Finite Group Databasebeta

← #7659503

Subgroups — #7659503

Order 512.

4838 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52248C213yesmaximal, complemented
2#42631C213yesmaximal, complemented
3#42601C213yesmaximal, complemented
4#42577C213yesmaximal, complemented
5#42556C213yesmaximal, complemented
6#42516C213yesmaximal, complemented
7#42501C213yesmaximal, complemented
8#40177C213yesmaximal, complemented
9#40165C213yesmaximal, complemented
10#40057C213yesmaximal, complemented
11#40048C213yesmaximal, complemented
12#39732C213yesmaximal, complemented
13#39604C213yesmaximal, complemented
14#37403C213yesmaximal, complemented
15#37350C213yesmaximal, complemented
16#37288C213yesmaximal, complemented
17Q8×#126C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#36432C211yesmaximal, characteristic, complemented
23#35996C211yesmaximal, characteristic, complemented
24#35845C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic
26#35816C211yesmaximal, characteristic, complemented
27#35816C211yesmaximal, characteristic, complemented
28#35801C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34312C211yesmaximal, characteristic, complemented
31#34183C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2864C2213yes—
42#2863C2213yes—
43#2860C2213yes—
44#2859C2213yes—
45#2855C2213yes—
46#2854C2213yes—
47#2827C2216yes—
48#2827C2216yes—
49#2795C2213yes—
50#2793C2216yes—
51#2792C2213yes—
52#2791C2216yes—
53#2790C2216yes—
54#2786C2216yes—
55#2785C2213yes—
56#2783C2213yes—
57#2783C2213yes—
58#2783C2216yes—
59#2782C2216yes—
60#2770C2216yes—
61#2769C2213yes—
62#2757C2216yes—
63#2747C2216yes—
64#2744C2216yes—
65#2744C2213yes—
66#2744C2213yes—
67#2743C2216yes—
68#2740C2216yes—
69#2737C2213yes—
70#2737C2213yes—
71#2723C2216yes—
72#2721C2211yescharacteristic
73#2721C2213yes—
74#2720C2216yes—
75#2718C2216yes—
76#2711C2216yes—
77#2707C2216yes—
78#2705C2213yes—
79#2705C2213yes—
80#2695C2216yes—
81#2694C2213yes—
82#2694C2213yes—
83#2681C2216yes—
84#2652C2216yes—
85#2649C2216yes—
86#2638C2216yes—
87#2630C2216yes—
88#2629C2213yes—
89#2629C2213yes—
90#2628C2213yes—
91#2627C2216yes—
92#2625C2213yes—
93#2624C2213yes—
94#2620C2213yes—
95#2618C2216yes—
96#2581C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2567C2213yes—
100#2566C2213yes—
101#2566C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2544C2213yes—
105#2538C2213yes—
106#2538C2213yes—
107#2537C2213yes—
108#2513C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2509C2213yes—
115#2508C2213yes—
116#2507C2213yes—
117#2507C2213yes—
118#2507C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2506C2213yes—
122#2502C2213yes—
123#2500C2213yes—
124#2500C2213yes—
125#2499C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2495C2213yes—
132#2486C2213yes—
133#2485C2213yes—
134#2485C2213yes—
135#2485C2213yes—
136#2481C2216yes—
137#2473C2216yes—
138#2466C2216yes—
139#2460C2216yes—
140#2454C2213yes—
141#2454C2213yes—
142#2453C2213yes—
143#2453C2213yes—
144#2452C2213yes—
145#2452C2213yes—
146#2449C2216yes—
147#2448C2213yes—
148#2448C2213yes—
149#2447C2213yes—
150#2447C2213yes—
151#2447C2213yes—
152#2447C2213yes—
153#2445C2213yes—
154#2445C2213yes—
155#2443C2216yes—
156#2442C2213yes—
157#2442C2213yes—
158#2441C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2428C2213yes—
163#2427C2213yes—
164#2423C2213yes—
165#2422C2213yes—
166#2422C2213yes—
167#2422C2213yes—
168#2422C2213yes—
169#2421C2213yes—
170#2420C2213yes—
171#2420C2213yes—
172#2417C2213yes—
173#2416C2213yes—
174#2396C2213yes—
175#2396C2213yes—
176#2396C2213yes—
177#2395C2213yes—
178#2395C2213yes—
179#2392C2213yes—
180#2367C2213yes—
181#2366C2213yes—
182#2363C2213yes—
183#2361C2213yes—
184#2361C2213yes—
185#2360C2213yes—
186#2352C2213yes—
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201D4×C4⋊C4C2213yes—
202D4×C4⋊C4C2213yes—
203D4×C4⋊C4C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2324C2213yes—
217#2324C2213yes—
218#2324C2213yes—
219#2323C2213yes—
220#2322C2216yes—
221#2322C2216yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×#125C2213yes—
227C4×#126C2213yes—
228C4×#126C2213yes—
229C4×#124C2213yes—
230C4×#123C2213yes—
231C4×#123C2213yes—
232#2293C2213yes—
233#2293C2213yes—
234#2285C2213yes—
235C2×#384C2213yes—
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242#550—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×#127C2313yes—
