Finite Group Databasebeta

← #8097177

Subgroups — #8097177

Order 512.

6447 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53102C216yesmaximal, complemented
2#53055C216yesmaximal, complemented
3#52969C213yesmaximal, complemented
4#52957C213yesmaximal, complemented
5#52297C213yesmaximal, complemented
6#46338C213yesmaximal, complemented
7#45992C216yesmaximal, complemented
8#45655C216yesmaximal, complemented
9#45487C216yesmaximal, complemented
10#45483C216yesmaximal, complemented
11#36592C211yesmaximal, characteristic, complemented
12#36458C212yesmaximal, complemented
13#36455C212yesmaximal, complemented
14#36455C212yesmaximal, complemented
15#36433C212yesmaximal, complemented
16#36091C211yesmaximal, characteristic, complemented
17#36091C212yesmaximal, complemented
18#36029C212yesmaximal, complemented
19#36005C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#560C22112yescomplemented
22C2×#550C2212yes—
23C2×#550C2212yes—
24C2×#550C2212yes—
25C2×#550C2212yes—
26C2×#550C2211yescharacteristic
27C2×#550C2211yescharacteristic, complemented
28C2×#550C2212yescomplemented
29C2×#520C2211yescharacteristic, complemented
30C2×C4×#41C2212yescomplemented
31#2867C2213yescomplemented
32#2860C2216yescomplemented
33#2856C2216yescomplemented
34#2856C2216yescomplemented
35#2854C2216yescomplemented
36#2828C2216yescomplemented
37#2828C22112yescomplemented
38#2824C2216yescomplemented
39#2818C22112yescomplemented
40#2815C22112yescomplemented
41#2813C22112yescomplemented
42#2812C2216yescomplemented
43#2803C2216yescomplemented
44#2795C2213yescomplemented
45#2792C2211yescharacteristic, complemented
46#2784C2213yescomplemented
47#2756C2216yescomplemented
48#2737C2216yescomplemented
49#2714C22112yescomplemented
50#2714C2216yescomplemented
51#2705C2216yescomplemented
52#2703C22112yescomplemented
53#2699C2213yescomplemented
54#2685C22112yescomplemented
55#2678C22112yescomplemented
56#2678C22112yescomplemented
57#2675C2216yescomplemented
58#2673C22112yescomplemented
59#2673C2216yescomplemented
60#2673C22112yescomplemented
61#2669C2216yescomplemented
62#2669C22112yescomplemented
63#2669C22112yescomplemented
64#2668C2216yescomplemented
65#2624C2213yescomplemented
66#2619C2216yescomplemented
67#2615C2213yes—
68#2615C2216yes—
69#2541C2216yescomplemented
70#2541C2213yescomplemented
71#2541C2216yescomplemented
72#2541C2216yescomplemented
73#2541C2216yescomplemented
74#2541C2216yescomplemented
75#2541C2213yescomplemented
76#2537C2216yescomplemented
77#2537C2216yescomplemented
78#2535C2216yescomplemented
79#2513C2216yescomplemented
80#2512C2216yescomplemented
81#2512C2216yescomplemented
82#2501C2213yescomplemented
83#2500C2216yescomplemented
84#2497C2216yescomplemented
85#2496C2216yescomplemented
86#2495C2216yescomplemented
87#2487C2213yescomplemented
88#2485C2216yescomplemented
89#2445C2216yescomplemented
90#2445C2216yescomplemented
91#2445C2216yescomplemented
92#2433C2216yes—
93#2433C2216yes—
94#2433C2216yes—
95#2433C2213yes—
96#2433C2216yes—
97#2428C2216yescomplemented
98#2428C2216yescomplemented
99#2428C2216yescomplemented
100#2428C2216yescomplemented
101#2428C2216yescomplemented
102#2428C2216yescomplemented
103#2422C2216yescomplemented
104#2422C2216yescomplemented
