Finite Group Databasebeta

← #33966821

Subgroups — #33966821

Order 18688.

1726 conjugacy classes of subgroups.

The subgroup lattice has 1580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623748C211yesmaximal, characteristic
2#22623738C211yesmaximal, characteristic, complemented
3#22622899C211yesmaximal, characteristic, complemented
4#22622897C211yesmaximal, characteristic, complemented
5#22622894C211yesmaximal, characteristic, complemented
6#22622866C211yesmaximal, characteristic, complemented
7#22622864C211yesmaximal, characteristic, complemented
8#22622855C211yesmaximal, characteristic, complemented
9#22622854C211yesmaximal, characteristic, complemented
10#22622849C211yesmaximal, characteristic, complemented
11#22622848C211yesmaximal, characteristic, complemented
12#22622844C211yesmaximal, characteristic, complemented
13#22622838C211yesmaximal, characteristic, complemented
14Q16×Dic146C211yesmaximal, characteristic, complemented
15#22622812C211yesmaximal, characteristic, complemented
16#22622809C211yesmaximal, characteristic, complemented
17#22622803C211yesmaximal, characteristic, complemented
18#22620476C211yesmaximal, characteristic, complemented
19#22620468C211yesmaximal, characteristic, complemented
20#22620466C211yesmaximal, characteristic, complemented
21#22619785C211yesmaximal, characteristic
22#22619779C211yesmaximal, characteristic
23#22619772C211yesmaximal, characteristic, complemented
24#22619770C211yesmaximal, characteristic, complemented
25#22619718C211yesmaximal, characteristic
26#477×D73C211yesmaximal, characteristic, complemented
27#22618876C211yesmaximal, characteristic, complemented
28#22618773C211yesmaximal, characteristic
29#22618769C211yesmaximal, characteristic
30#22618747C211yesmaximal, characteristic
31C73×#3390C211yesmaximal, characteristic, complemented
32C2×#14556623C2211yescharacteristic
33Q8×Dic146C2211yescharacteristic
34Q8×Dic146C2211yescharacteristic
35Q8×Dic146C2211yescharacteristic
36#17989317—21no—
37#17989317C2211yescharacteristic
38#17989316C2211yescharacteristic
39#17989315—21no—
40#17989315C2211yescharacteristic
41#17989314—21no—
42#17989314—21no—
43#17989314C2211yescharacteristic
44#17989314C2211yescharacteristic
45#17989313C2211yescharacteristic
46#17989313C2211yescharacteristic
47#17989293—21no—
48#17989293—21no—
49#17989293C2211yescharacteristic
50#17989293C2211yescharacteristic
51Q8×D292—21no—
52Q8×D292C2211yescharacteristic
53#17989252—21no—
54#17989252C2211yescharacteristic
55#17989217—21no—
56#17989217—21no—
57#17989217—21no—
58#17989217C2211yescharacteristic
59#17989217C2211yescharacteristic
60#17989217C2211yescharacteristic
61#17989214—21no—
62#17989214C2211yescharacteristic
63#17989143—21no—
64#17989143C2211yescharacteristic
65#17989141—21no—
66#17989141—21no—
67#17989141C2211yescharacteristic
68C4⋊Q8×D73—21no—
69C4⋊Q8×D73C2211yescharacteristic
70#17989069C2211yescharacteristic
71#17989069C2211yescharacteristic
72#17989063C2211yescharacteristic
73#17989063C2211yescharacteristic
74C4×#11924029C2211yescharacteristic
75C4×Q8×D73C2211yescharacteristic
76#17988997C2211yescharacteristic
77#17988997C2211yescharacteristic
78#17988997C2211yescharacteristic
79#17988996C2211yescharacteristic
80#17988996C2211yescharacteristic
81#17988995C2211yescharacteristic
82#17988994C2211yescharacteristic
83#17988994C2211yescharacteristic
84#17988994C2211yescharacteristic
85#17988993C2211yescharacteristic
86#17988992C2211yescharacteristic
87#17988991C2211yescharacteristic
88#17988991C2211yescharacteristic
89#17988991C2211yescharacteristic
90#17988991C2211yescharacteristic
91#17988990C2211yescharacteristic
92#17988988C2211yescharacteristic
93#17988987C2211yescharacteristic
94#17988986C2211yescharacteristic
95#17988984C2211yescharacteristic
96#17988984C2211yescharacteristic
97#17988897C2211yescharacteristic
98#17988896C2211yescharacteristic
99#17988896C2211yescharacteristic
100#17988894C2211yescharacteristic
101#17988894C2211yescharacteristic
102#17988893C2211yescharacteristic
103#17988892C2211yescharacteristic
104#17988892C2211yescharacteristic
105#17988891C2211yescharacteristic
106#17988891C2211yescharacteristic
107#17988890C2211yescharacteristic
108#17988888C2211yescharacteristic
109#17988888C2211yescharacteristic
110#17988886C2211yescharacteristic
111#17988884C2211yescharacteristic
112#17988884C2211yescharacteristic
113#17988883C2211yescharacteristic
114#17988883C2211yescharacteristic
115#17988882C2211yescharacteristic
116#17988882C2211yescharacteristic
117#17988882C2211yescharacteristic
118#17988881C2211yescharacteristic
119#17988881C2211yescharacteristic
120#17988881C2211yescharacteristic
121#17988880C2211yescharacteristic
122#17988880C2211yescharacteristic
123#17988880C2211yescharacteristic
124#17988880C2211yescharacteristic
