Finite Group Databasebeta

← #62197

Subgroups — #62197

Order 256.

851 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559C211yesmaximal, characteristic, complemented
2#3524C211yesmaximal, characteristic, complemented
3#3388C211yesmaximal, characteristic, complemented
4#3381C211yesmaximal, characteristic, complemented
5#3370C211yesmaximal, characteristic, complemented
6#3361C211yesmaximal, characteristic, complemented
7#3355C211yesmaximal, characteristic, complemented
8#3354C211yesmaximal, characteristic, complemented
9#3351C211yesmaximal, characteristic, complemented
10#3347C211yesmaximal, characteristic, complemented
11#3343C211yesmaximal, characteristic, complemented
12#3339C211yesmaximal, characteristic, complemented
13#3332C211yesmaximal, characteristic, complemented
14#3326C211yesmaximal, characteristic, complemented
15#3326C211yesmaximal, characteristic, complemented
16#3309C211yesmaximal, characteristic, complemented
17#3308C211yesmaximal, characteristic, complemented
18#3301C211yesmaximal, characteristic, complemented
19#3259C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3251C211yesmaximal, characteristic, complemented
22#3244C211yesmaximal, characteristic, complemented
23#3241C211yesmaximal, characteristic, complemented
24#3232C211yesmaximal, characteristic, complemented
25#3126C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3106C211yesmaximal, characteristic, complemented
28#3083C211yesmaximal, characteristic, complemented
29#3082C211yesmaximal, characteristic, complemented
30#3080C211yesmaximal, characteristic, complemented
31#2993C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#559—21no—
35#559C2211yescharacteristic
36#557C2211yescharacteristic
37#555—21no—
38#555C2211yescharacteristic
39#554C2211yescharacteristic
40#554C2211yescharacteristic
41#553—21no—
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#553C2211yescharacteristic
47#552—21no—
48#552C2211yescharacteristic
49#550C2211yescharacteristic
50#548C2211yescharacteristic
51#548C2211yescharacteristic
52#547—21no—
53#547—21no—
54#547C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic
58#542—21no—
59#542C2211yescharacteristic
60#540—21no—
61#540C2211yescharacteristic
62#540C2211yescharacteristic
63#540C2211yescharacteristic
64#539—21no—
65#539—21no—
66#539—21no—
67#537—21no—
68#532C2211yescharacteristic
69#529—21no—
70#529—21no—
71#529C2211yescharacteristic
72#529C2211yescharacteristic
73C2×#125C2211yescharacteristic
74#520C2211yescharacteristic
75#519C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic
78#501C2211yescharacteristic
79#499C2211yescharacteristic
80#499C2211yescharacteristic
81#499C2211yescharacteristic
82#498C2211yescharacteristic
83#490C2211yescharacteristic
84#489C2211yescharacteristic
85#488C2211yescharacteristic
86#488C2211yescharacteristic
87#488C2211yescharacteristic
88#486C2211yescharacteristic
89#485C2211yescharacteristic
90#484C2211yescharacteristic
91#483C2211yescharacteristic
92#483C2211yescharacteristic
93#482C2211yescharacteristic
94#482C2211yescharacteristic
95#482C2211yescharacteristic
96#482C2211yescharacteristic
97#482C2211yescharacteristic
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#481C2211yescharacteristic
101#481C2211yescharacteristic
102#481C2211yescharacteristic
103#481C2211yescharacteristic
104#480C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic
108#479C2211yescharacteristic
109#479C2211yescharacteristic
110#479C2211yescharacteristic
111#479C2211yescharacteristic
112#479C2211yescharacteristic
113#479C2211yescharacteristic
114#479C2211yescharacteristic
115#479C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic
125#478C2211yescharacteristic
126#478C2211yescharacteristic
127#477C2211yescharacteristic
128#477C2211yescharacteristic
129#477C2211yescharacteristic
130#476C2211yescharacteristic
131#476C2211yescharacteristic
132#475C2211yescharacteristic
133#475C2211yescharacteristic
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic
137#469C2211yescharacteristic
138#469C2211yescharacteristic
139#469C2211yescharacteristic
140#469C2211yescharacteristic
141#469C2211yescharacteristic
142#468C2211yescharacteristic
143#468C2211yescharacteristic
144#468C2211yescharacteristic
145#466C2211yescharacteristic
146#466C2211yescharacteristic
147#466C2211yescharacteristic
148#465C2211yescharacteristic
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#460C2211yescharacteristic
154#460C2211yescharacteristic
155#459C2211yescharacteristic
156#459C2211yescharacteristic
157#459C2211yescharacteristic
158#459C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#448C2211yescharacteristic
164#448C2211yescharacteristic
165#446C2211yescharacteristic
166C8×Q8C2211yescharacteristic
167#442C2211yescharacteristic
168#440C2211yescharacteristic
169#440C2211yescharacteristic
170#440C2211yescharacteristic
171C4×SD16C2211yescharacteristic
172C4×SD16C2211yescharacteristic
