Finite Group Databasebeta

← #33978701

Subgroups — #33978701

Order 18688.

1916 conjugacy classes of subgroups.

The subgroup lattice has 1786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623837C211yesmaximal, characteristic, complemented
2#22623536C211yesmaximal, characteristic, complemented
3#22623003C211yesmaximal, characteristic, complemented
4#22623001C211yesmaximal, characteristic, complemented
5#22622762C211yesmaximal, characteristic, complemented
6#22622754C211yesmaximal, characteristic, complemented
7#22622048C211yesmaximal, characteristic, complemented
8#22622046C211yesmaximal, characteristic, complemented
9#22621913C211yesmaximal, characteristic, complemented
10#22621911C211yesmaximal, characteristic, complemented
11#22621835C211yesmaximal, characteristic, complemented
12#22621833C211yesmaximal, characteristic, complemented
13#22621634C211yesmaximal, characteristic, complemented
14#22621460C211yesmaximal, characteristic, complemented
15#22621456C211yesmaximal, characteristic, complemented
16#22621430C211yesmaximal, characteristic, complemented
17#22621426C211yesmaximal, characteristic, complemented
18#22621301C211yesmaximal, characteristic, complemented
19#22621252C211yesmaximal, characteristic, complemented
20#22621242C211yesmaximal, characteristic, complemented
21#22620961C211yesmaximal, characteristic, complemented
22#22620923C211yesmaximal, characteristic, complemented
23#22620902C211yesmaximal, characteristic, complemented
24#22620086C211yesmaximal, characteristic, complemented
25#22620017C211yesmaximal, characteristic, complemented
26#22619937C211yesmaximal, characteristic, complemented
27#22619393C211yesmaximal, characteristic, complemented
28#22619382C211yesmaximal, characteristic, complemented
29C2×#17988790C211yesmaximal, characteristic, complemented
30#22619054C211yesmaximal, characteristic, complemented
31C73×#3282C211yesmaximal, characteristic, complemented
32C2×#14556618C2211yescharacteristic
33C2×#14556615C2211yescharacteristic
34C2×#14556611C2211yescharacteristic
35C22×#11924016C2211yescharacteristic
36#17989319C2211yescharacteristic
37#17989309C2211yescharacteristic, complemented
38#17989306C2211yescharacteristic, complemented
39#17989299—21no—
40#17989296C2211yescharacteristic
41#17989295C2211yescharacteristic
42#17989291—21no—
43#17989286—21no—
44#17989284C2211yescharacteristic
45#17989283C2211yescharacteristic
46#17989280—21no—
47#17989280—21no—
48#17989263—21no—
49#17989260—21no—
50#17989248C2211yescharacteristic
51#17989246C2211yescharacteristic, complemented
52#17989243C2211yescharacteristic
53#17989239C2211yescharacteristic, complemented
54#17989236C2211yescharacteristic, complemented
55#17989225C2211yescharacteristic
56#17989224—21no—
57D4×C22⋊D73C2211yescharacteristic
58#17989207—21no—
59#17989201—21no—
60#17989164—21no—
61#17989141C2211yescharacteristic, complemented
62#17989139C2211yescharacteristic, complemented
63#17989136C2211yescharacteristic, complemented
64#17989133C2211yescharacteristic, complemented
65#17989132C2211yescharacteristic
66#17989132C2211yescharacteristic, complemented
67C2×#14556589C2211yescharacteristic, complemented
68#17989123C2211yescharacteristic
69#17989116C2211yescharacteristic
70#17989114—21no—
71#17989097—21no—
72#17989093—21no—
73#17989066—21no—
74#41×Dic73C2211yescharacteristic
75C4×#11924027C2211yescharacteristic
76C2×D4×Dic73C2211yescharacteristic
77C2×#14556551—21no—
78C4×D4×D73C2211yescharacteristic
79#17988980C2211yescharacteristic, complemented
80#17988980C2211yescharacteristic, complemented
81#17988975C2211yescharacteristic
82#17988973C2211yescharacteristic
83#17988969C2211yescharacteristic, complemented
84#17988954C2211yescharacteristic, complemented
85#17988954C2211yescharacteristic, complemented
86#17988948C2211yescharacteristic, complemented
87#17988945C2211yescharacteristic, complemented
88#17988942C2211yescharacteristic, complemented
89#17988941C2211yescharacteristic, complemented
90#17988929C2211yescharacteristic, complemented
91#17988925C2211yescharacteristic, complemented
92#17988919C2211yescharacteristic, complemented
93#17988916C2211yescharacteristic, complemented
94#17988906C2211yescharacteristic, complemented
95#17988903C2211yescharacteristic, complemented
96#17988895C2211yescharacteristic, complemented
97#17988894C2211yescharacteristic, complemented
98#17988886C2211yescharacteristic, complemented
99#17988885C2211yescharacteristic, complemented
100#17988880C2211yescharacteristic, complemented
101#17988876C2211yescharacteristic, complemented
102#17988875C2211yescharacteristic
103#17988875C2211yescharacteristic, complemented
104#17988871C2211yescharacteristic, complemented
105#17988870C2211yescharacteristic, complemented
106#17988844C2211yescharacteristic, complemented
107#17988842C2211yescharacteristic, complemented
108#17988832C2211yescharacteristic
109#17988830C2211yescharacteristic
110#17988823C2211yescharacteristic
111#17988821C2211yescharacteristic
112#17988818C2211yescharacteristic, complemented
113#17988818C2211yescharacteristic, complemented
114#17988816C2211yescharacteristic, complemented
115#17988814C2211yescharacteristic, complemented
116#17988811C2211yescharacteristic, complemented
117#17988807C2211yescharacteristic, complemented
118#17988806C2211yescharacteristic, complemented
119#17988805C2211yescharacteristic, complemented
120#17988804C2211yescharacteristic
121#17988804C2211yescharacteristic, complemented
122#17988803C2211yescharacteristic, complemented
123#17988802C2211yescharacteristic
124#17988800C2211yescharacteristic
125#17988799C2211yescharacteristic, complemented
126#17988795C2211yescharacteristic, complemented
127#17988795C2211yescharacteristic, complemented
128#17988791C2211yescharacteristic, complemented
129#17988791C2211yescharacteristic, complemented