125#17988880C2211yescharacteristic
126#17988880C2211yescharacteristic
127#17988879C2211yescharacteristic
128#17988876C2211yescharacteristic
129#17988873C2211yescharacteristic
130#17988872C2211yescharacteristic
131#17988871C2211yescharacteristic
132#17988870C2211yescharacteristic
133#17988870C2211yescharacteristic
134#17988868C2211yescharacteristic
135#17988866C2211yescharacteristic
136#17988866C2211yescharacteristic
137#17988866C2211yescharacteristic
138#17988864C2211yescharacteristic
139#17988718C2211yescharacteristic
140#17988716C2211yescharacteristic
141#17988716C2211yescharacteristic
142#17988715C2211yescharacteristic
143#17988715C2211yescharacteristic
144C8×Dic146C2211yescharacteristic
145#17988711C2211yescharacteristic
146#17988694C2211yescharacteristic
147#17988692C2211yescharacteristic
148#17988692C2211yescharacteristic
149#17988691C2211yescharacteristic
150#17988690C2211yescharacteristic
151#17988689C2211yescharacteristic
152#17988689C2211yescharacteristic
153#17988686C2211yescharacteristic
154#17988685C2211yescharacteristic
155#17988685C2211yescharacteristic
156Q16×Dic73C2211yescharacteristic
157Q16×Dic73C2211yescharacteristic
158C4×#11924018C2211yescharacteristic
159#17988679C2211yescharacteristic
160#17988679C2211yescharacteristic
161C4×#11924017C2211yescharacteristic
162C4×#11924015C2211yescharacteristic
163#17988674C2211yescharacteristic
164#17988674C2211yescharacteristic
165#17988672C2211yescharacteristic
166#17988672C2211yescharacteristic
167#17988628C2211yescharacteristic
168#17988628C2211yescharacteristic
169#17988626C2211yescharacteristic
170#17988626C2211yescharacteristic
171#17988626C2211yescharacteristic
172#17988624C2211yescharacteristic
173#17988622C2211yescharacteristic
174#107×D73C2211yescharacteristic
175#107×D73C2211yescharacteristic
176#17988612C2211yescharacteristic
177#17988612C2211yescharacteristic
178C4⋊C8×D73C2211yescharacteristic
179#17988594C2211yescharacteristic
180#17988587C2211yescharacteristic
181#17988582C2211yescharacteristic
182#17988582C2211yescharacteristic
183#103×D73C2211yescharacteristic
184#103×D73C2211yescharacteristic
185#17988544C2211yescharacteristic
186#17988541C2211yescharacteristic
187#17988539C2211yescharacteristic
188#557×C73C2211yescharacteristic
189#557×C73C2211yescharacteristic
190#501×C73C2211yescharacteristic
191#501×C73C2211yescharacteristic
192#499×C73C2211yescharacteristic
193#479×C73C2211yescharacteristic
194#479×C73C2211yescharacteristic
195#479×C73C2211yescharacteristic
196#479×C73C2211yescharacteristic
197#477×C73C2211yescharacteristic
198#477×C73C2211yescharacteristic
199#446×C73C2211yescharacteristic
200#441×C73C2211yescharacteristic
201#441×C73C2211yescharacteristic
202C4×Q16×C73C2211yescharacteristic
203C2×#11924029C2311yescharacteristic
204C2×Q8×D73—21no—
205C2×Q8×D73—21no—
206C2×Q8×D73—21no—
207C2×Q8×D73C2311yescharacteristic
208#14556623Q818yescomplemented
209C2×#11924018C2311yescharacteristic
210C2×#11924017C2311yescharacteristic
211C2×#11924015C2311yescharacteristic
212C2×#11924011C2311yescharacteristic
213C2×#11924011C2311yescharacteristic
214C2×C8×D73C2311yescharacteristic
215C2×C8×D73C2311yescharacteristic
216#14556591—21no—
217#14556591—21no—
218#14556591—21no—
219#14556591—21no—
220#14556591C2311yescharacteristic
221#14556591C2311yescharacteristic
222#14556591C2311yescharacteristic
223#14556591C2311yescharacteristic
224#14556590—21no—
225#14556590—21no—
226#14556590—21no—
227#14556590—21no—
228#14556590—21no—
229#14556590—21no—
230#14556590—21no—
231#14556590—21no—
232#14556590—21no—
233#14556590—21no—
234#14556590—21no—
235#14556590—21no—
236#14556590—21no—
237#14556590—21no—
238#14556590—21no—
239#14556590D411yescharacteristic
240#14556590C2311yescharacteristic
241#14556590C2311yescharacteristic
242#14556590C2311yescharacteristic
243#14556590C2311yescharacteristic
244#14556590C2311yescharacteristic
245#14556590C2311yescharacteristic
246#14556590C2311yescharacteristic
247#14556590C2311yescharacteristic
248#14556589—21no—
249#14556589—21no—
250#14556589—21no—
251#14556589—21no—
252#14556589—21no—
253#14556589D411yescharacteristic
254#14556583—21no—
255#14556583—21no—
256#14556583C2311yescharacteristic
257#14556583C2311yescharacteristic
258#14556582—21no—
259#14556582—21no—
260#14556582—21no—
261#14556582—21no—
262#14556582C2311yescharacteristic
263#14556582C2311yescharacteristic
264#14556582C2311yescharacteristic
265#14556582C2311yescharacteristic
266#14556581—21no—
267#14556581—21no—
268#14556581—21no—
269#14556581—21no—
270#14556581—21no—
271#14556581—21no—
272#14556581—21no—
273#14556581—21no—
274#14556581—21no—
275#14556581—21no—
276#14556581D411yescharacteristic
277#14556581D411yescharacteristic
278#14556571—21no—
279#14556571—21no—
280#14556571—21no—
281#14556571—21no—