105#2420C2216yescomplemented
106#2416C2216yescomplemented
107#2416C2216yescomplemented
108#2414C2216yescomplemented
109#2414C2216yescomplemented
110#2414C2216yescomplemented
111#2414C2216yescomplemented
112#2408C2216yes—
113#2408C2213yes—
114#2408C2216yes—
115#2408C2216yes—
116#2408C2216yes—
117#2395C2213yescomplemented
118#2392C2216yescomplemented
119#2388C2216yes—
120#2388C2213yes—
121#2375C2216yescomplemented
122#2351C2212yescomplemented
123Q8×C4⋊C4C2212yescomplemented
124Q8×C4⋊C4C2212yescomplemented
125#2341C2211yescharacteristic
126#2341C2212yes—
127#2341C2212yes—
128#2341C2212yes—
129#2341C2212yes—
130#2341C2212yescomplemented
131#2341C2211yescharacteristic, complemented
132C4×#127C2213yescomplemented
133C4×#126C2216yescomplemented
134C4×#123C2216yescomplemented
135C4×#121C2216yescomplemented
136C4×#121C2216yescomplemented
137C42×Q8C2211yescharacteristic, complemented
138C2×H(5,𝔽2)—48no—
139C2×H(5,𝔽2)—44no—
140C22×#41C2311yescharacteristic
141C22×#41C2312yes—
142C22×#41C2312yes—
143C22×#41C2311yescharacteristic
144C22×#41C2313yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147#560—448no—
148#550—48no—
149#550—48no—
150#550—48no—
151#550—48no—
152#550—44no—
153#550—44no—
154#550—48no—
155C2×#127C2313yes—
156C2×#127C23112yes—
157C2×#127C2316yes—
158C2×#127C2316yes—
159C2×#127C2316yes—
160C2×#127C2313yes—
161C2×#127C2316yes—
162C2×#127C2313yes—
163C2×#127C2316yes—
164C2×#127C2316yes—
165C2×#126C2316yes—
166C2×#126C23112yes—
167C2×#123C2316yes—
168C2×#123C23112yes—
169C2×#123C23112yes—
170C2×#121C2316yes—
171C2×#121C2316yes—
172C2×#121C2316yes—
173C2×#121C2316yes—
174C2×#121C23112yes—
175C2×#121C23112yes—
176C2×#121C23112yes—
177C2×#121C2316yes—
178C2×#121C2316yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#121C2313yes—
184C2×#121C2316yes—
185C2×#121C2316yes—
186C2×#121C2313yes—
187C2×#121C2316yes—
188C2×#121C23112yes—
189C2×#121C23112yes—
190C2×#121C23112yes—
191C2×#120C2316yes—
192C2×#120C23112yes—
193C2×#120C23112yes—
194C2×#120C23112yes—
195C2×#120C23112yes—
196#520—44no—
197C4×#41—48no—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2312yes—
203C2×C4×D4C2313yes—
204C2×C4×D4C2316yes—
205C2×C4×D4C2316yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2316yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2316yes—
213C2×#117C2313yes—
214C2×#117C2316yes—
215C22×C4⋊C4C2313yes—
216C22×C42C2316yes—
217#400C23112yes—
218#400C2313yes—
219#399C2316yes—
220#399C2313yes—
221#398C2312yes—
222#398C2311yescharacteristic
223#397C23112yes—
224#397C2316yes—
225#397C23112yes—
226#397C2313yes—
227#397C2316yes—
228#397C23112yes—
229#396C2316yes—
230#396C2316yes—
231#396C23112yes—
232#395C2312yes—
233#395C2311yescharacteristic
234#394C2316yes—
235#394C23112yes—
236#394C23112yes—
237#394C23112yes—
238#394C23112yes—
239#394C23112yes—
240#394C2313yes—
241#394C2316yes—
242#394C23112yes—
243#394C23112yes—
244#394C23112yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2316yes—
250#394C2316yes—
251#394C23112yes—
252#393C2313yes—
253#393C2316yes—
254#392C2316yes—
255#392C23112yes—
256#392C23112yes—
257#392C23112yes—
258#392C23112yes—
259#392C23112yes—
260#392C2316yes—
261#392C23112yes—
262#392C23112yes—
263#392C23112yes—
264#392C23112yes—