130#17988790C2211yescharacteristic
131#17988790C2211yescharacteristic
132#17988790C2211yescharacteristic
133#17988790C2211yescharacteristic
134#17988790C2211yescharacteristic, complemented
135#17988790C2211yescharacteristic, complemented
136#17988790C2211yescharacteristic, complemented
137#17988790C2211yescharacteristic, complemented
138#17988786C2211yescharacteristic
139#17988785C2211yescharacteristic
140#17988785C2211yescharacteristic, complemented
141#17988781C2211yescharacteristic, complemented
142#17988780C2211yescharacteristic
143#17988780C2211yescharacteristic, complemented
144#17988749C2211yescharacteristic
145#17988748C2211yescharacteristic, complemented
146#17988746C2211yescharacteristic, complemented
147#17988742C2211yescharacteristic, complemented
148#17988739C2211yescharacteristic
149#17988736C2211yescharacteristic
150#17988734C2211yescharacteristic, complemented
151#17988732C2211yescharacteristic, complemented
152#17988731C2211yescharacteristic
153#17988730C2211yescharacteristic, complemented
154#17988729C2211yescharacteristic
155#17988728C2211yescharacteristic
156#17988726C2211yescharacteristic
157#17988721C2211yescharacteristic
158#17988717C2211yescharacteristic, complemented
159#17988714C2211yescharacteristic, complemented
160#17988699C2211yescharacteristic
161#17988699C2211yescharacteristic, complemented
162#17988696C2211yescharacteristic
163#17988696C2211yescharacteristic, complemented
164#17988694C2211yescharacteristic, complemented
165#17988691C2211yescharacteristic, complemented
166#17988688C2211yescharacteristic
167#17988684C2211yescharacteristic
168C4×#11924017C2211yescharacteristic, complemented
169C4×#11924015C2211yescharacteristic, complemented
170C4×#11924016C2211yescharacteristic
171#17988658C2211yescharacteristic
172#17988658C2211yescharacteristic, complemented
173#17988655C2211yescharacteristic
174#17988655C2211yescharacteristic, complemented
175D4×#10596831C2211yescharacteristic, complemented
176#17988641C2211yescharacteristic, complemented
177#17988641C2211yescharacteristic, complemented
178#17988638C2211yescharacteristic, complemented
179#17988609C2211yescharacteristic, complemented
180C2×#14556520C2211yescharacteristic, complemented
181C2×#14556520C2211yescharacteristic, complemented
182#17988587C2211yescharacteristic, complemented
183#17988585C2211yescharacteristic, complemented
184#17988584C2211yescharacteristic, complemented
185#17988583C2211yescharacteristic, complemented
186C2×#14556516C2211yescharacteristic, complemented
187C2×#14556515C2211yescharacteristic, complemented
188C2×#135×C73C2211yescharacteristic
189C22×SD16×C73C2211yescharacteristic
190#548×C73C2211yescharacteristic, complemented
191#546×C73C2211yescharacteristic
192#495×C73C2211yescharacteristic, complemented
193#465×C73C2211yescharacteristic, complemented
194#465×C73C2211yescharacteristic, complemented
195#464×C73C2211yescharacteristic, complemented
196#463×C73C2211yescharacteristic
197#452×C73C2211yescharacteristic
198#451×C73C2211yescharacteristic, complemented
199#449×C73C2211yescharacteristic, complemented
200#447×C73C2211yescharacteristic
201C4×SD16×C73C2211yescharacteristic
202C8×D4×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924028C2311yescharacteristic
205C2×#11924027—21no—
206C2×#11924027—21no—
207C2×#11924027D411yescharacteristic
208C2×#11924027C2311yescharacteristic
209C22×Dic146C2311yescharacteristic
210C22×C22⋊D73—21no—
211C2×D4×D73C2311yescharacteristic
212C23×Dic73—21no—
213C22×C4×D73—21no—
214#14556618—42no—
215#14556615—42no—
216#14556611—42no—
217C2×#11924018C2311yescharacteristic
218C2×#11924018C2311yescharacteristic
219C2×#11924017C2311yescharacteristic
220C2×#11924017C2311yescharacteristic
221C2×#11924016—42no—
222C2×#11924016C2311yescharacteristic
223C2×#11924016C2311yescharacteristic
224C2×#11924016C2311yescharacteristic
225C2×#11924016C2311yescharacteristic
226C2×#11924015C2311yescharacteristic
227C2×#11924015C2311yescharacteristic
228C2×#11924015C2311yescharacteristic
229C2×D584C2311yescharacteristic
230C2×#11924013C2311yescharacteristic
231C2×#11924013C2311yescharacteristic
232C2×#11924013C2311yescharacteristic
233C2×#11924011C2311yescharacteristic
234C2×#11924011C2311yescharacteristic
235C22×#10596831C2311yescharacteristic
236C22×#10596831C2311yescharacteristic
237#14556590C2311yescharacteristic
238#14556590C2311yescharacteristic
239#14556589—21no—
240#14556589—21no—
241#14556589C2311yescharacteristic
242#14556589C2311yescharacteristic
243#14556589C2311yescharacteristic
244#14556589C2311yescharacteristic
245#14556587C2311yescharacteristic
246#14556587C2311yescharacteristic
247#14556586—21no—
248#14556586—21no—
249#14556586—21no—
250#14556585—21no—
251#14556584—21no—
252#14556584—21no—
253#14556584—21no—
254#14556584—21no—
255#14556583C2311yescharacteristic
256#14556582C2311yescharacteristic
257#14556581—21no—
258#14556581—21no—
259#14556581—21no—
260#14556580—21no—
261#14556580C2311yescharacteristic
262#14556580C2311yescharacteristic
263#14556579C2311yescharacteristic
264#14556578C2311yescharacteristic
265#14556577—21no—
266#14556577—21no—
267#14556577—21no—
268#14556577—21no—
269#14556577—21no—
270#14556576—21no—
271#14556575—21no—
272#14556575—21no—
273#14556574—21no—
274#14556574—21no—
275#14556573—21no—
276#14556573—21no—
277#14556573—21no—
278#14556573—21no—
279#14556572—21no—
280#14556572—21no—
281#14556571—21no—
282#14556571C2311yescharacteristic
283#14556570—21no—
284#14556570C2311yescharacteristic
285#14556569—21no—
286#14556569—21no—
287#14556569—21no—
288#14556568—21no—
289#14556568—21no—
290#14556568—21no—
291#14556568—21no—
292#14556568—21no—
293#14556568—21no—
294#14556567—21no—
295#14556567C2311yescharacteristic
296#14556567C2311yescharacteristic
297#14556565—21no—
298#14556565C2311yescharacteristic
