21no—
285#14556576—21no—
286#14556576—21no—
287#14556576—21no—
288#14556575—21no—
289#14556573—21no—
290#14556573—21no—
291#14556573—21no—
292#14556573—21no—
293#14556573—21no—
294#14556573—21no—
295#14556571—21no—
296#14556571C2311yescharacteristic
297#14556570—21no—
298#14556570C2311yescharacteristic
299#14556569—21no—
300#14556569—21no—
301#14556567—21no—
302#14556567C2311yescharacteristic
303#14556567C2311yescharacteristic
304#14556567C2311yescharacteristic
305#14556566—21no—
306#14556566—21no—
307#14556566—21no—
308#14556566—21no—
309#14556566—21no—
310#14556566D411yescharacteristic
311#14556566C2311yescharacteristic
312#14556566C2311yescharacteristic
313#14556566C2311yescharacteristic
314#14556565—21no—
315#14556565—21no—
316#14556565C2311yescharacteristic
317#14556565C2311yescharacteristic
318#14556565C2311yescharacteristic
319#14556564—21no—
320#14556564—21no—
321#14556564—21no—
322#14556564—21no—
323#14556564—21no—
324#14556564—21no—
325#14556564—21no—
326#14556564D411yescharacteristic
327#14556564D411yescharacteristic
328#14556563—21no—
329#14556562—21no—
330#14556562—21no—
331#14556562D411yescharacteristic
332#14556562C2311yescharacteristic
333#14556561—21no—
334#14556561—21no—
335#14556561—21no—
336#14556559—21no—
337#14556559—21no—
338#14556559—21no—
339Q8×Dic73C2311yescharacteristic
340Q8×Dic73C2311yescharacteristic
341C4×Dic146—21no—
342#14556556—21no—
343C4×D292—21no—
344C4×D292—21no—
345C4×D292—21no—
346C4×D292—21no—
347C4×D292—21no—
348C4×D292C2311yescharacteristic
349C4×D292C2311yescharacteristic
350C4×D292C2311yescharacteristic
351#14556553—21no—
352#14556553—21no—
353#14556553—21no—
354#14556553—21no—
355#14556553C2311yescharacteristic
356#14556553C2311yescharacteristic
357C4×C22⋊D73—21no—
358C4×C22⋊D73—21no—
359C4×C22⋊D73—21no—
360C4×C22⋊D73—21no—
361C4×C22⋊D73—21no—
362C4×C22⋊D73C2311yescharacteristic
363C4×C22⋊D73C2311yescharacteristic
364#14556551—21no—
365#14556551—21no—
366#14556551—21no—
367#14556550C2311yescharacteristic
368#14556549—21no—
369#14556549—21no—
370#14556549—21no—
371#14556549C2311yescharacteristic
372#14556549C2311yescharacteristic
373#14556549C2311yescharacteristic
374#14556549C2311yescharacteristic
375#14556548—21no—
376#14556547—21no—
377C2×C4⋊Dic73C2311yescharacteristic
378C4⋊C4×D73—21no—
379C4⋊C4×D73—21no—
380C4⋊C4×D73C2311yescharacteristic
381C4⋊C4×D73C2311yescharacteristic
382C4⋊C4×D73C2311yescharacteristic
383C4⋊C4×D73C2311yescharacteristic
384C22⋊C4×D73—21no—
385C22⋊C4×D73—21no—
386C22⋊C4×D73—21no—
387C22⋊C4×D73—21no—
388C22⋊C4×D73—21no—
389C22⋊C4×D73—21no—
390C42×D73—21no—
391C42×D73—21no—
392C42×D73C2311yescharacteristic
393#14556525C2311yescharacteristic
394#14556525C2311yescharacteristic
395#14556524C2311yescharacteristic
396#14556524C2311yescharacteristic
397#14556523C2311yescharacteristic
398#14556522C2311yescharacteristic
399#14556522C2311yescharacteristic
400#14556522C2311yescharacteristic
401#14556522C2311yescharacteristic
402C4⋊#10596831C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556516C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556515C2311yescharacteristic
409#14556515C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556514C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556513C2311yescharacteristic
420#14556513C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556513C2311yescharacteristic
424#14556513C2311yescharacteristic
425#14556512C2311yescharacteristic
426#14556512C2311yescharacteristic
427#14556512C2311yescharacteristic
428#14556511C2311yescharacteristic
429#14556511C2311yescharacteristic
430#14556511C2311yescharacteristic
431#14556511C2311yescharacteristic
432#14556511C2311yescharacteristic
433#14556511C2311yescharacteristic
434#14556511C2311yescharacteristic
435C22⋊#10596831C2311yescharacteristic
436C22⋊#10596831C2311yescharacteristic
437#14556503C2311yescharacteristic
438#14556503C2311yescharacteristic
439#14556503C2311yescharacteristic
440#14556503C2311yescharacteristic
441C4×#10596831C2311yescharacteristic
442C8×Dic73C2311yescharacteristic
443C8×Dic73C2311yescharacteristic
444C2×#41×C73C2311yescharacteristic
445C22×Q8×C73C2311yescharacteristic
446C2×Q16×C73C2311yescharacteristic
447C2×Q16×C73C2311yescharacteristic
448C2×SD16×C73C2311yescharacteristic
449C2×M16×C73C2311yescharacteristic
450C2×M16×C73C2311yescharacteristic
451#126×C73—21no—
452#125×C73—21no—
453#125×C73C2311yescharacteristic
454#124×C73—21no—
455#124×C73C2311yescharacteristic
456#123×C73—21no—
457C22⋊Q8×C73—21no—