282#14556571—21no—
283#14556571—21no—
284#14556571—21no—
285#14556571—21no—
286#14556571D411yescharacteristic
287#14556569—21no—
288#14556569—21no—
289#14556569—21no—
290#14556569—21no—
291#14556569—21no—
292#14556569—21no—
293#14556569—21no—
294#14556569—21no—
295#14556569—21no—
296#14556569—21no—
297#14556569—21no—
298#14556569—21no—
299#14556569D411yescharacteristic
300#14556569D411yescharacteristic
301#14556567—21no—
302#14556567—21no—
303#14556567D411yescharacteristic
304Q8×Dic73C2311yescharacteristic
305Q8×Dic73C2311yescharacteristic
306Q8×Dic73C2311yescharacteristic
307Q8×Dic73C2311yescharacteristic
308Q8×Dic73C2311yescharacteristic
309Q8×Dic73C2311yescharacteristic
310C4×Dic146—21no—
311C4×Dic146—21no—
312C4×Dic146—21no—
313C4×Dic146—21no—
314C4×Dic146—21no—
315C4×Dic146—21no—
316C4×Dic146—21no—
317C4×Dic146—21no—
318C4×Dic146—21no—
319C4×Dic146C2311yescharacteristic
320C4×Dic146C2311yescharacteristic
321C4×Dic146C2311yescharacteristic
322C4×Dic146C2311yescharacteristic
323C4×Dic146C2311yescharacteristic
324C4×Dic146C2311yescharacteristic
325#14556556—21no—
326#14556556—21no—
327#14556556—21no—
328#14556556—21no—
329#14556556—21no—
330#14556556—21no—
331#14556556—21no—
332#14556556—21no—
333#14556556—21no—
334#14556556C2311yescharacteristic
335#14556556C2311yescharacteristic
336#14556556C2311yescharacteristic
337C4×D292—21no—
338C4×D292—21no—
339C4×D292—21no—
340C4×D292C2311yescharacteristic
341C4×D292C2311yescharacteristic
342C4×D292C2311yescharacteristic
343#14556553—21no—
344#14556553—21no—
345#14556553—21no—
346#14556553C2311yescharacteristic
347#14556553C2311yescharacteristic
348#14556553C2311yescharacteristic
349#14556549—21no—
350#14556549—21no—
351#14556549—21no—
352#14556549C2311yescharacteristic
353#14556549C2311yescharacteristic
354#14556549C2311yescharacteristic
355#14556548—21no—
356#14556548—21no—
357#14556548—21no—
358#14556548—21no—
359#14556548C2311yescharacteristic
360#14556548C2311yescharacteristic
361C4⋊C4×D73—21no—
362C4⋊C4×D73—21no—
363C4⋊C4×D73—21no—
364C4⋊C4×D73—21no—
365C4⋊C4×D73—21no—
366C4⋊C4×D73—21no—
367C4⋊C4×D73C2311yescharacteristic
368C4⋊C4×D73C2311yescharacteristic
369C4⋊C4×D73C2311yescharacteristic
370C42×D73—21no—
371C42×D73—21no—
372C42×D73C2311yescharacteristic
373#14556525C2311yescharacteristic
374#14556525C2311yescharacteristic
375#14556525C2311yescharacteristic
376#14556525C2311yescharacteristic
377#14556525C2311yescharacteristic
378#14556525C2311yescharacteristic
379#14556524C2311yescharacteristic
380#14556524C2311yescharacteristic
381#14556524C2311yescharacteristic
382#14556524C2311yescharacteristic
383#14556524C2311yescharacteristic
384#14556524C2311yescharacteristic
385#14556524C2311yescharacteristic
386#14556524C2311yescharacteristic
387#14556524C2311yescharacteristic
388#14556524C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556523C2311yescharacteristic
391#14556523C2311yescharacteristic
392#14556523C2311yescharacteristic
393#14556522C2311yescharacteristic
394#14556522C2311yescharacteristic
395#14556522C2311yescharacteristic
396#14556522C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556522C2311yescharacteristic
399#14556522C2311yescharacteristic
400C4⋊#10596831C2311yescharacteristic
401C4⋊#10596831C2311yescharacteristic
402C4⋊#10596831C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556520C2311yescharacteristic
407#14556520C2311yescharacteristic
408#14556520C2311yescharacteristic
409#14556516C2311yescharacteristic
410#14556516C2311yescharacteristic
411#14556516C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556515C2311yescharacteristic
416#14556515C2311yescharacteristic
417#14556515C2311yescharacteristic
418#14556514C2311yescharacteristic
419#14556514C2311yescharacteristic
420#14556514C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556513C2311yescharacteristic
424#14556511C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556511C2311yescharacteristic
427#14556502C2311yescharacteristic
428#14556502C2311yescharacteristic
429#14556501C2311yescharacteristic
430#14556501C2311yescharacteristic
431C4×#10596831C2311yescharacteristic
432C8×Dic73C2311yescharacteristic
433C8×Dic73C2311yescharacteristic
434C8×Dic73C2311yescharacteristic
435C8×Dic73C2311yescharacteristic
436C2×Q16×C73C2311yescharacteristic
437C4⋊Q8×C73—21no—
438C4⋊Q8×C73—21no—
439C4⋊Q8×C73C2311yescharacteristic
440C4⋊Q8×C73C2311yescharacteristic
441#125×C73—21no—
442#125×C73—21no—
443#125×C73—21no—
444#125×C73—21no—
445#125×C73C2311yescharacteristic
446#125×C73C2311yescharacteristic
447#125×C73C2311yescharacteristic
448#125×C73C2311yescharacteristic
449C4×Q8×C73—21no—
450C4×Q8×C73—21no—
451C4×Q8×C73C2311yescharacteristic
452C4×Q8×C73C2311yescharacteristic
453C4×Q8×C73C2311yescharacteristic
454C4×Q8×C73C2311yescharacteristic