299#14556565C2311yescharacteristic
300#14556565C2311yescharacteristic
301#14556564—21no—
302#14556564—21no—
303#14556564—21no—
304#14556563—21no—
305#14556563—21no—
306#14556563—21no—
307#14556563—21no—
308#14556563—21no—
309#14556563—21no—
310#14556563—21no—
311#14556563—21no—
312#14556563—21no—
313#14556563—21no—
314#14556562—21no—
315#14556562C2311yescharacteristic
316#14556560—21no—
317#14556559—21no—
318#14556559—21no—
319Q8×Dic73C2311yescharacteristic
320Q8×Dic73C2311yescharacteristic
321Q8×Dic73C2311yescharacteristic
322C4×Dic146—21no—
323C4×Dic146C2311yescharacteristic
324C4×Dic146C2311yescharacteristic
325#14556556—21no—
326#14556556D411yescharacteristic
327#14556556C2311yescharacteristic
328C4×D292C2311yescharacteristic
329D4×Dic73—21no—
330D4×Dic73—21no—
331D4×Dic73—21no—
332D4×Dic73—21no—
333D4×Dic73—21no—
334D4×Dic73D411yescharacteristic
335D4×Dic73C2311yescharacteristic
336D4×Dic73C2311yescharacteristic
337D4×Dic73C2311yescharacteristic
338D4×Dic73C2311yescharacteristic
339D4×Dic73C2311yescharacteristic
340D4×Dic73C2311yescharacteristic
341#14556553C2311yescharacteristic
342#14556553C2311yescharacteristic
343C4×C22⋊D73—21no—
344C4×C22⋊D73—21no—
345C4×C22⋊D73—21no—
346C4×C22⋊D73—21no—
347C4×C22⋊D73C2311yescharacteristic
348C4×C22⋊D73C2311yescharacteristic
349#14556551—21no—
350#14556551—21no—
351#14556551—21no—
352#14556551—21no—
353#14556551—21no—
354#14556551—21no—
355#14556551—21no—
356#14556551—21no—
357#14556551—21no—
358#14556551—21no—
359#14556551—21no—
360#14556551—21no—
361#14556551D411yescharacteristic
362#14556551D411yescharacteristic
363#14556550—21no—
364#14556550C2311yescharacteristic
365#14556549—21no—
366#14556549D411yescharacteristic
367#14556548—21no—
368#14556548—21no—
369#14556547—21no—
370#14556547—21no—
371#14556547—21no—
372#14556547D411yescharacteristic
373#14556547D411yescharacteristic
374C2×C4⋊Dic73C2311yescharacteristic
375C2×#11924007—21no—
376C2×#11924007—21no—
377C2×#11924007—21no—
378C2×#11924007—21no—
379C4⋊C4×D73—21no—
380C4⋊C4×D73C2311yescharacteristic
381C2×C22⋊Dic73—21no—
382C2×#11924005—21no—
383C22⋊C4×D73—21no—
384C2×C4×Dic73—21no—
385C2×C4×Dic73C2311yescharacteristic
386C2×C4×Dic73C2311yescharacteristic
387C42×D73C2311yescharacteristic
388#14556525C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556523C2311yescharacteristic
391#14556523C2311yescharacteristic
392#14556522C2311yescharacteristic
393#14556522C2311yescharacteristic
394#14556522C2311yescharacteristic
395C4⋊#10596831C2311yescharacteristic
396#14556520C2311yescharacteristic
397#14556520C2311yescharacteristic
398#14556520C2311yescharacteristic
399#14556520C2311yescharacteristic
400#14556520C2311yescharacteristic
401#14556520C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556516C2311yescharacteristic
405#14556516C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556516C2311yescharacteristic
409#14556516C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556515C2311yescharacteristic
416#14556515C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556514C2311yescharacteristic
419#14556513C2311yescharacteristic
420#14556513C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556512C2311yescharacteristic
424#14556512C2311yescharacteristic
425#14556512C2311yescharacteristic
426#14556512C2311yescharacteristic
427#14556512C2311yescharacteristic
428#14556511C2311yescharacteristic
429#14556511C2311yescharacteristic
430C22⋊#10596831C2311yescharacteristic
431C22⋊#10596831C2311yescharacteristic
432#14556503C2311yescharacteristic
433#14556503C2311yescharacteristic
434#14556501C2311yescharacteristic
435#14556501C2311yescharacteristic
436#14556501C2311yescharacteristic
437#14556501C2311yescharacteristic
438C4×#10596831C2311yescharacteristic
439C2×#41×C73C2311yescharacteristic
440C2×#41×C73C2311yescharacteristic
441C22×Q8×C73C2311yescharacteristic
442C22×D4×C73C2311yescharacteristic
443#135×C73—42no—
444C2×Q16×C73C2311yescharacteristic
445C2×Q16×C73C2311yescharacteristic
446C2×SD16×C73—42no—
447C2×SD16×C73C2311yescharacteristic
448C2×SD16×C73C2311yescharacteristic
449C2×SD16×C73C2311yescharacteristic
450C2×SD16×C73C2311yescharacteristic
451C2×SD16×C73C2311yescharacteristic
452C2×D8×C73C2311yescharacteristic
453C2×D8×C73C2311yescharacteristic
454C22×C8×C73C2311yescharacteristic
455C22×C8×C73C2311yescharacteristic
456#124×C73—21no—
457#124×C73C2311yescharacteristic
458#124×C73C2311yescharacteristic
459#123×C73—21no—
460C22⋊Q8×C73—21no—
461C22⋊Q8×C73C2311yescharacteristic
462C22⋊Q8×C73C2311yescharacteristic
463#121×C73—21no—
464#121×C73—21no—
465#121×C73C2311yescharacteristic
466#121×C73C2311yescharacteristic
467#120×C73—21no—
468C4×Q8×C73C2311yescharacteristic
469C4×D4×C73—21no—
470C4×D4×C73C2311yescharacteristic
471C4×D4×C73C2311yescharacteristic
472C2×C22⋊C4×C73—21no—
473#106×C73C2311yescharacteristic
474C4⋊C8×C73C2311yescharacteristic
475#103×C73C2311yescharacteristic
476#103×C73C2311yescharacteristic
477#103×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479#102×C73C2311yescharacteristic
480#102×C73C2311yescharacteristic
481C22⋊C8×C73C2311yescharacteristic
482C22⋊C8×C73C2311yescharacteristic
483C4×C8×C73C2311yescharacteristic
484C23×D73—21no—
485#11924029—41no—
486#11924029—41no—
487#11924028—41no—
488#11924028—41no—
489#11924027—41no—
490#11924027—41no—
491#11924027—42no—
492#11924027—44no—
493#11924027—82no—
494C2×Dic146—21no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—41no—
498C2×Dic146—41no—
499C2×Dic146C2×D411yescharacteristic
500C2×Dic146C2411yescharacteristic
501C2×Dic146C2411yescharacteristic
502C2×D292—21no—
503C2×D292C2411yescharacteristic
504C2×D292C2411yescharacteristic
505C2×C22⋊D73—21no—
506C2×C22⋊D73—21no—
507C2×C22⋊D73—21no—
508C2×C22⋊D73—21no—
509C2×C22⋊D73—21no—
510C2×C22⋊D73—21no—
511C2×C22⋊D73—21no—
512C2×C22⋊D73—21no—
