Finite Group Databasebeta

← #7659037

Subgroups — #7659037

Order 512.

5832 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42982C213yesmaximal, complemented
2#42977C213yesmaximal, complemented
3#42945C216yesmaximal, complemented
4#42589C216yesmaximal, complemented
5#42566C216yesmaximal, complemented
6#42539C216yesmaximal, complemented
7#42532C216yesmaximal, complemented
8#37513C213yesmaximal, complemented
9#37493C216yesmaximal, complemented
10#36670C213yesmaximal, complemented
11#36091C212yesmaximal, complemented
12#36076C212yesmaximal, complemented
13#36059C212yesmaximal, complemented
14#36049C212yesmaximal, complemented
15#36040C211yesmaximal, characteristic, complemented
16#36029C212yesmaximal, complemented
17#36029C211yesmaximal, characteristic, complemented
18#34295C212yesmaximal, complemented
19#34258C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#557C2211yescharacteristic, complemented
22C2×#550C2212yes—
23C2×#550C2212yes—
24C2×#550C2212yes—
25C2×#550C2211yescharacteristic, complemented
26C2×#520C2211yescharacteristic
27C2×#520C2212yescomplemented
28C2×C4×#41C2211yescharacteristic
29#2833C2211yescharacteristic, complemented
30#2832C2213yescomplemented
31#2831C2216yescomplemented
32#2830C2213yescomplemented
33#2829C2216yescomplemented
34#2828C2213yescomplemented
35#2828C2216yescomplemented
36#2827C2216yescomplemented
37#2826C2216yescomplemented
38#2825C2216yescomplemented
39#2824C2216yescomplemented
40#2756C22112yescomplemented
41#2749C22112yescomplemented
42#2735C2216yescomplemented
43#2703C22112yescomplemented
44#2688C22112yescomplemented
45#2684C22112yescomplemented
46#2678C22112yescomplemented
47#2670C2216yescomplemented
48#2668C2216yescomplemented
49#2668C2216yescomplemented
50#2661C22112yescomplemented
51#2648C22112yescomplemented
52#2644C2216yescomplemented
53#2641C2216yescomplemented
54#2635C22112yescomplemented
55#2631C22112yescomplemented
56#2628C2213yescomplemented
57#2624C2216yescomplemented
58#2622C22112yescomplemented
59#2619C2216yescomplemented
60#2619C2213yescomplemented
61#2617C22112yescomplemented
62#2615C2216yes—
63#2580C2213yescomplemented
64#2572C2216yescomplemented
65#2563C2213yescomplemented
66#2562C2216yescomplemented
67#2555C2216yescomplemented
68#2548C2216yescomplemented
69#2541C2213yescomplemented
70#2541C2216yescomplemented
71#2535C2216yescomplemented
72#2535C2213yescomplemented
73#2513C2216yescomplemented
74#2513C2216yescomplemented
75#2513C2216yescomplemented
76#2504C2216yescomplemented
77#2495C2216yescomplemented
78#2495C2216yescomplemented
79#2495C2216yescomplemented
80#2491C2216yescomplemented
81#2491C2216yescomplemented
82#2490C2216yescomplemented
83#2490C2216yescomplemented
84#2486C2216yescomplemented
85#2454C2216yescomplemented
86#2445C2216yescomplemented
87#2445C2216yescomplemented
88#2442C2216yescomplemented
89#2433C2216yes—
90#2433C2216yes—
91#2433C2216yes—
92#2428C2216yescomplemented
93#2428C2216yescomplemented
94#2428C2216yescomplemented
95#2424C22112yescomplemented
96#2420C2216yescomplemented