455C4×Q8×C73C2311yescharacteristic
456C4×Q8×C73C2311yescharacteristic
457C4×Q8×C73C2311yescharacteristic
458#107×C73C2311yescharacteristic
459#107×C73C2311yescharacteristic
460#107×C73C2311yescharacteristic
461#107×C73C2311yescharacteristic
462#107×C73C2311yescharacteristic
463#106×C73C2311yescharacteristic
464#106×C73C2311yescharacteristic
465#106×C73C2311yescharacteristic
466#106×C73C2311yescharacteristic
467C4⋊C8×C73C2311yescharacteristic
468C4⋊C8×C73C2311yescharacteristic
469C4⋊C8×C73C2311yescharacteristic
470#103×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#103×C73C2311yescharacteristic
474#103×C73C2311yescharacteristic
475#103×C73C2311yescharacteristic
476#97×C73C2311yescharacteristic
477#97×C73C2311yescharacteristic
478C4×C8×C73C2311yescharacteristic
479#11924029—22no—
480#11924029C2×Q814yes—
481C2×Dic146—21no—
482C2×Dic146—21no—
483C2×Dic146—21no—
484C2×Dic146—21no—
485C2×Dic146—21no—
486C2×Dic146—21no—
487C2×Dic146—21no—
488C2×Dic146—21no—
489C2×Dic146—21no—
490C2×Dic146—21no—
491C2×Dic146—21no—
492C2×Dic146—21no—
493C2×Dic146—21no—
494C2×Dic146C2×D411yescharacteristic
495C2×Dic146C2×D411yescharacteristic
496C2×Dic146C2×D411yescharacteristic
497C2×Dic146C2411yescharacteristic
498Q8×D73—22no—
499Q8×D73—82no—
500Q8×D73—82no—
501Q8×D73—82no—
502Q8×D73C2×Q814yescomplemented
503C2×D292—21no—
504C2×D292C2411yescharacteristic
505C2×C4×D73—21no—
506C2×C4×D73—21no—
507C2×C4×D73—21no—
508C2×C4×D73—21no—
509C2×C4×D73—21no—
510C2×C4×D73—21no—
511C2×C4×D73—21no—
512C2×C4×D73—21no—
513C2×C4×D73—21no—
514C2×C4×D73—21no—
515C2×C4×D73—21no—
516C2×C4×D73C2×D411yescharacteristic
517C2×C4×D73C2×D411yescharacteristic
518C2×C4×D73C2411yescharacteristic
519#11924018C2×Q814yescomplemented
520#11924017C2×Q814yescomplemented
521#11924015C2×Q814yescomplemented
522#11924011—22no—
523#11924011C2×Q814yescomplemented
524C2×#10596831C2411yescharacteristic
525C2×#10596831C2411yescharacteristic
526C2×#10596831C2411yescharacteristic
527C2×#10596831C2411yescharacteristic
528C8×D73—22no—
529C8×D73—22no—
530C4⋊Dic73—21no—
531C4⋊Dic73—21no—
532C4⋊Dic73—21no—
533C4⋊Dic73—21no—
534C4⋊Dic73—21no—
535C4⋊Dic73—21no—
536C4⋊Dic73—21no—
537C4⋊Dic73—21no—
538C4⋊Dic73—21no—
539C4⋊Dic73—21no—
540C4⋊Dic73—21no—
541C4⋊Dic73—21no—
542C4⋊Dic73—21no—
543C4⋊Dic73—21no—
544C4⋊Dic73C2×D411yescharacteristic
545C4⋊Dic73C2×D411yescharacteristic
546C4⋊Dic73C2×D411yescharacteristic
547C4⋊Dic73C2411yescharacteristic
548C4⋊Dic73C2411yescharacteristic
549C4⋊Dic73C2411yescharacteristic
550C4⋊Dic73C2411yescharacteristic
551C4⋊Dic73C2411yescharacteristic
552C4⋊Dic73C2411yescharacteristic
553#11924007—21no—
554#11924007—21no—
555#11924007—21no—
556#11924007—21no—
557#11924007—21no—
558#11924007—21no—
559#11924007—21no—
560#11924007—21no—
561#11924007—21no—
562#11924007—21no—
563#11924007—21no—
564#11924007—21no—
565#11924007—21no—
566#11924007—21no—
567#11924007—21no—
568#11924007—21no—
569#11924007—21no—
570#11924007—21no—
571#11924007—21no—
572#11924007—21no—
573#11924007—21no—
574#11924007—21no—
575#11924007—21no—
576#11924007—21no—
577#11924007—21no—
578#11924007C2×D411yescharacteristic
579#11924007C2×D411yescharacteristic
580#11924007C2×D411yescharacteristic
581#11924007C2×D411yescharacteristic
582#11924007C2×D411yescharacteristic
583#11924007C2×D411yescharacteristic
584#11924007C2×D411yescharacteristic
585#11924007C2×D411yescharacteristic
586#11924007C2×D411yescharacteristic
587#11924007C2×D411yescharacteristic
588#11924005—21no—
589#11924005—21no—
590#11924005—21no—
591#11924005—21no—
592#11924005—21no—
593#11924005—21no—
594#11924005—21no—
595#11924005—21no—
596#11924005—21no—
597#11924005C2×D411yescharacteristic
598#11924005C2×D411yescharacteristic
599#11924005C2×D411yescharacteristic
600#11924005C2×D411yescharacteristic
601C4×Dic73—21no—
602C4×Dic73—21no—
603C4×Dic73—21no—
604C4×Dic73—21no—
605C4×Dic73—21no—
606C4×Dic73—21no—
607C4×Dic73—21no—
608C4×Dic73—21no—
609C4×Dic73—21no—
610C4×Dic73—21no—
611C4×Dic73—21no—
612C4×Dic73—21no—
613C4×Dic73—21no—
614C4×Dic73—21no—
615C4×Dic73—21no—
616C4×Dic73C2×D411yescharacteristic
617C4×Dic73C2×D411yescharacteristic
618C4×Dic73C2411yescharacteristic
619C4×Dic73C2411yescharacteristic
620C4×Dic73C2411yescharacteristic
621C2×Q8×C73—21no—
622C2×Q8×C73—21no—
623C2×Q8×C73C2×D411yescharacteristic
624C2×Q8×C73C2411yescharacteristic
625C2×Q8×C73C2411yescharacteristic
626Q16×C73C2×Q814yescomplemented
627C2×C8×C73C2411yescharacteristic
628C2×C8×C73C2411yescharacteristic
629C2×C8×C73C2411yescharacteristic
630C2×C8×C73C2411yescharacteristic
631C4⋊C4×C73—21no—
632C4⋊C4×C73—21no—
633C4⋊C4×C73—21no—
634C4⋊C4×C73—21no—
635C4⋊C4×C73—21no—
636C4⋊C4×C73—21no—
637C4⋊C4×C73—21no—
638C4⋊C4×C73—21no—
639C4⋊C4×C73—21no—
640C4⋊C4×C73—21no—
641C4⋊C4×C73—21no—
642C4⋊C4×C73—21no—
643C4⋊C4×C73—21no—