458C22⋊Q8×C73C2311yescharacteristic
459C22⋊Q8×C73C2311yescharacteristic
460C22⋊Q8×C73C2311yescharacteristic
461#121×C73—21no—
462#121×C73C2311yescharacteristic
463C4×Q8×C73C2311yescharacteristic
464C4×Q8×C73C2311yescharacteristic
465C4×D4×C73—21no—
466C4×D4×C73C2311yescharacteristic
467#117×C73—21no—
468#117×C73C2311yescharacteristic
469C2×C4⋊C4×C73C2311yescharacteristic
470#107×C73C2311yescharacteristic
471#107×C73C2311yescharacteristic
472#106×C73C2311yescharacteristic
473C4⋊C8×C73C2311yescharacteristic
474#103×C73C2311yescharacteristic
475#103×C73C2311yescharacteristic
476#103×C73C2311yescharacteristic
477#103×C73C2311yescharacteristic
478#103×C73C2311yescharacteristic
479#103×C73C2311yescharacteristic
480#103×C73C2311yescharacteristic
481#102×C73C2311yescharacteristic
482#102×C73C2311yescharacteristic
483#102×C73C2311yescharacteristic
484C22⋊C8×C73C2311yescharacteristic
485C22⋊C8×C73C2311yescharacteristic
486C4×C8×C73C2311yescharacteristic
487C23×D73—21no—
488C23×D73—21no—
489C23×D73—21no—
490#11924029—22no—
491#11924029—22no—
492#11924029—22no—
493#11924029—22no—
494#11924029—22no—
495#11924029—41no—
496#11924029—41no—
497#11924029—44no—
498#11924029#4114yes—
499#11924028—22no—
500#11924028—22no—
501#11924028—22no—
502#11924028—22no—
503#11924028—22no—
504#11924028—44no—
505#11924028—41no—
506#11924028—44no—
507#11924028—44no—
508C2×Dic146—21no—
509C2×Dic146—21no—
510C2×Dic146C2×D411yescharacteristic
511C2×Dic146C2×D411yescharacteristic
512C2×Dic146C2411yescharacteristic
513Q8×D73—22no—
514Q8×D73—22no—
515Q8×D73—22no—
516Q8×D73—41no—
517Q8×D73—44no—
518C2×D292—21no—
519C2×D292—22no—
520C2×D292—21no—
521C2×D292—21no—
522C2×D292—21no—
523C2×D292—21no—
524C2×D292—21no—
525C2×D292—21no—
526C2×D292—21no—
527C2×D292—41no—
528C2×D292—44no—
529C2×D292C2×D411yescharacteristic
530C2×D292C2×D411yescharacteristic
531C2×D292C2×D411yescharacteristic
532C2×D292C2411yescharacteristic
533C2×D292C2411yescharacteristic
534C2×D292C2411yescharacteristic
535C2×C22⋊D73—21no—
536C2×C22⋊D73—21no—
537C2×C22⋊D73—21no—
538C2×C22⋊D73—21no—
539C2×C22⋊D73—21no—
540C2×C22⋊D73—21no—
541C2×C22⋊D73—21no—
542C2×C22⋊D73C2×D411yescharacteristic
543C2×C22⋊D73C2×D411yescharacteristic
544C2×C22⋊D73C2×D411yescharacteristic
545C2×C22⋊D73C2×D411yescharacteristic
546C2×C22⋊D73C2×D411yescharacteristic
547C2×C22⋊D73C2×D411yescharacteristic
548D4×D73—22no—
549D4×D73—22no—
550D4×D73—22no—
551D4×D73—41no—
552D4×D73—44no—
553D4×D73—44no—
554C22×Dic73—21no—
555C2×C4×D73—21no—
556C2×C4×D73—21no—
557C2×C4×D73—21no—
558C2×C4×D73—21no—
559C2×C4×D73—21no—
560C2×C4×D73—21no—
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—21no—
568C2×C4×D73—21no—
569C2×C4×D73—21no—
570C2×C4×D73C2×D411yescharacteristic
571C2×C4×D73C2×D411yescharacteristic
572C2×C4×D73C2411yescharacteristic
573C2×C4×D73C2411yescharacteristic
574C2×C4×D73C2411yescharacteristic
575#11924018—41no—
576#11924017—41no—
577#11924015—22no—
578#11924015—22no—
579#11924015—41no—
580#11924015—41no—
581D584—22no—
582D584—41no—
583#11924013—41no—
584#11924011—22no—
585#11924011—22no—
586#11924011—41no—
587#11924011—41no—
588C2×#10596831—41no—
589C2×#10596831—41no—
590C2×#10596831C2411yescharacteristic
591C2×#10596831C2411yescharacteristic
592C2×#10596831C2411yescharacteristic
593C2×#10596831C2411yescharacteristic
594C8×D73—22no—
595C8×D73—22no—
596C8×D73—41no—
597C8×D73—41no—
598C4⋊Dic73—21no—
599C4⋊Dic73—21no—
600C4⋊Dic73—21no—
601C4⋊Dic73—21no—
602C4⋊Dic73—21no—
603C4⋊Dic73—21no—
604C4⋊Dic73C2×D411yescharacteristic
605C4⋊Dic73C2411yescharacteristic
606C4⋊Dic73C2411yescharacteristic
607C4⋊Dic73C2411yescharacteristic
608C4⋊Dic73C2411yescharacteristic
609#11924007—21no—
610#11924007—21no—
611#11924007—21no—
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#11924007—21no—
621#11924007C2×D411yescharacteristic
622#11924007C2×D411yescharacteristic
623C22⋊Dic73—21no—
624C22⋊Dic73—21no—
625C22⋊Dic73—21no—
626C22⋊Dic73—21no—
627C22⋊Dic73—21no—
628C22⋊Dic73C2×D411yescharacteristic
629C22⋊Dic73C2×D411yescharacteristic
630#11924005—21no—
631#11924005—21no—
632#11924005—21no—
633#11924005—21no—
634#11924005—21no—
635#11924005—21no—
636#11924005—21no—
637#11924005—21no—
638#11924005—21no—
639#11924005—21no—
640#11924005—21no—
641#11924005—21no—
642#11924005—21no—
643#11924005—21no—
644#11924005—21no—
645#11924005—21no—
646#11924005—21no—
647#11924005—21no—
648#11924005—21no—
649#11924005—21no—
650#11924005—21no—
651#11924005—21no—
652#11924005C2×D411yescharacteristic
653#11924005C2×D411yescharacteristic