97#2420C2216yescomplemented
98#2418C22112yescomplemented
99#2416C2216yescomplemented
100#2416C2216yescomplemented
101#2416C2216yescomplemented
102#2408C2216yes—
103#2408C2216yes—
104#2408C2216yes—
105#2401C2216yescomplemented
106#2398C2216yescomplemented
107#2396C2213yescomplemented
108#2395C2216yescomplemented
109#2392C2216yescomplemented
110#2392C2213yescomplemented
111#2388C2216yes—
112#2366C2216yescomplemented
113#2363C2216yescomplemented
114#2361C2216yescomplemented
115#2352C2216yescomplemented
116#2351C2212yescomplemented
117#2351C2211yescharacteristic, complemented
118#2351C2211yescharacteristic, complemented
119#2351C2212yescomplemented
120#2341C2212yes—
121#2341C2212yes—
122#2341C2212yes—
123#2341C2212yes—
124#2341C2212yes—
125#2341C2212yescomplemented
126#2341C2212yescomplemented
127D4×C22⋊C4C2216yes—
128D4×C22⋊C4C2216yes—
129#2328C2216yescomplemented
130#2324C2216yescomplemented
131#2311C2213yes—
132#2309C2213yes—
133C4×#121C2216yescomplemented
134#2297C2213yes—
135C2×#390C2213yes—
136#2290C2216yescomplemented
137#2276C2212yescomplemented
138C2×H(5,𝔽2)—28no—
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—44no—
141C22×#41C2312yes—
142C22×#41C2312yes—
143C22×#41C2311yescharacteristic
144C22×#41C2313yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147#557—44no—
148#550—216no—
149#550—48no—
150#550—48no—
151#550—44no—
152C2×C4⋊Q8C2313yes—
153C2×#127C2316yes—
154C2×#127C2313yes—
155C2×#127C2316yes—
156C2×#127C2316yes—
157C2×#125C2316yes—
158C2×#124C23112yes—
159C2×#123C23112yes—
160C2×#121C2316yes—
161C2×#121C2316yes—
162C2×#121C2316yes—
163C2×#121C2316yes—
164C2×#121C2316yes—
165C2×#121C2316yes—
166C2×#121C2316yes—
167C2×#121C23112yes—
168C2×#121C23112yes—
169C2×#121C23112yes—
170C2×#120C23112yes—
171C2×#120C23112yes—
172C2×#120C23112yes—
173#520—44no—
174#520—48no—
175C4×#41—44no—
176C2×C4×Q8C2311yescharacteristic
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2311yescharacteristic
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2313yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2316yes—
185C2×C4×D4C2313yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C2316yes—
188C2×C4×D4C2313yes—
189C2×C4×D4C2316yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2313yes—
192C2×C4×D4C23112yes—
193C2×#117C2313yes—
194C2×#117C2313yes—
195C2×#117C2316yes—
196C22×C4⋊C4C2313yes—
197C22×C4⋊C4C2316yes—
198C22×C22⋊C4C23112yes—
199C22×C42C2313yes—
200#401C2312yes—
201#400C2316yes—
202#400C2312yes—
203#400C2316yes—
204#400C2312yes—
205#400C2316yes—
206#400C2316yes—
207#400C2316yes—
208#400C2311yescharacteristic
209#399C2313yes—
210#399C2316yes—
211#399C2316yes—
212#398C2312yes—
213#398C2316yes—
214#398C2316yes—
215#398C2311yescharacteristic
216#397C2316yes—
217#397C2316yes—
218#397C2316yes—
219#397C2316yes—
220#397C2316yes—
221#397C2316yes—
222#397C2316yes—
223#397C2313yes—
224#397C2316yes—
225#397C2316yes—
226#397C23112yes—
227#397C23112yes—
228#397C23112yes—
229#397C23112yes—
230#396C2316yes—
231#396C2316yes—