644C4⋊C4×C73—21no—
645C4⋊C4×C73—21no—
646C4⋊C4×C73—21no—
647C4⋊C4×C73C2×D411yescharacteristic
648C4⋊C4×C73C2×D411yescharacteristic
649C4⋊C4×C73C2×D411yescharacteristic
650C4⋊C4×C73C2411yescharacteristic
651C4⋊C4×C73C2411yescharacteristic
652C4⋊C4×C73C2411yescharacteristic
653C4⋊C4×C73C2411yescharacteristic
654C4⋊C4×C73C2411yescharacteristic
655C4⋊C4×C73C2411yescharacteristic
656C42×C73—21no—
657C42×C73—21no—
658C42×C73—21no—
659C42×C73—21no—
660C42×C73—21no—
661C42×C73—21no—
662C42×C73C2411yescharacteristic
663C42×C73C2411yescharacteristic
664C42×C73C2411yescharacteristic
665C22×D73—21no—
666C22×D73C22×D411yescharacteristic
667Q8×C73—21no—
668Q8×C73—21no—
669Q8×C73—41no—
670Q8×C73—42no—
671Q8×C73—81no—
672Q8×C73C22×Q812yes—
673Q8×C73C22×Q812yes—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73C22×D411yescharacteristic
683C2×C4×C73C22×D411yescharacteristic
684C2×C4×C73C22×D411yescharacteristic
685C2×C4×C73C22×D411yescharacteristic
686C2×C4×C73C22×D411yescharacteristic
687C2×C4×C73C22×D411yescharacteristic
688C2×C4×C73C2511yescharacteristic
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73C22×D411yescharacteristic
697C2×Dic73C22×D411yescharacteristic
698C2×Dic73C22×D411yescharacteristic
699C2×Dic73C22×D411yescharacteristic
700C2×Dic73C22×D411yescharacteristic
701C2×Dic73C22×D411yescharacteristic
702C2×Dic73C22×D411yescharacteristic
703D292—24no—
704D292—21no—
705D292C22×Q812yes—
706C4×D73—24no—
707C4×D73—24no—
708C4×D73—22no—
709C4×D73—41no—
710C4×D73—42no—
711C4×D73—42no—
712C4×D73—81no—
713C4×D73—81no—
714C4×D73—81no—
715C4×D73—81no—
716C4×D73—81no—
717C4×D73—81no—
718C4×D73—81no—
719C4×D73C22×Q812yes—
720C4×D732−1+412yes—
721Dic146—21no—
722Dic146—24no—
723Dic146—22no—
724Dic146—22no—
725Dic146—41no—
726Dic146—42no—
727Dic146—42no—
728Dic146—81no—
729Dic146—81no—
730Dic146—81no—
731Dic146—81no—
732Dic146—81no—
733Dic146—81no—
734Dic146—81no—
735Dic146—81no—
736Dic146—81no—
737Dic146—81no—
738Dic146C22×Q812yes—
739C8×C73—21no—
740C8×C73—21no—
741C8×C73—21no—
742C8×C73C22×Q812yes—
743#10596831—21no—
744#10596831—21no—
745#10596831—21no—
746#10596831C22×Q812yes—
747C22×C73C23×D411yescharacteristic
748C2×D73—21no—
749C2×D73—21no—
750C2×D73—22no—
751C2×D73—41no—
752C2×D73—41no—
753C2×D73D4×Q812yes—
754C4×C73—21no—
755C4×C73—21no—
756C4×C73—21no—
757C4×C73—22no—
758C4×C73—22no—
759C4×C73—21no—
760C4×C73—21no—
761C4×C73—21no—
762C4×C73—41no—
763C4×C73—41no—
764C4×C73—41no—
765C4×C73—41no—
766C4×C73—41no—
767C4×C73—41no—
768C4×C73C23×Q811yescharacteristic
769C4×C73C2×2−1+411yescharacteristic
770Dic73—21no—
771Dic73—21no—
772Dic73—21no—
773Dic73—22no—
774Dic73—21no—
775Dic73—21no—
776Dic73—41no—
777Dic73—41no—
778Dic73—41no—
779Dic73—41no—
780Dic73—41no—
781Dic73—41no—
782Dic73D4×Q812yes—
783Dic73#57812yes—
784#61384—731nomaximal, Sylow
785C2×C73C2×D4×Q811yescharacteristic
786C2×C73C2×#57811yescharacteristic
787C2×C73#358511yescharacteristic
788D73—22no—
789D73—42no—
790#3503—731no—
791#3502—731no—
792#3390—731no—
793#3390—731no—
794#3390—731no—
795#3390D7311yescharacteristic, complemented
796#3387—731no—
797#3387—731no—
798#3386—731no—
799#3386—731no—
800#3386—731no—
801#3386—731no—
802#3385—731no—
803#3385—731no—
804Q8×Q16—731no—
805Q8×Q16—731no—
806#3381—731no—
807#3381—731no—
808#3165—731no—
809#3164—731no—
810#3164—731no—
811#3083—731no—
812#3083—731no—
813#3082—731no—
814#3082—731no—
815#3076—731no—
816C2×#477—731no—
817#2962—731no—
818#2947—731no—
819#2947—731no—
820C4×#137—731no—
821C73#6138411yescharacteristic, complemented, Sylow
822C2×#137—731no—
823Q82—731no—
824Q82—731no—
825Q82—731no—
826Q82—731no—
827Q82—1461no—
828#557—731no—
829#557—731no—
830#557—731no—
831#557—731no—
832#557—731no—
833#557—731no—
834#557—1461no—
835#557—1461no—
836#557—1461no—
837#557C2×D7311yescharacteristic
838#557C2×D7311yescharacteristic
839#554—731no—
840#554—731no—
841#554—1461no—
842#554—1461no—
843D4×Q8—731no—
844D4×Q8—731no—
845D4×Q8—1461no—
846D4×Q8—1461no—
847#544—731no—
848#544—731no—
849#544—731no—
850#544—731no—
851#544—1461no—
852#544—1461no—
853#544—1461no—
854#544—1461no—
855#533—731no—
856#533—731no—
857#533—1461no—
858#533—1461no—
859#533—1461no—
860C2×C4⋊Q8—731no—
861C2×C4⋊Q8—1461no—
862#520—731no—
863#520—731no—
864#519—731no—
865#519—731no—
866C4×#41—731no—
867C2×C4×Q8—731no—
868#501—731no—
869#501—731no—
870#501—731no—
871#501—731no—
872#501—731no—
873#501—731no—
874#501—731no—
875#501—731no—
876#501—731no—
877#501—731no—
878#501C2×D7311yescharacteristic
879#501C2×D7311yescharacteristic
880#500—731no—
881#500—731no—
882#500—731no—
883#500—731no—
884#500—731no—
885#500—731no—
886#499—731no—
887#499—731no—
888#499—731no—
889#499C2×D7311yescharacteristic
890#498—731no—
891#498—731no—
892#479—731no—
893#479—731no—
894#479—731no—
895#479—731no—
896#479—731no—
