Finite Group Databasebeta

← #61761

Subgroups — #61761

Order 256.

876 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3539C211yesmaximal, characteristic, complemented
2#3494C211yesmaximal, characteristic, complemented
3#3355C211yesmaximal, characteristic, complemented
4#3351C211yesmaximal, characteristic, complemented
5#3348C211yesmaximal, characteristic, complemented
6#3347C211yesmaximal, characteristic, complemented
7#3345C211yesmaximal, characteristic, complemented
8#3343C211yesmaximal, characteristic, complemented
9#3339C211yesmaximal, characteristic, complemented
10#3337C211yesmaximal, characteristic, complemented
11#3332C211yesmaximal, characteristic, complemented
12#3330C211yesmaximal, characteristic, complemented
13#3309C211yesmaximal, characteristic, complemented
14#3309C211yesmaximal, characteristic, complemented
15#3307C211yesmaximal, characteristic, complemented
16#3307C211yesmaximal, characteristic, complemented
17#3305C211yesmaximal, characteristic, complemented
18#3303C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3198C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3194C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3122C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3093C211yesmaximal, characteristic, complemented
30#3091C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32#560—21no—
33#560—21no—
34#555C2211yescharacteristic
35#555C2211yescharacteristic
36#553—21no—
37#553—21no—
38#553C2211yescharacteristic
39#553C2211yescharacteristic
40#553C2211yescharacteristic
41#553C2211yescharacteristic
42#553C2211yescharacteristic, complemented
43#553C2211yescharacteristic, complemented
44#552C2211yescharacteristic, complemented
45#552C2211yescharacteristic, complemented
46#551—21no—
47#551—21no—
48#550C2211yescharacteristic, complemented
49#550C2211yescharacteristic, complemented
50#547C2211yescharacteristic
51#547C2211yescharacteristic
52#547C2211yescharacteristic, complemented
53#547C2211yescharacteristic, complemented
54#546—21no—
55#546—21no—
56#544C2211yescharacteristic
57#542—21no—
58#541C2211yescharacteristic
59#540—21no—
60#540—21no—
61#540—21no—
62#540C2211yescharacteristic
63#539—21no—
64#539—21no—
65#537C2211yescharacteristic
66#537C2211yescharacteristic
67#535C2211yescharacteristic
68#532—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic
73C2×#121C2211yescharacteristic
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C2×#117C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#491C2211yescharacteristic, complemented
82#490C2211yescharacteristic, complemented
83#487C2211yescharacteristic, complemented
84#486C2211yescharacteristic, complemented
85#485C2211yescharacteristic
86#485C2211yescharacteristic
87#485C2211yescharacteristic
88#485C2211yescharacteristic
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#481C2211yescharacteristic
112#481C2211yescharacteristic, complemented
113#481C2211yescharacteristic, complemented
114#481C2211yescharacteristic, complemented
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#480C2211yescharacteristic, complemented
118#480C2211yescharacteristic, complemented
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#478C2211yescharacteristic, complemented
128#478C2211yescharacteristic, complemented
129#477C2211yescharacteristic, complemented
130#476C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#469C2211yescharacteristic
134#469C2211yescharacteristic
135#469C2211yescharacteristic, complemented
136#469C2211yescharacteristic, complemented
137#468C2211yescharacteristic
138#468C2211yescharacteristic
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#466C2211yescharacteristic
142#466C2211yescharacteristic
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#465C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#461C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#450C2211yescharacteristic
154#450C2211yescharacteristic
155#449C2211yescharacteristic
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#442C2211yescharacteristic, complemented
166#442C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×SD16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×D8C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic, complemented
174#436C2211yescharacteristic, complemented
175#435C2211yescharacteristic, complemented
176#435C2211yescharacteristic, complemented
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic
182#433C2211yescharacteristic
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188#427C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#417C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic
202C2×C22⋊C8C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C22×D4—21no—
211C22×D4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×D8C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233#127—21no—
234#127—21no—
235#127—21no—
236#127C2311yescharacteristic
237#126—21no—
238#126—21no—
239#126—21no—
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#125C2311yescharacteristic
255#125C2311yescharacteristic
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
260#124—21no—
261#123—21no—
262#123—21no—
263#123—21no—
264#123—21no—
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
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#123D411yescharacteristic
282#123D411yescharacteristic
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8D411yescharacteristic
290C22⋊Q8D411yescharacteristic
291C22⋊Q8C2311yescharacteristic
292C22⋊Q8C2311yescharacteristic
293C22⋊Q8C2311yescharacteristic
294C22⋊Q8C2311yescharacteristic
