Finite Group Databasebeta

← #61774

Subgroups — #61774

Order 256.

869 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3539C211yesmaximal, characteristic, complemented
2#3492C211yesmaximal, characteristic, complemented
3#3355C211yesmaximal, characteristic, complemented
4#3352C211yesmaximal, characteristic, complemented
5#3351C211yesmaximal, characteristic, complemented
6#3351C211yesmaximal, characteristic, complemented
7#3346C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3344C211yesmaximal, characteristic, complemented
10#3343C211yesmaximal, characteristic, complemented
11#3333C211yesmaximal, characteristic, complemented
12#3332C211yesmaximal, characteristic, complemented
13#3331C211yesmaximal, characteristic, complemented
14#3330C211yesmaximal, characteristic, complemented
15#3317C211yesmaximal, characteristic, complemented
16#3315C211yesmaximal, characteristic, complemented
17#3309C211yesmaximal, characteristic, complemented
18#3307C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3204C211yesmaximal, characteristic, complemented
22#3203C211yesmaximal, characteristic, complemented
23#3197C211yesmaximal, characteristic, complemented
24#3197C211yesmaximal, characteristic, complemented
25#3120C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3098C211yesmaximal, characteristic, complemented
29#3092C211yesmaximal, characteristic, complemented
30#3092C211yesmaximal, characteristic, complemented
31#2978C211yesmaximal, characteristic, complemented
32#560—21no—
33#560—21no—
34#554—21no—
35#554C2211yescharacteristic
36#554C2211yescharacteristic
37#553—21no—
38#553—21no—
39#553—21no—
40#553C2211yescharacteristic
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#552—21no—
45#552C2211yescharacteristic
46#552C2211yescharacteristic
47#552C2211yescharacteristic
48#552C2211yescharacteristic
49#550C2211yescharacteristic
50#550C2211yescharacteristic
51#547—21no—
52#547C2211yescharacteristic
53#547C2211yescharacteristic
54#547C2211yescharacteristic
55#547C2211yescharacteristic
56#544C2211yescharacteristic
57#541C2211yescharacteristic
58#540—21no—
59#540—21no—
60#540C2211yescharacteristic
61#539—21no—
62#539—21no—
63#539—21no—
64#539—21no—
65#537C2211yescharacteristic
66#537C2211yescharacteristic
67#537C2211yescharacteristic
68#525—21no—
69#525—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic
73#525C2211yescharacteristic
74#520C2211yescharacteristic
75#520C2211yescharacteristic
76C22×C4⋊C4C2211yescharacteristic
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#484C2211yescharacteristic
92#484C2211yescharacteristic
93#484C2211yescharacteristic
94#484C2211yescharacteristic
95#484C2211yescharacteristic, complemented
96#484C2211yescharacteristic, complemented
97#483C2211yescharacteristic
98#483C2211yescharacteristic
99#483C2211yescharacteristic
100#483C2211yescharacteristic
101#483C2211yescharacteristic, complemented
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#482C2211yescharacteristic
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#481C2211yescharacteristic
110#481C2211yescharacteristic
111#481C2211yescharacteristic
112#481C2211yescharacteristic
113#481C2211yescharacteristic, complemented
114#481C2211yescharacteristic, complemented
115#480C2211yescharacteristic
116#480C2211yescharacteristic
117#480C2211yescharacteristic
118#480C2211yescharacteristic
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#479C2211yescharacteristic, complemented
124#479C2211yescharacteristic, 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#470C2211yescharacteristic
134#470C2211yescharacteristic
135#470C2211yescharacteristic, complemented
136#469C2211yescharacteristic
137#469C2211yescharacteristic
138#469C2211yescharacteristic, complemented
139#468C2211yescharacteristic
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#466C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#441C2211yescharacteristic, complemented
167#440C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×Q16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic
174#436C2211yescharacteristic
175#436C2211yescharacteristic
176#436C2211yescharacteristic
177#435C2211yescharacteristic
178#435C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#433C2211yescharacteristic
182#433C2211yescharacteristic
183#428C2211yescharacteristic
184#428C2211yescharacteristic
185#428C2211yescharacteristic
186#428C2211yescharacteristic
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#417C2211yescharacteristic
192#417C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic
195#417C2211yescharacteristic, complemented
196#417C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198#416C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic
202#407C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C23×C4—21no—
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×Q16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×SD16C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C2×M16C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C2×M16C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233#127—21no—
234#127—21no—
235#127C2311yescharacteristic
236#126—21no—
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#125—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#123—21no—
260#123—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#123D411yescharacteristic
281#123D411yescharacteristic
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8D411yescharacteristic
294C22⋊Q8D411yescharacteristic
295C22⋊Q8C2311yescharacteristic
296C22⋊Q8C2311yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
303C22⋊Q8C2311yescharacteristic
304C22⋊Q8C2311yescharacteristic
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#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121D411yescharacteristic
327#121D411yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#121C2311yescharacteristic
336#121C2311yescharacteristic
337#121C2311yescharacteristic
338#120—21no—