897#479—731no—
898#479—731no—
899#479—731no—
900#479—731no—
901#479—731no—
902#479C2×D7311yescharacteristic
903#479C2×D7311yescharacteristic
904#479C2×D7311yescharacteristic
905#479C2×D7311yescharacteristic
906#478—731no—
907#478—731no—
908#478—731no—
909#478—731no—
910#478—731no—
911#478—731no—
912#477—731no—
913#477—731no—
914#477—731no—
915#477—731no—
916#477—731no—
917#477—731no—
918#477—731no—
919#477—731no—
920#477—731no—
921#477—731no—
922#477—731no—
923#477—731no—
924#477—731no—
925#477—731no—
926#477—731no—
927#477C2×D7311yescharacteristic
928#477C2×D7311yescharacteristic
929#476—731no—
930#475—731no—
931#475—731no—
932#475—731no—
933#475—731no—
934#475—731no—
935#474—731no—
936#474—731no—
937#474—731no—
938#474—731no—
939#474—731no—
940#446—731no—
941#446—731no—
942#446—731no—
943#446—731no—
944#446—731no—
945#446C2×D7311yescharacteristic
946C8×Q8—731no—
947C8×Q8—731no—
948#441—731no—
949#441—731no—
950#441—731no—
951#441—731no—
952#441C2×D7311yescharacteristic
953#441C2×D7311yescharacteristic
954#440—731no—
955#440—731no—
956#440—731no—
957#440—731no—
958#440—731no—
959#440—731no—
960C4×Q16—731no—
961C4×Q16—731no—
962C4×Q16—731no—
963C4×Q16—731no—
964C4×Q16—731no—
965C4×Q16C2×D7311yescharacteristic
966C4×SD16—731no—
967C4×SD16—731no—
968C4×SD16—731no—
969C4×SD16—731no—
970C4×SD16—731no—
971C4×SD16—731no—
972#428—731no—
973#428—731no—
974#428—731no—
975#428—731no—
976#428—731no—
977#427—731no—
978#427—731no—
979C2×#107—731no—
980C2×#107—731no—
981#424—731no—
982#424—731no—
983C2×C4⋊C8—731no—
984#419—731no—
985#417—731no—
986#416—731no—
987#416—731no—
988C2×#103—731no—
989C2×#103—731no—
990#405—731no—
991#405—731no—
992C4×M16—731no—
993C2×#41—731no—
994C22×Q8—731no—
995C22×Q8—1461no—
996C22×Q8—1461no—
997C22×Q8—1461no—
998#137—738no—
999C2×Q16—731no—
1000C2×Q16C22×D7311yescharacteristic
1001C2×SD16—731no—
1002C2×SD16—731no—
1003C2×M16—731no—
1004C2×M16—731no—
1005C22×C8—731no—
1006C22×C8—731no—
1007C4⋊Q8—21no—
1008C4⋊Q8—21no—
1009C4⋊Q8—731no—
1010C4⋊Q8—731no—
1011C4⋊Q8—731no—
1012C4⋊Q8—731no—
1013C4⋊Q8—731no—
1014C4⋊Q8—731no—
1015C4⋊Q8—731no—
1016C4⋊Q8—731no—
1017C4⋊Q8—731no—
1018C4⋊Q8—731no—
1019C4⋊Q8—731no—
1020C4⋊Q8—731no—
1021C4⋊Q8—731no—
1022C4⋊Q8—731no—
1023C4⋊Q8—1461no—
1024C4⋊Q8—1461no—
1025C4⋊Q8—1461no—
1026C4⋊Q8—1461no—
1027C4⋊Q8—1461no—
1028C4⋊Q8—1461no—
1029C4⋊Q8—1461no—
1030C4⋊Q8—1461no—
1031C4⋊Q8—1461no—
1032C4⋊Q8—1461no—
1033C4⋊Q8—1461no—
1034C4⋊Q8—1461no—
1035C4⋊Q8—1461no—
1036C4⋊Q8—1461no—
1037C4⋊Q8—1461no—
1038C4⋊Q8—1461no—
1039C4⋊Q8—1461no—
1040C4⋊Q8—1461no—
1041C4⋊Q8—1461no—
1042C4⋊Q8—1461no—
1043C4⋊Q8—1461no—
1044C4⋊Q8—1461no—
1045C4⋊Q8—1461no—
1046C4⋊Q8—1461no—
1047C4⋊Q8C22×D7311yescharacteristic
1048C4⋊Q8C22×D7311yescharacteristic
1049#125—21no—
1050#125—21no—
1051#125—21no—
1052#125—21no—
1053#125—731no—
1054#125—731no—
1055#125—731no—
1056#125—731no—
1057#125—731no—
1058#125—731no—
1059#125—731no—
1060#125—731no—
1061#125—1461no—
1062#125—1461no—
1063#125—1461no—
1064#125—1461no—
1065#125—1461no—
1066#125—1461no—
1067#125—1461no—
1068#125—1461no—
1069#125—1461no—
1070#125—1461no—
1071#125—1461no—
1072#125—1461no—
1073#125—1461no—
1074#125—1461no—
1075#125—1461no—
1076#125—1461no—
1077#125C22×D7311yescharacteristic
1078#125C22×D7311yescharacteristic
1079#125C22×D7311yescharacteristic
1080#125C22×D7311yescharacteristic
1081C22⋊Q8—731no—
1082C22⋊Q8—731no—
1083C22⋊Q8—731no—
1084C22⋊Q8—731no—
1085C22⋊Q8—1461no—
1086C22⋊Q8—1461no—
1087C22⋊Q8—1461no—
1088C22⋊Q8—1461no—
1089C22⋊Q8—1461no—
1090C22⋊Q8—1461no—
1091C22⋊Q8—1461no—
1092C22⋊Q8—1461no—
1093C22⋊Q8—1461no—
1094C22⋊Q8—1461no—
1095C22⋊Q8—1461no—
1096C22⋊Q8—1461no—
1097C22⋊Q8—1461no—
1098C22⋊Q8—1461no—
1099C22⋊Q8—1461no—
1100C22⋊Q8—1461no—
1101C22⋊Q8—1461no—
1102C22⋊Q8—1461no—
1103C22⋊Q8—1461no—
1104C22⋊Q8—1461no—
1105C22⋊Q8—1461no—
1106C22⋊Q8—1461no—
1107C4×Q8—21no—
1108C4×Q8—21no—
1109C4×Q8—731no—
1110C4×Q8—731no—
1111C4×Q8—731no—
1112C4×Q8—731no—
1113C4×Q8—731no—
1114C4×Q8—731no—
1115C4×Q8—731no—
1116C4×Q8—731no—
1117C4×Q8—731no—
1118C4×Q8—731no—
1119C4×Q8—731no—
1120C4×Q8—731no—
1121C4×Q8—731no—
1122C4×Q8—731no—
1123C4×Q8—731no—
1124C4×Q8—1461no—
1125C4×Q8—1461no—
1126C4×Q8—1461no—
1127C4×Q8—1461no—
1128C4×Q8—1461no—
1129C4×Q8—1461no—
1130C4×Q8—1461no—
1131C4×Q8—1461no—
1132C4×Q8—1461no—
1133C4×Q8—1461no—
1134C4×Q8—1461no—
1135C4×Q8—1461no—
1136C4×Q8—1461no—
1137C4×Q8—1461no—
1138C4×Q8—1461no—
1139C4×Q8—1461no—
1140C4×Q8—1461no—
1141C4×Q8—1461no—
1142C4×Q8C22×D7311yescharacteristic
1143C4×Q8C22×D7311yescharacteristic
1144C4×Q8C22×D7311yescharacteristic
1145C4×Q8C22×D7311yescharacteristic
1146C4×Q8C22×D7311yescharacteristic
1147C4×Q8C22×D7311yescharacteristic
1148C4×Q8C22×D7311yescharacteristic
1149C4×D4—731no—
1150C4×D4—731no—
1151C4×D4—731no—
1152C4×D4—731no—
1153C4×D4—731no—
