Finite Group Databasebeta

← #7643495

Subgroups — #7643495

Order 512.

4950 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40390C214yesmaximal, complemented
2#40358C214yesmaximal, complemented
3#39317C214yesmaximal, complemented
4#39102C214yesmaximal, complemented
5#38889C214yesmaximal, complemented
6#38858C214yesmaximal, complemented
7#38353C214yesmaximal, complemented
8#38322C214yesmaximal, complemented
9#37431C212yesmaximal, complemented
10#37428C211yesmaximal, characteristic, complemented
11#37420C211yesmaximal, characteristic, complemented
12#37375C211yesmaximal, characteristic, complemented
13#37282C212yesmaximal, complemented
14#37270C211yesmaximal, characteristic
15#36621C212yesmaximal, complemented
16#35657C212yesmaximal, complemented
17#35636C212yesmaximal, complemented
18#35572C212yesmaximal, complemented
19#35552C212yesmaximal, complemented
20#35258C212yesmaximal, complemented
21#35197C212yesmaximal, complemented
22#35196C212yesmaximal, complemented
23#35110C212yesmaximal, complemented
24#35107C212yesmaximal, complemented
25#34281C211yesmaximal, characteristic, complemented
26#34280C211yesmaximal, characteristic, complemented
27C4×#525C211yesmaximal, characteristic, complemented
28C2×#542C2212yescomplemented
29C2×#541C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#529C2212yes—
32C2×#525C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2857C2212yescomplemented
36#2855C2212yes—
37#2855C2212yescomplemented
38#2854C2212yes—
39#2854C2212yescomplemented
40#2853C2214yes—
41#2852C2214yes—
42#2852C2214yes—
43#2851C2212yes—
44#2851C2212yes—
45#2850C2212yes—
46#2850C2212yes—
47#2850C2212yescomplemented
48#2849C2214yes—
49#2848C2212yes—
50#2847C2212yes—
51#2807C2214yes—
52#2803C2214yescomplemented
53#2797C2214yes—
54#2797C2214yescomplemented
55#2784C2214yes—
56#2779C2214yes—
57#2778C2214yes—
58#2775C2214yescomplemented
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2763C2214yes—
62#2753C2214yes—
63#2751C2214yes—
64#2750C2214yes—
65#2749C2214yes—
66#2745C2214yescomplemented
67#2743C2214yes—
68#2720C2214yes—
69#2718C2214yes—
70#2715C2214yes—
71#2711C2214yes—
72#2707C2214yescomplemented
73#2707C2214yescomplemented
74#2703C2214yes—
75#2696C2214yes—
76#2691C2214yes—
77#2691C2214yes—
78#2685C2214yes—
79#2685C2214yes—
80#2684C2214yes—
81#2673C2214yes—
82#2669C2214yes—
83#2655C2214yescomplemented
84#2650C2214yescomplemented
85#2649C2214yes—
86#2649C2214yescomplemented
87#2648C2214yes—
88#2648C2214yescomplemented
89#2638C2214yes—
90#2630C2214yes—
91#2628C2212yes—
92#2620C2212yes—
93#2616C2212yes—
94#2615C2212yes—
95#2610C2214yescomplemented
96#2603C2214yes—
97#2602C2214yes—
98#2601C2214yescomplemented
99#2597C2214yes—
100#2587C2214yes—
101#2576C2214yes—
102#2571C2212yescomplemented
103#2571C2212yescomplemented
104#2566C2212yescomplemented
105#2565C2212yescomplemented
106#2564C2214yes—
107#2562C2212yes—
108#2562C2212yes—
109#2560C2214yescomplemented
110#2559C2214yes—
111#2557C2214yes—
112#2554C2214yescomplemented
113#2553C2214yes—
114#2550C2212yescomplemented
115#2550C2212yescomplemented
116#2548C2212yescomplemented
117#2547C2212yescomplemented
118#2544C2214yes—
119#2542C2212yes—
120#2541C2212yes—
121#2538C2212yes—
122#2537C2212yes—
123#2536C2212yes—
124#2535C2212yes—
125#2533C2214yescomplemented
126#2533C2214yescomplemented
127#2530C2214yescomplemented
128#2530C2214yescomplemented
129#2529C2214yescomplemented
130#2527C2214yes—
131#2526C2214yes—
132#2526C2214yescomplemented
133#2525C2214yescomplemented
134#2525C2214yescomplemented
135#2521C2214yescomplemented
136#2520C2214yescomplemented
137#2518C2214yescomplemented
138#2516C2214yes—
139#2516C2214yescomplemented
140#2515C2214yes—
141#2513C2214yescomplemented
142#2499C2214yescomplemented
143#2498C2214yescomplemented
144#2497C2212yes—
145#2497C2214yescomplemented
146#2496C2212yes—
147#2496C2214yescomplemented
148#2495C2212yescomplemented
149#2494C2212yescomplemented
150#2493C2214yescomplemented
151#2492C2212yes—
152#2491C2212yes—
153#2490C2212yescomplemented
154#2489C2212yescomplemented
155#2477C2214yescomplemented
156#2470C2214yes—
157#2469C2214yescomplemented
158#2468C2214yes—
159#2467C2214yes—
160#2466C2214yes—
161#2465C2214yescomplemented
162#2463C2214yes—
163#2461C2214yes—
