Finite Group Databasebeta

← #62195

Subgroups — #62195

Order 256.

854 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559C211yesmaximal, characteristic, complemented
2#3521C211yesmaximal, characteristic, complemented
3#3389C211yesmaximal, characteristic, complemented
4#3380C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3360C211yesmaximal, characteristic, complemented
7#3355C211yesmaximal, characteristic, complemented
8#3353C211yesmaximal, characteristic, complemented
9#3351C211yesmaximal, characteristic, complemented
10#3350C211yesmaximal, characteristic, complemented
11#3345C211yesmaximal, characteristic, complemented
12#3337C211yesmaximal, characteristic, complemented
13#3330C211yesmaximal, characteristic, complemented
14#3322C211yesmaximal, characteristic, complemented
15#3322C211yesmaximal, characteristic, complemented
16#3307C211yesmaximal, characteristic, complemented
17#3306C211yesmaximal, characteristic, complemented
18#3297C211yesmaximal, characteristic, complemented
19#3260C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3251C211yesmaximal, characteristic, complemented
22#3243C211yesmaximal, characteristic, complemented
23#3242C211yesmaximal, characteristic, complemented
24#3232C211yesmaximal, characteristic, complemented
25#3122C211yesmaximal, characteristic, complemented
26#3119C211yesmaximal, characteristic, complemented
27#3106C211yesmaximal, characteristic, complemented
28#3084C211yesmaximal, characteristic, complemented
29#3081C211yesmaximal, characteristic, complemented
30#3080C211yesmaximal, characteristic, complemented
31#2993C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#556C2211yescharacteristic
35#556C2211yescharacteristic
36#554C2211yescharacteristic
37#554C2211yescharacteristic, complemented
38#554C2211yescharacteristic, complemented
39#553—21no—
40#553C2211yescharacteristic
41#553C2211yescharacteristic
42#553C2211yescharacteristic
43#553C2211yescharacteristic
44#553C2211yescharacteristic, complemented
45#552—21no—
46#552C2211yescharacteristic
47#551—21no—
48#551—21no—
49#547—21no—
50#547—21no—
51#547C2211yescharacteristic
52#547C2211yescharacteristic
53#547C2211yescharacteristic, complemented
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic, complemented
58#542C2211yescharacteristic
59#541C2211yescharacteristic
60#540C2211yescharacteristic
61#540C2211yescharacteristic, complemented
62#539—21no—
63#539—21no—
64#539—21no—
65#539—21no—
66#538—21no—
67#537—21no—
68#532C2211yescharacteristic, complemented
69#529—21no—
70#529C2211yescharacteristic
71#529C2211yescharacteristic
72C2×#126—21no—
73C2×#125C2211yescharacteristic, complemented
74#520C2211yescharacteristic
75#518C2211yescharacteristic
76C4×#41C2211yescharacteristic
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#499C2211yescharacteristic, complemented
82#499C2211yescharacteristic, complemented
83#491C2211yescharacteristic, complemented
84#489C2211yescharacteristic
85#488C2211yescharacteristic
86#488C2211yescharacteristic
87#488C2211yescharacteristic
88#487C2211yescharacteristic, complemented
89#485C2211yescharacteristic
90#485C2211yescharacteristic
91#485C2211yescharacteristic, complemented
92#484C2211yescharacteristic
93#484C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#483C2211yescharacteristic
96#483C2211yescharacteristic, complemented
97#482C2211yescharacteristic
98#482C2211yescharacteristic
99#482C2211yescharacteristic
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#481C2211yescharacteristic
103#481C2211yescharacteristic, complemented
104#480C2211yescharacteristic
105#480C2211yescharacteristic
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#479C2211yescharacteristic, complemented
109#479C2211yescharacteristic, complemented
110#479C2211yescharacteristic, complemented
111#479C2211yescharacteristic, complemented
112#479C2211yescharacteristic, complemented
113#479C2211yescharacteristic, complemented
114#478C2211yescharacteristic
115#478C2211yescharacteristic
116#478C2211yescharacteristic
117#478C2211yescharacteristic
118#478C2211yescharacteristic
119#478C2211yescharacteristic
120#478C2211yescharacteristic
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#476C2211yescharacteristic
129#476C2211yescharacteristic
130#476C2211yescharacteristic
131#476C2211yescharacteristic, complemented
132#475C2211yescharacteristic, complemented
133#475C2211yescharacteristic, complemented
134#474C2211yescharacteristic
135#474C2211yescharacteristic
136#474C2211yescharacteristic, complemented
137#469C2211yescharacteristic
138#469C2211yescharacteristic
139#469C2211yescharacteristic
140#468C2211yescharacteristic
141#468C2211yescharacteristic
142#468C2211yescharacteristic, complemented
143#468C2211yescharacteristic, complemented
144#468C2211yescharacteristic, complemented
145#466C2211yescharacteristic
146#465C2211yescharacteristic
147#465C2211yescharacteristic
148#465C2211yescharacteristic, complemented
149#463C2211yescharacteristic
150#463C2211yescharacteristic
151#463C2211yescharacteristic
152#463C2211yescharacteristic