265#392C23112yes—
266#392C2316yes—
267#392C2316yes—
268#392C2316yes—
269#392C2313yes—
270#392C2316yes—
271#392C2316yes—
272#392C2316yes—
273#392C23112yes—
274#390C2313yes—
275#390C2313yes—
276#390C2316yes—
277#390C2316yes—
278#390C23112yes—
279#390C2316yes—
280#390C2316yes—
281#390C2316yes—
282#390C2316yes—
283#390C2316yes—
284#390C2316yes—
285#390C2316yes—
286#390C2316yes—
287#390C2316yes—
288#390C2316yes—
289#390C2316yes—
290#390C2316yes—
291#390C2316yes—
292#390C2316yes—
293#390C23112yes—
294#389C2316yes—
295#389C2316yes—
296#389C2316yes—
297#389C2316yes—
298#389C2316yes—
299#389C2316yes—
300#389C2312yes—
301#389C2312yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#388C23112yes—
307#388C23112yes—
308#388C2316yes—
309#388C23112yes—
310#388C2316yes—
311#388C2316yes—
312#388C2316yes—
313#388C2316yes—
314#387C2312yes—
315#387C2316yes—
316#387C2316yes—
317#387C2312yes—
318#387C2316yes—
319#386C23112yes—
320#386C23112yes—
321#386C2316yes—
322#386C23112yes—
323#386C2316yes—
324#386C2316yes—
325#386C2316yes—
326#386C2316yes—
327#386C2316yes—
328#385C2316yes—
329#385C2316yes—
330#384C2311yescharacteristic
331#384C2316yes—
332#384C2316yes—
333#383C2316yes—
334#382C2316yes—
335#381C2316yes—
336#380C2316yes—
337#380C2316yes—
338#380C2316yes—
339#380C2313yes—
340#380C2316yes—
341#380C2316yes—
342#380C2313yes—
343#380C2316yes—
344#380C2316yes—
345#379C23112yes—
346#379C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2313yes—
357C4×C22⋊C4C2316yes—
358C4×C22⋊C4C2313yes—
359C43C2313yes—
360C25C2416yes—
361H(5,𝔽2)—464no—
362C2×#41—28no—
363C2×#41—24no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—28no—
369C2×#41—28no—
370C2×#41—28no—
371C2×#41—24no—
372C2×#41—412no—
373C2×#41—46no—
374C22×Q8C2411yescharacteristic
375C22×Q8C2411yescharacteristic
376C22×D4—412no—
377C22×D4—46no—
378C22×D4—412no—
379C22×D4—412no—
380C22×D4—412no—
381C22×D4C2416yes—
382C22×D4C2413yes—
383C22×D4C2413yes—
384C22×D4C2416yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2413yes—
389C22×D4C2416yes—
390C22×D4C2413yes—
391C22×D4C2416yes—
392C22×D4C24112yes—
393C22×D4C24112yes—
394C22×D4C24112yes—
395C22×D4C2416yes—
396C22×D4C24112yes—
397C22×D4C2416yes—
398C22×D4C24112yes—
399C22×D4C2416yes—
400C22×D4C2413yes—
401C23×C4C2413yes—
402C23×C4C2416yes—
403C23×C4C2413yes—
404C23×C4C2416yes—
405C23×C4C2416yes—
406C23×C4C2416yes—
407C23×C4C2416yes—
408#127—46no—
409#127—412no—
410#127—412no—
411#127—412no—
412#127—412no—
413#127—46no—
414#127—412no—
415#127—46no—
416#127—424no—
417#127—86no—
418#126—224no—
419#126—424no—
420#123—224no—
421#123—424no—
422#123—424no—
423#121—224no—
424#121—424no—
425#121—424no—
426#121—412no—
427#121—424no—
428#121—424no—
429#121—412no—
430#121—412no—
431#121—412no—
432#121—412no—
433#121—412no—
434#121—412no—
435#121—412no—
436#121—46no—
437#121—412no—
438#121—412no—
439#121—412no—
440#121—412no—
441#121—46no—
442#121—424no—
443#121—812no—
444#120—412no—
445#120—424no—
446#120—424no—
447#120—424no—
448#120—812no—
449C4×Q8—28no—
450C4×Q8—28no—
451C4×Q8—28no—
452C4×Q8—24no—
453C4×Q8—28no—
454C4×D4—412no—
455C4×D4—412no—
456C4×D4—412no—
457C4×D4—412no—
458C4×D4—412no—
459C4×D4—412no—
460C4×D4—412no—
461C4×D4—46no—
462C4×D4—412no—
463C4×D4—46no—
464#117—46no—
