Finite Group Databasebeta

← #62172

Subgroups — #62172

Order 256.

826 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3555C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic
3#3388C211yesmaximal, characteristic, complemented
4#3385C211yesmaximal, characteristic, complemented
5#3377C211yesmaximal, characteristic, complemented
6#3369C211yesmaximal, characteristic, complemented
7#3350C211yesmaximal, characteristic, complemented
8#3349C211yesmaximal, characteristic, complemented
9#3349C211yesmaximal, characteristic, complemented
10#3344C211yesmaximal, characteristic, complemented
11#3342C211yesmaximal, characteristic, complemented
12#3337C211yesmaximal, characteristic, complemented
13#3315C211yesmaximal, characteristic, complemented
14#3314C211yesmaximal, characteristic, complemented
15#3311C211yesmaximal, characteristic, complemented
16#3311C211yesmaximal, characteristic, complemented
17#3302C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3261C211yesmaximal, characteristic, complemented
20#3258C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3242C211yesmaximal, characteristic, complemented
24#3240C211yesmaximal, characteristic, complemented
25#3123C211yesmaximal, characteristic, complemented
26#3120C211yesmaximal, characteristic, complemented
27#3116C211yesmaximal, characteristic, complemented
28#3084C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3076C211yesmaximal, characteristic, complemented
31#2992C211yesmaximal, characteristic, complemented
32#563—21no—
33#563—21no—
34Q82C2211yescharacteristic, complemented
35#557—21no—
36#557C2211yescharacteristic, complemented
37#556—21no—
38#556C2211yescharacteristic
39#556C2211yescharacteristic
40#556C2211yescharacteristic
41#556C2211yescharacteristic
42#556C2211yescharacteristic, complemented
43#554C2211yescharacteristic
44#554C2211yescharacteristic
45#553—21no—
46#553C2211yescharacteristic
47#552—21no—
48#552C2211yescharacteristic
49#552C2211yescharacteristic
50#552C2211yescharacteristic, complemented
51#551—21no—
52#551—21no—
53#547C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542C2211yescharacteristic
60#541—21no—
61#541—21no—
62#541—21no—
63#541C2211yescharacteristic
64#541C2211yescharacteristic
65#541C2211yescharacteristic, complemented
66#539—21no—
67#538—21no—
68#533C2211yescharacteristic, complemented
69#533C2211yescharacteristic, complemented
70#529—21no—
71#529C2211yescharacteristic
72#529C2211yescharacteristic
73C2×#126—21no—
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#501C2211yescharacteristic, complemented
80#501C2211yescharacteristic, complemented
81#500C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#489C2211yescharacteristic
85#489C2211yescharacteristic
86#489C2211yescharacteristic
87#488C2211yescharacteristic
88#487C2211yescharacteristic, complemented
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic
92#485C2211yescharacteristic
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#484C2211yescharacteristic
99#484C2211yescharacteristic, complemented
100#484C2211yescharacteristic, complemented
101#483C2211yescharacteristic
102#483C2211yescharacteristic, complemented
103#482C2211yescharacteristic
104#482C2211yescharacteristic
105#482C2211yescharacteristic
106#480C2211yescharacteristic
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#479C2211yescharacteristic, complemented
114#479C2211yescharacteristic, complemented
115#479C2211yescharacteristic, complemented
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#477C2211yescharacteristic, complemented
124#477C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic
127#476C2211yescharacteristic
128#476C2211yescharacteristic
129#476C2211yescharacteristic
130#475C2211yescharacteristic, complemented
131#475C2211yescharacteristic, complemented
132#475C2211yescharacteristic, complemented
133#475C2211yescharacteristic, complemented
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic
137#470C2211yescharacteristic
138#470C2211yescharacteristic
139#470C2211yescharacteristic, complemented
140#468C2211yescharacteristic
141#467C2211yescharacteristic
142#467C2211yescharacteristic
143#467C2211yescharacteristic, complemented
144#467C2211yescharacteristic, complemented
145#467C2211yescharacteristic, complemented
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic
149#464C2211yescharacteristic
150#464C2211yescharacteristic
151#464C2211yescharacteristic
152#464C2211yescharacteristic
153#462C2211yescharacteristic, complemented
154#462C2211yescharacteristic, complemented
155#462C2211yescharacteristic, complemented
156#462C2211yescharacteristic, complemented