164#2461C2214yes—
165#2461C2214yescomplemented
166#2459C2214yes—
167#2457C2214yes—
168#2457C2214yescomplemented
169#2457C2214yescomplemented
170#2455C2214yes—
171#2445C2214yes—
172#2445C2214yes—
173#2444C2214yes—
174#2427C2212yes—
175#2427C2212yescomplemented
176#2426C2212yes—
177#2426C2212yescomplemented
178#2421C2212yes—
179#2421C2212yescomplemented
180#2420C2214yes—
181#2420C2212yes—
182#2420C2212yescomplemented
183#2374C2214yescomplemented
184#2373C2214yes—
185#2373C2214yes—
186#2371C2214yescomplemented
187#2370C2214yescomplemented
188#2364C2214yes—
189#2363C2214yes—
190#2359C2214yescomplemented
191#2337C2214yes—
192#2335C2214yescomplemented
193#2334C2214yes—
194#2332C2214yescomplemented
195#2330C2211yescharacteristic, complemented
196#2330C2211yescharacteristic, complemented
197#2328C2214yes—
198#2328C2211yescharacteristic, complemented
199#2327C2211yescharacteristic, complemented
200#2324C2212yes—
201#2324C2214yes—
202#2324C2212yescomplemented
203#2323C2212yes—
204#2323C2212yescomplemented
205#2319C2214yescomplemented
206#2314C2211yescharacteristic
207#2314C2211yescharacteristic
208#2314C2212yescomplemented
209#2314C2214yescomplemented
210C4×C4⋊Q8C2211yescharacteristic, complemented
211C4×#127C2211yescharacteristic, complemented
212C4×#125C2211yescharacteristic, complemented
213C4×#125C2211yescharacteristic, complemented
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218C4×#123C2214yes—
219C4×#123C2212yes—
220C4×#123C2212yes—
221C4×#121C2212yes—
222C4×#121C2212yes—
223C4×#121C2212yes—
224C4×#121C2212yes—
225C4×#120C2214yes—
226C4×#120C2212yes—
227C4×#120C2212yes—
228#2297C2211yescharacteristic
229#2296C2211yescharacteristic
230#2295C2212yescomplemented
231#2293C2212yescomplemented
232#2290C2214yes—
233#2290C2214yes—
234#2290C2212yes—
235#2290C2212yes—
236#2283C2212yes—
237#2280C2211yescharacteristic
238#2276C2212yescomplemented
239#2275C2212yescomplemented
240C42×D4C2212yes—
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C24×C4C2311yescharacteristic
245C24×C4C2312yes—
246#542—48no—
247#541—28no—
248#540—28no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2312yes—
251C2×#127C2311yescharacteristic
252C2×#127C2314yes—
253#529—48no—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#125C2314yes—
261C2×#125C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266#525—28no—
267C2×#123C2314yes—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#120C2312yes—
290C2×#120C2314yes—
291C4×#41—44no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2311yescharacteristic
315C2×#117C2314yes—
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C22×C42—44no—
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321C22×C42C2311yescharacteristic
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2312yes—
327#401C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#390C2314yes—
418#390C2312yes—
419#390C2314yes—
420#390C2312yes—
421#390C2312yes—
422#390C2314yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
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#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#387C2312yes—
501#387C2314yes—
502#387C2314yes—
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#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2312yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
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#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2312yes—
559#386C2312yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2312yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2312yes—
583#385C2312yes—
584#385C2312yes—
585#384C2311yescharacteristic
586#384C2311yescharacteristic
587#384C2312yes—
588#384C2314yes—
589#383C2314yes—
590#383C2314yes—
591#382C2311yescharacteristic
592#382C2311yescharacteristic
593#382C2312yes—
594#382C2312yes—
595#382C2314yes—
596#382C2312yes—
597#382C2314yes—
598#382C2314yes—
599#381C2314yes—
600#381C2314yes—
601#381C2314yes—
602#381C2314yes—
603#381C2314yes—
604#381C2311yescharacteristic
605#381C2311yescharacteristic
606#380C2312yes—
607#380C2312yes—
608#380C2312yes—
609#380C2312yes—
610#380C2312yes—
611#380C2312yes—
612#380C2312yes—
613#380C2312yes—
614#380C2314yes—
615#380C2314yes—
616#380C2312yes—
