Finite Group Databasebeta

← #62554

Subgroups — #62554

Order 256.

842 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3565C211yesmaximal, characteristic, complemented
2#3562C211yesmaximal, characteristic, complemented
3#3377C211yesmaximal, characteristic, complemented
4#3370C211yesmaximal, characteristic, complemented
5#3365C211yesmaximal, characteristic, complemented
6#3360C211yesmaximal, characteristic, complemented
7#3327C211yesmaximal, characteristic, complemented
8#3322C211yesmaximal, characteristic, complemented
9#3321C211yesmaximal, characteristic, complemented
10#3317C211yesmaximal, characteristic, complemented
11#3311C211yesmaximal, characteristic, complemented
12#3307C211yesmaximal, characteristic, complemented
13#3305C211yesmaximal, characteristic, complemented
14#3302C211yesmaximal, characteristic, complemented
15#3301C211yesmaximal, characteristic, complemented
16#3300C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3296C211yesmaximal, characteristic, complemented
19#3242C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3240C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3224C211yesmaximal, characteristic, complemented
24#3219C211yesmaximal, characteristic, complemented
25#3179C211yesmaximal, characteristic, complemented
26#3178C211yesmaximal, characteristic, complemented
27#3168C211yesmaximal, characteristic, complemented
28#3137C211yesmaximal, characteristic, complemented
29#3136C211yesmaximal, characteristic, complemented
30#3131C211yesmaximal, characteristic, complemented
31#2966C211yesmaximal, characteristic, complemented
32#563—21no—
33#562—21no—
34#562—21no—
35#560—21no—
36#559C2211yescharacteristic
37#557C2211yescharacteristic, complemented
38#556—21no—
39#556C2211yescharacteristic
40#556C2211yescharacteristic
41#555C2211yescharacteristic, complemented
42#554C2211yescharacteristic, complemented
43#553—21no—
44#553C2211yescharacteristic
45#553C2211yescharacteristic
46#552—21no—
47#552C2211yescharacteristic
48#552C2211yescharacteristic, complemented
49#551—21no—
50#550C2211yescharacteristic
51#548C2211yescharacteristic
52#548C2211yescharacteristic
53#547C2211yescharacteristic
54#546C2211yescharacteristic
55#546C2211yescharacteristic
56#544C2211yescharacteristic
57#544C2211yescharacteristic, complemented
58#542—21no—
59#542—21no—
60#542C2211yescharacteristic
61#542C2211yescharacteristic, complemented
62#541—21no—
63#541C2211yescharacteristic
64#540—21no—
65#540C2211yescharacteristic
66#539—21no—
67#539—21no—
68#538—21no—
69#538—21no—
70#536C2211yescharacteristic
71#535C2211yescharacteristic
72#533C2211yescharacteristic, complemented
73#532C2211yescharacteristic
74#529C2211yescharacteristic
75#529C2211yescharacteristic
76#529C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#499C2211yescharacteristic, complemented
80#497C2211yescharacteristic, complemented
81#496C2211yescharacteristic
82#495C2211yescharacteristic
83#491C2211yescharacteristic, complemented
84#491C2211yescharacteristic, complemented
85#490C2211yescharacteristic
86#490C2211yescharacteristic
87#489C2211yescharacteristic
88#489C2211yescharacteristic
89#489C2211yescharacteristic
90#489C2211yescharacteristic
91#488C2211yescharacteristic
92#488C2211yescharacteristic
93#488C2211yescharacteristic
94#488C2211yescharacteristic
95#488C2211yescharacteristic
96#488C2211yescharacteristic, complemented
97#488C2211yescharacteristic, complemented
98#488C2211yescharacteristic, complemented
99#487C2211yescharacteristic, complemented
100#487C2211yescharacteristic, complemented
101#487C2211yescharacteristic, complemented
102#486C2211yescharacteristic
103#486C2211yescharacteristic
104#486C2211yescharacteristic
105#485C2211yescharacteristic
106#485C2211yescharacteristic
107#485C2211yescharacteristic, complemented
108#485C2211yescharacteristic, complemented
109#484C2211yescharacteristic
110#483C2211yescharacteristic
111#482C2211yescharacteristic
112#482C2211yescharacteristic
113#482C2211yescharacteristic
114#482C2211yescharacteristic, complemented
115#481C2211yescharacteristic, complemented
116#480C2211yescharacteristic
117#479C2211yescharacteristic, complemented
118#479C2211yescharacteristic, complemented
119#479C2211yescharacteristic, complemented
120#479C2211yescharacteristic, complemented
121#478C2211yescharacteristic
