Finite Group Databasebeta

← #7681591

Subgroups — #7681591

Order 512.

4777 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60020C214yesmaximal, complemented
2#59976C214yesmaximal, complemented
3#59619C214yesmaximal, complemented
4#59592C214yesmaximal, complemented
5#44422C214yesmaximal, complemented
6#44307C214yesmaximal, complemented
7#44284C214yesmaximal, complemented
8#44156C214yesmaximal, complemented
9#39545C212yesmaximal, complemented
10#39483C211yesmaximal, characteristic, complemented
11#39426C212yesmaximal, complemented
12#39366C211yesmaximal, characteristic, complemented
13#39152C212yesmaximal, complemented
14#38074C212yesmaximal, complemented
15#38067C212yesmaximal, complemented
16#36609C211yesmaximal, characteristic, complemented
17#36567C211yesmaximal, characteristic, complemented
18#36361C212yesmaximal, complemented
19#35603C212yesmaximal, complemented
20#35598C212yesmaximal, complemented
21#35337C211yesmaximal, characteristic, complemented
22#35296C212yesmaximal, complemented
23#34893C212yesmaximal, complemented
24#34319C212yesmaximal, complemented
25#34272C212yesmaximal, complemented
26#34125C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#544C2212yes—
30C2×#540C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2864C2212yes—
33#2862C2211yescharacteristic
34#2859C2211yescharacteristic
35#2858C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2786C2214yes—
40#2783C2214yes—
41#2777C2214yes—
42#2775C2214yes—
43#2774C2214yes—
44#2773C2214yes—
45#2773C2214yes—
46#2771C2214yes—
47#2768C2214yes—
48#2751C2214yes—
49#2751C2214yes—
50#2750C2214yes—
51#2738C2214yes—
52#2727C2214yes—
53#2715C2214yes—
54#2713C2214yes—
55#2711C2214yes—
56#2707C2214yes—
57#2696C2214yes—
58#2692C2214yes—
59#2687C2214yes—
60#2682C2214yes—
61#2676C2214yes—
62#2674C2214yes—
63#2647C2211yescharacteristic
64#2647C2211yescharacteristic
65#2644C2212yes—
66#2644C2212yes—
67#2628C2212yes—
68#2628C2212yes—
69#2619C2212yes—
70#2604C2214yes—
71#2599C2214yes—
72#2597C2214yes—
73#2596C2214yes—
74#2595C2214yes—
75#2595C2214yes—
76#2595C2214yes—
77#2593C2214yes—
78#2592C2214yes—
79#2590C2214yes—
80#2589C2214yes—
81#2589C2214yes—
82#2589C2214yes—
83#2589C2214yes—
84#2588C2214yes—
85#2588C2214yes—
86#2587C2214yes—
87#2585C2214yes—
88#2584C2212yes—
89#2580C2212yes—
90#2578C2214yes—
91#2573C2214yes—
92#2566C2212yes—
93#2558C2214yes—
94#2557C2214yes—
95#2557C2214yes—
96#2557C2214yes—
97#2556C2214yes—
98#2554C2214yes—
99#2550C2212yes—
100#2540C2214yes—
101#2533C2214yes—
102#2532C2214yes—
103#2529C2214yes—
104#2525C2214yes—
105#2523C2214yes—
106#2522C2214yes—
107#2515C2214yes—
108#2513C2212yes—
109#2513C2212yes—
110#2509C2212yes—
111#2507C2212yes—
112#2507C2212yes—
113#2506C2212yes—
114#2501C2212yes—
115#2500C2212yes—
116#2498C2214yes—
117#2496C2212yes—
118#2495C2212yes—
119#2492C2214yes—
120#2491C2212yes—
121#2491C2214yes—
122#2490C2212yes—
123#2490C2214yes—
124#2489C2214yes—
125#2487C2212yes—
126#2486C2214yes—
127#2485C2212yes—
128#2479C2214yes—
129#2479C2214yes—
130#2479C2214yes—
131#2476C2214yes—
132#2475C2214yes—
133#2474C2214yes—
134#2474C2214yes—
135#2471C2214yes—
136#2471C2214yes—
137#2470C2214yes—
138#2470C2214yes—
139#2469C2214yes—
140#2466C2214yes—
141#2465C2214yes—
142#2462C2214yes—
143#2461C2214yes—
144#2458C2214yes—
145#2455C2214yes—
146#2455C2214yes—
147#2455C2214yes—
148#2454C2212yes—
149#2452C2212yes—
150#2448C2214yes—
151#2448C2214yes—
152#2447C2214yes—
153#2447C2214yes—
154#2443C2214yes—
155#2442C2212yes—
156#2439C2212yes—
157#2430C2214yes—
158#2419C2214yes—
159#2416C2212yes—
160#2414C2212yes—
161#2413C2214yes—
162#2396C2214yes—
163#2396C2214yes—
164#2374C2214yes—
165#2373C2214yes—
166#2370C2212yes—
167#2370C2214yes—
168#2370C2214yes—
169#2370C2214yes—
170#2369C2214yes—
171#2368C2214yes—
172#2368C2214yes—
173#2367C2214yes—
174#2365C2214yes—
175#2363C2212yes—
176#2363C2214yes—
177#2361C2212yes—
178#2361C2214yes—
179#2360C2214yes—
180#2360C2214yes—
181#2359C2214yes—
182#2357C2212yes—
183#2357C2214yes—
184#2357C2212yes—
185#2357C2212yes—
186#2357C2212yes—
187#2352C2212yes—
188#2351C2212yes—
189#2347C2212yes—
190#2347C2212yes—
191#2347C2212yes—
192#2346C2212yes—
193#2344C2212yes—
194#2341C2212yes—
195#2335C2214yes—
196#2334C2214yes—
197#2333C2214yes—