232#396C2316yes—
233#396C2316yes—
234#396C2316yes—
235#395C2313yes—
236#395C2312yes—
237#394C23112yes—
238#394C2316yes—
239#394C2316yes—
240#394C2316yes—
241#394C2316yes—
242#394C2316yes—
243#394C2316yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2313yes—
250#394C23112yes—
251#394C23112yes—
252#394C2316yes—
253#394C23112yes—
254#394C23112yes—
255#394C23112yes—
256#393C2313yes—
257#393C2316yes—
258#393C2316yes—
259#393C2316yes—
260#393C2316yes—
261#392C2316yes—
262#392C2313yes—
263#392C2316yes—
264#392C2316yes—
265#392C2316yes—
266#392C23112yes—
267#392C23112yes—
268#392C23112yes—
269#392C23112yes—
270#392C23112yes—
271#392C2316yes—
272#392C2316yes—
273#391C2313yes—
274#391C2311yescharacteristic
275#390C2316yes—
276#390C2313yes—
277#390C2316yes—
278#390C2316yes—
279#390C2316yes—
280#390C2313yes—
281#390C23112yes—
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#388C23112yes—
301#388C23112yes—
302#388C2316yes—
303#388C2316yes—
304#388C23112yes—
305#388C23112yes—
306#388C23112yes—
307#388C23112yes—
308#387C2312yes—
309#387C2316yes—
310#386C23112yes—
311#386C2316yes—
312#386C2316yes—
313#386C2316yes—
314#386C2316yes—
315#386C23112yes—
316#386C23112yes—
317#386C23112yes—
318#386C23112yes—
319#386C23112yes—
320#386C23112yes—
321#386C23112yes—
322#386C23112yes—
323#385C2316yes—
324#385C2316yes—
325#385C23112yes—
326#383C23112yes—
327#382C2316yes—
328#382C2313yes—
329#382C2316yes—
330#382C2313yes—
331#381C23112yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#380C23112yes—
337#380C2316yes—
338#380C2316yes—
339#380C2316yes—
340#379C2316yes—
341#379C2316yes—
342#379C23112yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2313yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2313yes—
349C4×C4⋊C4C2316yes—
350C4×C22⋊C4C23112yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358#376C2316yes—
359C25C2416yes—
360H(5,𝔽2)—464no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—28no—
369C2×#41—212no—
370C2×#41—46no—
371C2×#41—46no—
372C2×#41#4118yes—
373C22×Q8C2411yescharacteristic
374C22×Q8C2413yes—
375C22×Q8C2411yescharacteristic
376C22×D4—224no—
377C22×D4—212no—
378C22×D4—46no—
379C22×D4—46no—
380C22×D4—412no—
381C22×D4—412no—
382C22×D4C2416yes—
383C22×D4C2416yes—
384C22×D4C2413yes—
385C22×D4C24112yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2413yes—
389C22×D4C2416yes—
390C22×D4C2416yes—
391C22×D4C2413yes—
392C22×D4C24112yes—
393C22×D4C24112yes—
394C22×D4C2416yes—
395C23×C4C2416yes—
396C23×C4C2416yes—
397C23×C4C2413yes—
398C23×C4C2416yes—
399C23×C4C2416yes—
400C23×C4C24112yes—
401C4⋊Q8—46no—
402#127—224no—
403#127—412no—
404#127—46no—
405#127—412no—
406#125—412no—
407#124—812no—
408#123—812no—
409#121—224no—
410#121—224no—
411#121—412no—
412#121—412no—
413#121—412no—
414#121—412no—
415#121—412no—
416#121—812no—
417#121—812no—
418#121—812no—
419#120—812no—
420#120—812no—
421#120—812no—
422C4×Q8—28no—
423C4×Q8—28no—
424C4×Q8—24no—
425C4×Q8—28no—
426C4×Q8—24no—
427C4×Q8—28no—
428C4×Q8—46no—
429C4×D4—224no—
430C4×D4—412no—