153#461C2211yescharacteristic, complemented
154#461C2211yescharacteristic, complemented
155#460C2211yescharacteristic, complemented
156#460C2211yescharacteristic, complemented
157#459C2211yescharacteristic
158#459C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#447C2211yescharacteristic
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#442C2211yescharacteristic
168#442C2211yescharacteristic
169#442C2211yescharacteristic
170#440C2211yescharacteristic, complemented
171C4×SD16C2211yescharacteristic, complemented
172C4×SD16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic, complemented
174C4×D8C2211yescharacteristic
175C4×D8C2211yescharacteristic
176C4×D8C2211yescharacteristic
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#436C2211yescharacteristic
181#436C2211yescharacteristic, complemented
182#435C2211yescharacteristic
183#435C2211yescharacteristic, complemented
184C8×D4C2211yescharacteristic
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#431C2211yescharacteristic, complemented
188#428C2211yescharacteristic
189#428C2211yescharacteristic, complemented
190#428C2211yescharacteristic, complemented
191#428C2211yescharacteristic, complemented
192#427C2211yescharacteristic
193C2×#106C2211yescharacteristic, complemented
194#424C2211yescharacteristic
195#424C2211yescharacteristic, complemented
196#423C2211yescharacteristic, complemented
197#418C2211yescharacteristic
198#417C2211yescharacteristic
199#417C2211yescharacteristic
200#417C2211yescharacteristic
201#416C2211yescharacteristic
202C2×#102C2211yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C2×SD16C2311yescharacteristic
210C2×SD16C2311yescharacteristic
211C2×SD16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×D8C2311yescharacteristic
214C2×D8C2311yescharacteristic
215C2×D8C2311yescharacteristic
216C2×D8C2311yescharacteristic
217C2×M16C2311yescharacteristic
218C2×M16C2311yescharacteristic
219C2×M16C2311yescharacteristic
220C2×M16C2311yescharacteristic
221C22×C8C2311yescharacteristic
222C22×C8C2311yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8C2311yescharacteristic
226C4⋊Q8C2311yescharacteristic
227C4⋊Q8C2311yescharacteristic
228C4⋊Q8C2311yescharacteristic
229C4⋊Q8C2311yescharacteristic
230#127C2311yescharacteristic
231#126—21no—
232#126—21no—
233#126—21no—
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#126D411yescharacteristic
246#126D411yescharacteristic
247#125—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125D411yescharacteristic
255#125C2311yescharacteristic
256#125C2311yescharacteristic
257#125C2311yescharacteristic
258#125C2311yescharacteristic
259#125C2311yescharacteristic
260#125C2311yescharacteristic
261#125C2311yescharacteristic
262#125C2311yescharacteristic
263#124—21no—
264#124—21no—
265#124—21no—
266#124D411yescharacteristic
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#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123D411yescharacteristic
290#123D411yescharacteristic
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
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⋊Q8D411yescharacteristic
309C22⋊Q8C2311yescharacteristic
310C22⋊Q8C2311yescharacteristic
311C22⋊Q8C2311yescharacteristic
312C22⋊Q8C2311yescharacteristic
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#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#120—21no—
336#120—21no—
337C4×Q8—21no—
338C4×Q8C2311yescharacteristic
339C4×Q8C2311yescharacteristic
340C4×Q8C2311yescharacteristic
341C4×Q8C2311yescharacteristic
342C4×Q8C2311yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4C2311yescharacteristic
357C4×D4C2311yescharacteristic
358C4×D4C2311yescharacteristic
359C4×D4C2311yescharacteristic
360C4×D4C2311yescharacteristic
361C4×D4C2311yescharacteristic
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#117C2311yescharacteristic
377#117C2311yescharacteristic
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
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#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
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472#97C2311yescharacteristic
473#97C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—22no—
480#41—22no—
481#41—41no—
482#41—41no—
483#41—82no—
484#41—82no—
485#41—82no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×D411yescharacteristic
491C2×Q8C2411yescharacteristic
492C2×Q8C2411yescharacteristic
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
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—41no—
508C2×D4C2×D411yescharacteristic
509C2×D4C2×D411yescharacteristic
510C2×D4C2×D411yescharacteristic
511C2×D4C2411yescharacteristic
512C2×D4C2411yescharacteristic
513C2×D4C2411yescharacteristic
514C2×D4C2411yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
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×C4C2×D411yescharacteristic
535C22×C4C2×D411yescharacteristic
536C22×C4C2411yescharacteristic
537C22×C4C2411yescharacteristic
538C22×C4C2411yescharacteristic
539SD16—41no—
540SD16—41no—
541SD16—41no—
542SD16—41no—
543D8—22no—