247C2×#126C2311yescharacteristic
248C2×#126C2313yes—
249C2×#126C2316yes—
250C2×#125C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#123C2313yes—
258C2×#123C2316yes—
259C2×#123C2313yes—
260C2×#123C2316yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2316yes—
270#520—44no—
271#520—44no—
272#520—44no—
273#519—44no—
274C4×#41—28no—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2316yes—
302C2×C4×D4C2316yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2316yes—
313C22×C4⋊C4C2316yes—
314C22×C42C2313yes—
315#400C2316yes—
316#400C2316yes—
317#400C2313yes—
318#400C2316yes—
319#400C2316yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#399C2316yes—
328#399C2316yes—
329#399C2313yes—
330#399C2311yescharacteristic
331#399C2313yes—
332#399C2311yescharacteristic
333#399C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2316yes—
342#398C2313yes—
343#398C2313yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2313yes—
348#398C2311yescharacteristic
349#398C2311yescharacteristic
350#398C2313yes—
351#398C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2316yes—
368#396C2313yes—
369#396C2313yes—
370#396C2316yes—
371#396C2316yes—
372#396C2313yes—
373#396C2313yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2313yes—
379#396C2316yes—
380#396C2316yes—
381#396C2313yes—
382#396C2311yescharacteristic
383#395C2313yes—
384#395C2316yes—
385#395C2313yes—
386#395C2313yes—
387#394C2313yes—
388#394C2316yes—
389#394C2316yes—
390#394C2316yes—
391#394C2313yes—
392#394C2316yes—
393#394C2316yes—
394#394C2313yes—
395#394C2316yes—
396#394C2313yes—
397#394C2313yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#393C2313yes—
402#393C2313yes—
403#393C2313yes—
404#392C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2316yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2311yescharacteristic
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2316yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2311yescharacteristic
495#388C2311yescharacteristic
496#387C2311yescharacteristic
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2311yescharacteristic
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2311yescharacteristic
523#387C2313yes—
524#387C2313yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2316yes—
529#386C2316yes—
530#386C2316yes—
531#386C2313yes—
532#386C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2316yes—
537#385C2316yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2313yes—
548#385C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2316yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2311yescharacteristic
561#384C2313yes—
562#383C2313yes—
563#383C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#381C2313yes—
573#381C2316yes—
574#381C2313yes—
575#381C2316yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2316yes—
591#380C2316yes—
592#380C2316yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41#4118yes—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2413yes—
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2416yes—
644C22×D4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2416yes—
651C23×C4C2416yes—
652C23×C4C2416yes—
653C4⋊Q8—46no—
654#127—212no—
655#126—24no—
656#126—46no—
657#126—86no—
658#125—24no—
659#125—46no—
660#125—46no—
661#125—46no—
662#125—86no—
663#124—212no—
664#124—46no—
665#123—212no—
666#123—46no—
667#123—412no—
668#123—86no—
669C22⋊Q8—212no—
670C22⋊Q8—46no—
671C22⋊Q8—86no—
672C22⋊Q8—86no—
673#121—212no—
674#121—212no—
675#121—212no—
676#121—46no—
677#121—86no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×D4—212no—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—86no—
705C4×D4—86no—
706#117—212no—
707#117—46no—
708#117—46no—
709#117—46no—
710#117—46no—
711#117—46no—
712C2×C4⋊C4—46no—
713C2×C4⋊C4—46no—
714C2×C4⋊C4—46no—
715C2×C4⋊C4—86no—
716C2×C4⋊C4—86no—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C42—212no—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2416yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2416yes—
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2416yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907C24C2511yescharacteristic
908C24C2513yes—
909C24C2513yes—
910#41—232no—
911#41—416no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—43no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—416no—
919C2×Q8C2×#4114yes—