617#380C2312yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#379C2314yes—
625#379C2311yescharacteristic
626#379C2311yescharacteristic
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673#376C2314yes—
674#376C2311yescharacteristic
675#376C2311yescharacteristic
676#376C2314yes—
677#376C2314yes—
678C2×#95C2314yes—
679C43C2311yescharacteristic
680C43C2311yescharacteristic
681C25C2411yescharacteristic
682C2×#41—24no—
683C2×#41—42no—
684C2×#41—42no—
685C22×Q8C2412yes—
686C22×Q8C2411yescharacteristic
687C22×Q8C2414yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2412yes—
692C22×D4C2411yescharacteristic
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C23×C4—24no—
700C23×C4—42no—
701C23×C4—44no—
702C23×C4—42no—
703C23×C4—44no—
704C23×C4—44no—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2412yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2412yes—
717C23×C4C2412yes—
718C23×C4C2411yescharacteristic
719C23×C4C2414yes—
720C23×C4C2412yes—
721C4⋊Q8—24no—
722C4⋊Q8—44no—
723#127—24no—
724#127—48no—
725#126—216no—
726#126—48no—
727#126—48no—
728#126—48no—
729#125—216no—
730#125—24no—
731#125—24no—
732#125—44no—
733#124—48no—
734#124—44no—
735#124—44no—
736#124—48no—
737#123—216no—
738#123—28no—
739#123—48no—
740#123—48no—
741#123—48no—
742#123—48no—
743C22⋊Q8—28no—
744C22⋊Q8—28no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—44no—
751#121—28no—
752#121—28no—
753#121—216no—
754#121—48no—
755#121—44no—
756#121—44no—
757#121—44no—
758#121—44no—
759#120—28no—
760#120—48no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—48no—
770C4×D4—44no—
771C4×D4—44no—
772C4×D4—44no—
773C4×D4—44no—
774C4×D4—48no—
775C4×D4—48no—
776C4×D4—44no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—48no—
780C4×D4—44no—
781#117—28no—
782#117—42no—
783#117—42no—
784#117—48no—
785#117—48no—
786#117#4118yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C42—24no—
886C2×C42—28no—
887C2×C42—44no—
888C2×C42—44no—
889C2×C42—44no—
890C2×C42—44no—
891C2×C42—44no—
892C2×C42—42no—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2414yes—
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979C24—22no—
980C24—24no—
981C24—41no—
982C24—42no—
983C24—41no—
984C24C2512yes—
985C24C2514yes—
986C24C2511yescharacteristic
987C24C2512yes—
988#41—416no—
989C2×Q8—24no—
990C2×Q8—22no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—41no—
994C2×Q8—41no—
995C2×Q8—44no—
996C2×Q8—44no—
997C2×Q8—44no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—28no—
1002C2×D4—28no—
1003C2×D4—28no—
1004C2×D4—24no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—22no—
1008C2×D4—28no—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—41no—
1012C2×D4—42no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—41no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—41no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—416no—
1079C22×C4—432no—
1080C22×C4C2×#4114yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4C2×#4118yes—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—41no—
1165C22⋊C4—44no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4C2×#4118yes—
1202C42—28no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—28no—
1210C42—24no—
1211C42—22no—
1212C42—22no—
1213C42—24no—
1214C42—42no—
1215C42—42no—
1216C42—41no—
1217C42—41no—
1218C42—42no—
1219C42—42no—
1220C42—44no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42C2×#4114yes—
1230C42C2×#4114yes—
1231C42H(5,𝔽2)14yes—
1232C23—22no—
1233C23—22no—
1234C23—21no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—21no—
1240C23—22no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—22no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23—24no—
1254C23—24no—
1255C23—22no—
1256C23—48no—
1257C23—44no—
1258C23—48no—
1259C23—44no—
1260C23—44no—
1261C23C22×#4112yes—
1262C23#58514yes—
1263C23C2611yescharacteristic
1264Q8—44no—
1265Q8—48no—
1266Q8—164no—
1267D4—48no—
1268D4—48no—
1269D4—44no—
1270D4—48no—
1271D4—48no—
1272D4—88no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—164no—
1277D4—164no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—28no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—48no—
1337C2×C4—48no—
1338C2×C4—48no—
1339C2×C4—48no—
1340C2×C4—48no—
1341C2×C4—48no—
