Finite Group Databasebeta

← #61749

Subgroups — #61749

Order 256.

878 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3493C211yesmaximal, characteristic, complemented
3#3353C211yesmaximal, characteristic, complemented
4#3351C211yesmaximal, characteristic, complemented
5#3349C211yesmaximal, characteristic, complemented
6#3348C211yesmaximal, characteristic, complemented
7#3347C211yesmaximal, characteristic, complemented
8#3345C211yesmaximal, characteristic, complemented
9#3341C211yesmaximal, characteristic, complemented
10#3337C211yesmaximal, characteristic, complemented
11#3324C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3319C211yesmaximal, characteristic, complemented
14#3318C211yesmaximal, characteristic, complemented
15#3317C211yesmaximal, characteristic, complemented
16#3311C211yesmaximal, characteristic, complemented
17#3305C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3203C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3197C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3099C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3094C211yesmaximal, characteristic, complemented
30#3091C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32#562—21no—
33#560—21no—
34#556—21no—
35#556C2211yescharacteristic
36#556C2211yescharacteristic, complemented
37#555—21no—
38#555C2211yescharacteristic
39#555C2211yescharacteristic, complemented
40#555C2211yescharacteristic, complemented
41#553—21no—
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic
47#552C2211yescharacteristic, complemented
48#552C2211yescharacteristic, complemented
49#551—21no—
50#550C2211yescharacteristic
51#547C2211yescharacteristic
52#546—21no—
53#546C2211yescharacteristic
54#546C2211yescharacteristic
55D42C2211yescharacteristic
56#544C2211yescharacteristic, complemented
57#542C2211yescharacteristic
58#540—21no—
59#540C2211yescharacteristic
60#538—21no—
61#538—21no—
62#538—21no—
63#537C2211yescharacteristic
64#537C2211yescharacteristic, complemented
65#535—21no—
66#535C2211yescharacteristic
67#534—21no—
68#529—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic, complemented
73C2×#121C2211yescharacteristic
74#520C2211yescharacteristic, complemented
75#520C2211yescharacteristic, complemented
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#490C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#486C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#484C2211yescharacteristic, complemented
92#484C2211yescharacteristic, complemented
93#484C2211yescharacteristic, complemented
94#483C2211yescharacteristic, complemented
95#483C2211yescharacteristic, complemented
96#482C2211yescharacteristic
97#482C2211yescharacteristic
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#482C2211yescharacteristic, complemented
105#482C2211yescharacteristic, complemented
106#482C2211yescharacteristic, complemented
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#482C2211yescharacteristic, complemented
110#481C2211yescharacteristic
111#481C2211yescharacteristic, complemented
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#477C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#475C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#470C2211yescharacteristic, complemented
134#469C2211yescharacteristic
135#469C2211yescharacteristic, complemented
136#468C2211yescharacteristic
137#468C2211yescharacteristic, complemented
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#467C2211yescharacteristic, complemented
142#466C2211yescharacteristic
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#466C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#464C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#450C2211yescharacteristic
157#450C2211yescharacteristic, complemented
158#449C2211yescharacteristic
159#449C2211yescharacteristic, complemented
160#449C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#447C2211yescharacteristic
164#447C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#442C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×SD16C2211yescharacteristic, complemented
170C4×SD16C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#436C2211yescharacteristic
174#436C2211yescharacteristic, complemented
175#435C2211yescharacteristic
176#435C2211yescharacteristic, complemented
177#435C2211yescharacteristic, complemented
178#435C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic, complemented
182#433C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#428C2211yescharacteristic, complemented
186#428C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188#427C2211yescharacteristic, complemented
189#427C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#418C2211yescharacteristic
192#418C2211yescharacteristic
193#418C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201#407C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×D4—21no—
209C22×D4—21no—
210C22×D4C2311yescharacteristic
211C22×D4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C2×Q16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
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#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#126—21no—
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125C2311yescharacteristic
252#125C2311yescharacteristic
253#125C2311yescharacteristic
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124—21no—
264#124C2311yescharacteristic
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⋊Q8D411yescharacteristic
289C22⋊Q8D411yescharacteristic
290C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
319#121D411yescharacteristic
320#121C2311yescharacteristic
321#121C2311yescharacteristic
322#121C2311yescharacteristic
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#120—21no—
334#120—21no—
335#120—21no—
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340#120—21no—
341#120D411yescharacteristic
342#120D411yescharacteristic
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
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