431C4×D4—412no—
432C4×D4—412no—
433C4×D4—46no—
434C4×D4—46no—
435C4×D4—412no—
436C4×D4—46no—
437C4×D4—412no—
438C4×D4—812no—
439#117—412no—
440#117—46no—
441#117—46no—
442C2×C4⋊C4—412no—
443C2×C4⋊C4—46no—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2413yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2413yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2413yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C2416yes—
463C2×C4⋊C4C2416yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2416yes—
467C2×C22⋊C4—812no—
468C2×C22⋊C4C2416yes—
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C24112yes—
473C2×C22⋊C4C24112yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2413yes—
476C2×C22⋊C4C2413yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C24112yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C24112yes—
498C2×C22⋊C4C24112yes—
499C2×C22⋊C4C2416yes—
500C2×C22⋊C4C2416yes—
501C2×C42—46no—
502C2×C42C2413yes—
503C2×C42C2416yes—
504C2×C42C2416yes—
505C2×C42C2413yes—
506C2×C42C2416yes—
507C2×C42C2416yes—
508C2×C42C2413yes—
509C2×C42C24112yes—
510C2×C42C2411yescharacteristic
511#95C2412yes—
512#95C2416yes—
513#95C2416yes—
514#95C2416yes—
515#95C2416yes—
516#95C2412yes—
517#95C2412yes—
518#95C2412yes—
519#95C2412yes—
520#95C2412yes—
521#95C2412yes—
522#95C2412yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C24112yes—
530#95C2412yes—
531#95C2412yes—
532#95C2411yescharacteristic
533#95C2411yescharacteristic
534#95C2416yes—
535#95C2416yes—
536#95C2413yes—
537#95C2413yes—
538#95C24112yes—
539#95C2416yes—
540#95C2416yes—
541C24—212no—
542C24—46no—
543C24—46no—
544C24—412no—
545C24—412no—
546C24C2516yes—
547C24C2516yes—
548C24C2513yes—
549#41—232no—
550#41—448no—
551#41—432no—
552#41—432no—
553C2×Q8—22no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—43no—
557C2×Q8—46no—
558C2×Q8C2×#4114yes—
559C2×Q8H(5,𝔽2)14yes—
560C2×Q8H(5,𝔽2)14yes—
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—224no—
564C2×D4—212no—
565C2×D4—26no—
566C2×D4—212no—
567C2×D4—26no—
568C2×D4—26no—
569C2×D4—212no—
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—212no—
573C2×D4—43no—
574C2×D4—43no—
575C2×D4—46no—
576C2×D4—46no—
577C2×D4—448no—
578C2×D4—46no—
579C2×D4—43no—
580C2×D4—46no—
581C2×D4—412no—
582C2×D4—46no—
583C2×D4—46no—
584C2×D4—46no—
585C2×D4—412no—
586C2×D4—46no—
587C2×D4—46no—
588C2×D4—46no—
589C2×D4—46no—
590C2×D4—412no—
591C2×D4—412no—
592C2×D4—412no—
593C2×D4—412no—
594C2×D4—412no—
595C2×D4—46no—
596C2×D4—412no—
597C2×D4—412no—
598C2×D4—496no—
599C2×D4C2×#41112yes—
600C22×C4—26no—
601C22×C4—26no—
602C22×C4—212no—
603C22×C4—212no—
604C22×C4—212no—
605C22×C4—212no—
606C22×C4—212no—
607C22×C4—212no—
608C22×C4—46no—
609C22×C4—46no—
610C22×C4—46no—
611C22×C4—412no—
612C22×C4—412no—
613C22×C4—46no—
614C22×C4—412no—
615C22×C4—412no—
616C22×C4C2×#41112yes—
617C22×C4C2512yes—
618C22×C4C2512yes—
619C22×C4C2516yes—
620C22×C4C2516yes—
621C22×C4C2513yes—
622C22×C4C2512yes—
623C22×C4C2516yes—
624C22×C4C2511yescharacteristic
625C22×C4C2516yes—