513C2×C22⋊D73—21no—
514C2×C22⋊D73—21no—
515C2×C22⋊D73—21no—
516C2×C22⋊D73—44no—
517C2×C22⋊D73C2×D411yescharacteristic
518C2×C22⋊D73C2×D411yescharacteristic
519D4×D73—22no—
520D4×D73—41no—
521C22×Dic73—21no—
522C22×Dic73—21no—
523C22×Dic73—21no—
524C22×Dic73—21no—
525C22×Dic73—21no—
526C22×Dic73—21no—
527C22×Dic73—21no—
528C22×Dic73—21no—
529C22×Dic73—21no—
530C22×Dic73—82no—
531C22×Dic73C2×D411yescharacteristic
532C22×Dic73C2×D411yescharacteristic
533C22×Dic73C2×D411yescharacteristic
534C22×Dic73C2×D411yescharacteristic
535C2×C4×D73—21no—
536C2×C4×D73—21no—
537C2×C4×D73—21no—
538C2×C4×D73—21no—
539C2×C4×D73—21no—
540C2×C4×D73—21no—
541C2×C4×D73—82no—
542C2×C4×D73C2×D411yescharacteristic
543C2×C4×D73C2×D411yescharacteristic
544C2×C4×D73C2411yescharacteristic
545#11924018—41no—
546#11924018—41no—
547#11924017—41no—
548#11924017—41no—
549#11924016—22no—
550#11924016—22no—
551#11924016—41no—
552#11924016—41no—
553#11924015—41no—
554#11924015—41no—
555#11924015—41no—
556D584—41no—
557#11924013—22no—
558#11924013—41no—
559#11924013—41no—
560#11924011—41no—
561#11924011—41no—
562C2×#10596831—41no—
563C2×#10596831—41no—
564C2×#10596831C2411yescharacteristic
565C2×#10596831C2411yescharacteristic
566C2×#10596831C2411yescharacteristic
567C2×#10596831C2411yescharacteristic
568C4⋊Dic73—21no—
569C4⋊Dic73—21no—
570C4⋊Dic73—21no—
571C4⋊Dic73—21no—
572C4⋊Dic73—21no—
573C4⋊Dic73—21no—
574C4⋊Dic73C2×D411yescharacteristic
575C4⋊Dic73C2411yescharacteristic
576C4⋊Dic73C2411yescharacteristic
577C4⋊Dic73C2411yescharacteristic
578C4⋊Dic73C2411yescharacteristic
579#11924007—21no—
580#11924007—21no—
581#11924007—21no—
582#11924007—21no—
583#11924007—21no—
584#11924007—21no—
585#11924007—21no—
586#11924007—21no—
587#11924007—21no—
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007—21no—
592#11924007—21no—
593#11924007—21no—
594#11924007—21no—
595#11924007—21no—
596#11924007—21no—
597#11924007—21no—
598#11924007C2×D411yescharacteristic
599#11924007C2×D411yescharacteristic
600#11924007C2×D411yescharacteristic
601#11924007C2×D411yescharacteristic
602C22⋊Dic73—21no—
603C22⋊Dic73—21no—
604C22⋊Dic73—21no—
605C22⋊Dic73—21no—
606C22⋊Dic73—21no—
607C22⋊Dic73—21no—
608C22⋊Dic73—21no—
609C22⋊Dic73—21no—
610C22⋊Dic73—21no—
611C22⋊Dic73—21no—
612C22⋊Dic73—21no—
613C22⋊Dic73C2×D411yescharacteristic
614C22⋊Dic73C2×D411yescharacteristic
615#11924005—21no—
616#11924005—21no—
617#11924005—21no—
618#11924005—21no—
619#11924005—21no—
620#11924005—21no—
621#11924005—21no—
622#11924005—21no—
623#11924005—21no—
624#11924005—21no—
625#11924005—21no—
626#11924005—21no—
627#11924005—21no—
628#11924005—21no—
629#11924005—21no—
630#11924005C2×D411yescharacteristic
631#11924005C2×D411yescharacteristic
632C4×Dic73—21no—
633C4×Dic73—21no—
634C4×Dic73—21no—
635C4×Dic73—21no—
636C4×Dic73—21no—
637C4×Dic73—21no—
638C4×Dic73C2×D411yescharacteristic
639C4×Dic73C2×D411yescharacteristic
640C4×Dic73C2×D411yescharacteristic
641C4×Dic73C2×D411yescharacteristic
642C4×Dic73C2×D411yescharacteristic
643C4×Dic73C2×D411yescharacteristic
644C4×Dic73C2411yescharacteristic
645C4×Dic73C2411yescharacteristic
646C4×Dic73C2411yescharacteristic
647C24×C73—21no—
648#41×C73—22no—
649#41×C73—41no—
650#41×C73—41no—
651#41×C73—41no—
652C2×Q8×C73—21no—
653C2×Q8×C73—41no—
654C2×Q8×C73—41no—
655C2×Q8×C73C2411yescharacteristic
656C2×Q8×C73C2411yescharacteristic
657C2×Q8×C73C2411yescharacteristic
658C2×D4×C73—22no—
659C2×D4×C73—21no—
660C2×D4×C73—21no—
661C2×D4×C73—21no—
662C2×D4×C73—21no—
663C2×D4×C73—21no—
664C2×D4×C73—41no—
665C2×D4×C73C2×D411yescharacteristic
666C2×D4×C73C2411yescharacteristic
667C2×D4×C73C2411yescharacteristic
668C2×D4×C73C2411yescharacteristic
669C22×C4×C73—21no—
670C22×C4×C73—21no—
671C22×C4×C73—21no—
672C22×C4×C73—21no—
673C22×C4×C73C2411yescharacteristic
674C22×C4×C73C2411yescharacteristic
675Q16×C73—41no—
676Q16×C73—41no—
677SD16×C73—22no—
678SD16×C73—22no—
679SD16×C73—41no—
680SD16×C73—41no—
681SD16×C73—41no—
682D8×C73—22no—
683D8×C73—41no—
684C2×C8×C73—41no—
685C2×C8×C73—41no—
686C2×C8×C73C2411yescharacteristic
687C2×C8×C73C2411yescharacteristic
688C2×C8×C73C2411yescharacteristic
689C2×C8×C73C2411yescharacteristic
690C4⋊C4×C73—21no—
691C4⋊C4×C73—21no—
692C4⋊C4×C73—21no—
693C4⋊C4×C73C2×D411yescharacteristic
694C4⋊C4×C73C2411yescharacteristic
695C4⋊C4×C73C2411yescharacteristic
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C22⋊C4×C73—21no—
699C22⋊C4×C73—21no—
700C22⋊C4×C73—21no—
701C22⋊C4×C73—21no—
702C22⋊C4×C73—21no—
703C22⋊C4×C73—21no—
704C22⋊C4×C73—21no—
705C22⋊C4×C73C2×D411yescharacteristic
706C22⋊C4×C73C2×D411yescharacteristic
707C42×C73—21no—
708C42×C73C2411yescharacteristic
709C23×C73—21no—
710C23×C73—21no—
711C23×C73—21no—
712C23×C73—42no—
713C23×C73—42no—
714C23×C73—81no—
715C23×C73C22×D411yescharacteristic
716C23×C73C22×D411yescharacteristic
717C22×D73—21no—
718C22×D73—21no—
719C22×D73—42no—
720C22×D73—42no—
721C22×D73—81no—
722C22×D73C22×D411yescharacteristic
723Q8×C73—21no—
724Q8×C73—21no—
725Q8×C73—21no—
726Q8×C73—21no—
727Q8×C73—21no—
728Q8×C73—21no—
729Q8×C73—81no—
730D4×C73—22no—
731D4×C73—21no—
732D4×C73—21no—
733D4×C73—21no—
734D4×C73—21no—
735D4×C73—21no—
736D4×C73—42no—
737D4×C73—42no—
738D4×C73—42no—
739D4×C73—81no—
740D4×C73—81no—
741D4×C73H(5,𝔽2)12yes—
742C2×C4×C73—21no—
743C2×C4×C73—21no—
744C2×C4×C73—21no—
745C2×C4×C73—21no—
746C2×C4×C73—21no—
747C2×C4×C73—21no—
748C2×C4×C73—21no—
749C2×C4×C73—21no—
750C2×C4×C73—21no—
751C2×C4×C73—42no—
752C2×C4×C73—81no—
753C2×C4×C73—81no—
754C2×C4×C73—81no—
755C2×C4×C73C22×D411yescharacteristic
756C2×C4×C73C22×D411yescharacteristic
757C2×C4×C73C22×D411yescharacteristic
758C2×C4×C73C22×D411yescharacteristic
759C2×C4×C73C2511yescharacteristic
760C22⋊D73—22no—
761C22⋊D73—41no—
762C22⋊D73—42no—
763C22⋊D73—42no—
764C22⋊D73—42no—
765C22⋊D73—42no—