920C2×Q8H(5,𝔽2)14yes—
921C2×Q82−1+414yes—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—212no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—46no—
934C2×D4—43no—
935C2×D4—43no—
936C2×D4—43no—
937C2×D4—46no—
938C2×D4—43no—
939C2×D4C2×#41112yes—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—43no—
953C22×C4—43no—
954C22×C4—46no—
955C22×C4—46no—
956C22×C4—46no—
957C22×C4—46no—
958C22×C4—46no—
959C22×C4—46no—
960C22×C4—46no—
961C22×C4—46no—
962C22×C4—46no—
963C22×C4C2×#41112yes—
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2513yes—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—46no—
1037C4⋊C4—41no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—46no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—46no—
1044C4⋊C4—46no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C42−1+414yes—
1057C22⋊C4—212no—
1058C22⋊C4—26no—
1059C22⋊C4—26no—
1060C22⋊C4—212no—
1061C22⋊C4—22no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—26no—
1071C22⋊C4—41no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—41no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—43no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—46no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C42—22no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—22no—
1115C42—22no—
1116C42—46no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42—43no—
1122C42—43no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
1128C23—23no—
1129C23—21no—
1130C23—23no—
1131C23—21no—
1132C23—23no—
1133C23—21no—
1134C23—23no—
1135C23—21no—
1136C23—23no—
1137C23—23no—
1138C23—21no—
1139C23—21no—
1140C23—23no—
1141C23—23no—
1142C23—21no—
1143C23C22×#4116yes—
1144C23C2611yescharacteristic
1145Q8—412no—
1146Q8—86no—
1147Q8#539116yes—
1148D4—224no—
1149D4—412no—
1150D4—412no—
1151D4—86no—
1152D4—812no—
1153D4—86no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—224no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—412no—
1232C2×C4—412no—
1233C2×C4—412no—
1234C2×C4—412no—
1235C2×C4—166no—
1236C2×C4—166no—
1237C2×C4—166no—
1238C2×C4C22×#4112yes—
1239C2×C4C22×#4116yes—
1240C2×C4C2×H(5,𝔽2)16yes—
1241C2×C4C2×2−1+412yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C2×C4C2×2−1+416yes—
1245C2×C4#58512yes—
1246C22—26no—
1247C22—26no—
1248C22—26no—
1249C22—43no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
1254C22—41no—
1255C22—41no—
1256C22—43no—
1257C22—41no—
1258C22—43no—
1259C22—43no—
1260C22—41no—
1261C22—41no—
1262C22—43no—
1263C22—41no—
1264C22—43no—
1265C22—41no—
1266C22—43no—
1267C22C23×#4111yescharacteristic
1268C22C22×H(5,𝔽2)11yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22H(7,𝔽2)11yescharacteristic
1273C22H(7,𝔽2)11yescharacteristic
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—41no—
1280C4—43no—
1281C4—43no—
1282C4—43no—
1283C4—43no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—43no—
1293C4—43no—
1294C4—43no—
1295C4—41no—
1296C4—41no—
1297C4—43no—
1298C4—41no—
1299C4—43no—
1300C4—43no—
1301C4C2×#539112yes—
1302C2—46no—
1303C2—83no—
1304C2—81no—
1305C2C22×#53911yescharacteristic
1306C2#6294311yescharacteristic
1307C2#6295211yescharacteristic
1308C2#6300011yescharacteristic
1309C2#6300811yescharacteristic
1310C2#6303911yescharacteristic
1311C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35831C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52248C2semidirect
2. #42631C2semidirect
3. #42601C2semidirect
4. #42577C2semidirect
5. #42556C2semidirect
6. #42516C2semidirect
7. #42501C2semidirect
8. #40177C2semidirect
9. #40165C2semidirect
10. #40057C2semidirect
11. #40048C2semidirect
12. #39732C2semidirect
13. #39604C2semidirect
14. #37403C2semidirect
15. #37350C2semidirect
16. #37288C2semidirect
17. Q8×#126C2semidirect
18. Q8×#125C2semidirect
19. #36475C2semidirect
20. #36458C2semidirect
21. #36433C2semidirect
22. #36432C2semidirect
23. #35996C2semidirect
24. #35845C2semidirect
26. #35816C2semidirect
27. #35816C2semidirect
28. #35801C2semidirect
29. #34313C2semidirect
30. #34312C2semidirect
31. #34183C2semidirect

Maximal subgroups

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

subgroupindex
#522482
#426312
#426012
#425772
#425562
#425162
#425012
#401772
#401652
#400572
#400482
#397322
#396042
#374032
#373502
#372882
Q8×#1262
Q8×#1252
#364752
#364582
#364332
#364322
#359962
#358452
#358312
#358162
#358012
#343132
#343122
#341832