465#117—412no—
466C2×C4⋊C4—46no—
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2416yes—
471C2×C4⋊C4C2413yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2416yes—
474C2×C4⋊C4C2416yes—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C2413yes—
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2411yescharacteristic
482C2×C4⋊C4C2412yes—
483C2×C4⋊C4C2411yescharacteristic
484C2×C4⋊C4C2412yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C24112yes—
487C2×C4⋊C4C24112yes—
488C2×C4⋊C4C2412yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C24112yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C2413yes—
505C2×C22⋊C4C2416yes—
506C2×C22⋊C4C2416yes—
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C2416yes—
509C2×C22⋊C4C2416yes—
510C2×C22⋊C4C2413yes—
511C2×C22⋊C4C2416yes—
512C2×C22⋊C4C2416yes—
513C2×C22⋊C4C2416yes—
514C2×C22⋊C4C2416yes—
515C2×C22⋊C4C24112yes—
516C2×C22⋊C4C24112yes—
517C2×C22⋊C4C24112yes—
518C2×C22⋊C4C24112yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C24112yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C42—412no—
524C2×C42C2416yes—
525C2×C42C2416yes—
526C2×C42C2413yes—
527C2×C42C2416yes—
528C2×C42C2416yes—
529C2×C42C2416yes—
530C2×C42C2411yescharacteristic
531C2×C42C2416yes—
532C2×C42C2413yes—
533C2×C42C2412yes—
534#95C2412yes—
535#95C2412yes—
536#95C2411yescharacteristic
537#95C2411yescharacteristic
538#95C2412yes—
539#95C2412yes—
540#95C2412yes—
541#95C2413yes—
542#95C2416yes—
543#95C2416yes—
544#95C2416yes—
545#95C2413yes—
546#95C2416yes—
547#95C2416yes—
548#95C2412yes—
549#95C2416yes—
550#95C2416yes—
551#95C2416yes—
552#95C2416yes—
553#95C2416yes—
554#95C2416yes—
555#95C24112yes—
556C24—412no—
557C24—46no—
558C24—412no—
559C24—46no—
560C24—46no—
561C24C2516yes—
562C24C2513yes—
563C24C2516yes—
564C24C2513yes—
565#41—448no—
566#41—432no—
567#41—416no—
568#41—432no—
569#41—416no—
570C2×Q8—42no—
571C2×Q8—41no—
572C2×Q8H(5,𝔽2)18yes—
573C2×Q8H(5,𝔽2)14yes—
574C2×D4—212no—
575C2×D4—26no—
576C2×D4—212no—
577C2×D4—212no—
578C2×D4—212no—
579C2×D4—212no—
580C2×D4—212no—
581C2×D4—212no—
582C2×D4—212no—
583C2×D4—26no—
584C2×D4—212no—
585C2×D4—212no—
586C2×D4—212no—
587C2×D4—212no—
588C2×D4—26no—
589C2×D4—26no—
590C2×D4—46no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—46no—
594C2×D4—43no—
595C2×D4—46no—
596C2×D4—46no—
597C2×D4—46no—
598C2×D4—43no—
599C2×D4—46no—
600C2×D4—43no—
601C2×D4—46no—
602C2×D4—46no—
603C2×D4—46no—
604C2×D4—46no—
605C2×D4—46no—
606C2×D4—46no—
607C2×D4—46no—
608C2×D4—43no—
609C2×D4—43no—
610C2×D4—412no—
611C2×D4—412no—
612C2×D4—412no—
613C2×D4—412no—
614C2×D4—412no—
615C2×D4—412no—
616C2×D4—412no—
617C2×D4—412no—
618C2×D4—412no—
619C2×D4—412no—
620C2×D4—412no—
621C2×D4—412no—
622C2×D4—412no—
623C2×D4—46no—
624C2×D4—412no—
625C2×D4—46no—
626C2×D4—412no—
627C2×D4—412no—
628C2×D4—412no—
629C2×D4—448no—
630C2×D4—496no—
631C22×C4—212no—
632C22×C4—26no—
633C22×C4—212no—
634C22×C4—212no—
635C22×C4—212no—
636C22×C4—212no—
637C22×C4—212no—
638C22×C4—212no—
639C22×C4—212no—
640C22×C4—26no—
641C22×C4—212no—
642C22×C4—212no—
643C22×C4—46no—
644C22×C4—46no—
645C22×C4—46no—
646C22×C4—46no—
647C22×C4—46no—
648C22×C4—412no—
649C22×C4C2511yescharacteristic