766C22⋊D73—42no—
767C22⋊D73—42no—
768C22⋊D73—42no—
769C22⋊D73—81no—
770C22⋊D73—81no—
771C22⋊D73—81no—
772C22⋊D73—81no—
773C2×Dic73—22no—
774C2×Dic73—22no—
775C2×Dic73—22no—
776C2×Dic73—21no—
777C2×Dic73—21no—
778C2×Dic73—21no—
779C2×Dic73—21no—
780C2×Dic73—21no—
781C2×Dic73—21no—
782C2×Dic73—41no—
783C2×Dic73—42no—
784C2×Dic73—42no—
785C2×Dic73—42no—
786C2×Dic73—42no—
787C2×Dic73—81no—
788C2×Dic73—81no—
789C2×Dic73—81no—
790C2×Dic73—81no—
791C2×Dic73—81no—
792C2×Dic73C22×D411yescharacteristic
793C2×Dic73C22×D411yescharacteristic
794C2×Dic73C22×D411yescharacteristic
795C2×Dic73C22×D411yescharacteristic
796C2×Dic73C22×D411yescharacteristic
797C2×Dic73C22×D411yescharacteristic
798C2×Dic73C22×D411yescharacteristic
799D292—21no—
800D292—21no—
801D292—21no—
802D292—21no—
803D292—81no—
804C4×D73—21no—
805C4×D73—21no—
806C4×D73—22no—
807C4×D73—41no—
808C4×D73—42no—
809C4×D73—42no—
810C4×D73—81no—
811C4×D73—81no—
812C4×D73—81no—
813C4×D73—81no—
814Dic146—21no—
815Dic146—21no—
816Dic146—21no—
817Dic146—21no—
818Dic146—41no—
819Dic146—42no—
820Dic146—81no—
821Dic146—81no—
822C8×C73—21no—
823C8×C73—21no—
824C8×C73—21no—
825C8×C73—21no—
826#10596831—21no—
827#10596831—21no—
828#10596831—21no—
829#10596831—21no—
830C22×C73—21no—
831C22×C73—21no—
832C22×C73—22no—
833C22×C73—21no—
834C22×C73—21no—
835C22×C73—21no—
836C22×C73—41no—
837C22×C73—41no—
838C22×C73—41no—
839C22×C73—41no—
840C22×C73—41no—
841C22×C73—41no—
842C22×C73—41no—
843C22×C73—41no—
844C22×C73—84no—
845C22×C73#57512yes—
846C22×C73C23×D411yescharacteristic
847C2×D73—21no—
848C2×D73—21no—
849C2×D73—21no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—41no—
854C2×D73—41no—
855C2×D73—41no—
856C2×D73—84no—
857C4×C73—21no—
858C4×C73—21no—
859C4×C73—21no—
860C4×C73—21no—
861C4×C73—41no—
862C4×C73—41no—
863C4×C73—41no—
864C4×C73—41no—
865C4×C73—41no—
866C4×C73C2×H(5,𝔽2)11yescharacteristic
867C4×C73#58511yescharacteristic
868Dic73—21no—
869Dic73—21no—
870Dic73—21no—
871Dic73—21no—
872Dic73—21no—
873Dic73—21no—
874Dic73—41no—
875Dic73—41no—
876Dic73—41no—
877Dic73—41no—
878Dic73—41no—
879Dic73—41no—
880Dic73#57712yes—
881#61978—731nomaximal, Sylow
882C2×C73—22no—
883C2×C73—42no—
884C2×C73—41no—
885C2×C73—81no—
886C2×C73—81no—
887C2×C73#348811yescharacteristic
888C2×C73C2×#57511yescharacteristic
889C2×C73C2×#57711yescharacteristic
890D73—41no—
891D73—81no—
892D73—81no—
893#3511—731no—
894#3481—731no—
895#3401—731no—
896#3401—731no—
897#3376—731no—
898#3376—731no—
899#3316—731no—
900#3316—731no—
901#3307—731no—
902#3307—731no—
903#3301—731no—
904#3301—731no—
905#3282—731no—
906#3282D7311yescharacteristic, complemented
907#3267—731no—
908#3267—731no—
909#3265—731no—
910#3265—731no—
911#3252—731no—
912#3247—731no—
913#3246—731no—
914#3218—731no—
915#3214—731no—
916#3212—731no—
917#3116—731no—
918#3109—731no—
919#3101—731no—
920#3036—731no—
921#3035—731no—
922C2×#461—731no—
923#2990—731no—
924C73#6197811yescharacteristic, complemented, Sylow
925C2×AGL(1,ℤ/8)—731no—
926C2×AGL(1,ℤ/8)—731no—
927C2×#135—731no—
928C2×#135C2×D7311yescharacteristic
929C22×SD16—731no—
930C22×SD16C2×D7311yescharacteristic
931#559—731no—
932#556—731no—
933#556—731no—
934#555—1461no—
935#554—731no—
936#554—731no—
937#554—1461no—
938#553—731no—
939#553—731no—
940#553—1461no—
941#553—1461no—
942#553—1461no—
943#551—1461no—
944#551—1461no—
945#548—731no—
946#548—731no—
947#548—731no—
948#548C2×D7311yescharacteristic, complemented
949#547—731no—
950#547—731no—
951#546—731no—
952#546—1461no—
953#546C2×D7311yescharacteristic
954D42—731no—
955#542—1461no—
956#542—1461no—
957#537—1461no—
958#533—731no—
959#533—731no—
960#532—731no—
961#532—731no—
962#532—731no—
963#532—731no—
964C2×C4⋊Q8—731no—
965#529—731no—
966#529—731no—
967#529—1461no—
968#525—1461no—
969#525—1461no—
970#520—1461no—
971C4×#41—731no—
972C4×#41—731no—
973C2×C4×D4—731no—
974C2×C4×D4—731no—
975C2×C4×D4—1461no—
976#497—731no—
977#497—731no—
978#496—731no—
979#496—731no—
980#495—731no—
981#495C2×D7311yescharacteristic, complemented
982#491—731no—
983#491—731no—
984#489—731no—
985#489—731no—
986#488—731no—
987#488—731no—
988#485—731no—
989#485—731no—
990#483—731no—
991#483—731no—
992#481—731no—
993#481—731no—
994#479—731no—
995#479—731no—
996#478—731no—
997#478—731no—
998#477—731no—
999#476—731no—
1000#476—731no—
1001#476—731no—
1002#475—731no—
1003#475—731no—
1004#470—731no—
1005#470—731no—
1006#468—731no—
1007#468—731no—
1008#466—731no—
1009#466—731no—
1010#465—731no—
1011#465—731no—
1012#465—731no—
1013#465—731no—
1014#465C2×D7311yescharacteristic, complemented
1015#465C2×D7311yescharacteristic, complemented
1016#464—731no—
1017#464—731no—
1018#464—731no—
1019#464C2×D7311yescharacteristic, complemented
1020#463—731no—
1021#463—731no—
1022#463—731no—
1023#463—731no—
1024#463—731no—
1025#463—731no—
1026#463—731no—
1027#463C2×D7311yescharacteristic
1028#462—731no—
1029#462—731no—
1030#461—731no—
1031#461—731no—
1032#461—731no—
1033#461—731no—
1034#461—731no—
1035#461—731no—
1036#461—731no—
1037#461—731no—
1038#461—731no—
1039#461—731no—
1040#460—731no—
1041#460—731no—
1042#460—731no—
1043#459—731no—
1044#459—731no—
1045#459—731no—
1046#452—731no—
1047#452—731no—
1048#452—731no—
1049#452C2×D7311yescharacteristic
1050#451—731no—
1051#451C2×D7311yescharacteristic, complemented
1052#450—731no—
1053#450—731no—
1054#449—731no—
1055#449—731no—
1056#449—731no—
1057#449—731no—
1058#449—731no—
1059#449C2×D7311yescharacteristic, complemented
1060#448—731no—
1061#448—731no—
1062#447—731no—
1063#447C2×D7311yescharacteristic
1064#446—731no—
1065#446—731no—
1066#442—731no—
1067#442—731no—
1068#442—731no—
1069#442—731no—
1070#441—731no—
1071#441—731no—
1072#440—731no—
1073#440—731no—
1074C4×SD16—731no—
1075C4×SD16—731no—
1076C4×SD16—731no—
1077C4×SD16C2×D7311yescharacteristic
1078#435—731no—
1079#435—731no—
1080#435—731no—