654#11924005C2×D411yescharacteristic
655#11924005C2×D411yescharacteristic
656C4×Dic73—21no—
657C4×Dic73—21no—
658C4×Dic73—21no—
659C4×Dic73—21no—
660C4×Dic73—21no—
661C4×Dic73—21no—
662C4×Dic73—21no—
663C4×Dic73C2×D411yescharacteristic
664C4×Dic73C2×D411yescharacteristic
665C4×Dic73C2411yescharacteristic
666#41×C73—22no—
667#41×C73—41no—
668C2×Q8×C73—21no—
669C2×Q8×C73—22no—
670C2×Q8×C73—41no—
671C2×Q8×C73C2411yescharacteristic
672C2×Q8×C73C2411yescharacteristic
673C2×Q8×C73C2411yescharacteristic
674C2×D4×C73—21no—
675C2×D4×C73—21no—
676C2×D4×C73C2×D411yescharacteristic
677C2×D4×C73C2411yescharacteristic
678C22×C4×C73—21no—
679C22×C4×C73—21no—
680C22×C4×C73—21no—
681C22×C4×C73C2411yescharacteristic
682C22×C4×C73C2411yescharacteristic
683Q16×C73—22no—
684Q16×C73—41no—
685SD16×C73—41no—
686M16×C73—41no—
687M16×C73—41no—
688C2×C8×C73C2411yescharacteristic
689C2×C8×C73C2411yescharacteristic
690C2×C8×C73C2411yescharacteristic
691C2×C8×C73C2411yescharacteristic
692C4⋊C4×C73—21no—
693C4⋊C4×C73—21no—
694C4⋊C4×C73—21no—
695C4⋊C4×C73—21no—
696C4⋊C4×C73—21no—
697C4⋊C4×C73—21no—
698C4⋊C4×C73—21no—
699C4⋊C4×C73—21no—
700C4⋊C4×C73C2×D411yescharacteristic
701C4⋊C4×C73C2411yescharacteristic
702C4⋊C4×C73C2411yescharacteristic
703C4⋊C4×C73C2411yescharacteristic
704C4⋊C4×C73C2411yescharacteristic
705C22⋊C4×C73—21no—
706C22⋊C4×C73—21no—
707C22⋊C4×C73—21no—
708C22⋊C4×C73—21no—
709C22⋊C4×C73—21no—
710C22⋊C4×C73—21no—
711C22⋊C4×C73—21no—
712C22⋊C4×C73C2×D411yescharacteristic
713C22⋊C4×C73C2×D411yescharacteristic
714C42×C73—21no—
715C42×C73—21no—
716C42×C73—21no—
717C42×C73C2411yescharacteristic
718C23×C73—21no—
719C23×C73C22×D411yescharacteristic
720C23×C73C22×D411yescharacteristic
721C22×D73—21no—
722C22×D73—21no—
723C22×D73—21no—
724C22×D73—42no—
725C22×D73—42no—
726C22×D73—42no—
727C22×D73—81no—
728C22×D73—81no—
729C22×D73—81no—
730C22×D73—81no—
731C22×D73—81no—
732C22×D73—81no—
733C22×D73C22×D411yescharacteristic
734C22×D73C22×D411yescharacteristic
735C22×D73C22×D411yescharacteristic
736Q8×C73—21no—
737Q8×C73—21no—
738Q8×C73—21no—
739Q8×C73—21no—
740Q8×C73—21no—
741Q8×C73—42no—
742Q8×C73C2×#4112yes—
743D4×C73—21no—
744D4×C73—21no—
745D4×C73—41no—
746D4×C73—42no—
747D4×C73—81no—
748C2×C4×C73—21no—
749C2×C4×C73—21no—
750C2×C4×C73—21no—
751C2×C4×C73—21no—
752C2×C4×C73—21no—
753C2×C4×C73—21no—
754C2×C4×C73—21no—
755C2×C4×C73—21no—
756C2×C4×C73—21no—
757C2×C4×C73—21no—
758C2×C4×C73—21no—
759C2×C4×C73—42no—
760C2×C4×C73—42no—
761C2×C4×C73—81no—
762C2×C4×C73C22×D411yescharacteristic
763C2×C4×C73C22×D411yescharacteristic
764C2×C4×C73C22×D411yescharacteristic
765C2×C4×C73C22×D411yescharacteristic
766C2×C4×C73C2511yescharacteristic
767C22⋊D73—22no—
768C22⋊D73—22no—
769C22⋊D73—22no—
770C22⋊D73—22no—
771C22⋊D73—41no—
772C22⋊D73—41no—
773C22⋊D73—42no—
774C22⋊D73—42no—
775C22⋊D73—42no—
776C22⋊D73—81no—
777C22⋊D73—81no—
778C22⋊D73—81no—
779C22⋊D73—81no—
780C2×Dic73—21no—
781C2×Dic73—21no—
782C2×Dic73—21no—
783C2×Dic73—21no—
784C2×Dic73—21no—
785C2×Dic73—81no—
786C2×Dic73C22×D411yescharacteristic
787C2×Dic73C22×D411yescharacteristic
788C2×Dic73C22×D411yescharacteristic
789C2×Dic73C22×D411yescharacteristic
790C2×Dic73C22×D411yescharacteristic
791D292—24no—
792D292—22no—
793D292—22no—
794D292—21no—
795D292—21no—
796D292—21no—
797D292—21no—
798D292—21no—
799D292—41no—
800D292—42no—
801D292—42no—
802D292—42no—
803D292—42no—
804D292—81no—
805D292—81no—
806D292—81no—
807D292C2×#4112yes—
808C4×D73—21no—
809C4×D73—21no—
810C4×D73—21no—
811C4×D73—21no—
812C4×D73—24no—
813C4×D73—41no—
814C4×D73—41no—
815C4×D73—42no—
816C4×D73—42no—
817C4×D73—42no—
818C4×D73—42no—
819C4×D73—42no—
820C4×D73—42no—
821C4×D73—81no—
822C4×D73—81no—
823C4×D73—81no—
824C4×D73—81no—
825C4×D73—81no—
826C4×D73—81no—
827C4×D73—81no—
828C4×D73—81no—
829C4×D73C2×#4112yes—
830C4×D73H(5,𝔽2)12yes—
831Dic146—22no—
832Dic146—22no—
833Dic146—21no—
834Dic146—21no—
835Dic146—42no—
836Dic146—42no—
837C8×C73—21no—
838C8×C73—21no—
839C8×C73—21no—
840C8×C73—21no—
841#10596831—21no—
842#10596831—21no—
843#10596831—21no—
844#10596831—21no—
845C22×C73—21no—
846C22×C73—21no—
847C22×C73—21no—
848C22×C73—21no—
849C22×C73—21no—
850C22×C73—21no—
851C22×C73—41no—
852C22×C73—41no—
853C22×C73—41no—
854C22×C73C23×D411yescharacteristic
855C2×D73—21no—
856C2×D73—21no—
857C2×D73—21no—
858C2×D73—21no—
859C2×D73—21no—
860C2×D73—21no—
861C2×D73—22no—
862C2×D73—21no—
863C2×D73—21no—
864C2×D73—41no—
865C2×D73—41no—
866C2×D73—41no—
867C2×D73—41no—
868C2×D73—41no—
869C2×D73—41no—
870C2×D73—41no—
871C2×D73—41no—