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2516yes—
653C22×C4C2516yes—
654C22×C4C2513yes—
655C22×C4C2516yes—
656C22×C4C2516yes—
657C22×C4C2512yes—
658C22×C4C2511yescharacteristic
659C22×C4C2512yes—
660C22×C4C2512yes—
661C22×C4C2512yes—
662C22×C4C2511yescharacteristic
663C22×C4C2513yes—
664C4⋊C4—212no—
665C4⋊C4—212no—
666C4⋊C4—212no—
667C4⋊C4—212no—
668C4⋊C4—26no—
669C4⋊C4—212no—
670C4⋊C4—212no—
671C4⋊C4—212no—
672C4⋊C4—24no—
673C4⋊C4—43no—
674C4⋊C4—41no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—41no—
679C4⋊C4—42no—
680C4⋊C4—41no—
681C4⋊C4—42no—
682C4⋊C4—412no—
683C4⋊C4—412no—
684C4⋊C4—46no—
685C4⋊C4H(5,𝔽2)18yescomplemented
686C22⋊C4—212no—
687C22⋊C4—212no—
688C22⋊C4—212no—
689C22⋊C4—212no—
690C22⋊C4—212no—
691C22⋊C4—212no—
692C22⋊C4—212no—
693C22⋊C4—212no—
694C22⋊C4—212no—
695C22⋊C4—46no—
696C22⋊C4—412no—
697C22⋊C4—46no—
698C22⋊C4—46no—
699C22⋊C4—46no—
700C22⋊C4—46no—
701C22⋊C4—46no—
702C22⋊C4—46no—
703C22⋊C4—46no—
704C22⋊C4—46no—
705C22⋊C4—43no—
706C22⋊C4—46no—
707C22⋊C4—43no—
708C22⋊C4—46no—
709C22⋊C4—46no—
710C22⋊C4—46no—
711C22⋊C4—412no—
712C22⋊C4—412no—
713C22⋊C4—412no—
714C22⋊C4—46no—
715C22⋊C4—46no—
716C22⋊C4—412no—
717C22⋊C4—46no—
718C22⋊C4—412no—
719C22⋊C4—46no—
720C42—212no—
721C42—212no—
722C42—212no—
723C42—212no—
724C42—26no—
725C42—212no—
726C42—22no—
727C42—42no—
728C42—46no—
729C42—43no—
730C23—26no—
731C23—26no—
732C23—26no—
733C23—26no—
734C23—26no—
735C23—26no—
736C23—23no—
737C23—26no—
738C23—26no—
739C23—26no—
740C23—26no—
741C23—26no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—23no—
746C23—26no—
747C23—23no—
748C23—26no—
749C23—23no—
750C23—26no—
751C23—23no—
752C23—23no—
753C23—26no—
754C23—424no—
755C23—1612no—
756C23—166no—
757C23—166no—
758C23—1612no—
759C23C2611yescharacteristic
760Q8—44no—
761Q8#560116yescomplemented
762D4—424no—
763D4—412no—
764D4—412no—
765D4—424no—
766D4—424no—
767D4—412no—
768D4—812no—
769D4—812no—
770D4—812no—
771D4—86no—
772D4—86no—
773D4—812no—
774D4—812no—
775D4—1612no—
776D4—1612no—
777D4—166no—
778D4—166no—
779D4—1612no—
780D4—1612no—
781D4—1612no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—26no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—23no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—22no—
799C2×C4—26no—
800C2×C4—26no—
801C2×C4—26no—
802C2×C4—26no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—26no—
813C2×C4—22no—
814C2×C4—26no—
815C2×C4—22no—
816C2×C4—26no—
817C2×C4—412no—
818C2×C4—424no—
819C2×C4—424no—
820C2×C4—412no—
821C2×C4—812no—
822C2×C4—812no—
823C2×C4—166no—
824C2×C4C2×H(5,𝔽2)14yes—
825C2×C4C2×H(5,𝔽2)14yes—
826C2×C4C2×H(5,𝔽2)14yes—
827C2×C4C2×H(5,𝔽2)112yes—
828C2×C4C2×H(5,𝔽2)16yes—
829C2×C4#58512yes—
830C22—46no—
831C22—46no—
832C22—46no—
833C22—46no—
834C22—46no—
835C22—46no—
836C22—43no—
837C22—46no—
838C22—46no—
839C22—43no—
840C22—46no—
841C22—43no—
842C22—43no—
843C22—46no—
844C22—46no—
845C22—46no—
846C22—46no—
847C22—46no—
848C22—46no—
849C22—46no—
850C22—43no—
851C22—46no—
852C22—46no—
853C22—43no—
854C22—1624no—
855C22C22×H(5,𝔽2)12yes—
856C22C22×H(5,𝔽2)12yes—
857C22C22×H(5,𝔽2)11yescharacteristic
858C22C2×#58511yescharacteristic
859C22H(7,𝔽2)11yescharacteristic
860C4—24no—
861C4—24no—
862C4—22no—
863C4—24no—
864C4—46no—
865C4—46no—
866C4—43no—