157#461C2211yescharacteristic
158#461C2211yescharacteristic
159#452C2211yescharacteristic
160#452C2211yescharacteristic
161#452C2211yescharacteristic
162#452C2211yescharacteristic
163#450C2211yescharacteristic
164#450C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166#446C2211yescharacteristic, complemented
167#441C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#441C2211yescharacteristic, complemented
170#440C2211yescharacteristic
171#440C2211yescharacteristic
172#440C2211yescharacteristic
173#440C2211yescharacteristic
174#440C2211yescharacteristic
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic
177C4×SD16C2211yescharacteristic
178C4×SD16C2211yescharacteristic
179#435C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic
182#435C2211yescharacteristic, complemented
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#428C2211yescharacteristic
189#428C2211yescharacteristic, complemented
190#427C2211yescharacteristic
191#427C2211yescharacteristic, complemented
192#427C2211yescharacteristic, complemented
193C2×#106C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#417C2211yescharacteristic
199#416C2211yescharacteristic
200#416C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C2×Q16C2311yescharacteristic
207C2×Q16C2311yescharacteristic
208C2×Q16C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×M16C2311yescharacteristic
215C2×M16C2311yescharacteristic
216C22×C8C2311yescharacteristic
217C22×C8C2311yescharacteristic
218C22×C8C2311yescharacteristic
219C22×C8C2311yescharacteristic
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234#126—21no—
235#126—21no—
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#126—21no—
248#126—21no—
249#126—21no—
250#126—21no—
251#126—21no—
252#126—21no—
253#126—21no—
254#126—21no—
255#126—21no—
256#126D411yescharacteristic
257#126D411yescharacteristic
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125—21no—
268#125—21no—
269#125—21no—
270#125—21no—
271#125—21no—
272#125—21no—
273#125D411yescharacteristic
274#125C2311yescharacteristic
275#125C2311yescharacteristic
276#125C2311yescharacteristic
277#125C2311yescharacteristic
278#125C2311yescharacteristic
279#125C2311yescharacteristic
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124D411yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123D411yescharacteristic
299#123D411yescharacteristic
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8D411yescharacteristic
315C22⋊Q8C2311yescharacteristic
316C22⋊Q8C2311yescharacteristic
317C22⋊Q8C2311yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325#121—21no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121D411yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#120—21no—
333#120—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8C2311yescharacteristic
344C4×Q8C2311yescharacteristic
345C4×Q8C2311yescharacteristic
346C4×Q8C2311yescharacteristic
347C4×Q8C2311yescharacteristic
348C4×Q8C2311yescharacteristic
349C4×Q8C2311yescharacteristic
350C4×Q8C2311yescharacteristic
351C4×Q8C2311yescharacteristic
352C4×Q8C2311yescharacteristic
353C4×Q8C2311yescharacteristic
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
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
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
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#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#103C2311yescharacteristic
453#103C2311yescharacteristic
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
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—22no—
480#41—22no—
481#41—41no—
482#41—41no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×D411yescharacteristic
490C2×Q8C2411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×Q8C2411yescharacteristic
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—41no—
501C2×D4C2×D411yescharacteristic
502C2×D4C2×D411yescharacteristic
503C2×D4C2×D411yescharacteristic
504C2×D4C2411yescharacteristic
505C2×D4C2411yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4C2×D411yescharacteristic
518C22×C4C2×D411yescharacteristic
519C22×C4C2411yescharacteristic
520C22×C4C2411yescharacteristic
521C22×C4C2411yescharacteristic
522Q16—41no—
523Q16—41no—
524Q16—41no—
525Q16—41no—
526SD16—22no—
527SD16—22no—
528SD16—41no—
529SD16—41no—
530M16—41no—
531M16—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8C2411yescharacteristic
537C2×C8C2411yescharacteristic
538C2×C8C2411yescharacteristic
539C2×C8C2411yescharacteristic
540C2×C8C2411yescharacteristic
541C2×C8C2411yescharacteristic
542C2×C8C2411yescharacteristic
543C2×C8C2411yescharacteristic
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