198#2333C2214yes—
199#2331C2212yes—
200#2331C2212yes—
201#2330C2211yescharacteristic
202#2330C2212yes—
203#2328C2211yescharacteristic
204#2324C2212yes—
205#2324C2212yes—
206#2324C2212yes—
207#2319C2212yes—
208#2317C2212yes—
209#2314C2211yescharacteristic
210#2314C2211yescharacteristic
211#2314C2211yescharacteristic
212C4×C4⋊Q8C2212yes—
213C4×C4⋊Q8C2212yes—
214C4×#127C2211yescharacteristic
215C4×#125C2212yes—
216C4×#125C2212yes—
217C4×#125C2212yes—
218C4×#125C2211yescharacteristic
219C4×C22⋊Q8C2214yes—
220C4×#123C2214yes—
221C4×#123C2214yes—
222C4×#121C2212yes—
223C4×#121C2214yes—
224#2296C2212yes—
225#2296C2214yes—
226#2293C2212yes—
227#2293C2212yes—
228#2293C2212yes—
229#2293C2211yescharacteristic
230#2293C2212yes—
231#2293C2211yescharacteristic
232C2×#389C2212yes—
233#2290C2214yes—
234#2283C2212yes—
235#2283C2211yescharacteristic
236#2274C2212yes—
237#2274C2212yes—
238C42×Q8C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C42×D4C2212yes—
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243C22×#41C2311yescharacteristic
244#553—216no—
245#544—216no—
246#540—28no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×#127C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2311yescharacteristic
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C4×#41—28no—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2314yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2314yes—
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310C22×C42C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#392C2314yes—
381#392C2314yes—
382#392C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2312yes—
402#390C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2314yes—
410#390C2312yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2314yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2312yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2314yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2314yes—
502#388C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#384C2311yescharacteristic
570#384C2312yes—
571#384C2311yescharacteristic
572#384C2311yescharacteristic
573#383C2311yescharacteristic
574#383C2314yes—
575#383C2312yes—
576#383C2312yes—
577#383C2311yescharacteristic
578#382C2312yes—
579#382C2311yescharacteristic
580#382C2312yes—
581#382C2312yes—
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#382C2314yes—
585#382C2312yes—
586#382C2312yes—
587#382C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2312yes—
592#381C2311yescharacteristic
593#381C2311yescharacteristic
594#381C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2312yes—
605#380C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2311yescharacteristic
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2312yes—
672#376C2314yes—
673C2×#95C2314yes—
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2312yes—
678C2×#41—24no—
679C2×#41—44no—
680C22×Q8C2411yescharacteristic
681C22×Q8C2414yes—
682C22×Q8C2414yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2414yes—
700C23×C4C2414yes—
701C4⋊Q8—216no—
702C4⋊Q8—28no—
703C4⋊Q8—28no—
704#127—24no—
705#126—216no—
706#126—84no—
707#125—216no—
708#125—28no—
709#125—28no—
710#125—48no—
711#125#4118yescomplemented
712#124—48no—
713#124—84no—
714#124—84no—
715#123—216no—
716#123—216no—
717#123—48no—
718#123—84no—
719#123—84no—
720#123—84no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—48no—
724#121—216no—
725#121—28no—
726#121—28no—
727#121—216no—
728#121—28no—
729#121—48no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×Q8—84no—
735C4×Q8—84no—
736C4×D4—24no—
737C4×D4—28no—
738C4×D4—28no—
739C4×D4—28no—
740C4×D4—216no—
741C4×D4—28no—
742C4×D4—28no—
743C4×D4—84no—
744C4×D4—84no—
745C4×D4—84no—
746C4×D4#4118yes—
747#117—28no—
748#117—24no—
749#117—28no—
750#117—28no—
751#117—24no—
752#117—28no—
753#117—28no—
754#117—24no—
755#117—48no—
756#117—84no—
757#117—84no—
758C2×C4⋊C4—28no—
759C2×C4⋊C4—28no—
760C2×C4⋊C4—84no—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2414yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C42—28no—
859C2×C42—24no—
860C2×C42—84no—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2411yescharacteristic
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2411yescharacteristic