122#478C2211yescharacteristic
123#478C2211yescharacteristic
124#478C2211yescharacteristic, complemented
125#477C2211yescharacteristic, complemented
126#476C2211yescharacteristic
127#475C2211yescharacteristic, complemented
128#474C2211yescharacteristic, complemented
129#470C2211yescharacteristic
130#469C2211yescharacteristic
131#468C2211yescharacteristic
132#468C2211yescharacteristic, complemented
133#467C2211yescharacteristic
134#467C2211yescharacteristic, complemented
135#466C2211yescharacteristic
136#466C2211yescharacteristic, complemented
137#465C2211yescharacteristic
138#465C2211yescharacteristic
139#465C2211yescharacteristic
140#465C2211yescharacteristic, complemented
141#464C2211yescharacteristic
142#464C2211yescharacteristic
143#464C2211yescharacteristic
144#464C2211yescharacteristic, complemented
145#463C2211yescharacteristic
146#463C2211yescharacteristic
147#463C2211yescharacteristic
148#463C2211yescharacteristic, complemented
149#462C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic
152#459C2211yescharacteristic
153#452C2211yescharacteristic
154#452C2211yescharacteristic
155#452C2211yescharacteristic
156#452C2211yescharacteristic, complemented
157#451C2211yescharacteristic, complemented
158#450C2211yescharacteristic
159#449C2211yescharacteristic
160#449C2211yescharacteristic
161#449C2211yescharacteristic
162#449C2211yescharacteristic, complemented
163#448C2211yescharacteristic, complemented
164#447C2211yescharacteristic
165#446C2211yescharacteristic, complemented
166C8×Q8C2211yescharacteristic, complemented
167#442C2211yescharacteristic, complemented
168#441C2211yescharacteristic, complemented
169#440C2211yescharacteristic
170#440C2211yescharacteristic, complemented
171C4×Q16C2211yescharacteristic, complemented
172C4×Q16C2211yescharacteristic, complemented
173C4×SD16C2211yescharacteristic
174C4×SD16C2211yescharacteristic, complemented
175C4×SD16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic
178C4×D8C2211yescharacteristic
179#436C2211yescharacteristic
180#435C2211yescharacteristic
181#435C2211yescharacteristic, complemented
182C8×D4C2211yescharacteristic
183C8×D4C2211yescharacteristic
184C8×D4C2211yescharacteristic, complemented
185#433C2211yescharacteristic
186#433C2211yescharacteristic, complemented
187#432C2211yescharacteristic, complemented
188#419C2211yescharacteristic, complemented
189#418C2211yescharacteristic
190#417C2211yescharacteristic
191#417C2211yescharacteristic
192#416C2211yescharacteristic
193#416C2211yescharacteristic
194#416C2211yescharacteristic
195#416C2211yescharacteristic
196#416C2211yescharacteristic, complemented
197#416C2211yescharacteristic, complemented
198C2×#103C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic
200#405C2211yescharacteristic
201#405C2211yescharacteristic, complemented
202C2×C4×C8C2211yescharacteristic, complemented
203C2×#41C2311yescharacteristic
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×D4C2311yescharacteristic
209C2×Q16C2311yescharacteristic
210C2×Q16C2311yescharacteristic
211C2×Q16C2311yescharacteristic
212C2×SD16C2311yescharacteristic
213C2×SD16C2311yescharacteristic
214C2×SD16C2311yescharacteristic
215C2×SD16C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×M16C2311yescharacteristic
222C2×M16C2311yescharacteristic
223C22×C8C2311yescharacteristic
224C22×C8C2311yescharacteristic
225C22×C8C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8C2311yescharacteristic
231C4⋊Q8C2311yescharacteristic
232C4⋊Q8C2311yescharacteristic
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127—21no—
237#127C2311yescharacteristic
238#127C2311yescharacteristic
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#126D411yescharacteristic
254#126D411yescharacteristic
255#125—21no—
256#125—21no—
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125D411yescharacteristic
264#125C2311yescharacteristic
265#125C2311yescharacteristic
266#125C2311yescharacteristic
267#125C2311yescharacteristic
268#125C2311yescharacteristic
269#125C2311yescharacteristic
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277#124—21no—
278#124D411yescharacteristic
279#124C2311yescharacteristic
280#124C2311yescharacteristic
281#124C2311yescharacteristic
282#124C2311yescharacteristic
283#124C2311yescharacteristic
284#124C2311yescharacteristic
285#123—21no—
286#123—21no—