872C2×D73—162no—
873C2×D73—162no—
874C2×D73—162no—
875C2×D73#54612yes—
876C4×C73—21no—
877C4×C73—21no—
878C4×C73—21no—
879C4×C73—21no—
880C4×C73—22no—
881C4×C73—41no—
882C4×C73—41no—
883C4×C73—41no—
884C4×C73—41no—
885C4×C73—41no—
886C4×C73—41no—
887C4×C73C22×#4111yescharacteristic
888C4×C73C2×H(5,𝔽2)11yescharacteristic
889Dic73—21no—
890Dic73—21no—
891Dic73—21no—
892Dic73—21no—
893Dic73—41no—
894Dic73—41no—
895Dic73—41no—
896Dic73—41no—
897Dic73—41no—
898Dic73#54612yes—
899#61216—731nomaximal, Sylow
900C2×C73—41no—
901C2×C73—41no—
902C2×C73—81no—
903C2×C73C2×#54611yescharacteristic
904C2×C73#358411yescharacteristic
905C2×C73#358411yescharacteristic
906D73—22no—
907D73—41no—
908D73—41no—
909D73—42no—
910D73—81no—
911D73—81no—
912#3512—731no—
913#3500—731no—
914#3327—731no—
915#3327D7311yescharacteristic, complemented
916#3326—731no—
917#3326—731no—
918#3323—731no—
919#3323—731no—
920#3322—731no—
921#3322—731no—
922#3301—731no—
923#3301—731no—
924#3300—731no—
925#3300—731no—
926#3297—731no—
927#3297—731no—
928#3296—731no—
929#3296—731no—
930C2×#488—731no—
931#3097—731no—
932#3096—731no—
933#3080—731no—
934#3063—731no—
935#3062—731no—
936#3040—731no—
937#3013—731no—
938#3012—731no—
939C4×#135—731no—
940#2931—731no—
941#2898—731no—
942#2897—731no—
943C73#6121611yescharacteristic, complemented, Sylow
944C2×2−1+4—731no—
945C2×H(5,𝔽2)—731no—
946C2×#137—731no—
947C2×AGL(1,ℤ/8)—731no—
948C2×#135—731no—
949C2×#131—731no—
950C2×#131—731no—
951#553—731no—
952#553—731no—
953#553—731no—
954#553—731no—
955#553—1461no—
956#553—1461no—
957#553—1461no—
958#553—1461no—
959#552—731no—
960#552—731no—
961#552—731no—
962#552C2×D7311yescharacteristic, complemented
963#548—731no—
964#548—731no—
965#548—731no—
966#548C2×D7311yescharacteristic
967#546—731no—
968#546—731no—
969#546—731no—
970#546—731no—
971#546—1461no—
972#546—1461no—
973#546—1461no—
974#546—1461no—
975#541—1461no—
976#540—1461no—
977#537—731no—
978#537—731no—
979#536—731no—
980#536—1461no—
981#535—731no—
982#535—1461no—
983#532—731no—
984#532—1461no—
985#529—1461no—
986#529—1461no—
987C2×#125—731no—
988C2×#124—731no—
989C2×#124—1461no—
990#520—731no—
991#520—731no—
992C4×#41—731no—
993C4×#41—731no—
994#488—731no—
995#488—731no—
996#488—731no—
997#488—731no—
998#488—731no—
999#488—731no—
1000#488—731no—
1001#488C2×D7311yescharacteristic, complemented
1002#485—731no—
1003#485—731no—
1004#485—731no—
1005#485—731no—
1006#484—731no—
1007#484C2×D7311yescharacteristic, complemented
1008#483—731no—
1009#483—731no—
1010#482—731no—
1011#482—731no—
1012#482—731no—
1013#482C2×D7311yescharacteristic, complemented
1014#481—731no—
1015#481—731no—
1016#480—731no—
1017#480—731no—
1018#479—731no—
1019#479—731no—
1020#479—731no—
1021#479C2×D7311yescharacteristic, complemented
1022#478—731no—
1023#478—731no—
1024#478—731no—
1025#478—731no—
1026#470—731no—
1027#470C2×D7311yescharacteristic, complemented
1028#469—731no—
1029#469—731no—
1030#468—731no—
1031#468—731no—
1032#468—731no—
1033#468C2×D7311yescharacteristic, complemented
1034#467—731no—
1035#467—731no—
1036#466—731no—
1037#466—731no—
1038#465—731no—
1039#465—731no—
1040#465—731no—
1041#465—731no—
1042#464—731no—
1043#464—731no—
1044#464—731no—
1045#464C2×D7311yescharacteristic, complemented
1046#463—731no—
1047#463—731no—
1048#463—731no—
1049#463—731no—
1050#452—731no—
1051#452—731no—
1052#452—731no—
1053#452C2×D7311yescharacteristic
1054#451—731no—
1055#451C2×D7311yescharacteristic, complemented
1056#450—731no—
1057#450—731no—
1058#449—731no—
1059#449—731no—
1060#449—731no—
1061#449—731no—
1062#448—731no—
1063#448—731no—
1064#447—731no—
1065#447—731no—
1066C4×Q16—731no—
1067C4×Q16C2×D7311yescharacteristic, complemented
1068C4×SD16—731no—
1069C4×SD16—731no—
1070C4×SD16—731no—
1071C4×SD16—731no—
1072C4×D8—731no—
1073C4×D8—731no—
1074#436—731no—
1075#436—731no—
1076#436—731no—
1077#436C2×D7311yescharacteristic, complemented
1078C8×D4—731no—
1079C8×D4—731no—
1080C8×D4—731no—
1081C8×D4—731no—
1082#428—731no—
1083#428—731no—
1084#427—731no—
1085#423—731no—
1086#419—731no—
1087#419—731no—
1088#419C2×D7311yescharacteristic, complemented
1089#418—731no—
1090#418—731no—
1091#418—731no—
1092#417—731no—
1093#417—731no—
1094#417—731no—
1095#417—731no—
1096#417—731no—
1097#417C2×D7311yescharacteristic
1098#416—731no—
1099#416—731no—
1100#416—731no—
1101#416—731no—
1102#416—731no—
1103#416—731no—
1104C2×#103—731no—
1105C2×#103—731no—
1106C2×#103—731no—
1107C2×#103—731no—
1108C2×#102—731no—
1109C2×#102—731no—
1110C2×#102—731no—