1154C4×D4—731no—
1155C4×D4—1461no—
1156C4×D4—1461no—
1157C4×D4—1461no—
1158C4×D4—1461no—
1159C4×D4—1461no—
1160C4×D4—1461no—
1161#117—731no—
1162#117—731no—
1163#117—731no—
1164#117—731no—
1165#117—731no—
1166#117—1461no—
1167#117—1461no—
1168#117—1461no—
1169#117—1461no—
1170#117—1461no—
1171#117—1461no—
1172#117—1461no—
1173C2×C4⋊C4—731no—
1174C2×C4⋊C4—731no—
1175C2×C4⋊C4—731no—
1176C2×C4⋊C4—1461no—
1177C2×C4⋊C4—1461no—
1178C2×C4⋊C4—1461no—
1179C2×C4⋊C4—1461no—
1180C2×C4⋊C4—1461no—
1181C2×C4⋊C4—1461no—
1182C2×C42—731no—
1183C2×C42—1461no—
1184C2×C42—1461no—
1185#107—731no—
1186#107—731no—
1187#107—731no—
1188#107—731no—
1189#107—731no—
1190#107—731no—
1191#107—731no—
1192#107—731no—
1193#107—731no—
1194#107—731no—
1195#107—731no—
1196#107—731no—
1197#107—731no—
1198#107—731no—
1199#107—731no—
1200#107—731no—
1201#107—731no—
1202#107C22×D7311yescharacteristic
1203#107C22×D7311yescharacteristic
1204#107C22×D7311yescharacteristic
1205#107C22×D7311yescharacteristic
1206#107C22×D7311yescharacteristic
1207#106—731no—
1208#106—731no—
1209#106—731no—
1210#106—731no—
1211#106—731no—
1212#106—731no—
1213#106—731no—
1214#106—731no—
1215#106—731no—
1216#106—731no—
1217#106C22×D7311yescharacteristic
1218#106C22×D7311yescharacteristic
1219#106C22×D7311yescharacteristic
1220#106C22×D7311yescharacteristic
1221C4⋊C8—731no—
1222C4⋊C8—731no—
1223C4⋊C8—731no—
1224C4⋊C8—731no—
1225C4⋊C8—731no—
1226C4⋊C8—731no—
1227C4⋊C8—731no—
1228C4⋊C8—731no—
1229C4⋊C8—731no—
1230C4⋊C8C22×D7311yescharacteristic
1231C4⋊C8C22×D7311yescharacteristic
1232C4⋊C8C22×D7311yescharacteristic
1233#103—731no—
1234#103—731no—
1235#103—731no—
1236#103—731no—
1237#103—731no—
1238#103—731no—
1239#103—731no—
1240#103—731no—
1241#103—731no—
1242#103—731no—
1243#103—731no—
1244#103—731no—
1245#103C22×D7311yescharacteristic
1246#103C22×D7311yescharacteristic
1247#103C22×D7311yescharacteristic
1248#103C22×D7311yescharacteristic
1249#103C22×D7311yescharacteristic
1250#103C22×D7311yescharacteristic
1251#102—731no—
1252#102—731no—
1253#102—731no—
1254#102—731no—
1255#102—731no—
1256#102—731no—
1257#97—731no—
1258#97—731no—
1259#97—731no—
1260#97—731no—
1261#97C22×D7311yescharacteristic
1262#97C22×D7311yescharacteristic
1263C4×C8—731no—
1264C4×C8—731no—
1265C4×C8—731no—
1266C4×C8—731no—
1267C4×C8—731no—
1268C4×C8C22×D7311yescharacteristic
1269#41—734no—
1270#41—1462no—
1271C2×Q8—21no—
1272C2×Q8—21no—
1273C2×Q8—5842no—
1274C2×Q8—5842no—
1275C2×Q8—5842no—
1276C2×Q8—731no—
1277C2×Q8—731no—
1278C2×Q8—731no—
1279C2×Q8—734no—
1280C2×Q8—731no—
1281C2×Q8—1461no—
1282C2×Q8—1461no—
1283C2×Q8—1461no—
1284C2×Q8—1461no—
1285C2×Q8—1461no—
1286C2×Q8—1461no—
1287C2×Q8—1461no—
1288C2×Q8—1461no—
1289C2×Q8—1461no—
1290C2×Q8—1462no—
1291C2×Q8—1461no—
1292C2×Q8—1461no—
1293C2×Q8—1461no—
1294C2×Q8—1461no—
1295C2×Q8D4×D7311yescharacteristic
1296C2×Q8C23×D7311yescharacteristic
1297C2×Q8C23×D7311yescharacteristic
1298C2×D4—731no—
1299C2×D4—1461no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—1461no—
1304C22×C4—1461no—
1305C22×C4—1461no—
1306C22×C4—1461no—
1307C22×C4—1461no—
1308C22×C4—1461no—
1309C22×C4—1461no—
1310C22×C4—1461no—
1311C22×C4—1461no—
1312C22×C4—1461no—
1313C22×C4—1461no—
1314Q16—734no—
1315Q16Q8×D7314yescomplemented
1316SD16—734no—
1317SD16—734no—
1318M16—734no—
1319M16—1462no—
1320C2×C8—731no—
1321C2×C8—731no—
1322C2×C8—731no—
1323C2×C8—731no—
1324C2×C8—1462no—
1325C2×C8—1462no—
1326C2×C8C23×D7311yescharacteristic
1327C2×C8C23×D7311yescharacteristic
1328C2×C8C23×D7311yescharacteristic
1329C2×C8C23×D7311yescharacteristic
1330C4⋊C4—21no—
1331C4⋊C4—21no—
1332C4⋊C4—21no—
1333C4⋊C4—21no—
1334C4⋊C4—21no—
1335C4⋊C4—21no—
1336C4⋊C4—21no—
1337C4⋊C4—21no—
1338C4⋊C4—21no—
1339C4⋊C4—21no—
1340C4⋊C4—21no—
1341C4⋊C4—21no—
1342C4⋊C4—21no—
1343C4⋊C4—21no—
1344C4⋊C4—21no—
1345C4⋊C4—21no—
1346C4⋊C4—731no—
1347C4⋊C4—731no—
1348C4⋊C4—731no—
1349C4⋊C4—731no—
1350C4⋊C4—731no—
1351C4⋊C4—731no—
1352C4⋊C4—731no—
1353C4⋊C4—731no—
1354C4⋊C4—731no—
1355C4⋊C4—731no—
1356C4⋊C4—731no—
1357C4⋊C4—731no—
1358C4⋊C4—731no—
1359C4⋊C4—731no—
1360C4⋊C4—731no—
1361C4⋊C4—731no—
1362C4⋊C4—731no—
1363C4⋊C4—731no—
1364C4⋊C4—731no—
1365C4⋊C4—1461no—
1366C4⋊C4—1461no—
1367C4⋊C4—1461no—
1368C4⋊C4—1461no—
1369C4⋊C4—1461no—
1370C4⋊C4—1461no—
1371C4⋊C4—1461no—
1372C4⋊C4—1461no—
1373C4⋊C4—1461no—
1374C4⋊C4—1461no—
1375C4⋊C4—1461no—
1376C4⋊C4—1461no—
1377C4⋊C4—1461no—
1378C4⋊C4—1461no—
1379C4⋊C4—1461no—
1380C4⋊C4—1461no—
1381C4⋊C4—1461no—
1382C4⋊C4—1461no—
1383C4⋊C4—1461no—
1384C4⋊C4—1461no—
1385C4⋊C4—1461no—
1386C4⋊C4—1461no—
1387C4⋊C4—1461no—
1388C4⋊C4—1461no—
1389C4⋊C4—1461no—
1390C4⋊C4—1461no—
1391C4⋊C4—1461no—
1392C4⋊C4—1461no—
1393C4⋊C4—1461no—
1394C4⋊C4—1461no—
1395C4⋊C4—1461no—
1396C4⋊C4—1461no—
1397C4⋊C4—1461no—
1398C4⋊C4—1461no—
1399C4⋊C4—1461no—
1400C4⋊C4—1461no—