1081#435—731no—
1082C8×D4—731no—
1083C8×D4C2×D7311yescharacteristic, complemented
1084#432—731no—
1085#432—731no—
1086#431—731no—
1087#423—731no—
1088C2×C4⋊C8—731no—
1089C2×C4⋊C8—731no—
1090#417—731no—
1091#417—731no—
1092#416—731no—
1093#416—731no—
1094C2×#103—731no—
1095C2×#103—731no—
1096C2×#41—731no—
1097C2×#41—731no—
1098C2×#41—731no—
1099C2×#41—731no—
1100C2×#41—1461no—
1101C2×#41—1461no—
1102C2×#41C22×D7311yescharacteristic
1103C2×#41C22×D7311yescharacteristic
1104C22×Q8—731no—
1105C22×Q8C22×D7311yescharacteristic
1106C22×D4—731no—
1107C22×D4—1461no—
1108C22×D4C22×D7311yescharacteristic
1109C23×C4—1461no—
1110C23×C4—1461no—
1111AGL(1,ℤ/8)—2922no—
1112AGL(1,ℤ/8)—2922no—
1113#135—42no—
1114#135—2922no—
1115C2×Q16—731no—
1116C2×Q16—731no—
1117C2×Q16C22×D7311yescharacteristic
1118C2×Q16C22×D7311yescharacteristic
1119C2×SD16—42no—
1120C2×SD16—2922no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16—731no—
1125C2×SD16—731no—
1126C2×SD16—731no—
1127C2×SD16—731no—
1128C2×SD16—731no—
1129C2×SD16—731no—
1130C2×SD16C22×D7311yescharacteristic
1131C2×SD16C22×D7311yescharacteristic
1132C2×SD16C22×D7311yescharacteristic
1133C2×SD16C22×D7311yescharacteristic
1134C2×SD16C22×D7311yescharacteristic
1135C2×D8—731no—
1136C2×D8—731no—
1137C2×D8—731no—
1138C2×D8—731no—
1139C2×D8C22×D7311yescharacteristic
1140C2×D8C22×D7311yescharacteristic
1141C2×M16—731no—
1142C2×M16—731no—
1143C22×C8—731no—
1144C22×C8—731no—
1145C22×C8C22×D7311yescharacteristic
1146C22×C8C22×D7311yescharacteristic
1147C4⋊Q8—731no—
1148C4⋊Q8—731no—
1149C4⋊Q8—731no—
1150C4⋊Q8—731no—
1151C4⋊Q8—731no—
1152C4⋊Q8—731no—
1153C4⋊Q8—1461no—
1154C4⋊Q8—1461no—
1155#127—731no—
1156#127—731no—
1157#126—1461no—
1158#126—1461no—
1159#126—1461no—
1160#126—1461no—
1161#126—1461no—
1162#126—1461no—
1163#126—1461no—
1164#126—1461no—
1165#125—731no—
1166#125—731no—
1167#125—1461no—
1168#125—1461no—
1169#125—1461no—
1170#124—21no—
1171#124—731no—
1172#124—731no—
1173#124—731no—
1174#124—731no—
1175#124—1461no—
1176#124—1461no—
1177#124—1461no—
1178#124—1461no—
1179#124—1461no—
1180#124—1461no—
1181#124C22×D7311yescharacteristic
1182#124C22×D7311yescharacteristic
1183#123—21no—
1184#123—1461no—
1185#123—1461no—
1186#123—1461no—
1187#123—1461no—
1188#123—1461no—
1189#123—1461no—
1190#123—1461no—
1191#123—1461no—
1192#123—1461no—
1193#123—1461no—
1194#123—1461no—
1195C22⋊Q8—21no—
1196C22⋊Q8—731no—
1197C22⋊Q8—731no—
1198C22⋊Q8—731no—
1199C22⋊Q8—731no—
1200C22⋊Q8—1461no—
1201C22⋊Q8—1461no—
1202C22⋊Q8—1461no—
1203C22⋊Q8—1461no—
1204C22⋊Q8—1461no—
1205C22⋊Q8—1461no—
1206C22⋊Q8—1461no—
1207C22⋊Q8—1461no—
1208C22⋊Q8—1461no—
1209C22⋊Q8—1461no—
1210C22⋊Q8—1461no—
1211C22⋊Q8—1461no—
1212C22⋊Q8C22×D7311yescharacteristic
1213C22⋊Q8C22×D7311yescharacteristic
1214#121—21no—
1215#121—21no—
1216#121—731no—
1217#121—731no—
1218#121—731no—
1219#121—731no—
1220#121—1461no—
1221#121—1461no—
1222#121—1461no—
1223#121—1461no—
1224#121—1461no—
1225#121—1461no—
1226#121—1461no—
1227#121—1461no—
1228#121—1461no—
1229#121—1461no—
1230#121—1461no—
1231#121—1461no—
1232#121—1461no—
1233#121—1461no—
1234#121—1461no—
1235#121C22×D7311yescharacteristic
1236#121C22×D7311yescharacteristic
1237#120—21no—
1238#120—1461no—
1239#120—1461no—
1240#120—1461no—
1241C4×Q8—731no—
1242C4×Q8—731no—
1243C4×Q8—731no—
1244C4×Q8—731no—
1245C4×Q8—731no—
1246C4×Q8—731no—
1247C4×Q8—731no—
1248C4×Q8—1461no—
1249C4×Q8—1461no—
1250C4×Q8C22×D7311yescharacteristic
1251C4×D4—21no—
1252C4×D4—731no—
1253C4×D4—731no—
1254C4×D4—731no—
1255C4×D4—731no—
1256C4×D4—731no—
1257C4×D4—731no—
1258C4×D4—731no—
1259C4×D4—731no—
1260C4×D4—731no—
1261C4×D4—731no—
1262C4×D4—731no—
1263C4×D4—731no—
1264C4×D4—731no—
1265C4×D4—731no—
1266C4×D4—1461no—
1267C4×D4—1461no—
1268C4×D4—1461no—
1269C4×D4—1461no—
1270C4×D4—1461no—
1271C4×D4—1461no—
1272C4×D4—1461no—
1273C4×D4—1461no—
1274C4×D4—1461no—
1275C4×D4—1461no—
1276C4×D4—1461no—
1277C4×D4—1461no—
1278C4×D4—1461no—
1279C4×D4—1461no—
1280C4×D4—1461no—
1281C4×D4—1461no—
1282C4×D4—1461no—
1283C4×D4—1461no—
1284C4×D4—1461no—
1285C4×D4—1461no—
1286C4×D4—1461no—
1287C4×D4C22×D7311yescharacteristic
1288C4×D4C22×D7311yescharacteristic
1289#117—731no—
1290#117—731no—
1291#117—731no—
1292#117—731no—
1293#117—1461no—
1294#117—1461no—
1295#117—1461no—
1296#117—1461no—
1297#117—1461no—
1298#117—1461no—
1299#117—1461no—
1300C2×C4⋊C4—731no—
1301C2×C4⋊C4—731no—
1302C2×C4⋊C4—1461no—
1303C2×C4⋊C4—1461no—
1304C2×C4⋊C4—1461no—
1305C2×C4⋊C4—1461no—
1306C2×C4⋊C4—1461no—
1307C2×C22⋊C4—21no—
1308C2×C22⋊C4—1461no—
1309C2×C22⋊C4—1461no—
1310C2×C22⋊C4—1461no—
1311C2×C42—731no—
1312C2×C42—731no—
1313C2×C42—731no—
1314C2×C42—1461no—
1315#107—731no—
1316#107—731no—
1317#106—731no—
1318#106—731no—
1319#106—731no—
1320#106—731no—
1321#106—731no—
1322#106C22×D7311yescharacteristic
1323C4⋊C8—731no—
1324C4⋊C8—731no—
1325C4⋊C8—731no—
1326C4⋊C8—731no—
1327C4⋊C8—731no—
1328C4⋊C8—731no—
1329C4⋊C8—731no—
1330C4⋊C8—731no—
1331C4⋊C8—731no—
1332C4⋊C8C22×D7311yescharacteristic
1333#103—731no—
1334#103—731no—
1335#103—731no—
1336#103—731no—
1337#103—731no—
1338#103—731no—
1339#103—731no—
1340#103—731no—
1341#103—731no—
1342#103—731no—
1343#103—731no—
1344#103—731no—
1345#103—731no—
1346#103—731no—
1347#103—731no—
1348#103C22×D7311yescharacteristic
1349#103C22×D7311yescharacteristic
1350#103C22×D7311yescharacteristic
1351#102—731no—
1352#102—731no—
1353#102—731no—
1354#102—731no—
1355#102—731no—
1356#102—731no—
1357#102—731no—
1358#102—731no—
1359#102—731no—
1360#102—731no—
1361#102—731no—
1362#102C22×D7311yescharacteristic
1363#102C22×D7311yescharacteristic
1364#102C22×D7311yescharacteristic
1365C22⋊C8—731no—
1366C22⋊C8—731no—
1367C22⋊C8—731no—
1368C22⋊C8—731no—
1369C22⋊C8C22×D7311yescharacteristic
1370C22⋊C8C22×D7311yescharacteristic
1371#97—731no—
1372#97—731no—
1373#97—731no—
1374#97—731no—