1111C2×#102—731no—
1112#408—731no—
1113#408—731no—
1114C2×C4×C8—731no—
11152−1+4—2922no—
11162−1+4—1464no—
1117H(5,𝔽2)—2922no—
1118H(5,𝔽2)—1464no—
1119C2×#41—731no—
1120C2×#41—731no—
1121C2×#41—731no—
1122C2×#41—731no—
1123C2×#41—731no—
1124C2×#41—731no—
1125C2×#41—731no—
1126C2×#41—1461no—
1127C2×#41—1461no—
1128C2×#41—1461no—
1129C2×#41—1461no—
1130C2×#41C22×D7311yescharacteristic
1131C22×Q8—731no—
1132C22×Q8—731no—
1133C22×Q8—1461no—
1134C22×Q8C22×D7311yescharacteristic
1135C22×D4—731no—
1136C22×D4—731no—
1137C22×D4—731no—
1138C22×D4—1461no—
1139C22×D4—1461no—
1140C22×D4—1461no—
1141#137—2922no—
1142AGL(1,ℤ/8)—2922no—
1143#135—1464no—
1144C2×Q16—731no—
1145C2×Q16C22×D7311yescharacteristic
1146C2×Q16C22×D7311yescharacteristic
1147C2×SD16—731no—
1148C2×SD16—731no—
1149C2×SD16—731no—
1150C2×SD16—731no—
1151C2×SD16—731no—
1152C2×SD16C22×D7311yescharacteristic
1153C2×D8—731no—
1154C2×D8—731no—
1155C2×D8—731no—
1156#131—2922no—
1157#131—2922no—
1158C2×M16—731no—
1159C2×M16—731no—
1160C2×M16—731no—
1161C2×M16—731no—
1162C2×M16C22×D7311yescharacteristic
1163C2×M16C22×D7311yescharacteristic
1164C22×C8—731no—
1165C22×C8—731no—
1166C22×C8—731no—
1167C22×C8—731no—
1168C22×C8—731no—
1169C22×C8—731no—
1170C4⋊Q8—731no—
1171C4⋊Q8—1461no—
1172#127—731no—
1173#127—1461no—
1174#126—21no—
1175#126—1461no—
1176#126—1461no—
1177#126—1461no—
1178#126—1461no—
1179#126—1461no—
1180#126—1461no—
1181#126—1461no—
1182#125—21no—
1183#125—731no—
1184#125—731no—
1185#125—731no—
1186#125—1461no—
1187#125—1461no—
1188#125—1461no—
1189#125—1461no—
1190#125—1461no—
1191#125C22×D7311yescharacteristic
1192#124—21no—
1193#124—731no—
1194#124—731no—
1195#124—731no—
1196#124—731no—
1197#124—731no—
1198#124—1461no—
1199#124—1461no—
1200#124—1461no—
1201#124—1461no—
1202#124—1461no—
1203#124—1461no—
1204#124—1461no—
1205#124C22×D7311yescharacteristic
1206#123—21no—
1207#123—1461no—
1208#123—1461no—
1209#123—1461no—
1210#123—1461no—
1211#123—1461no—
1212#123—1461no—
1213#123—1461no—
1214#123—1461no—
1215#123—1461no—
1216#123—1461no—
1217#123—1461no—
1218#123—1461no—
1219#123—1461no—
1220C22⋊Q8—21no—
1221C22⋊Q8—731no—
1222C22⋊Q8—731no—
1223C22⋊Q8—731no—
1224C22⋊Q8—731no—
1225C22⋊Q8—731no—
1226C22⋊Q8—1461no—
1227C22⋊Q8—1461no—
1228C22⋊Q8—1461no—
1229C22⋊Q8—1461no—
1230C22⋊Q8—1461no—
1231C22⋊Q8C22×D7311yescharacteristic
1232C22⋊Q8C22×D7311yescharacteristic
1233C22⋊Q8C22×D7311yescharacteristic
1234#121—21no—
1235#121—731no—
1236#121—731no—
1237#121—731no—
1238#121—731no—
1239#121—731no—
1240#121—731no—
1241#121—731no—
1242#121—731no—
1243#121—731no—
1244#121—731no—
1245#121—731no—
1246#121—1461no—
1247#121—1461no—
1248#121—1461no—
1249#121—1461no—
1250#121—1461no—
1251#121—1461no—
1252#121—1461no—
1253#121—1461no—
1254#121—1461no—
1255#121—1461no—
1256#121—1461no—
1257#121—1461no—
1258#121—1461no—
1259#121—1461no—
1260#121—1461no—
1261#121—1461no—
1262#121—1461no—
1263#121C22×D7311yescharacteristic
1264#120—1461no—
1265#120—1461no—
1266#120—1461no—
1267#120—1461no—
1268#120—1461no—
1269#120—1461no—
1270C4×Q8—731no—
1271C4×Q8—731no—
1272C4×Q8—1461no—
1273C4×Q8—1461no—
1274C4×Q8C22×D7311yescharacteristic
1275C4×Q8C22×D7311yescharacteristic
1276C4×D4—21no—
1277C4×D4—731no—
1278C4×D4—731no—
1279C4×D4—731no—
1280C4×D4—731no—
1281C4×D4—731no—
1282C4×D4—731no—
1283C4×D4—731no—
1284C4×D4—1461no—
1285C4×D4—1461no—
1286C4×D4—1461no—
1287C4×D4—1461no—
1288C4×D4—1461no—
1289C4×D4—1461no—
1290C4×D4—1461no—
1291C4×D4—1461no—
1292C4×D4—1461no—
1293C4×D4—1461no—
1294C4×D4—1461no—
1295C4×D4—1461no—
1296C4×D4—1461no—
1297C4×D4—1461no—
1298C4×D4—1461no—
1299C4×D4—1461no—
1300C4×D4—1461no—
1301C4×D4C22×D7311yescharacteristic
1302#117—21no—
1303#117—731no—
1304#117—731no—
1305#117—731no—
1306#117—731no—
1307#117—731no—
1308#117—1461no—
1309#117—1461no—
1310#117—1461no—
1311#117—1461no—
1312#117—1461no—
1313#117C22×D7311yescharacteristic
1314C2×C4⋊C4—731no—
1315C2×C4⋊C4—731no—
1316C2×C4⋊C4—731no—
1317C2×C4⋊C4—731no—
1318C2×C4⋊C4—731no—
1319C2×C4⋊C4—1461no—
1320C2×C4⋊C4—1461no—
1321C2×C4⋊C4C22×D7311yescharacteristic
1322C2×C22⋊C4—1461no—
1323C2×C22⋊C4—1461no—
1324C2×C22⋊C4—1461no—
1325C2×C22⋊C4—1461no—
1326C2×C22⋊C4—1461no—
1327C2×C22⋊C4—1461no—
1328C2×C42—731no—
1329C2×C42—1461no—
1330C2×C42—1461no—
1331#107—731no—
1332#107—731no—
1333#107—731no—
1334#107—731no—
1335#107C22×D7311yescharacteristic
1336#107C22×D7311yescharacteristic
1337#106—731no—
1338#106—731no—
1339#106—731no—
1340#106—731no—
1341#106—731no—
1342#106C22×D7311yescharacteristic
1343C4⋊C8—731no—