626C22×C4C2512yes—
627C22×C4C2511yescharacteristic
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2513yes—
631C22×C4C2511yescharacteristic
632C22×C4C2513yes—
633C4⋊C4—24no—
634C4⋊C4—212no—
635C4⋊C4—212no—
636C4⋊C4—212no—
637C4⋊C4—26no—
638C4⋊C4—26no—
639C4⋊C4—212no—
640C4⋊C4—43no—
641C4⋊C4—46no—
642C4⋊C4—41no—
643C4⋊C4—42no—
644C4⋊C4—41no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—46no—
648C4⋊C4—41no—
649C4⋊C4—46no—
650C4⋊C4—46no—
651C4⋊C4—46no—
652C4⋊C4—46no—
653C4⋊C4—46no—
654C4⋊C4—46no—
655C4⋊C4—46no—
656C22⋊C4—212no—
657C22⋊C4—212no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—412no—
661C22⋊C4—412no—
662C22⋊C4—46no—
663C22⋊C4—46no—
664C22⋊C4—43no—
665C22⋊C4—43no—
666C22⋊C4—46no—
667C22⋊C4—46no—
668C22⋊C4—46no—
669C22⋊C4—46no—
670C22⋊C4—46no—
671C22⋊C4—46no—
672C22⋊C4—46no—
673C22⋊C4—412no—
674C22⋊C4—46no—
675C22⋊C4—46no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C22⋊C4—46no—
679C22⋊C4—46no—
680C22⋊C4—412no—
681C22⋊C4—412no—
682C22⋊C4—46no—
683C22⋊C4—46no—
684C22⋊C4—46no—
685C22⋊C4—412no—
686C22⋊C4—412no—
687C22⋊C4—46no—
688C22⋊C4—46no—
689C42—212no—
690C42—212no—
691C42—212no—
692C42—26no—
693C42—26no—
694C42—212no—
695C42—41no—
696C42—43no—
697C42—412no—
698C23—23no—
699C23—23no—
700C23—26no—
701C23—26no—
702C23—26no—
703C23—26no—
704C23—26no—
705C23—26no—
706C23—26no—
707C23—26no—
708C23—26no—
709C23—26no—
710C23—26no—
711C23—26no—
712C23—26no—
713C23—26no—
714C23—26no—
715C23—26no—
716C23—424no—
717C23—824no—
718C23—1612no—
719C23—166no—
720C23—166no—
721C23C22×#4116yes—
722C23C2611yescharacteristic
723Q8—44no—
724Q8—86no—
725Q8#538116yes—
726D4—224no—
727D4—412no—
728D4—424no—
729D4—424no—
730D4—424no—
731D4—824no—
732D4—812no—
733D4—812no—
734D4—86no—
735D4—812no—
736D4—166no—
737D4—1612no—
738D4—1612no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—224no—
742C2×C4—22no—
743C2×C4—26no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—26no—
752C2×C4—26no—
753C2×C4—23no—
754C2×C4—26no—
755C2×C4—23no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—26no—
761C2×C4—26no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—26no—
770C2×C4—26no—
771C2×C4—26no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—22no—
780C2×C4—424no—
781C2×C4—424no—
782C2×C4—812no—
783C2×C4—1612no—
784C2×C4—166no—
785C2×C4C22×#4112yes—
786C2×C4C22×#4116yes—
787C2×C4C2×H(5,𝔽2)16yes—
788C2×C4C2×H(5,𝔽2)16yes—
789C22—212no—
790C22—26no—
791C22—46no—
792C22—43no—
793C22—43no—
794C22—46no—
795C22—46no—
796C22—46no—
797C22—46no—
798C22—46no—
799C22—46no—
800C22—46no—
801C22—46no—
802C22—46no—
803C22—46no—
804C22—46no—
805C22—46no—
806C22—46no—
807C22—46no—
808C22—1624no—
809C22C23×#4111yescharacteristic
810C22C22×H(5,𝔽2)11yescharacteristic
811C22C22×H(5,𝔽2)11yescharacteristic
812C22H(7,𝔽2)12yes—
813C22H(7,𝔽2)12yes—
814C4—22no—
815C4—42no—
816C4—46no—
817C4—43no—
818C4—46no—
819C4—43no—
820C4—42no—
821C4—41no—
822C4—42no—
823C4—46no—
824C4—41no—
825C4—46no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4C2×#538112yes—
