Finite Group Databasebeta

← #7687442

Subgroups — #7687442

Order 512.

4798 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59509C213yesmaximal, complemented
2#59497C213yesmaximal, complemented
3#59446C213yesmaximal, complemented
4#59332C213yesmaximal, complemented
5#59260C213yesmaximal, complemented
6#45379C213yesmaximal, complemented
7#45007C213yesmaximal, complemented
8#44990C213yesmaximal, complemented
9#44902C213yesmaximal, complemented
10#39474C213yesmaximal, complemented
11#39080C213yesmaximal, complemented
12#39076C213yesmaximal, complemented
13#38926C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36458C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36370C213yesmaximal, complemented
20#36171C213yesmaximal, complemented
21#36076C211yesmaximal, characteristic
22#36005C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35868C211yesmaximal, characteristic, complemented
25#34898C213yesmaximal, complemented
26#34263C211yesmaximal, characteristic, complemented
27#34263C211yesmaximal, characteristic, complemented
28#34197C211yesmaximal, characteristic, complemented
29#34184C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2864C2213yes—
39#2860C2213yes—
40#2860C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2793C2216yes—
44#2781C2216yes—
45#2779C2216yes—
46#2773C2216yes—
47#2765C2216yes—
48#2761C2216yes—
49#2754C2216yes—
50#2750C2216yes—
51#2744C2216yes—
52#2743C2216yes—
53#2721C2216yes—
54#2707C2216yes—
55#2695C2216yes—
56#2687C2216yes—
57#2647C2213yes—
58#2647C2213yes—
59#2624C2213yes—
60#2624C2213yes—
61#2611C2216yes—
62#2601C2216yes—
63#2580C2213yes—
64#2580C2213yes—
65#2577C2213yes—
66#2577C2213yes—
67#2575C2213yes—
68#2575C2216yes—
69#2575C2213yes—
70#2571C2213yes—
71#2570C2213yes—
72#2570C2213yes—
73#2570C2213yes—
74#2570C2213yes—
75#2570C2213yes—
76#2566C2213yes—
77#2566C2213yes—
78#2565C2213yes—
79#2562C2213yes—
80#2558C2216yes—
81#2552C2213yes—
82#2536C2213yes—
83#2528C2216yes—
84#2527C2216yes—
85#2524C2213yes—
86#2524C2211yescharacteristic
87#2517C2216yes—
88#2513C2213yes—
89#2513C2213yes—
90#2513C2213yes—
91#2513C2213yes—
92#2512C2213yes—
93#2512C2213yes—
94#2509C2213yes—
95#2509C2213yes—
96#2509C2213yes—
97#2508C2213yes—
98#2508C2213yes—
99#2508C2213yes—
100#2507C2213yes—
101#2507C2213yes—
102#2507C2213yes—
103#2506C2213yes—
104#2506C2213yes—
105#2506C2213yes—
106#2504C2213yes—
107#2501C2213yes—
108#2498C2216yes—
109#2497C2213yes—
110#2496C2213yes—
111#2496C2213yes—
112#2495C2213yes—
113#2495C2213yes—
114#2494C2213yes—
115#2494C2213yes—
116#2494C2213yes—
117#2493C2216yes—
118#2488C2216yes—
119#2487C2213yes—
120#2486C2213yes—
121#2479C2216yes—
122#2479C2216yes—
123#2468C2216yes—
124#2468C2213yes—
125#2468C2213yes—
126#2460C2216yes—
127#2458C2216yes—
128#2458C2216yes—
129#2454C2213yes—
130#2454C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2445C2213yes—
134#2445C2213yes—
135#2445C2213yes—
136#2445C2213yes—
137#2441C2213yes—
138#2441C2213yes—
139#2439C2213yes—
140#2439C2213yes—
141#2423C2213yes—
142#2422C2213yes—
143#2422C2213yes—
144#2421C2213yes—
145#2420C2213yes—
146#2420C2213yes—
147#2419C2216yes—
148#2419C2216yes—
149#2402C2213yes—
150#2402C2213yes—
151#2395C2213yes—
152#2395C2213yes—
153#2370C2213yes—
154#2370C2213yes—
155#2366C2213yes—
156#2365C2213yes—
157#2363C2213yes—
158#2363C2213yes—
159#2359C2216yes—
160#2359C2216yes—
161#2357C2213yes—
162#2357C2213yes—
163#2357C2213yes—
164#2357C2213yes—
165#2355C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2354C2213yes—
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185#2349C2213yes—
186#2349C2213yes—
187#2349C2213yes—
188#2349C2213yes—
189#2346C2213yes—
190#2346C2213yes—
191#2345C2213yes—
192#2345C2213yes—
193#2344C2213yes—
194#2344C2213yes—
195#2343C2216yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2319C2213yes—
205#2319C2213yes—
206#2319C2213yes—
207#2319C2213yes—
208#2317C2213yes—
209#2317C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#127C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×#126C2213yes—
218C4×#126C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×#121C2213yes—
222C4×#121C2213yes—
223#2298C2213yes—
224#2298C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2285C2213yes—
228#2283C2213yes—
229#2283C2213yes—
230C2×#382C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2213yes—
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#550—28no—
242C2×C4⋊Q8C2313yes—
243C2×#127C2313yes—
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2316yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#123C2316yes—
252C2×#123C2316yes—
253C2×#123C2316yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×#121C2313yes—
257C2×#121C2313yes—
258#520—28no—
259#520—28no—