1344C4⋊C8—731no—
1345C4⋊C8—731no—
1346C4⋊C8C22×D7311yescharacteristic
1347#103—731no—
1348#103—731no—
1349#103—731no—
1350#103—731no—
1351#103—731no—
1352#103—731no—
1353#103—731no—
1354#103—731no—
1355#103—731no—
1356#103—731no—
1357#103—731no—
1358#103—731no—
1359#103—731no—
1360#103C22×D7311yescharacteristic
1361#103C22×D7311yescharacteristic
1362#103C22×D7311yescharacteristic
1363#103C22×D7311yescharacteristic
1364#103C22×D7311yescharacteristic
1365#103C22×D7311yescharacteristic
1366#103C22×D7311yescharacteristic
1367#102—731no—
1368#102—731no—
1369#102—731no—
1370#102—731no—
1371#102—731no—
1372#102—731no—
1373#102—731no—
1374#102—731no—
1375#102—731no—
1376#102—731no—
1377#102—731no—
1378#102—731no—
1379#102—731no—
1380#102—731no—
1381#102—731no—
1382#102—731no—
1383#102—731no—
1384#102C22×D7311yescharacteristic
1385#102C22×D7311yescharacteristic
1386#102C22×D7311yescharacteristic
1387C22⋊C8—731no—
1388C22⋊C8—731no—
1389C22⋊C8—731no—
1390C22⋊C8—731no—
1391C22⋊C8—731no—
1392C22⋊C8—731no—
1393C22⋊C8C22×D7311yescharacteristic
1394C22⋊C8C22×D7311yescharacteristic
1395C4×C8—731no—
1396C4×C8—731no—
1397C4×C8—731no—
1398C4×C8C22×D7311yescharacteristic
1399C24—1461no—
1400C24—1461no—
1401C24—1461no—
1402#41—22no—
1403#41—41no—
1404#41—2921no—
1405#41—2924no—
1406#41—2924no—
1407#41—2924no—
1408#41—2924no—
1409#41—2921no—
1410#41—2921no—
1411#41—734no—
1412#41—1462no—
1413#41—1462no—
1414#41—1462no—
1415#41—1462no—
1416#41—1462no—
1417#41—1462no—
1418#41—1462no—
1419#41—1462no—
1420#41—1462no—
1421#41—1462no—
1422C2×Q8—21no—
1423C2×Q8—22no—
1424C2×Q8—41no—
1425C2×Q8—2921no—
1426C2×Q8—2924no—
1427C2×Q8—731no—
1428C2×Q8—731no—
1429C2×Q8—731no—
1430C2×Q8—1461no—
1431C2×Q8—1461no—
1432C2×Q8—1462no—
1433C2×Q8—1462no—
1434C2×Q8—1462no—
1435C2×Q8C23×D7311yescharacteristic
1436C2×Q8C23×D7311yescharacteristic
1437C2×Q8C23×D7311yescharacteristic
1438C2×D4—21no—
1439C2×D4—21no—
1440C2×D4—2921no—
1441C2×D4—2924no—
1442C2×D4—2924no—
1443C2×D4—2921no—
1444C2×D4—2924no—
1445C2×D4—731no—
1446C2×D4—731no—
1447C2×D4—731no—
1448C2×D4—731no—
1449C2×D4—731no—
1450C2×D4—731no—
1451C2×D4—731no—
1452C2×D4—731no—
1453C2×D4—731no—
1454C2×D4—731no—
1455C2×D4—731no—
1456C2×D4—731no—
1457C2×D4—1461no—
1458C2×D4—1461no—
1459C2×D4—1461no—
1460C2×D4—1462no—
1461C2×D4—1461no—
1462C2×D4—1461no—
1463C2×D4—1461no—
1464C2×D4—1461no—
1465C2×D4—1462no—
1466C2×D4—1462no—
1467C2×D4—1461no—
1468C2×D4—1461no—
1469C2×D4—1462no—
1470C2×D4—1461no—
1471C2×D4—1461no—
1472C2×D4—1461no—
1473C2×D4—1461no—
1474C2×D4—1461no—
1475C2×D4—1461no—
1476C2×D4D4×D7311yescharacteristic
1477C2×D4C23×D7311yescharacteristic
1478C22×C4—21no—
1479C22×C4—21no—
1480C22×C4—21no—
1481C22×C4—731no—
1482C22×C4—731no—
1483C22×C4—731no—
1484C22×C4—731no—
1485C22×C4—731no—
1486C22×C4—1461no—
1487C22×C4—1461no—
1488C22×C4—1461no—
1489C22×C4—1461no—
1490C22×C4—1461no—
1491C22×C4—1461no—
1492C22×C4—1461no—
1493C22×C4—1461no—
1494C22×C4—1461no—
1495C22×C4—1461no—
1496C22×C4—1461no—
1497C22×C4—1461no—
1498C22×C4—1461no—
1499C22×C4—1461no—
1500C22×C4—1461no—
1501C22×C4—1461no—
1502C22×C4C23×D7311yescharacteristic
1503C22×C4C23×D7311yescharacteristic
1504Q16—22no—
1505Q16—41no—
1506Q16—2921no—
1507SD16—41no—
1508SD16—2921no—
1509SD16—2921no—
1510SD16—2921no—
1511SD16—1462no—
1512SD16—1462no—
1513D8—2921no—
1514D8—2921no—
1515D8—1462no—
1516M16—41no—
1517M16—41no—
1518M16—2921no—
1519M16—2921no—
1520M16—1462no—
1521M16—1462no—
1522C2×C8—2921no—
1523C2×C8—2921no—
1524C2×C8—2921no—
1525C2×C8—2921no—
1526C2×C8—731no—
1527C2×C8—731no—
1528C2×C8—731no—
1529C2×C8—731no—
1530C2×C8—1462no—
1531C2×C8—1462no—
1532C2×C8C23×D7311yescharacteristic
1533C2×C8C23×D7311yescharacteristic
1534C2×C8C23×D7311yescharacteristic
1535C2×C8C23×D7311yescharacteristic
1536C4⋊C4—21no—
1537C4⋊C4—21no—
1538C4⋊C4—21no—
1539C4⋊C4—21no—
1540C4⋊C4—21no—
1541C4⋊C4—21no—
1542C4⋊C4—21no—
1543C4⋊C4—21no—
1544C4⋊C4—731no—
1545C4⋊C4—731no—
1546C4⋊C4—731no—
1547C4⋊C4—731no—
1548C4⋊C4—731no—
1549C4⋊C4—731no—
1550C4⋊C4—731no—
1551C4⋊C4—1461no—
1552C4⋊C4—1461no—
1553C4⋊C4—1461no—
1554C4⋊C4—1461no—
1555C4⋊C4—1461no—
1556C4⋊C4—1461no—
1557C4⋊C4—1461no—
1558C4⋊C4—1461no—
1559C4⋊C4—1461no—
1560C4⋊C4—1461no—
1561C4⋊C4—1461no—
1562C4⋊C4—1461no—
1563C4⋊C4—1461no—
1564C4⋊C4—1461no—
1565C4⋊C4—1461no—
1566C4⋊C4—1461no—
1567C4⋊C4—1461no—
1568C4⋊C4—1461no—
1569C4⋊C4D4×D7311yescharacteristic
1570C4⋊C4C23×D7311yescharacteristic
1571C4⋊C4C23×D7311yescharacteristic
1572C4⋊C4C23×D7311yescharacteristic
1573C4⋊C4C23×D7311yescharacteristic
1574C22⋊C4—21no—