287#123—21no—
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#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123D411yescharacteristic
304#123D411yescharacteristic
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⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8D411yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327C22⋊Q8C2311yescharacteristic
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121D411yescharacteristic
345#121C2311yescharacteristic
346#121C2311yescharacteristic
347#121C2311yescharacteristic
348#121C2311yescharacteristic
349#121C2311yescharacteristic
350#121C2311yescharacteristic
351#120—21no—
352#120—21no—
353#120—21no—
354#120—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8C2311yescharacteristic
360C4×Q8C2311yescharacteristic
361C4×Q8C2311yescharacteristic
362C4×Q8C2311yescharacteristic
363C4×Q8C2311yescharacteristic
364C4×Q8C2311yescharacteristic
365C4×Q8C2311yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2311yescharacteristic
377C4×D4C2311yescharacteristic
378C4×D4C2311yescharacteristic
379C4×D4C2311yescharacteristic
380C4×D4C2311yescharacteristic
381C4×D4C2311yescharacteristic
382C4×D4C2311yescharacteristic
383C4×D4C2311yescharacteristic
384C4×D4C2311yescharacteristic
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117C2311yescharacteristic
392#117C2311yescharacteristic
393#117C2311yescharacteristic
394#117C2311yescharacteristic
395#117C2311yescharacteristic
396#117C2311yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C2311yescharacteristic
400C2×C4⋊C4C2311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#106C2311yescharacteristic
411#106C2311yescharacteristic
412#106C2311yescharacteristic
413#106C2311yescharacteristic
414#106C2311yescharacteristic
415#106C2311yescharacteristic
416C4⋊C8C2311yescharacteristic
417C4⋊C8C2311yescharacteristic
418C4⋊C8C2311yescharacteristic
419C4⋊C8C2311yescharacteristic
420C4⋊C8C2311yescharacteristic
421C4⋊C8C2311yescharacteristic
422#103C2311yescharacteristic
423#103C2311yescharacteristic
424#103C2311yescharacteristic
425#103C2311yescharacteristic
426#103C2311yescharacteristic
427#103C2311yescharacteristic
428#103C2311yescharacteristic
429#103C2311yescharacteristic
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
468#97C2311yescharacteristic
469#97C2311yescharacteristic
470#97C2311yescharacteristic
471#97C2311yescharacteristic
472C4×C8C2311yescharacteristic
473C4×C8C2311yescharacteristic
474C4×C8C2311yescharacteristic
475C4×C8C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479#41—41no—
480#41—41no—
481#41—41no—
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×Q8C2411yescharacteristic
497C2×Q8C2411yescharacteristic
498C2×Q8C2411yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4C2×D411yescharacteristic
517C2×D4C2×D411yescharacteristic
518C2×D4C2×D411yescharacteristic
519C2×D4C2411yescharacteristic
520C2×D4C2411yescharacteristic
521C2×D4C2411yescharacteristic
522C2×D4C2411yescharacteristic
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×C4—21no—
535C22×C4—21no—
536C22×C4C2×D411yescharacteristic
537C22×C4C2×D411yescharacteristic
538C22×C4C2411yescharacteristic
539C22×C4C2411yescharacteristic
540C22×C4C2411yescharacteristic
541Q16—41no—
542Q16—41no—
543Q16—41no—
544SD16—41no—
545SD16—41no—
546SD16—41no—
547SD16—41no—
548SD16—41no—
549SD16—41no—
550D8—41no—
551D8—41no—
552D8—41no—
553M16—41no—
554M16—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8C2411yescharacteristic
560C2×C8C2411yescharacteristic
561C2×C8C2411yescharacteristic
562C2×C8C2411yescharacteristic
563C2×C8C2411yescharacteristic
564C2×C8C2411yescharacteristic
565C2×C8C2411yescharacteristic
566C2×C8C2411yescharacteristic
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⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4C2×D411yescharacteristic
602C4⋊C4C2×D411yescharacteristic
603C4⋊C4C2×D411yescharacteristic
604C4⋊C4C2×D411yescharacteristic
605C4⋊C4C2×D411yescharacteristic
606C4⋊C4C2×D411yescharacteristic
607C4⋊C4C2×D411yescharacteristic
608C4⋊C4C2×D411yescharacteristic
609C4⋊C4C2×D411yescharacteristic
610C4⋊C4C2×D411yescharacteristic
611C4⋊C4C2411yescharacteristic
612C4⋊C4C2411yescharacteristic
613C4⋊C4C2411yescharacteristic
614C4⋊C4C2411yescharacteristic
615C4⋊C4C2411yescharacteristic