295C22⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297#121—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
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#121D411yescharacteristic
322#121D411yescharacteristic
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#120—21no—
338#120—21no—
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×D4—21no—
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×D4—21no—
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372C4×D4C2311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#103C2311yescharacteristic
437#103C2311yescharacteristic
438#103C2311yescharacteristic
439#103C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
445#102C2311yescharacteristic
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
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24C2×D411yescharacteristic
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—41no—
489#41—41no—
490#41—82no—
491#41—82no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
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×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—82no—
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2411yescharacteristic
529C2×D4C2411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4C2×D411yescharacteristic
552C22×C4C2×D411yescharacteristic
553C22×C4C2×D411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556C22×C4C2411yescharacteristic
557C22×C4C2411yescharacteristic
558C22×C4C2411yescharacteristic
559SD16—41no—
560SD16—41no—
561SD16—41no—
562SD16—41no—
563D8—41no—
564D8—41no—
565D8—41no—
566D8—41no—
567M16—41no—
568M16—41no—
569M16—41no—
570M16—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
580C2×C8C2411yescharacteristic
581C2×C8C2411yescharacteristic
582C2×C8C2411yescharacteristic
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⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
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⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42C2411yescharacteristic
681C42C2411yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—81no—
691C23—81no—
692C23C22×D411yescharacteristic
693C23C22×D411yescharacteristic
694C23C22×D411yescharacteristic
695C23C22×D411yescharacteristic
696C23C22×D411yescharacteristic
697Q8—21no—
698Q8—21no—
699Q8—21no—
700Q8—21no—
701Q8—41no—
702Q8—81no—
703Q8—81no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C22×D411yescharacteristic
787C2×C4C22×D411yescharacteristic
788C2×C4C22×D411yescharacteristic
789C2×C4C22×D411yescharacteristic
790C2×C4C22×D411yescharacteristic
791C2×C4C2511yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—21no—
798C8—21no—
799C8—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—82no—
828C22—162no—
829C22C23×D411yescharacteristic
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4#58511yescharacteristic
852C4#58511yescharacteristic
853C2—41no—
854C2—41no—
855C2—41no—
856C2—41no—
857C2—41no—
858C2—81no—
859C2—81no—
860C2—81no—
861C2—81no—
862C2#348511yescharacteristic
863C2#358411yescharacteristic
864C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3539C2semidirect
2. #3494C2semidirect
3. #3355C2semidirect
4. #3351C2semidirect
5. #3348C2semidirect
6. #3347C2semidirect
7. #3345C2semidirect
8. #3343C2semidirect
9. #3339C2semidirect
10. #3337C2semidirect
11. #3332C2semidirect
12. #3330C2semidirect
13. #3309C2semidirect
14. #3309C2semidirect
15. #3307C2semidirect
16. #3307C2semidirect
17. #3305C2semidirect
18. #3303C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3198C2semidirect
22. #3198C2semidirect
23. #3194C2semidirect
24. #3188C2semidirect
25. #3123C2semidirect
26. #3122C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3093C2semidirect
30. #3091C2semidirect
31. #2976C2semidirect
42. #553C22semidirect
43. #553C22semidirect
44. #552C22semidirect
45. #552C22semidirect
48. #550C22semidirect
49. #550C22semidirect
52. #547C22semidirect
53. #547C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #499C22semidirect
81. #491C22semidirect
82. #490C22semidirect
83. #487C22semidirect
84. #486C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
97. #483C22semidirect
98. #483C22semidirect
107. #482C22semidirect
108. #482C22semidirect
109. #482C22semidirect
110. #482C22semidirect
112. #481C22semidirect
113. #481C22semidirect
114. #481C22semidirect
115. #481C22semidirect
117. #480C22semidirect
118. #480C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #478C22semidirect
128. #478C22semidirect
129. #477C22semidirect
130. #476C22semidirect
131. #475C22semidirect
132. #474C22semidirect
135. #469C22semidirect
136. #469C22semidirect
139. #468C22semidirect
140. #468C22semidirect
143. #466C22semidirect
144. #466C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #461C22semidirect
150. #461C22semidirect
151. #459C22semidirect
152. #459C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #449C22semidirect
162. #449C22semidirect
165. #442C22semidirect
166. #442C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×SD16C22semidirect
170. C4×SD16C22semidirect
171. C4×D8C22semidirect
172. C4×D8C22semidirect
173. #436C22semidirect
174. #436C22semidirect
175. #435C22semidirect
176. #435C22semidirect
177. #435C22semidirect
178. #435C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #417C22semidirect
192. #417C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. #416C22semidirect

Maximal subgroups

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

subgroupindex
#35392
#34942
#33552
#33512
#33482
#33472
#33452
#33432
#33392
#33372
#33322
#33302
#33092
#33072
#33052
#33032
#32422
#32412
#31982
#31942
#31882
#31232
#31222
#30992
#30982
#30932
#30912
#29762