260C4×#41—28no—
261C4×#41—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2316yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2316yes—
295C2×#117C2316yes—
296C22×C4⋊C4C2313yes—
297C22×C4⋊C4C2313yes—
298C22×C42C2313yes—
299C22×C42C2313yes—
300#401C2316yes—
301#400C2311yescharacteristic
302#400C2313yes—
303#400C2311yescharacteristic
304#400C2313yes—
305#400C2316yes—
306#400C2313yes—
307#400C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2316yes—
311#400C2316yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2316yes—
317#399C2313yes—
318#399C2316yes—
319#399C2313yes—
320#399C2316yes—
321#399C2316yes—
322#398C2311yescharacteristic
323#398C2313yes—
324#398C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2313yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2311yescharacteristic
336#398C2313yes—
337#397C2313yes—
338#397C2316yes—
339#397C2313yes—
340#397C2313yes—
341#397C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2316yes—
352#396C2316yes—
353#396C2316yes—
354#394C2313yes—
355#394C2313yes—
356#394C2316yes—
357#394C2316yes—
358#394C2316yes—
359#394C2316yes—
360#394C2313yes—
361#394C2313yes—
362#393C2316yes—
363#393C2316yes—
364#391C2316yes—
365#391C2313yes—
366#391C2313yes—
367#390C2313yes—
368#390C2313yes—
369#390C2316yes—
370#390C2316yes—
371#390C2313yes—
372#390C2313yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2316yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2316yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#388C2313yes—
425#388C2313yes—
426#388C2313yes—
427#388C2313yes—
428#388C2313yes—
429#388C2313yes—
430#388C2313yes—
431#388C2313yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2313yes—
437#388C2316yes—
438#388C2316yes—
439#388C2316yes—
440#388C2316yes—
441#388C2316yes—
442#388C2316yes—
443#388C2313yes—
444#388C2313yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2313yes—
449#388C2316yes—
450#388C2316yes—
451#388C2313yes—
452#388C2313yes—
453#387C2311yescharacteristic
454#387C2313yes—
455#387C2313yes—
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2311yescharacteristic
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2316yes—
464#387C2316yes—
465#387C2316yes—
466#387C2316yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2316yes—
483#387C2316yes—
484#387C2311yescharacteristic
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2311yescharacteristic
489#387C2311yescharacteristic
490#386C2316yes—
491#386C2316yes—
492#386C2316yes—
493#386C2316yes—
494#386C2316yes—
495#385C2313yes—
496#385C2313yes—
497#385C2316yes—
498#385C2316yes—
499#385C2316yes—
500#385C2316yes—
501#385C2316yes—
502#385C2316yes—
503#385C2313yes—
504#385C2316yes—
505#385C2313yes—
506#385C2316yes—
507#385C2316yes—
508#384C2313yes—
509#384C2313yes—
510#384C2313yes—
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#384C2313yes—
516#383C2311yescharacteristic
517#383C2313yes—
518#383C2311yescharacteristic
519#383C2313yes—
520#382C2313yes—
521#382C2313yes—
522#382C2313yes—
523#382C2313yes—
524#382C2313yes—
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2316yes—
533#382C2313yes—
534#382C2316yes—
535#382C2311yescharacteristic
536#382C2313yes—
537#381C2316yes—
538#381C2316yes—
539#381C2316yes—
540#381C2313yes—
541#381C2313yes—
542#381C2316yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2316yes—
552#380C2316yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2311yescharacteristic
600C4×C4⋊C4C2311yescharacteristic
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616#376C2313yes—
617#376C2313yes—
618#376C2316yes—
619C2×#95C2316yes—
620C2×#95C2316yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×D4C2413yes—
633C22×D4C2413yes—
634C22×D4C2413yes—
635C22×D4C2416yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2416yes—
639C23×C4C2416yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C4⋊Q8—212no—
645#127—212no—
646#126—46no—
647#126—46no—
648#126—86no—
649#125—212no—
650#125—212no—
651#125—46no—
652#125—86no—
653#123—412no—
654#123—412no—
655#123—86no—
656C22⋊Q8—46no—
657C22⋊Q8—46no—
658#121—212no—
659#121—212no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—212no—
673C4×Q8—46no—
674C4×Q8—46no—
675C4×Q8#4118yes—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682C4×D4—212no—
683C4×D4—212no—
684C4×D4—212no—
685C4×D4—46no—
686C4×D4—46no—
687C4×D4—86no—
688#117—212no—
689#117—212no—
690#117—212no—
691#117—212no—
692#117—412no—
693#117—86no—
694C2×C4⋊C4—212no—
695C2×C4⋊C4—212no—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2416yes—
770C2×C22⋊C4C2416yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C42—212no—
789C2×C42—212no—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2411yescharacteristic