616C4⋊C4C2411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
654C22⋊C4C2×D411yescharacteristic
655C22⋊C4C2×D411yescharacteristic
656C22⋊C4C2×D411yescharacteristic
657C22⋊C4C2×D411yescharacteristic
658C22⋊C4C2×D411yescharacteristic
659C22⋊C4C2×D411yescharacteristic
660C22⋊C4C2×D411yescharacteristic
661C22⋊C4C2×D411yescharacteristic
662C22⋊C4C2×D411yescharacteristic
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42C2×D411yescharacteristic
674C42C2×D411yescharacteristic
675C42C2411yescharacteristic
676C42C2411yescharacteristic
677C42C2411yescharacteristic
678C42C2411yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23C22×D411yescharacteristic
687C23C22×D411yescharacteristic
688C23C22×D411yescharacteristic
689Q8—21no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—41no—
698Q8—81no—
699Q8—81no—
700Q8—81no—
701Q8—81no—
702Q8—81no—
703D4—21no—
704D4—21no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—81no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—81no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4C22×D411yescharacteristic
763C2×C4C22×D411yescharacteristic
764C2×C4C22×D411yescharacteristic
765C2×C4C22×D411yescharacteristic
766C2×C4C22×D411yescharacteristic
767C2×C4C22×D411yescharacteristic
768C2×C4C22×D411yescharacteristic
769C2×C4C22×D411yescharacteristic
770C2×C4C22×D411yescharacteristic
771C2×C4C22×D411yescharacteristic
772C2×C4C22×D411yescharacteristic
773C2×C4C2511yescharacteristic
774C8—21no—
775C8—21no—
776C8—21no—
777C8—21no—
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—162no—
804C22C23×D411yescharacteristic
805C4—21no—
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4#58511yescharacteristic
829C4#58511yescharacteristic
830C2—41no—
831C2—41no—
832C2—41no—
833C2—81no—
834C2—81no—
835C2—81no—
836C2—81no—
837C2#350011yescharacteristic
838C2#358411yescharacteristic
839C2#358411yescharacteristic
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. #3565C2semidirect
2. #3562C2semidirect
3. #3377C2semidirect
4. #3370C2semidirect
5. #3365C2semidirect
6. #3360C2semidirect
7. #3327C2semidirect
8. #3322C2semidirect
9. #3321C2semidirect
10. #3317C2semidirect
11. #3311C2semidirect
12. #3307C2semidirect
13. #3305C2semidirect
14. #3302C2semidirect
15. #3301C2semidirect
16. #3300C2semidirect
17. #3297C2semidirect
18. #3296C2semidirect
19. #3242C2semidirect
20. #3241C2semidirect
21. #3240C2semidirect
22. #3225C2semidirect
23. #3224C2semidirect
24. #3219C2semidirect
25. #3179C2semidirect
26. #3178C2semidirect
27. #3168C2semidirect
28. #3137C2semidirect
29. #3136C2semidirect
30. #3131C2semidirect
31. #2966C2semidirect
37. #557C22semidirect
41. #555C22semidirect
42. #554C22semidirect
48. #552C22semidirect
57. #544C22semidirect
61. #542C22semidirect
72. #533C22semidirect
76. #529C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #499C22semidirect
80. #497C22semidirect
83. #491C22semidirect
84. #491C22semidirect
96. #488C22semidirect
97. #488C22semidirect
98. #488C22semidirect
99. #487C22semidirect
100. #487C22semidirect
101. #487C22semidirect
107. #485C22semidirect
108. #485C22semidirect
114. #482C22semidirect
115. #481C22semidirect
117. #479C22semidirect
118. #479C22semidirect
119. #479C22semidirect
120. #479C22semidirect
124. #478C22semidirect
125. #477C22semidirect
127. #475C22semidirect
128. #474C22semidirect
132. #468C22semidirect
134. #467C22semidirect
136. #466C22semidirect
140. #465C22semidirect
144. #464C22semidirect
148. #463C22semidirect
149. #462C22semidirect
150. #461C22semidirect
156. #452C22semidirect
157. #451C22semidirect
162. #449C22semidirect
163. #448C22semidirect
165. #446C22semidirect
166. C8×Q8C22semidirect
167. #442C22semidirect
168. #441C22semidirect
170. #440C22semidirect
171. C4×Q16C22semidirect
172. C4×Q16C22semidirect
174. C4×SD16C22semidirect
175. C4×SD16C22semidirect
176. C4×SD16C22semidirect
181. #435C22semidirect
184. C8×D4C22semidirect
186. #433C22semidirect
187. #432C22semidirect
188. #419C22semidirect
196. #416C22semidirect
197. #416C22semidirect
198. C2×#103C22semidirect
201. #405C22semidirect
202. C2×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#35652
#35622
#33772
#33702
#33652
#33602
#33272
#33222
#33212
#33172
#33112
#33072
#33052
#33022
#33012
#33002
#32972
#32962
#32422
#32412
#32402
#32252
#32242
#32192
#31792
#31782
#31682
#31372
#31362
#31312
#29662