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
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×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
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#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C4⋊C4C2311yescharacteristic
396C2×C4⋊C4C2311yescharacteristic
397C2×C4⋊C4C2311yescharacteristic
398C2×C4⋊C4C2311yescharacteristic
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C4⋊C4C2311yescharacteristic
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#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
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
478C24C2×D411yescharacteristic
479#41—41no—
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—41no—
491#41—82no—
492#41—82no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×D411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
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×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2×D411yescharacteristic
520C2×D4C2×D411yescharacteristic
521C2×D4C2×D411yescharacteristic
522C2×D4C2×D411yescharacteristic
523C2×D4C2411yescharacteristic
524C2×D4C2411yescharacteristic
525C2×D4C2411yescharacteristic
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×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—41no—
546C22×C4—41no—
547C22×C4—82no—
548C22×C4C2×D411yescharacteristic
549C22×C4C2×D411yescharacteristic
550C22×C4C2×D411yescharacteristic
551C22×C4C2411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556Q16—41no—
557Q16—41no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561SD16—41no—
562D8—41no—
563D8—41no—
564M16—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568M16—41no—
569M16—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8C2411yescharacteristic
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
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⋊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⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2×D411yescharacteristic
618C4⋊C4C2×D411yescharacteristic
619C4⋊C4C2×D411yescharacteristic
620C4⋊C4C2×D411yescharacteristic
621C4⋊C4C2×D411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C4⋊C4C2411yescharacteristic
628C4⋊C4C2411yescharacteristic
629C4⋊C4C2411yescharacteristic
630C4⋊C4C2411yescharacteristic
631C4⋊C4C2411yescharacteristic
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⋊C4—21no—
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
670C22⋊C4C2×D411yescharacteristic
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—41no—
686C23—41no—
687C23—41no—
688C23C22×D411yescharacteristic
689C23C22×D411yescharacteristic
690C23C22×D411yescharacteristic
691C23C22×D411yescharacteristic
692C23C22×D411yescharacteristic
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698Q8—21no—
699Q8—41no—
700Q8—81no—
701Q8—81no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
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—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
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×C4C22×D411yescharacteristic
778C2×C4C22×D411yescharacteristic
779C2×C4C22×D411yescharacteristic
780C2×C4C22×D411yescharacteristic
781C2×C4C22×D411yescharacteristic
782C2×C4C22×D411yescharacteristic
783C2×C4C22×D411yescharacteristic
784C2×C4C22×D411yescharacteristic
785C2×C4C22×D411yescharacteristic
786C2×C4C2511yescharacteristic
787C8—21no—
788C8—21no—
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—44no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22C23×D411yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4#58511yescharacteristic
844C4#58511yescharacteristic
845C2—41no—
846C2—41no—
847C2—41no—
848C2—41no—
849C2—41no—
850C2—81no—
851C2—81no—
852C2—81no—
853C2#348511yescharacteristic
854C2#358511yescharacteristic
855C2#358611yescharacteristic
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. #3492C2semidirect
3. #3355C2semidirect
4. #3352C2semidirect
5. #3351C2semidirect
6. #3351C2semidirect
7. #3346C2semidirect
8. #3345C2semidirect
9. #3344C2semidirect
10. #3343C2semidirect
11. #3333C2semidirect
12. #3332C2semidirect
13. #3331C2semidirect
14. #3330C2semidirect
15. #3317C2semidirect
16. #3315C2semidirect
17. #3309C2semidirect
18. #3307C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3204C2semidirect
22. #3203C2semidirect
23. #3197C2semidirect
24. #3197C2semidirect
25. #3120C2semidirect
26. #3119C2semidirect
27. #3099C2semidirect
28. #3098C2semidirect
29. #3092C2semidirect
30. #3092C2semidirect
31. #2978C2semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #499C22semidirect
81. #491C22semidirect
82. #490C22semidirect
83. #487C22semidirect
84. #486C22semidirect
89. #485C22semidirect
90. #485C22semidirect
95. #484C22semidirect
96. #484C22semidirect
101. #483C22semidirect
102. #483C22semidirect
107. #482C22semidirect
108. #482C22semidirect
113. #481C22semidirect
114. #481C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #479C22semidirect
124. #479C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #478C22semidirect
128. #478C22semidirect
129. #477C22semidirect
130. #476C22semidirect
131. #475C22semidirect
132. #474C22semidirect
135. #470C22semidirect
138. #469C22semidirect
143. #468C22semidirect
144. #468C22semidirect
145. #467C22semidirect
146. #466C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #462C22semidirect
150. #461C22semidirect
151. #460C22semidirect
152. #459C22semidirect
157. #452C22semidirect
158. #452C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #442C22semidirect
166. #441C22semidirect
167. #440C22semidirect
168. #440C22semidirect
169. C4×Q16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
195. #417C22semidirect
196. #417C22semidirect
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
#34922
#33552
#33522
#33512
#33462
#33452
#33442
#33432
#33332
#33322
#33312
#33302
#33172
#33152
#33092
#33072
#32422
#32412
#32042
#32032
#31972
#31202
#31192
#30992
#30982
#30922
#29782