867C4—42no—
868C4—46no—
869C4—46no—
870C4—42no—
871C4—41no—
872C4—42no—
873C4—41no—
874C4C2×#560112yes—
875C2—86no—
876C2—83no—
877C2—83no—
878C2—86no—
879C2C22×#56011yescharacteristic
880C2#6289911yescharacteristic
881C2#6291612yes—
882C2#6301412yes—
883C2#6304011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53102C2semidirect
2. #53055C2semidirect
3. #52969C2semidirect
4. #52957C2semidirect
5. #52297C2semidirect
6. #46338C2semidirect
7. #45992C2semidirect
8. #45655C2semidirect
9. #45487C2semidirect
10. #45483C2semidirect
11. #36592C2semidirect
12. #36458C2semidirect
13. #36455C2semidirect
14. #36455C2semidirect
15. #36433C2semidirect
16. #36091C2semidirect
17. #36091C2semidirect
18. #36029C2semidirect
19. #36005C2semidirect
21. C2×#560C22semidirect
27. C2×#550C22semidirect
28. C2×#550C22semidirect
29. C2×#520C22semidirect
30. C2×C4×#41C22semidirect
31. #2867C22semidirect
32. #2860C22semidirect
33. #2856C22semidirect
34. #2856C22semidirect
35. #2854C22semidirect
36. #2828C22semidirect
37. #2828C22semidirect
38. #2824C22semidirect
39. #2818C22semidirect
40. #2815C22semidirect
41. #2813C22semidirect
42. #2812C22semidirect
43. #2803C22semidirect
44. #2795C22semidirect
45. #2792C22semidirect
46. #2784C22semidirect
47. #2756C22semidirect
48. #2737C22semidirect
49. #2714C22semidirect
50. #2714C22semidirect
51. #2705C22semidirect
52. #2703C22semidirect
53. #2699C22semidirect
54. #2685C22semidirect
55. #2678C22semidirect
56. #2678C22semidirect
57. #2675C22semidirect
58. #2673C22semidirect
59. #2673C22semidirect
60. #2673C22semidirect
61. #2669C22semidirect
62. #2669C22semidirect
63. #2669C22semidirect
64. #2668C22semidirect
65. #2624C22semidirect
66. #2619C22semidirect
69. #2541C22semidirect
70. #2541C22semidirect
71. #2541C22semidirect
72. #2541C22semidirect
73. #2541C22semidirect
74. #2541C22semidirect
75. #2541C22semidirect
76. #2537C22semidirect
77. #2537C22semidirect
78. #2535C22semidirect
79. #2513C22semidirect
80. #2512C22semidirect
81. #2512C22semidirect
82. #2501C22semidirect
83. #2500C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2495C22semidirect
87. #2487C22semidirect
88. #2485C22semidirect
89. #2445C22semidirect
90. #2445C22semidirect
91. #2445C22semidirect
97. #2428C22semidirect
98. #2428C22semidirect
99. #2428C22semidirect
100. #2428C22semidirect
101. #2428C22semidirect
102. #2428C22semidirect
103. #2422C22semidirect
104. #2422C22semidirect
105. #2420C22semidirect
106. #2416C22semidirect
107. #2416C22semidirect
108. #2414C22semidirect
109. #2414C22semidirect
110. #2414C22semidirect
111. #2414C22semidirect
117. #2395C22semidirect
118. #2392C22semidirect
121. #2375C22semidirect
122. #2351C22semidirect
123. Q8×C4⋊C4C22semidirect
124. Q8×C4⋊C4C22semidirect
130. #2341C22semidirect
131. #2341C22semidirect
132. C4×#127C22semidirect
133. C4×#126C22semidirect
134. C4×#123C22semidirect
135. C4×#121C22semidirect
136. C4×#121C22semidirect
137. C42×Q8C22semidirect
685. C4⋊C4H(5,𝔽2)semidirect
761. Q8#560semidirect

Maximal subgroups

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

subgroupindex
#531022
#530552
#529692
#529572
#522972
#463382
#459922
#456552
#454872
#454832
#365922
#364582
#364552
#364332
#360912
#360292
#360052