830C2—46no—
831C2—86no—
832C2—86no—
833C2C22×#53811yescharacteristic
834C2#6285812yes—
835C2#6306612yes—
836C2#6306611yescharacteristic
837C2#6306611yescharacteristic
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. #42982C2semidirect
2. #42977C2semidirect
3. #42945C2semidirect
4. #42589C2semidirect
5. #42566C2semidirect
6. #42539C2semidirect
7. #42532C2semidirect
8. #37513C2semidirect
9. #37493C2semidirect
10. #36670C2semidirect
11. #36091C2semidirect
12. #36076C2semidirect
13. #36059C2semidirect
14. #36049C2semidirect
15. #36040C2semidirect
16. #36029C2semidirect
17. #36029C2semidirect
18. #34295C2semidirect
19. #34258C2semidirect
21. C2×#557C22semidirect
25. C2×#550C22semidirect
27. C2×#520C22semidirect
29. #2833C22semidirect
30. #2832C22semidirect
31. #2831C22semidirect
32. #2830C22semidirect
33. #2829C22semidirect
34. #2828C22semidirect
35. #2828C22semidirect
36. #2827C22semidirect
37. #2826C22semidirect
38. #2825C22semidirect
39. #2824C22semidirect
40. #2756C22semidirect
41. #2749C22semidirect
42. #2735C22semidirect
43. #2703C22semidirect
44. #2688C22semidirect
45. #2684C22semidirect
46. #2678C22semidirect
47. #2670C22semidirect
48. #2668C22semidirect
49. #2668C22semidirect
50. #2661C22semidirect
51. #2648C22semidirect
52. #2644C22semidirect
53. #2641C22semidirect
54. #2635C22semidirect
55. #2631C22semidirect
56. #2628C22semidirect
57. #2624C22semidirect
58. #2622C22semidirect
59. #2619C22semidirect
60. #2619C22semidirect
61. #2617C22semidirect
63. #2580C22semidirect
64. #2572C22semidirect
65. #2563C22semidirect
66. #2562C22semidirect
67. #2555C22semidirect
68. #2548C22semidirect
69. #2541C22semidirect
70. #2541C22semidirect
71. #2535C22semidirect
72. #2535C22semidirect
73. #2513C22semidirect
74. #2513C22semidirect
75. #2513C22semidirect
76. #2504C22semidirect
77. #2495C22semidirect
78. #2495C22semidirect
79. #2495C22semidirect
80. #2491C22semidirect
81. #2491C22semidirect
82. #2490C22semidirect
83. #2490C22semidirect
84. #2486C22semidirect
85. #2454C22semidirect
86. #2445C22semidirect
87. #2445C22semidirect
88. #2442C22semidirect
92. #2428C22semidirect
93. #2428C22semidirect
94. #2428C22semidirect
95. #2424C22semidirect
96. #2420C22semidirect
97. #2420C22semidirect
98. #2418C22semidirect
99. #2416C22semidirect
100. #2416C22semidirect
101. #2416C22semidirect
105. #2401C22semidirect
106. #2398C22semidirect
107. #2396C22semidirect
108. #2395C22semidirect
109. #2392C22semidirect
110. #2392C22semidirect
112. #2366C22semidirect
113. #2363C22semidirect
114. #2361C22semidirect
115. #2352C22semidirect
116. #2351C22semidirect
117. #2351C22semidirect
118. #2351C22semidirect
119. #2351C22semidirect
125. #2341C22semidirect
126. #2341C22semidirect
129. #2328C22semidirect
130. #2324C22semidirect
133. C4×#121C22semidirect
136. #2290C22semidirect
137. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#429822
#429772
#429452
#425892
#425662
#425392
#425322
#375132
#374932
#366702
#360912
#360762
#360592
#360492
#360402
#360292
#342952
#342582