Finite Group Databasebeta

← #61762

Subgroups — #61762

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#3540C211yesmaximal, characteristic, complemented
2#3494C211yesmaximal, characteristic, complemented
3#3354C211yesmaximal, characteristic, complemented
4#3353C211yesmaximal, characteristic, complemented
5#3350C211yesmaximal, characteristic, complemented
6#3350C211yesmaximal, characteristic, complemented
7#3347C211yesmaximal, characteristic, complemented
8#3347C211yesmaximal, characteristic, complemented
9#3341C211yesmaximal, characteristic, complemented
10#3340C211yesmaximal, characteristic, complemented
11#3326C211yesmaximal, characteristic, complemented
12#3322C211yesmaximal, characteristic, complemented
13#3321C211yesmaximal, characteristic, complemented
14#3319C211yesmaximal, characteristic, complemented
15#3308C211yesmaximal, characteristic, complemented
16#3306C211yesmaximal, characteristic, complemented
17#3301C211yesmaximal, characteristic, complemented
18#3297C211yesmaximal, characteristic, complemented
19#3244C211yesmaximal, characteristic, complemented
20#3243C211yesmaximal, characteristic, complemented
21#3200C211yesmaximal, characteristic, complemented
22#3199C211yesmaximal, characteristic, complemented
23#3194C211yesmaximal, characteristic, complemented
24#3188C211yesmaximal, characteristic, complemented
25#3118C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3097C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3093C211yesmaximal, characteristic, complemented
30#3091C211yesmaximal, characteristic, complemented
31#2976C211yesmaximal, characteristic, complemented
32H(3,𝔽4)—21no—
33#560—21no—
34#559—21no—
35#556C2211yescharacteristic, complemented
36#556C2211yescharacteristic, complemented
37#555C2211yescharacteristic
38#555C2211yescharacteristic, complemented
39#555C2211yescharacteristic, complemented
40#555C2211yescharacteristic, complemented
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic, complemented
44#553C2211yescharacteristic, complemented
45#551—21no—
46#551—21no—
47#551—21no—
48#548C2211yescharacteristic, complemented
49#548C2211yescharacteristic, complemented
50#547C2211yescharacteristic
51#547C2211yescharacteristic, complemented
52#546—21no—
53#546—21no—
54#546C2211yescharacteristic, complemented
55#546C2211yescharacteristic, complemented
56#544C2211yescharacteristic, complemented
57#542—21no—
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic
62#540—21no—
63#538—21no—
64#538—21no—
65#536C2211yescharacteristic
66#535C2211yescharacteristic
67#535C2211yescharacteristic
68#532—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72#525C2211yescharacteristic
73C2×#121C2211yescharacteristic, complemented
74#520C2211yescharacteristic
75#518C2211yescharacteristic, complemented
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#498C2211yescharacteristic, complemented
81#489C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#488C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#485C2211yescharacteristic, complemented
89#485C2211yescharacteristic, complemented
90#485C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#484C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic
100#482C2211yescharacteristic
101#482C2211yescharacteristic
102#482C2211yescharacteristic
103#482C2211yescharacteristic, complemented
104#482C2211yescharacteristic, complemented
105#482C2211yescharacteristic, complemented
106#482C2211yescharacteristic, complemented
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#482C2211yescharacteristic, complemented
110#482C2211yescharacteristic, complemented
111#482C2211yescharacteristic, complemented
112#482C2211yescharacteristic, complemented
113#482C2211yescharacteristic, complemented
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic
116#481C2211yescharacteristic, complemented
117#481C2211yescharacteristic, complemented
118#480C2211yescharacteristic
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#479C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic, complemented
127#476C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#475C2211yescharacteristic, complemented
130#474C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#469C2211yescharacteristic
134#469C2211yescharacteristic
135#469C2211yescharacteristic, complemented
136#469C2211yescharacteristic, complemented
137#468C2211yescharacteristic, complemented
138#468C2211yescharacteristic, complemented
139#468C2211yescharacteristic, complemented
140#468C2211yescharacteristic, complemented
141#466C2211yescharacteristic
142#466C2211yescharacteristic
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#463C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#450C2211yescharacteristic, complemented
154#450C2211yescharacteristic, complemented
155#449C2211yescharacteristic
156#449C2211yescharacteristic
157#449C2211yescharacteristic
158#449C2211yescharacteristic
159#448C2211yescharacteristic, complemented
160#448C2211yescharacteristic, complemented
161#447C2211yescharacteristic
162#447C2211yescharacteristic
163#447C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
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, 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