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
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
386#117C2311yescharacteristic
387#117C2311yescharacteristic
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390C2×C4⋊C4—21no—
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#102C2311yescharacteristic
441#102C2311yescharacteristic
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—
479C24—21no—
480C24C2×D411yescharacteristic
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—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8C2×D411yescharacteristic
494C2×Q8C2411yescharacteristic
495C2×Q8C2411yescharacteristic
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×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—82no—
521C2×D4—82no—
522C2×D4C2×D411yescharacteristic
523C2×D4C2×D411yescharacteristic
524C2×D4C2×D411yescharacteristic
525C2×D4C2×D411yescharacteristic
526C2×D4C2×D411yescharacteristic
527C2×D4C2×D411yescharacteristic
528C2×D4C2×D411yescharacteristic
529C2×D4C2411yescharacteristic
530C2×D4C2411yescharacteristic
531C2×D4C2411yescharacteristic
532C2×D4C2411yescharacteristic
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—41no—
548C22×C4—41no—
549C22×C4C2×D411yescharacteristic
550C22×C4C2×D411yescharacteristic
551C22×C4C2×D411yescharacteristic
552C22×C4C2411yescharacteristic
553C22×C4C2411yescharacteristic
554C22×C4C2411yescharacteristic
555C22×C4C2411yescharacteristic
556C22×C4C2411yescharacteristic
557Q16—41no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561SD16—41no—
562D8—41no—
563D8—41no—
564D8—41no—
565M16—41no—
566M16—41no—
567M16—41no—
568M16—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8C2411yescharacteristic
574C2×C8C2411yescharacteristic
575C2×C8C2411yescharacteristic
576C2×C8C2411yescharacteristic
577C2×C8C2411yescharacteristic
578C2×C8C2411yescharacteristic
579C2×C8C2411yescharacteristic
580C2×C8C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C22⋊C4C2×D411yescharacteristic
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C42—21no—
669C42—21no—
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—
692C23—81no—
693C23—81no—
694C23—81no—
695C23C22×D411yescharacteristic
696C23C22×D411yescharacteristic
697C23C22×D411yescharacteristic
698C23C22×D411yescharacteristic
699C23C22×D411yescharacteristic
700Q8—21no—
701Q8—21no—
702Q8—21no—
703Q8—21no—
704Q8—41no—
705Q8—81no—
706Q8—81no—
707Q8—81no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—42no—
724D4—42no—
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—
740D4—81no—
741D4—81no—
742D4—81no—
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—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
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—
829C22—162no—
830C22C23×D411yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4#58511yescharacteristic
853C4#58511yescharacteristic
854C2—41no—
855C2—41no—
856C2—41no—
857C2—41no—
858C2—41no—
859C2—81no—
860C2—81no—
861C2—81no—
862C2—81no—
863C2#348511yescharacteristic
864C2#358411yescharacteristic
865C2#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. #3542C2semidirect
2. #3493C2semidirect
3. #3353C2semidirect
4. #3351C2semidirect
5. #3349C2semidirect
6. #3348C2semidirect
7. #3347C2semidirect
8. #3345C2semidirect
9. #3341C2semidirect
10. #3337C2semidirect
11. #3324C2semidirect
12. #3322C2semidirect
13. #3319C2semidirect
14. #3318C2semidirect
15. #3317C2semidirect
16. #3311C2semidirect
17. #3305C2semidirect
18. #3296C2semidirect
19. #3243C2semidirect
20. #3241C2semidirect
21. #3203C2semidirect
22. #3198C2semidirect
23. #3197C2semidirect
24. #3188C2semidirect
25. #3125C2semidirect
26. #3119C2semidirect
27. #3099C2semidirect
28. #3096C2semidirect
29. #3094C2semidirect
30. #3091C2semidirect
31. #2976C2semidirect
36. #556C22semidirect
39. #555C22semidirect
40. #555C22semidirect
44. #553C22semidirect
47. #552C22semidirect
48. #552C22semidirect
56. #544C22semidirect
64. #537C22semidirect
72. #525C22semidirect
74. #520C22semidirect
75. #520C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #490C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #486C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #484C22semidirect
92. #484C22semidirect
93. #484C22semidirect
94. #483C22semidirect
95. #483C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #482C22semidirect
105. #482C22semidirect
106. #482C22semidirect
107. #482C22semidirect
108. #482C22semidirect
109. #482C22semidirect
111. #481C22semidirect
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. #477C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #475C22semidirect
131. #474C22semidirect
132. #474C22semidirect
133. #470C22semidirect
135. #469C22semidirect
137. #468C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
141. #467C22semidirect
143. #466C22semidirect
144. #466C22semidirect
145. #466C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #464C22semidirect
150. #463C22semidirect
151. #460C22semidirect
152. #459C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #452C22semidirect
157. #450C22semidirect
159. #449C22semidirect
160. #449C22semidirect
161. #449C22semidirect
162. #449C22semidirect
164. #447C22semidirect
165. #442C22semidirect
166. #442C22semidirect
167. #441C22semidirect
168. #440C22semidirect
169. C4×SD16C22semidirect
170. C4×SD16C22semidirect
171. C4×SD16C22semidirect
172. C4×D8C22semidirect
174. #436C22semidirect
176. #435C22semidirect
177. #435C22semidirect
178. #435C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. #427C22semidirect
190. C2×#106C22semidirect
193. #418C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#102C22semidirect
199. #408C22semidirect
200. #408C22semidirect
201. #407C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35422
#34932
#33532
#33512
#33492
#33482
#33472
#33452
#33412
#33372
#33242
#33222
#33192
#33182
#33172
#33112
#33052
#32962
#32432
#32412
#32032
#31982
#31972
#31882
#31252
#31192
#30992
#30962
#30942
#30912
#29762