1342C2×C4—44no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—88no—
1347C2×C4—88no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—164no—
1351C2×C4C22×#4114yes—
1352C2×C4C22×#4114yes—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4112yes—
1355C2×C4C2×H(5,𝔽2)14yes—
1356C2×C4C2×H(5,𝔽2)12yes—
1357C2×C4#58514yes—
1358C2×C4#58512yes—
1359C22—24no—
1360C22—24no—
1361C22—24no—
1362C22—24no—
1363C22—22no—
1364C22—416no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—42no—
1372C22—44no—
1373C22—42no—
1374C22—42no—
1375C22—44no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—44no—
1380C22—44no—
1381C22—42no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22C23×#4111yescharacteristic
1387C22C22×H(5,𝔽2)11yescharacteristic
1388C22C2×#58512yes—
1389C22C2×#58512yes—
1390C22C2×#58511yescharacteristic
1391C4—24no—
1392C4—24no—
1393C4—24no—
1394C4—24no—
1395C4—22no—
1396C4—44no—
1397C4—44no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—44no—
1404C4—41no—
1405C4—41no—
1406C4—44no—
1407C4—41no—
1408C4—44no—
1409C4—41no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4#346014yes—
1414C2—44no—
1415C2—42no—
1416C2—84no—
1417C2—82no—
1418C2C2×#346011yescharacteristic
1419C2#6281012yes—
1420C2#6282112yes—
1421C2#6282911yescharacteristic
1422C2#6283911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37270C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40390C2semidirect
2. #40358C2semidirect
3. #39317C2semidirect
4. #39102C2semidirect
5. #38889C2semidirect
6. #38858C2semidirect
7. #38353C2semidirect
8. #38322C2semidirect
9. #37431C2semidirect
10. #37428C2semidirect
11. #37420C2semidirect
12. #37375C2semidirect
13. #37282C2semidirect
15. #36621C2semidirect
16. #35657C2semidirect
17. #35636C2semidirect
18. #35572C2semidirect
19. #35552C2semidirect
20. #35258C2semidirect
21. #35197C2semidirect
22. #35196C2semidirect
23. #35110C2semidirect
24. #35107C2semidirect
25. #34281C2semidirect
26. #34280C2semidirect
27. C4×#525C2semidirect
28. C2×#542C22semidirect
35. #2857C22semidirect
37. #2855C22semidirect
39. #2854C22semidirect
47. #2850C22semidirect
52. #2803C22semidirect
54. #2797C22semidirect
58. #2775C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
66. #2745C22semidirect
72. #2707C22semidirect
73. #2707C22semidirect
83. #2655C22semidirect
84. #2650C22semidirect
86. #2649C22semidirect
88. #2648C22semidirect
95. #2610C22semidirect
98. #2601C22semidirect
102. #2571C22semidirect
103. #2571C22semidirect
104. #2566C22semidirect
105. #2565C22semidirect
109. #2560C22semidirect
112. #2554C22semidirect
114. #2550C22semidirect
115. #2550C22semidirect
116. #2548C22semidirect
117. #2547C22semidirect
125. #2533C22semidirect
126. #2533C22semidirect
127. #2530C22semidirect
128. #2530C22semidirect
129. #2529C22semidirect
132. #2526C22semidirect
133. #2525C22semidirect
134. #2525C22semidirect
135. #2521C22semidirect
136. #2520C22semidirect
137. #2518C22semidirect
139. #2516C22semidirect
141. #2513C22semidirect
142. #2499C22semidirect
143. #2498C22semidirect
145. #2497C22semidirect
147. #2496C22semidirect
148. #2495C22semidirect
149. #2494C22semidirect
150. #2493C22semidirect
153. #2490C22semidirect
154. #2489C22semidirect
155. #2477C22semidirect
157. #2469C22semidirect
161. #2465C22semidirect
165. #2461C22semidirect
168. #2457C22semidirect
169. #2457C22semidirect
175. #2427C22semidirect
177. #2426C22semidirect
179. #2421C22semidirect
182. #2420C22semidirect
183. #2374C22semidirect
186. #2371C22semidirect
187. #2370C22semidirect
190. #2359C22semidirect
192. #2335C22semidirect
194. #2332C22semidirect
195. #2330C22semidirect
196. #2330C22semidirect
198. #2328C22semidirect
199. #2327C22semidirect
202. #2324C22semidirect
204. #2323C22semidirect
205. #2319C22semidirect
208. #2314C22semidirect
209. #2314C22semidirect
210. C4×C4⋊Q8C22semidirect
211. C4×#127C22semidirect
212. C4×#125C22semidirect
213. C4×#125C22semidirect
230. #2295C22semidirect
231. #2293C22semidirect
238. #2276C22semidirect
239. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#403902
#403582
#393172
#391022
#388892
#388582
#383532
#383222
#374312
#374282
#374202
#373752
#372822
#372702
#366212
#356572
#356362
#355722
#355522
#352582
#351972
#351962
#351102
#351072
#342812
#342802
C4×#5252