190#427C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#407C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×D4—21no—
210C22×D4C2311yescharacteristic
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⋊Q8—21no—
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235#127—21no—
236#127—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#125C2311yescharacteristic
249#125C2311yescharacteristic
250#124—21no—
251#124—21no—
252#124—21no—
253#124—21no—
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#124—21no—
265#124—21no—
266#124—21no—
267#124C2311yescharacteristic
268#124C2311yescharacteristic
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123D411yescharacteristic
286#123D411yescharacteristic
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8D411yescharacteristic
296C22⋊Q8D411yescharacteristic
297C22⋊Q8C2311yescharacteristic
298C22⋊Q8C2311yescharacteristic
299C22⋊Q8C2311yescharacteristic
300C22⋊Q8C2311yescharacteristic
301C22⋊Q8C2311yescharacteristic
302C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
318#121D411yescharacteristic
319#121C2311yescharacteristic
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×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
388#117C2311yescharacteristic
389#117C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C4⋊C4C2311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
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—
479C24—21no—
480C24C2×D411yescharacteristic
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—82no—
488#41—82no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8C2×D411yescharacteristic
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×D4—21no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
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
557SD16—41no—
558SD16—41no—
559SD16—41no—
560SD16—41no—
561D8—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⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊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—
708Q8—81no—
709Q8—81no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—21no—
714D4—21no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—42no—
726D4—42no—
727D4—42no—
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—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—
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. #3540C2semidirect
2. #3494C2semidirect
3. #3354C2semidirect
4. #3353C2semidirect
5. #3350C2semidirect
6. #3350C2semidirect
7. #3347C2semidirect
8. #3347C2semidirect
9. #3341C2semidirect
10. #3340C2semidirect
11. #3326C2semidirect
12. #3322C2semidirect
13. #3321C2semidirect
14. #3319C2semidirect
15. #3308C2semidirect
16. #3306C2semidirect
17. #3301C2semidirect
18. #3297C2semidirect
19. #3244C2semidirect
20. #3243C2semidirect
21. #3200C2semidirect
22. #3199C2semidirect
23. #3194C2semidirect
24. #3188C2semidirect
25. #3118C2semidirect
26. #3118C2semidirect
27. #3097C2semidirect
28. #3096C2semidirect
29. #3093C2semidirect
30. #3091C2semidirect
31. #2976C2semidirect
35. #556C22semidirect
36. #556C22semidirect
38. #555C22semidirect
39. #555C22semidirect
40. #555C22semidirect
43. #553C22semidirect
44. #553C22semidirect
48. #548C22semidirect
49. #548C22semidirect
51. #547C22semidirect
54. #546C22semidirect
55. #546C22semidirect
56. #544C22semidirect
73. C2×#121C22semidirect
75. #518C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #498C22semidirect
81. #489C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #488C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #485C22semidirect
89. #485C22semidirect
90. #485C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #484C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #483C22semidirect
97. #483C22semidirect
98. #483C22semidirect
103. #482C22semidirect
104. #482C22semidirect
105. #482C22semidirect
106. #482C22semidirect
107. #482C22semidirect
108. #482C22semidirect
109. #482C22semidirect
110. #482C22semidirect
111. #482C22semidirect
112. #482C22semidirect
113. #482C22semidirect
114. #482C22semidirect
116. #481C22semidirect
117. #481C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #477C22semidirect
126. #476C22semidirect
127. #476C22semidirect
128. #476C22semidirect
129. #475C22semidirect
130. #474C22semidirect
131. #474C22semidirect
132. #474C22semidirect
135. #469C22semidirect
136. #469C22semidirect
137. #468C22semidirect
138. #468C22semidirect
139. #468C22semidirect
140. #468C22semidirect
143. #466C22semidirect
144. #466C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #450C22semidirect
154. #450C22semidirect
159. #448C22semidirect
160. #448C22semidirect
163. #447C22semidirect
164. #447C22semidirect
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
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #428C22semidirect
186. #428C22semidirect
187. #427C22semidirect
188. #427C22semidirect
189. #427C22semidirect
190. #427C22semidirect
191. #419C22semidirect
192. #418C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #416C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#102C22semidirect
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
#35402
#34942
#33542
#33532
#33502
#33472
#33412
#33402
#33262
#33222
#33212
#33192
#33082
#33062
#33012
#32972
#32442
#32432
#32002
#31992
#31942
#31882
#31182
#30972
#30962
#30932
#30912
#29762