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic
175C4×SD16C2211yescharacteristic
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#436C2211yescharacteristic
182#435C2211yescharacteristic
183#435C2211yescharacteristic
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic
187#431C2211yescharacteristic
188#428C2211yescharacteristic
189#428C2211yescharacteristic
190#428C2211yescharacteristic
191#428C2211yescharacteristic
192#427C2211yescharacteristic
193C2×#107C2211yescharacteristic
194#424C2211yescharacteristic
195#424C2211yescharacteristic
196#423C2211yescharacteristic
197#419C2211yescharacteristic
198#417C2211yescharacteristic
199#417C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#103C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×D8C2311yescharacteristic
214C2×D8C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230#127—21no—
231#127C2311yescharacteristic
232#127C2311yescharacteristic
233#126—21no—
234#126—21no—
235#126—21no—
236#126—21no—
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126D411yescharacteristic
242#126D411yescharacteristic
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125D411yescharacteristic
251#125C2311yescharacteristic
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124D411yescharacteristic
267#124C2311yescharacteristic
268#124C2311yescharacteristic
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123D411yescharacteristic
290#123D411yescharacteristic
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8D411yescharacteristic
307C22⋊Q8C2311yescharacteristic
308C22⋊Q8C2311yescharacteristic
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121D411yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373C4×D4C2311yescharacteristic
374C4×D4C2311yescharacteristic
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C42—21no—
399C2×C42C2311yescharacteristic
400#107C2311yescharacteristic
401#107C2311yescharacteristic
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424C4⋊C8C2311yescharacteristic
425C4⋊C8C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478#41—22no—
479#41—22no—
480#41—41no—
481#41—41no—
482#41—82no—
483#41—82no—
484#41—82no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×Q8—41no—
492C2×Q8C2×D411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×D411yescharacteristic
512C2×D4C2×D411yescharacteristic
513C2×D4C2×D411yescharacteristic
514C2×D4C2411yescharacteristic
515C2×D4C2411yescharacteristic
516C2×D4C2411yescharacteristic
517C2×D4C2411yescharacteristic
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4C2×D411yescharacteristic
537C22×C4C2×D411yescharacteristic
538C22×C4C2411yescharacteristic
539C22×C4C2411yescharacteristic
540C22×C4C2411yescharacteristic
541SD16—22no—
542SD16—22no—
543SD16—41no—
544SD16—41no—
545D8—41no—
546D8—41no—
547D8—41no—
548D8—41no—
549M16—41no—
550M16—41no—
551M16—41no—
552M16—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4C2×D411yescharacteristic
647C22⋊C4C2×D411yescharacteristic
648C22⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23C22×D411yescharacteristic
677C23C22×D411yescharacteristic
678C23C22×D411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—41no—
683Q8—42no—
684Q8—81no—
685Q8—81no—
686Q8—81no—
687Q8—81no—
688Q82−1+412yes—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—81no—
705D4—81no—
706D4—81no—
707D4—81no—
708D4—81no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D4—81no—
715D4—81no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
760C2×C4C22×D411yescharacteristic
761C2×C4C22×D411yescharacteristic
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C2511yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22C23×D411yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4C2×2−1+411yescharacteristic
820C4#58511yescharacteristic
821C2—41no—
822C2—41no—
823C2—41no—
824C2—81no—
825C2—81no—
826C2—81no—
827C2—81no—
828C2#348911yescharacteristic
829C2#358411yescharacteristic
830C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3559C2semidirect
2. #3524C2semidirect
3. #3388C2semidirect
4. #3381C2semidirect
5. #3370C2semidirect
6. #3361C2semidirect
7. #3355C2semidirect
8. #3354C2semidirect
9. #3351C2semidirect
10. #3347C2semidirect
11. #3343C2semidirect
12. #3339C2semidirect
13. #3332C2semidirect
14. #3326C2semidirect
15. #3326C2semidirect
16. #3309C2semidirect
17. #3308C2semidirect
18. #3301C2semidirect
19. #3259C2semidirect
20. #3257C2semidirect
21. #3251C2semidirect
22. #3244C2semidirect
23. #3241C2semidirect
24. #3232C2semidirect
25. #3126C2semidirect
26. #3119C2semidirect
27. #3106C2semidirect
28. #3083C2semidirect
29. #3082C2semidirect
30. #3080C2semidirect
31. #2993C2semidirect

Maximal subgroups

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

subgroupindex
#35592
#35242
#33882
#33812
#33702
#33612
#33552
#33542
#33512
#33472
#33432
#33392
#33322
#33262
#33092
#33082
#33012
#32592
#32572
#32512
#32442
#32412
#32322
#31262
#31192
#31062
#30832
#30822
#30802
#29932