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2411yescharacteristic
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2416yes—
826#95C2416yes—
827#95C2416yes—
828#95C2416yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2416yes—
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2416yes—
860#95C2416yes—
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2416yes—
869#95C2416yes—
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2416yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2416yes—
890C24C2513yes—
891C24C2513yes—
892#41—232no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—43no—
897C2×Q8C2×#4114yes—
898C2×Q8C2×#4114yes—
899C2×Q82−1+414yes—
900C2×D4—26no—
901C2×D4—212no—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—43no—
909C2×D4—46no—
910C2×D4—46no—
911C2×D4C2×#41112yes—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—212no—
915C22×C4—212no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—46no—
924C22×C4—46no—
925C22×C4—43no—
926C22×C4—43no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—43no—
933C22×C4—46no—
934C22×C4—46no—
935C22×C4C2×#41112yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—212no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—46no—
997C4⋊C4—43no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—46no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—46no—
1009C4⋊C4—43no—
1010C4⋊C4—46no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—46no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4C2×#41112yes—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—212no—
1031C22⋊C4—212no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—26no—
1037C22⋊C4—46no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—46no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—46no—
1046C22⋊C4—46no—
1047C22⋊C4—46no—
1048C22⋊C4—46no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C42—22no—
1058C42—22no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—22no—
1075C42—26no—
1076C42—22no—
1077C42—22no—
1078C42—46no—
1079C42—43no—
1080C42—46no—
1081C42—43no—
1082C42—43no—
1083C42—43no—
1084C42—43no—
1085C42—43no—
1086C42—43no—
1087C42C2×#41112yes—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23—23no—
1097C23—23no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23C22×#4116yes—
1102C23C2611yescharacteristic
1103Q8—412no—
1104Q8#552116yes—
1105D4—224no—
1106D4—412no—
1107D4—412no—
1108D4—812no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—224no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—412no—
1189C2×C4—86no—
1190C2×C4—86no—
1191C2×C4—86no—
1192C2×C4—86no—
1193C2×C4—812no—
1194C2×C4—812no—
1195C2×C4C22×#4112yes—
1196C2×C4C22×#4116yes—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4116yes—
1200C2×C4C2×2−1+416yes—
1201C2×C4#58512yes—
1202C2×C4#58512yes—
1203C2×C4#58512yes—
1204C22—26no—
1205C22—26no—
1206C22—26no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22C23×#4111yescharacteristic
1219C22C23×#4111yescharacteristic
1220C22C22×2−1+411yescharacteristic
1221C22C2×#58511yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22C2×#58511yescharacteristic
1224C22H(7,𝔽2)11yescharacteristic
1225C4—22no—
1226C4—22no—
1227C4—22no—
1228C4—26no—
1229C4—22no—
1230C4—22no—
1231C4—41no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—41no—
1236C4—41no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—41no—
1241C4—43no—
1242C4—41no—
1243C4—41no—
1244C4—43no—
1245C4—43no—
1246C4—41no—
1247C4—41no—
1248C4—43no—
1249C4—41no—
1250C4—43no—
1251C4—43no—
1252C4—41no—
1253C4C2×#552112yes—
1254C2—46no—
1255C2—83no—
1256C2C22×#55211yescharacteristic
1257C2#6281011yescharacteristic
1258C2#6281611yescharacteristic
1259C2#6295211yescharacteristic
1260C2#6300611yescharacteristic
1261C2#6301011yescharacteristic
1262C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59509C2semidirect
2. #59497C2semidirect
3. #59446C2semidirect
4. #59332C2semidirect
5. #59260C2semidirect
6. #45379C2semidirect
7. #45007C2semidirect
8. #44990C2semidirect
9. #44902C2semidirect
10. #39474C2semidirect
11. #39080C2semidirect
12. #39076C2semidirect
13. #38926C2semidirect
14. #36585C2semidirect
15. #36475C2semidirect
16. #36458C2semidirect
17. #36431C2semidirect
18. #36431C2semidirect
19. #36370C2semidirect
20. #36171C2semidirect
23. #35971C2semidirect
24. #35868C2semidirect
25. #34898C2semidirect
26. #34263C2semidirect
27. #34263C2semidirect
28. #34197C2semidirect
29. #34184C2semidirect
30. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#595092
#594972
#594462
#593322
#592602
#453792
#450072
#449902
#449022
#394742
#390802
#390762
#389262
#365852
#364752
#364582
#364312
#363702
#361712
#360762
#360052
#359712
#358682
#348982
#342632
#341972
#341842
C4×#5572
C4×#5502