1375C4×C8—731no—
1376C4×C8C22×D7311yescharacteristic
1377C24—21no—
1378C24—1461no—
1379#41—22no—
1380#41—41no—
1381#41—41no—
1382#41—41no—
1383#41—2921no—
1384#41—2921no—
1385#41—2922no—
1386#41—2924no—
1387#41—2921no—
1388#41—2921no—
1389#41—2921no—
1390#41—2921no—
1391#41—5842no—
1392C2×Q8—21no—
1393C2×Q8—41no—
1394C2×Q8—41no—
1395C2×Q8—2921no—
1396C2×Q8—2921no—
1397C2×Q8—731no—
1398C2×Q8—731no—
1399C2×Q8—731no—
1400C2×Q8—1461no—
1401C2×Q8—1461no—
1402C2×Q8—1461no—
1403C2×Q8C23×D7311yescharacteristic
1404C2×Q8C23×D7311yescharacteristic
1405C2×Q8C23×D7311yescharacteristic
1406C2×D4—22no—
1407C2×D4—21no—
1408C2×D4—21no—
1409C2×D4—21no—
1410C2×D4—21no—
1411C2×D4—21no—
1412C2×D4—41no—
1413C2×D4—2924no—
1414C2×D4—2921no—
1415C2×D4—731no—
1416C2×D4—731no—
1417C2×D4—731no—
1418C2×D4—731no—
1419C2×D4—1461no—
1420C2×D4—1461no—
1421C2×D4—1461no—
1422C2×D4—1461no—
1423C2×D4—1461no—
1424C2×D4—1461no—
1425C2×D4—1461no—
1426C2×D4—1461no—
1427C2×D4—1461no—
1428C2×D4—1462no—
1429C2×D4—1461no—
1430C2×D4—1461no—
1431C2×D4—1461no—
1432C2×D4D4×D7311yescharacteristic
1433C2×D4C23×D7311yescharacteristic
1434C2×D4C23×D7311yescharacteristic
1435C2×D4C23×D7311yescharacteristic
1436C22×C4—21no—
1437C22×C4—21no—
1438C22×C4—21no—
1439C22×C4—21no—
1440C22×C4—5842no—
1441C22×C4—5842no—
1442C22×C4—731no—
1443C22×C4—731no—
1444C22×C4—731no—
1445C22×C4—731no—
1446C22×C4—731no—
1447C22×C4—731no—
1448C22×C4—731no—
1449C22×C4—1461no—
1450C22×C4—1461no—
1451C22×C4—1461no—
1452C22×C4—1461no—
1453C22×C4—1461no—
1454C22×C4—1461no—
1455C22×C4—1461no—
1456C22×C4—1461no—
1457C22×C4—1461no—
1458C22×C4—1461no—
1459C22×C4—1461no—
1460C22×C4—1461no—
1461C22×C4—1461no—
1462C22×C4—1461no—
1463C22×C4—1461no—
1464C22×C4C23×D7311yescharacteristic
1465C22×C4C23×D7311yescharacteristic
1466Q16—41no—
1467Q16—41no—
1468Q16—2921no—
1469Q16—2921no—
1470SD16—22no—
1471SD16—22no—
1472SD16—41no—
1473SD16—41no—
1474SD16—41no—
1475SD16—2921no—
1476SD16—2921no—
1477SD16—2921no—
1478SD16—2921no—
1479SD16—2921no—
1480SD16—2921no—
1481SD16—2921no—
1482SD16—1462no—
1483SD16—1462no—
1484D8—22no—
1485D8—41no—
1486D8—2921no—
1487D8—2921no—
1488D8—2921no—
1489D8—1462no—
1490M16—2921no—
1491M16—2921no—
1492C2×C8—41no—
1493C2×C8—41no—
1494C2×C8—2921no—
1495C2×C8—2921no—
1496C2×C8—731no—
1497C2×C8—731no—
1498C2×C8—731no—
1499C2×C8—731no—
1500C2×C8C23×D7311yescharacteristic
1501C2×C8C23×D7311yescharacteristic
1502C2×C8C23×D7311yescharacteristic
1503C2×C8C23×D7311yescharacteristic
1504C4⋊C4—21no—
1505C4⋊C4—21no—
1506C4⋊C4—21no—
1507C4⋊C4—731no—
1508C4⋊C4—731no—
1509C4⋊C4—731no—
1510C4⋊C4—731no—
1511C4⋊C4—731no—
1512C4⋊C4—731no—
1513C4⋊C4—731no—
1514C4⋊C4—731no—
1515C4⋊C4—731no—
1516C4⋊C4—1461no—
1517C4⋊C4—1461no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4—1461no—
1522C4⋊C4—1461no—
1523C4⋊C4—1461no—
1524C4⋊C4—1461no—
1525C4⋊C4—1461no—
1526C4⋊C4—1461no—
1527C4⋊C4—1461no—
1528C4⋊C4—1461no—
1529C4⋊C4—1461no—
1530C4⋊C4—1461no—
1531C4⋊C4—1461no—
1532C4⋊C4—1461no—
1533C4⋊C4—1461no—
1534C4⋊C4—1461no—
1535C4⋊C4—1461no—
1536C4⋊C4—1461no—
1537C4⋊C4—1461no—
1538C4⋊C4—1461no—
1539C4⋊C4—1461no—
1540C4⋊C4—1461no—
1541C4⋊C4D4×D7311yescharacteristic
1542C4⋊C4C23×D7311yescharacteristic
1543C4⋊C4C23×D7311yescharacteristic
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
1547C22⋊C4—21no—
1548C22⋊C4—21no—
1549C22⋊C4—21no—
1550C22⋊C4—21no—
1551C22⋊C4—21no—
1552C22⋊C4—21no—
1553C22⋊C4—731no—
1554C22⋊C4—731no—
1555C22⋊C4—731no—
1556C22⋊C4—731no—
1557C22⋊C4—1461no—
1558C22⋊C4—1461no—
1559C22⋊C4—1461no—
1560C22⋊C4—1461no—
1561C22⋊C4—1461no—
1562C22⋊C4—1461no—
1563C22⋊C4—1461no—
1564C22⋊C4—1461no—
1565C22⋊C4—1461no—
1566C22⋊C4—1461no—
1567C22⋊C4—1461no—
1568C22⋊C4—1461no—
1569C22⋊C4—1461no—
1570C22⋊C4—1461no—
1571C22⋊C4—1461no—
1572C22⋊C4—1461no—
1573C22⋊C4—1461no—
1574C22⋊C4—1461no—
1575C22⋊C4—1461no—
1576C22⋊C4—1461no—
1577C22⋊C4—1461no—
1578C22⋊C4—1461no—
1579C22⋊C4—1461no—
1580C22⋊C4—1461no—
1581C22⋊C4—1461no—
1582C22⋊C4—1461no—
1583C22⋊C4D4×D7311yescharacteristic
1584C22⋊C4D4×D7311yescharacteristic
1585C42—21no—
1586C42—731no—
1587C42—731no—
1588C42—731no—
1589C42—731no—
1590C42—731no—
1591C42—731no—
1592C42—731no—
1593C42—731no—
1594C42—731no—
1595C42—1461no—
1596C42—1461no—
1597C42—1461no—
1598C42—1461no—
1599C42—1461no—
1600C42—1461no—
1601C42C23×D7311yescharacteristic
1602C23—21no—
1603C23—21no—
1604C23—21no—
1605C23—42no—
1606C23—42no—
1607C23—81no—
1608C23—2922no—
1609C23—2922no—
1610C23—5841no—
1611C23—731no—
1612C23—1461no—
1613C23—1461no—
1614C23C2×D4×D7311yescharacteristic
1615C23C2×D4×D7311yescharacteristic
1616Q8—21no—
1617Q8—21no—
1618Q8—21no—
1619Q8—21no—
1620Q8—21no—
1621Q8—21no—
1622Q8—81no—
1623Q8—2921no—
1624Q8—2922no—
1625Q8—5841no—
1626Q8—5841no—
1627Q8—1461no—
1628Q8—1461no—
1629Q8—1461no—
1630Q8—1461no—
1631D4—22no—
1632D4—21no—
1633D4—21no—
1634D4—21no—
1635D4—21no—
1636D4—21no—
1637D4—42no—
1638D4—42no—
1639D4—42no—
1640D4—81no—
1641D4—81no—
1642D4—2922no—
1643D4—2922no—
1644D4—2922no—
1645D4—2922no—
1646D4—2922no—
1647D4—2921no—
1648D4—2922no—
1649D4—2922no—
1650D4—5841no—
1651D4—5841no—
1652D4—5841no—
1653D4—5841no—
1654D4—5841no—
1655D4—1462no—
1656D4—1461no—
1657D4—1461no—
1658D4—1461no—
1659D4—1461no—
1660D4#1455663612yes—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—42no—
1671C2×C4—81no—
1672C2×C4—81no—
1673C2×C4—81no—
1674C2×C4—2921no—
1675C2×C4—2922no—
1676C2×C4—2922no—
1677C2×C4—2922no—
1678C2×C4—2922no—
1679C2×C4—2922no—
1680C2×C4—2922no—
1681C2×C4—2921no—
1682C2×C4—5841no—
1683C2×C4—5841no—
1684C2×C4—5841no—
1685C2×C4—5841no—
1686C2×C4—5841no—
1687C2×C4—5841no—
1688C2×C4—5841no—
1689C2×C4—5841no—
1690C2×C4—5841no—
1691C2×C4—731no—
1692C2×C4—731no—
1693C2×C4—731no—
1694C2×C4—731no—
1695C2×C4—731no—
1696C2×C4—731no—
1697C2×C4—731no—
1698C2×C4—1462no—
1699C2×C4—1461no—
1700C2×C4—1461no—
1701C2×C4—1461no—