1575C22⋊C4—21no—
1576C22⋊C4—21no—
1577C22⋊C4—21no—
1578C22⋊C4—21no—
1579C22⋊C4—21no—
1580C22⋊C4—21no—
1581C22⋊C4—731no—
1582C22⋊C4—731no—
1583C22⋊C4—731no—
1584C22⋊C4—731no—
1585C22⋊C4—731no—
1586C22⋊C4—731no—
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⋊C4—1461no—
1599C22⋊C4—1461no—
1600C22⋊C4—1461no—
1601C22⋊C4—1461no—
1602C22⋊C4—1461no—
1603C22⋊C4—1461no—
1604C22⋊C4—1461no—
1605C22⋊C4—1461no—
1606C22⋊C4—1461no—
1607C22⋊C4—1461no—
1608C22⋊C4—1461no—
1609C22⋊C4—1461no—
1610C22⋊C4—1461no—
1611C22⋊C4—1461no—
1612C22⋊C4—1461no—
1613C22⋊C4—1461no—
1614C22⋊C4D4×D7311yescharacteristic
1615C22⋊C4D4×D7311yescharacteristic
1616C42—21no—
1617C42—21no—
1618C42—21no—
1619C42—731no—
1620C42—731no—
1621C42—731no—
1622C42—1461no—
1623C42—1461no—
1624C42—1461no—
1625C42—1461no—
1626C42—1461no—
1627C42—1461no—
1628C42—1461no—
1629C42C23×D7311yescharacteristic
1630C23—21no—
1631C23—2922no—
1632C23—2922no—
1633C23—2922no—
1634C23—5841no—
1635C23—5841no—
1636C23—5841no—
1637C23—5841no—
1638C23—5841no—
1639C23—5841no—
1640C23—731no—
1641C23—731no—
1642C23—731no—
1643C23—1461no—
1644C23—1461no—
1645C23—1461no—
1646C23C2×D4×D7311yescharacteristic
1647C23C2×D4×D7311yescharacteristic
1648Q8—21no—
1649Q8—21no—
1650Q8—21no—
1651Q8—21no—
1652Q8—21no—
1653Q8—42no—
1654Q8—2922no—
1655Q8—2922no—
1656Q8—1462no—
1657Q8—1462no—
1658Q8—1461no—
1659Q8—1461no—
1660Q8#41×D7312yes—
1661D4—21no—
1662D4—21no—
1663D4—41no—
1664D4—42no—
1665D4—81no—
1666D4—2922no—
1667D4—2922no—
1668D4—2921no—
1669D4—2922no—
1670D4—2922no—
1671D4—2922no—
1672D4—2922no—
1673D4—2921no—
1674D4—2921no—
1675D4—2922no—
1676D4—5841no—
1677D4—5841no—
1678D4—5841no—
1679D4—5841no—
1680D4—5841no—
1681D4—5841no—
1682D4—5841no—
1683D4—732no—
1684D4—1462no—
1685D4—1464no—
1686D4—1462no—
1687D4—1462no—
1688D4—1462no—
1689D4—1462no—
1690D4—1462no—
1691D4—1461no—
1692D4—1461no—
1693D4—1461no—
1694D4—1461no—
1695D4—1461no—
1696C2×C4—21no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—21no—
1705C2×C4—21no—
1706C2×C4—21no—
1707C2×C4—42no—
1708C2×C4—42no—
1709C2×C4—81no—
1710C2×C4—2922no—
1711C2×C4—2922no—
1712C2×C4—2922no—
1713C2×C4—2921no—
1714C2×C4—2921no—
1715C2×C4—2922no—
1716C2×C4—2922no—
1717C2×C4—2922no—
1718C2×C4—5841no—
1719C2×C4—5841no—
1720C2×C4—5841no—
1721C2×C4—5841no—
1722C2×C4—5841no—
1723C2×C4—5841no—
1724C2×C4—5841no—
1725C2×C4—5841no—
1726C2×C4—5841no—
1727C2×C4—731no—
1728C2×C4—732no—
1729C2×C4—732no—
1730C2×C4—731no—
1731C2×C4—731no—
1732C2×C4—731no—
1733C2×C4—731no—
1734C2×C4—1464no—
1735C2×C4—1461no—
1736C2×C4—1461no—
1737C2×C4—1461no—
1738C2×C4—1461no—
1739C2×C4—1461no—
1740C2×C4—1461no—
1741C2×C4—1461no—
1742C2×C4—1461no—
1743C2×C4—1461no—
1744C2×C4C2×D4×D7311yescharacteristic
1745C2×C4C2×D4×D7311yescharacteristic
1746C2×C4C2×D4×D7311yescharacteristic
1747C2×C4C2×D4×D7311yescharacteristic
1748C2×C4C24×D7311yescharacteristic
1749C8—21no—
1750C8—21no—
1751C8—21no—
1752C8—21no—
1753C8—1461no—
1754C8—1461no—
1755C8—1461no—
1756C8—1461no—
1757C22—21no—
1758C22—21no—
1759C22—21no—
1760C22—21no—
1761C22—21no—
1762C22—21no—
1763C22—41no—
1764C22—41no—
1765C22—41no—
1766C22—2921no—
1767C22—2921no—
1768C22—2921no—
1769C22—2921no—
1770C22—2921no—
1771C22—2921no—
1772C22—2921no—
1773C22—2921no—
1774C22—732no—
1775C22—11682no—
1776C22—11682no—
1777C22—11682no—
1778C22—1462no—
1779C22—1461no—
1780C22—1461no—
1781C22—1461no—
1782C22—1461no—
1783C22—1461no—
1784C22—1461no—
1785C22—1461no—
1786C22—1461no—
1787C22C22×D4×D7311yescharacteristic
1788C4—21no—
1789C4—21no—
1790C4—22no—
1791C4—21no—
1792C4—21no—
1793C4—41no—
1794C4—41no—
1795C4—41no—
1796C4—41no—
1797C4—41no—
1798C4—41no—
1799C4—2921no—
1800C4—2921no—
1801C4—2921no—
1802C4—2921no—
1803C4—2921no—
1804C4—732no—
1805C4—1461no—
1806C4—1461no—
1807C4—1461no—
1808C4—1461no—
1809C4C2×#41×D7311yescharacteristic
1810C4H(5,𝔽2)×D7311yescharacteristic
1811C2—41no—
1812C2—41no—
1813C2—81no—
1814C2—2922no—
1815C2—2921no—
1816C2—2921no—
1817C2—5841no—
1818C2—5841no—
1819C2—1462no—
1820C2#546×D7311yescharacteristic
1821C2#2262470111yescharacteristic
1822C2#2262470411yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3327C2
socleC22×C73C23×D4
hypercenter#3327D73
hypocenterC73#61216
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3327

Complements

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

NH ≅ G/Ntype
1. #22623845C2semidirect
2. #22623722C2semidirect
3. #22622204C2semidirect
4. #22622185C2semidirect
5. #22622180C2semidirect
6. #22622153C2semidirect
7. #22622142C2semidirect