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958C24C2514yes—
959C24C2511yescharacteristic
960C24C2512yes—
961#41—416no—
962C2×Q8—22no—
963C2×Q8—28no—
964C2×Q8—28no—
965C2×Q8—24no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×D4—24no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—42no—
980C2×D4—42no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4C2×#4114yes—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—28no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—28no—
1000C22×C4—24no—
1001C22×C4—22no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—28no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—42no—
1020C22×C4C2×#4118yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—22no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4C2×#4118yes—
1096C4⋊C4C2×#4114yes—
1097C4⋊C4C2×#41116yes—
1098C22⋊C4—24no—
1099C22⋊C4—28no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—24no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4C2×#4118yes—
1142C42—22no—
1143C42—24no—
1144C42—22no—
1145C42—24no—
1146C42—24no—
1147C42—22no—
1148C42—22no—
1149C42—28no—
1150C42—28no—
1151C42—24no—
1152C42—24no—
1153C42—22no—
1154C42—24no—
1155C42—24no—
1156C42—42no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—42no—
1162C42—44no—
1163C42—44no—
1164C42—42no—
1165C42—44no—
1166C42—42no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—44no—
1173C42—42no—
1174C42—44no—
1175C42C2×#4114yes—
1176C42C2×#4114yes—
1177C422−1+414yes—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—24no—
1185C23—21no—
1186C23—24no—
1187C23—21no—
1188C23—21no—
1189C23—24no—
1190C23—24no—
1191C23—24no—
1192C23—22no—
1193C23—22no—
1194C23—24no—
1195C23—24no—
1196C23C22×#4114yes—
1197C23C2611yescharacteristic
1198Q8—28no—
1199Q8—88no—
1200Q8—88no—
1201D4—44no—
1202D4—48no—
1203D4—48no—
1204D4—88no—
1205D4—88no—
1206D4—88no—
1207D4—88no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—216no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—21no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—48no—
1268C2×C4—416no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4—88no—
1274C2×C4—82no—
1275C2×C4—84no—
1276C2×C4—88no—
1277C2×C4C22×#4114yes—
1278C2×C4C22×#4112yes—
1279C2×C4C22×#4112yes—
1280C2×C4C22×#4118yes—
1281C2×C4C22×#4114yes—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4112yes—
1284C2×C4C2×2−1+414yes—
1285C2×C4C2×2−1+412yes—
1286C2×C4#58514yes—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—42no—
1297C22—41no—
1298C22—44no—
1299C22—44no—
1300C22—41no—
1301C22—44no—
1302C22—42no—
1303C22—44no—
1304C22—41no—
1305C22—44no—
1306C22C23×#4111yescharacteristic
1307C22C23×#4111yescharacteristic
1308C22C22×2−1+411yescharacteristic
1309C22C2×#58512yes—
1310C22H(7,𝔽2)12yes—
1311C4—28no—
1312C4—24no—
1313C4—22no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—42no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—44no—
1323C4—41no—
1324C4—44no—
1325C4—42no—
1326C4—44no—
1327C4—41no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—41no—
1334C4#348214yes—
1335C2—44no—
1336C2—84no—
1337C2—81no—
1338C2C2×#348211yescharacteristic
1339C2#6281411yescharacteristic
1340C2#6285811yescharacteristic
1341C2#6292612yes—
1342C2#6301012yes—
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. #60020C2semidirect
2. #59976C2semidirect
3. #59619C2semidirect
4. #59592C2semidirect
5. #44422C2semidirect
6. #44307C2semidirect
7. #44284C2semidirect
8. #44156C2semidirect
9. #39545C2semidirect
10. #39483C2semidirect
11. #39426C2semidirect
12. #39366C2semidirect
13. #39152C2semidirect
14. #38074C2semidirect
15. #38067C2semidirect
16. #36609C2semidirect
17. #36567C2semidirect
18. #36361C2semidirect
19. #35603C2semidirect
20. #35598C2semidirect
21. #35337C2semidirect
22. #35296C2semidirect
23. #34893C2semidirect
24. #34319C2semidirect
25. #34272C2semidirect
26. #34125C2semidirect
27. C4×#540C2semidirect
711. #125#41semidirect

Maximal subgroups

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

subgroupindex
#600202
#599762
#596192
#595922
#444222
#443072
#442842
#441562
#395452
#394832
#394262
#393662
#391522
#380742
#380672
#366092
#365672
#363612
#356032
#355982
#353372
#352962
#348932
#343192
#342722
#341252
C4×#5402