544D8—22no—
545D8—41no—
546D8—41no—
547M16—41no—
548M16—41no—
549M16—41no—
550M16—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8C2411yescharacteristic
554C2×C8C2411yescharacteristic
555C2×C8C2411yescharacteristic
556C2×C8C2411yescharacteristic
557C2×C8C2411yescharacteristic
558C2×C8C2411yescharacteristic
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
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⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4C2×D411yescharacteristic
597C4⋊C4C2×D411yescharacteristic
598C4⋊C4C2×D411yescharacteristic
599C4⋊C4C2×D411yescharacteristic
600C4⋊C4C2×D411yescharacteristic
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2411yescharacteristic
607C4⋊C4C2411yescharacteristic
608C4⋊C4C2411yescharacteristic
609C4⋊C4C2411yescharacteristic
610C4⋊C4C2411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2×D411yescharacteristic
649C22⋊C4C2×D411yescharacteristic
650C22⋊C4C2×D411yescharacteristic
651C22⋊C4C2×D411yescharacteristic
652C22⋊C4C2×D411yescharacteristic
653C22⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42C2×D411yescharacteristic
667C42C2×D411yescharacteristic
668C42C2411yescharacteristic
669C42C2411yescharacteristic
670C42C2411yescharacteristic
671C42C2411yescharacteristic
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—42no—
677C23—81no—
678C23—81no—
679C23C22×D411yescharacteristic
680C23C22×D411yescharacteristic
681C23C22×D411yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—41no—
687Q8—81no—
688Q8—81no—
689Q8—81no—
690Q8—81no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—81no—
707D4—81no—
708D4—81no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—81no—
714D42−1+412yes—
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—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C22×D411yescharacteristic
755C2×C4C22×D411yescharacteristic
756C2×C4C22×D411yescharacteristic
757C2×C4C22×D411yescharacteristic
758C2×C4C22×D411yescharacteristic
759C2×C4C22×D411yescharacteristic
760C2×C4C22×D411yescharacteristic
761C2×C4C22×D411yescharacteristic
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C2511yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—21no—
771C8—21no—
772C8—21no—
773C8—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—162no—
796C22C23×D411yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—21no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4C2×2−1+411yescharacteristic
821C4#58511yescharacteristic
822C2—41no—
823C2—41no—
824C2—41no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—81no—
829C2#348911yescharacteristic
830C2#358411yescharacteristic
831C2#358511yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
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. #3559C2semidirect
2. #3521C2semidirect
3. #3389C2semidirect
4. #3380C2semidirect
5. #3376C2semidirect
6. #3360C2semidirect
7. #3355C2semidirect
8. #3353C2semidirect
9. #3351C2semidirect
10. #3350C2semidirect
11. #3345C2semidirect
12. #3337C2semidirect
13. #3330C2semidirect
14. #3322C2semidirect
15. #3322C2semidirect
16. #3307C2semidirect
17. #3306C2semidirect
18. #3297C2semidirect
19. #3260C2semidirect
20. #3257C2semidirect
21. #3251C2semidirect
22. #3243C2semidirect
23. #3242C2semidirect
24. #3232C2semidirect
25. #3122C2semidirect
26. #3119C2semidirect
27. #3106C2semidirect
28. #3084C2semidirect
29. #3081C2semidirect
30. #3080C2semidirect
31. #2993C2semidirect
37. #554C22semidirect
38. #554C22semidirect
44. #553C22semidirect
53. #547C22semidirect
57. #544C22semidirect
61. #540C22semidirect
68. #532C22semidirect
73. C2×#125C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #499C22semidirect
82. #499C22semidirect
83. #491C22semidirect
88. #487C22semidirect
91. #485C22semidirect
93. #484C22semidirect
94. #484C22semidirect
96. #483C22semidirect
100. #482C22semidirect
101. #482C22semidirect
103. #481C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #479C22semidirect
109. #479C22semidirect
110. #479C22semidirect
111. #479C22semidirect
112. #479C22semidirect
113. #479C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
131. #476C22semidirect
132. #475C22semidirect
133. #475C22semidirect
136. #474C22semidirect
142. #468C22semidirect
143. #468C22semidirect
144. #468C22semidirect
148. #465C22semidirect
153. #461C22semidirect
154. #461C22semidirect
155. #460C22semidirect
156. #460C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
170. #440C22semidirect
171. C4×SD16C22semidirect
172. C4×SD16C22semidirect
173. C4×SD16C22semidirect
181. #436C22semidirect
183. #435C22semidirect
186. #433C22semidirect
187. #431C22semidirect
189. #428C22semidirect
190. #428C22semidirect
191. #428C22semidirect
193. C2×#106C22semidirect
195. #424C22semidirect
196. #423C22semidirect

Maximal subgroups

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

subgroupindex
#35592
#35212
#33892
#33802
#33762
#33602
#33552
#33532
#33512
#33502
#33452
#33372
#33302
#33222
#33072
#33062
#32972
#32602
#32572
#32512
#32432
#32422
#32322
#31222
#31192
#31062
#30842
#30812
#30802
#29932