1401C4⋊C4—1461no—
1402C4⋊C4—1461no—
1403C4⋊C4—1461no—
1404C4⋊C4D4×D7311yescharacteristic
1405C4⋊C4D4×D7311yescharacteristic
1406C4⋊C4D4×D7311yescharacteristic
1407C4⋊C4C23×D7311yescharacteristic
1408C4⋊C4C23×D7311yescharacteristic
1409C4⋊C4C23×D7311yescharacteristic
1410C4⋊C4C23×D7311yescharacteristic
1411C4⋊C4C23×D7311yescharacteristic
1412C4⋊C4C23×D7311yescharacteristic
1413C22⋊C4—731no—
1414C22⋊C4—731no—
1415C22⋊C4—731no—
1416C22⋊C4—731no—
1417C22⋊C4—1461no—
1418C22⋊C4—1461no—
1419C22⋊C4—1461no—
1420C22⋊C4—1461no—
1421C22⋊C4—1461no—
1422C22⋊C4—1461no—
1423C22⋊C4—1461no—
1424C22⋊C4—1461no—
1425C22⋊C4—1461no—
1426C42—21no—
1427C42—21no—
1428C42—21no—
1429C42—21no—
1430C42—21no—
1431C42—21no—
1432C42—731no—
1433C42—731no—
1434C42—731no—
1435C42—731no—
1436C42—731no—
1437C42—1461no—
1438C42—1461no—
1439C42—1461no—
1440C42—1461no—
1441C42—1461no—
1442C42—1461no—
1443C42—1461no—
1444C42—1461no—
1445C42—1461no—
1446C42—1461no—
1447C42—1461no—
1448C42—1461no—
1449C42—1461no—
1450C42—1461no—
1451C42—1461no—
1452C42C23×D7311yescharacteristic
1453C42C23×D7311yescharacteristic
1454C42C23×D7311yescharacteristic
1455C23—731no—
1456C23—1461no—
1457Q8—21no—
1458Q8—21no—
1459Q8—41no—
1460Q8—42no—
1461Q8—81no—
1462Q8—2922no—
1463Q8—2921no—
1464Q8—2922no—
1465Q8—5841no—
1466Q8—5841no—
1467Q8—5841no—
1468Q8—5841no—
1469Q8—5841no—
1470Q8—5841no—
1471Q8—5841no—
1472Q8—5841no—
1473Q8—5841no—
1474Q8—5841no—
1475Q8—732no—
1476Q8—1464no—
1477Q8—1462no—
1478Q8—1462no—
1479Q8—1461no—
1480Q8C2×Q8×D7312yes—
1481Q8C2×Q8×D7312yes—
1482D4—732no—
1483D4—1464no—
1484D4—1461no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—2922no—
1494C2×C4—2921no—
1495C2×C4—2922no—
1496C2×C4—5841no—
1497C2×C4—5841no—
1498C2×C4—5841no—
1499C2×C4—5841no—
1500C2×C4—5841no—
1501C2×C4—5841no—
1502C2×C4—5841no—
1503C2×C4—731no—
1504C2×C4—731no—
1505C2×C4—732no—
1506C2×C4—732no—
1507C2×C4—731no—
1508C2×C4—731no—
1509C2×C4—731no—
1510C2×C4—731no—
1511C2×C4—731no—
1512C2×C4—1462no—
1513C2×C4—1464no—
1514C2×C4—1464no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4—1461no—
1521C2×C4—1461no—
1522C2×C4C2×D4×D7311yescharacteristic
1523C2×C4C2×D4×D7311yescharacteristic
1524C2×C4C2×D4×D7311yescharacteristic
1525C2×C4C2×D4×D7311yescharacteristic
1526C2×C4C2×D4×D7311yescharacteristic
1527C2×C4C2×D4×D7311yescharacteristic
1528C2×C4C24×D7311yescharacteristic
1529C8—21no—
1530C8—21no—
1531C8—21no—
1532C8—732no—
1533C8—1461no—
1534C8—1461no—
1535C8—1461no—
1536C8C2×Q8×D7312yes—
1537C22—2921no—
1538C22—2921no—
1539C22—732no—
1540C22—1462no—
1541C22—1461no—
1542C22—1461no—
1543C22C22×D4×D7311yescharacteristic
1544C4—22no—
1545C4—22no—
1546C4—21no—
1547C4—21no—
1548C4—21no—
1549C4—21no—
1550C4—21no—
1551C4—21no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—2921no—
1559C4—2921no—
1560C4—2921no—
1561C4—2921no—
1562C4—2921no—
1563C4—2921no—
1564C4—732no—
1565C4—732no—
1566C4—1462no—
1567C4—1461no—
1568C4—1461no—
1569C4—1461no—
1570C4—1461no—
1571C4—1461no—
1572C4C22×Q8×D7311yescharacteristic
1573C42−1+4×D7311yescharacteristic
1574C2—2922no—
1575C2—1462no—
1576C2D4×Q8×D7311yescharacteristic
1577C2#578×D7311yescharacteristic
1578C2#2262470811yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3390C2
socleC22×C73C23×D4
prime radicalC2×#11924029C23
hypercenter#3390D73
hypocenterC73#61384
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3390

Complements

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

NH ≅ G/Ntype
2. #22623738C2semidirect
3. #22622899C2semidirect
4. #22622897C2semidirect
5. #22622894C2semidirect
6. #22622866C2semidirect
7. #22622864C2semidirect
8. #22622855C2semidirect
9. #22622854C2semidirect
10. #22622849C2semidirect
11. #22622848C2semidirect
12. #22622844C2semidirect
13. #22622838C2semidirect
14. Q16×Dic146C2semidirect
15. #22622812C2semidirect
16. #22622809C2semidirect
17. #22622803C2semidirect
18. #22620476C2semidirect
19. #22620468C2semidirect
20. #22620466C2semidirect
23. #22619772C2semidirect
24. #22619770C2semidirect
26. #477×D73C2semidirect
27. #22618876C2semidirect
31. C73×#3390C2semidirect
208. #14556623Q8semidirect
502. Q8×D73C2×Q8semidirect
519. #11924018C2×Q8semidirect
520. #11924017C2×Q8semidirect
521. #11924015C2×Q8semidirect
523. #11924011C2×Q8semidirect
626. Q16×C73C2×Q8semidirect
795. #3390D73semidirect
821. C73#61384semidirect
1315. Q16Q8×D73semidirect

Maximal subgroups

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

subgroupindex
#226237482
#226237382
#226228992
#226228972
#226228942
#226228662
#226228642
#226228552
#226228542
#226228492
#226228482
#226228442
#226228382
Q16×Dic1462
#226228122
#226228092
#226228032
#226204762
#226204682
#226204662
#226197852
#226197792
#226197722
#226197702
#226197182
#477×D732
#226188762
#226187732
#226187692
#226187472
C73×#33902
#6138473