8. #22622134C2semidirect
9. #22622131C2semidirect
10. #22621833C2semidirect
11. #22621830C2semidirect
12. #22621822C2semidirect
13. #22621811C2semidirect
14. #22621784C2semidirect
15. #22621779C2semidirect
16. #22621773C2semidirect
17. #22621760C2semidirect
18. #488×D73C2semidirect
19. #22619899C2semidirect
20. #22619886C2semidirect
21. #22619750C2semidirect
22. #22619619C2semidirect
23. #22619606C2semidirect
24. #22619422C2semidirect
25. #22619247C2semidirect
26. #22619239C2semidirect
27. C4×#14556614C2semidirect
28. #22618640C2semidirect
29. #22618463C2semidirect
30. #22618455C2semidirect
31. C73×#3327C2semidirect
34. C2×#14556623C22semidirect
38. C2×#14556599C22semidirect
40. #17989290C22semidirect
42. #17989285C22semidirect
43. #17989283C22semidirect
46. #17989281C22semidirect
47. #17989279C22semidirect
48. #17989278C22semidirect
49. #17989271C22semidirect
64. #17989167C22semidirect
73. #125×D73C22semidirect
77. #17989067C22semidirect
79. C4×#11924029C22semidirect
80. #17988944C22semidirect
81. #17988943C22semidirect
82. #17988943C22semidirect
83. #17988942C22semidirect
84. #17988941C22semidirect
85. #17988940C22semidirect
86. #17988940C22semidirect
87. #17988930C22semidirect
88. #17988929C22semidirect
89. #17988927C22semidirect
90. #17988925C22semidirect
91. #17988924C22semidirect
92. #17988917C22semidirect
93. #17988916C22semidirect
94. #17988914C22semidirect
95. #17988911C22semidirect
96. #17988909C22semidirect
97. #17988907C22semidirect
98. #17988903C22semidirect
99. #17988901C22semidirect
100. #17988899C22semidirect
101. #17988896C22semidirect
102. #17988894C22semidirect
103. #17988892C22semidirect
104. #17988890C22semidirect
105. #17988888C22semidirect
106. #17988886C22semidirect
107. #17988884C22semidirect
108. #17988844C22semidirect
109. #17988840C22semidirect
110. #17988839C22semidirect
111. #17988836C22semidirect
112. #17988836C22semidirect
113. #17988833C22semidirect
114. #17988826C22semidirect
115. #17988825C22semidirect
116. #17988824C22semidirect
117. #17988821C22semidirect
118. #17988818C22semidirect
119. #17988818C22semidirect
120. #17988817C22semidirect
121. #17988813C22semidirect
122. #17988811C22semidirect
123. #17988809C22semidirect
124. #17988807C22semidirect
125. #17988805C22semidirect
126. #17988803C22semidirect
127. #17988801C22semidirect
128. #17988799C22semidirect
130. #17988748C22semidirect
131. #17988747C22semidirect
132. #17988741C22semidirect
136. #17988735C22semidirect
137. #17988734C22semidirect
139. #17988727C22semidirect
140. #17988726C22semidirect
143. Q16×Dic73C22semidirect
144. C4×#11924015C22semidirect
145. C4×#11924015C22semidirect
146. #17988672C22semidirect
147. #17988672C22semidirect
148. C4×D584C22semidirect
149. #17988669C22semidirect
150. #17988666C22semidirect
151. #17988663C22semidirect
152. #17988663C22semidirect
153. D4×#10596831C22semidirect
154. #17988652C22semidirect
155. #17988650C22semidirect
156. #17988650C22semidirect
157. #17988628C22semidirect
158. #17988626C22semidirect
159. #17988624C22semidirect
160. #17988609C22semidirect
161. #17988594C22semidirect
162. #17988594C22semidirect
166. #17988589C22semidirect
170. #17988587C22semidirect
174. #17988582C22semidirect
175. #17988582C22semidirect
176. #17988581C22semidirect
177. C2×#14556515C22semidirect
178. #103×D73C22semidirect
179. #103×D73C22semidirect
180. #103×D73C22semidirect
186. #17988552C22semidirect
187. C4×C8×D73C22semidirect
188. #552×C73C22semidirect
190. #488×C73C22semidirect
191. #484×C73C22semidirect
192. #482×C73C22semidirect
193. #479×C73C22semidirect
194. #470×C73C22semidirect
195. #468×C73C22semidirect
196. #464×C73C22semidirect
198. #451×C73C22semidirect
199. C4×Q16×C73C22semidirect
200. #436×C73C22semidirect
201. #419×C73C22semidirect
915. #3327D73semidirect
943. C73#61216semidirect
962. #552C2×D73semidirect
1001. #488C2×D73semidirect
1007. #484C2×D73semidirect
1013. #482C2×D73semidirect
1021. #479C2×D73semidirect
1027. #470C2×D73semidirect
1033. #468C2×D73semidirect
1045. #464C2×D73semidirect
1055. #451C2×D73semidirect
1067. C4×Q16C2×D73semidirect
1077. #436C2×D73semidirect
1088. #419C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238452
#226237222
#226222042
#226221852
#226221802
#226221532
#226221422
#226221342
#226221312
#226218332
#226218302
#226218222
#226218112
#226217842
#226217792
#226217732
#226217602
#488×D732
#226198992
#226198862
#226197502
#226196192
#226196062
#226194222
#226192472
#226192392
C4×#145566142
#226186402
#226184632
#226184552
C73×#33272
#6121673