590C4⋊C4C2×D411yescharacteristic
591C4⋊C4C2×D411yescharacteristic
592C4⋊C4C2×D411yescharacteristic
593C4⋊C4C2×D411yescharacteristic
594C4⋊C4C2×D411yescharacteristic
595C4⋊C4C2×D411yescharacteristic
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2411yescharacteristic
600C4⋊C4C2411yescharacteristic
601C4⋊C4C2411yescharacteristic
602C4⋊C4C2411yescharacteristic
603C4⋊C4C2411yescharacteristic
604C4⋊C4C2411yescharacteristic
605C4⋊C4C2411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
638C22⋊C4C2×D411yescharacteristic
639C22⋊C4C2×D411yescharacteristic
640C22⋊C4C2×D411yescharacteristic
641C22⋊C4C2×D411yescharacteristic
642C22⋊C4C2×D411yescharacteristic
643C22⋊C4C2×D411yescharacteristic
644C22⋊C4C2×D411yescharacteristic
645C22⋊C4C2×D411yescharacteristic
646C22⋊C4C2×D411yescharacteristic
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42C2×D411yescharacteristic
664C42C2×D411yescharacteristic
665C42C2411yescharacteristic
666C42C2411yescharacteristic
667C42C2411yescharacteristic
668C42C2411yescharacteristic
669C23—21no—
670C23—21no—
671C23—42no—
672C23—81no—
673C23—81no—
674C23C22×D411yescharacteristic
675C23C22×D411yescharacteristic
676C23C22×D411yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—41no—
686Q8—42no—
687Q8—81no—
688Q8—81no—
689Q8—81no—
690Q8—81no—
691Q8—81no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—81no—
702D4—81no—
703D42−1+412yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
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—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4C22×D411yescharacteristic
738C2×C4C22×D411yescharacteristic
739C2×C4C22×D411yescharacteristic
740C2×C4C22×D411yescharacteristic
741C2×C4C22×D411yescharacteristic
742C2×C4C22×D411yescharacteristic
743C2×C4C22×D411yescharacteristic
744C2×C4C22×D411yescharacteristic
745C2×C4C22×D411yescharacteristic
746C2×C4C22×D411yescharacteristic
747C2×C4C22×D411yescharacteristic
748C2×C4C2511yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—21no—
754C8—21no—
755C8—21no—
756C8—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—162no—
773C22C23×D411yescharacteristic
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4C2×2−1+411yescharacteristic
800C4#58511yescharacteristic
801C2—41no—
802C2—41no—
803C2—41no—
804C2—42no—
805C2—81no—
806C2#348911yescharacteristic
807C2#358411yescharacteristic
808C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
prime radical#3521C2
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. #3555C2semidirect
3. #3388C2semidirect
4. #3385C2semidirect
5. #3377C2semidirect
6. #3369C2semidirect
7. #3350C2semidirect
8. #3349C2semidirect
9. #3349C2semidirect
10. #3344C2semidirect
11. #3342C2semidirect
12. #3337C2semidirect
13. #3315C2semidirect
14. #3314C2semidirect
15. #3311C2semidirect
16. #3311C2semidirect
17. #3302C2semidirect
18. #3296C2semidirect
19. #3261C2semidirect
20. #3258C2semidirect
21. #3248C2semidirect
22. #3243C2semidirect
23. #3242C2semidirect
24. #3240C2semidirect
25. #3123C2semidirect
26. #3120C2semidirect
27. #3116C2semidirect
28. #3084C2semidirect
29. #3081C2semidirect
30. #3076C2semidirect
31. #2992C2semidirect
34. Q82C22semidirect
36. #557C22semidirect
42. #556C22semidirect
50. #552C22semidirect
57. #544C22semidirect
65. #541C22semidirect
68. #533C22semidirect
69. #533C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #501C22semidirect
80. #501C22semidirect
81. #500C22semidirect
82. #499C22semidirect
83. #491C22semidirect
88. #487C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
99. #484C22semidirect
100. #484C22semidirect
102. #483C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #479C22semidirect
114. #479C22semidirect
115. #479C22semidirect
123. #477C22semidirect
124. #477C22semidirect
125. #477C22semidirect
130. #475C22semidirect
131. #475C22semidirect
132. #475C22semidirect
133. #475C22semidirect
139. #470C22semidirect
143. #467C22semidirect
144. #467C22semidirect
145. #467C22semidirect
153. #462C22semidirect
154. #462C22semidirect
155. #462C22semidirect
156. #462C22semidirect
165. #446C22semidirect
166. #446C22semidirect
167. #441C22semidirect
168. #441C22semidirect
169. #441C22semidirect
175. C4×Q16C22semidirect
182. #435C22semidirect
184. C8×D4C22semidirect
186. #433C22semidirect
187. #432C22semidirect
189. #428C22semidirect
191. #427C22semidirect
192. #427C22semidirect
193. C2×#106C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#35552
#35212
#33882
#33852
#33772
#33692
#33502
#33492
#33442
#33422
#33372
#33152
#33142
#33112
#33022
#32962
#32612
#32582
#32482
#32432
#32422
#32402
#31232
#31202
#31162
#30842
#30812
#30762
#29922