1702C2×C4—1461no—
1703C2×C4—1461no—
1704C2×C4—1461no—
1705C2×C4—1462no—
1706C2×C4—1462no—
1707C2×C4—1462no—
1708C2×C4—1461no—
1709C2×C4—1461no—
1710C2×C4C2×D4×D7311yescharacteristic
1711C2×C4C2×D4×D7311yescharacteristic
1712C2×C4C2×D4×D7311yescharacteristic
1713C2×C4C2×D4×D7311yescharacteristic
1714C2×C4C24×D7311yescharacteristic
1715C8—21no—
1716C8—21no—
1717C8—21no—
1718C8—21no—
1719C8—1461no—
1720C8—1461no—
1721C8—1461no—
1722C8—1461no—
1723C22—21no—
1724C22—21no—
1725C22—21no—
1726C22—22no—
1727C22—21no—
1728C22—21no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—84no—
1738C22—2921no—
1739C22—2921no—
1740C22—2921no—
1741C22—2921no—
1742C22—2921no—
1743C22—2921no—
1744C22—5844no—
1745C22—1461no—
1746C22—1461no—
1747C22—1461no—
1748C22#1798938412yes—
1749C22C22×D4×D7311yescharacteristic
1750C4—21no—
1751C4—21no—
1752C4—21no—
1753C4—21no—
1754C4—41no—
1755C4—41no—
1756C4—41no—
1757C4—41no—
1758C4—41no—
1759C4—2921no—
1760C4—2921no—
1761C4—2921no—
1762C4—2921no—
1763C4—2921no—
1764C4—2921no—
1765C4—732no—
1766C4—1461no—
1767C4—1461no—
1768C4—1461no—
1769C4—1461no—
1770C4—1461no—
1771C4—1461no—
1772C4C2×#1455663611yescharacteristic
1773C4#1798942211yescharacteristic
1774C2—22no—
1775C2—41no—
1776C2—42no—
1777C2—81no—
1778C2—81no—
1779C2—2921no—
1780C2—5841no—
1781C2—5841no—
1782C2#2262359111yescharacteristic
1783C2C2×#1798938411yescharacteristic
1784C2#577×D7311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3282C2
socleC22×C73C23×D4
hypercenter#3282D73
hypocenterC73#61978
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3282

Complements

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

NH ≅ G/Ntype
1. #22623837C2semidirect
2. #22623536C2semidirect
3. #22623003C2semidirect
4. #22623001C2semidirect
5. #22622762C2semidirect
6. #22622754C2semidirect
7. #22622048C2semidirect
8. #22622046C2semidirect
9. #22621913C2semidirect
10. #22621911C2semidirect
11. #22621835C2semidirect
12. #22621833C2semidirect
13. #22621634C2semidirect
14. #22621460C2semidirect
15. #22621456C2semidirect
16. #22621430C2semidirect
17. #22621426C2semidirect
18. #22621301C2semidirect
19. #22621252C2semidirect
20. #22621242C2semidirect
21. #22620961C2semidirect
22. #22620923C2semidirect
23. #22620902C2semidirect
24. #22620086C2semidirect
25. #22620017C2semidirect
26. #22619937C2semidirect
27. #22619393C2semidirect
28. #22619382C2semidirect
29. C2×#17988790C2semidirect
30. #22619054C2semidirect
31. C73×#3282C2semidirect
37. #17989309C22semidirect
38. #17989306C22semidirect
51. #17989246C22semidirect
53. #17989239C22semidirect
54. #17989236C22semidirect
61. #17989141C22semidirect
62. #17989139C22semidirect
63. #17989136C22semidirect
64. #17989133C22semidirect
66. #17989132C22semidirect
67. C2×#14556589C22semidirect
79. #17988980C22semidirect
80. #17988980C22semidirect
83. #17988969C22semidirect
84. #17988954C22semidirect
85. #17988954C22semidirect
86. #17988948C22semidirect
87. #17988945C22semidirect
88. #17988942C22semidirect
89. #17988941C22semidirect
90. #17988929C22semidirect
91. #17988925C22semidirect
92. #17988919C22semidirect
93. #17988916C22semidirect
94. #17988906C22semidirect
95. #17988903C22semidirect
96. #17988895C22semidirect
97. #17988894C22semidirect
98. #17988886C22semidirect
99. #17988885C22semidirect
100. #17988880C22semidirect
101. #17988876C22semidirect
103. #17988875C22semidirect
104. #17988871C22semidirect
105. #17988870C22semidirect
106. #17988844C22semidirect
107. #17988842C22semidirect
112. #17988818C22semidirect
113. #17988818C22semidirect
114. #17988816C22semidirect
115. #17988814C22semidirect
116. #17988811C22semidirect
117. #17988807C22semidirect
118. #17988806C22semidirect
119. #17988805C22semidirect
121. #17988804C22semidirect
122. #17988803C22semidirect
125. #17988799C22semidirect
126. #17988795C22semidirect
127. #17988795C22semidirect
128. #17988791C22semidirect
129. #17988791C22semidirect
134. #17988790C22semidirect
135. #17988790C22semidirect
136. #17988790C22semidirect
137. #17988790C22semidirect
140. #17988785C22semidirect
141. #17988781C22semidirect
143. #17988780C22semidirect
145. #17988748C22semidirect
146. #17988746C22semidirect
147. #17988742C22semidirect
150. #17988734C22semidirect
151. #17988732C22semidirect
153. #17988730C22semidirect
158. #17988717C22semidirect
159. #17988714C22semidirect
161. #17988699C22semidirect
163. #17988696C22semidirect
164. #17988694C22semidirect
165. #17988691C22semidirect
168. C4×#11924017C22semidirect
169. C4×#11924015C22semidirect
172. #17988658C22semidirect
174. #17988655C22semidirect
175. D4×#10596831C22semidirect
176. #17988641C22semidirect
177. #17988641C22semidirect
178. #17988638C22semidirect
179. #17988609C22semidirect
180. C2×#14556520C22semidirect
181. C2×#14556520C22semidirect
182. #17988587C22semidirect
183. #17988585C22semidirect
184. #17988584C22semidirect
185. #17988583C22semidirect
186. C2×#14556516C22semidirect
187. C2×#14556515C22semidirect
190. #548×C73C22semidirect
192. #495×C73C22semidirect
193. #465×C73C22semidirect
194. #465×C73C22semidirect
195. #464×C73C22semidirect
198. #451×C73C22semidirect
199. #449×C73C22semidirect
202. C8×D4×C73C22semidirect
906. #3282D73semidirect
924. C73#61978semidirect
948. #548C2×D73semidirect
981. #495C2×D73semidirect
1014. #465C2×D73semidirect
1015. #465C2×D73semidirect
1019. #464C2×D73semidirect
1051. #451C2×D73semidirect
1059. #449C2×D73semidirect
1083. C8×D4C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238372
#226235362
#226230032
#226230012
#226227622
#226227542
#226220482
#226220462
#226219132
#226219112
#226218352
#226218332
#226216342
#226214602
#226214562
#226214302
#226214262
#226213012
#226212522
#226212422
#226209612
#226209232
#226209022
#226200862
#226200172
#226199372
#226193932
#226193822
C2×#179887902
#226190542
C73×#32822
#6197873