Finite Group Databasebeta

← #7715636

Subgroups — #7715636

Order 512.

4330 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48979C214yesmaximal, complemented
2#48921C214yesmaximal, complemented
3#48124C214yesmaximal, complemented
4#48056C214yesmaximal, complemented
5#47333C214yesmaximal, complemented
6#47329C214yesmaximal, complemented
7#47326C214yesmaximal, complemented
8#47322C214yesmaximal, complemented
9#39159C212yesmaximal, complemented
10#39158C212yesmaximal, complemented
11#39143C212yesmaximal, complemented
12#39142C212yesmaximal, complemented
13#38285C212yesmaximal, complemented
14#38284C212yesmaximal, complemented
15#38277C212yesmaximal, complemented
16#38276C212yesmaximal, complemented
17#37514C211yesmaximal, characteristic, complemented
18#37513C211yesmaximal, characteristic
19#37421C211yesmaximal, characteristic, complemented
20#37325C212yesmaximal, complemented
21#37308C211yesmaximal, characteristic, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35296C211yesmaximal, characteristic, complemented
24#35270C212yesmaximal, complemented
25#35258C212yesmaximal, complemented
26#34419C212yesmaximal, complemented
27#34056C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×C4×#41C2211yescharacteristic
30#2864C2211yescharacteristic
31#2864C2211yescharacteristic
32#2862C2211yescharacteristic
33#2858C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2833C2212yes—
41#2832C2212yes—
42#2830C2212yes—
43#2828C2212yes—
44#2805C2214yes—
45#2803C2214yes—
46#2803C2214yes—
47#2788C2214yes—
48#2785C2214yes—
49#2784C2214yes—
50#2783C2214yes—
51#2783C2214yes—
52#2782C2214yes—
53#2781C2214yes—
54#2780C2214yes—
55#2779C2214yes—
56#2778C2214yes—
57#2778C2214yes—
58#2776C2214yes—
59#2775C2214yes—
60#2773C2214yes—
61#2765C2214yes—
62#2762C2214yes—
63#2759C2214yes—
64#2759C2214yes—
65#2759C2214yes—
66#2758C2214yes—
67#2758C2214yes—
68#2756C2214yes—
69#2754C2214yes—
70#2751C2214yes—
71#2747C2214yes—
72#2745C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2742C2212yes—
76#2742C2212yes—
77#2741C2214yes—
78#2734C2214yes—
79#2731C2214yes—
80#2731C2214yes—
81#2730C2214yes—
82#2712C2212yes—
83#2712C2212yes—
84#2710C2214yes—
85#2708C2214yes—
86#2702C2214yes—
87#2702C2214yes—
88#2700C2214yes—
89#2700C2214yes—
90#2696C2214yes—
91#2693C2212yes—
92#2693C2212yes—
93#2686C2214yes—
94#2677C2212yes—
95#2677C2212yes—
96#2653C2214yes—
97#2649C2214yes—
98#2647C2212yes—
99#2645C2212yes—
100#2645C2212yes—
101#2644C2212yes—
102#2644C2212yes—
103#2640C2212yes—
104#2635C2214yes—
105#2631C2214yes—
106#2628C2212yes—
107#2628C2211yescharacteristic
108#2628C2211yescharacteristic
109#2621C2211yescharacteristic
110#2620C2212yes—
111#2619C2211yescharacteristic
112#2616C2212yes—
113#2615C2212yes—
114#2610C2214yes—
115#2599C2214yes—
116#2596C2214yes—
117#2595C2214yes—
118#2593C2212yes—
119#2588C2214yes—
120#2586C2212yes—
121#2578C2214yes—
122#2576C2214yes—
123#2575C2214yes—
124#2574C2214yes—
125#2572C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2568C2212yes—
129#2568C2214yes—
130#2563C2212yes—
131#2557C2214yes—
132#2555C2212yes—
133#2551C2212yes—
134#2551C2212yes—
135#2547C2214yes—
136#2545C2212yes—
137#2544C2212yes—
138#2533C2214yes—
139#2532C2214yes—
140#2532C2214yes—
141#2530C2214yes—
142#2529C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2527C2214yes—
146#2526C2214yes—
147#2525C2214yes—
148#2520C2214yes—
149#2518C2214yes—
150#2516C2214yes—
151#2515C2214yes—
152#2514C2214yes—
153#2510C2214yes—
154#2510C2214yes—
155#2498C2214yes—
156#2495C2212yes—
157#2495C2212yes—
158#2494C2212yes—
159#2494C2212yes—
160#2494C2214yes—
161#2493C2214yes—
162#2492C2214yes—
163#2492C2212yes—
164#2492C2212yes—
165#2491C2214yes—
166#2491C2212yes—
167#2491C2212yes—
168#2488C2214yes—
169#2485C2214yes—
170#2474C2214yes—
171#2474C2214yes—
172#2474C2214yes—
173#2471C2214yes—
174#2469C2214yes—
175#2467C2214yes—
176#2465C2214yes—
177#2463C2214yes—
178#2461C2214yes—
179#2459C2214yes—
180#2458C2214yes—
181#2457C2214yes—
182#2457C2214yes—
183#2455C2214yes—
184#2450C2214yes—
185#2444C2214yes—
186#2439C2214yes—
187#2439C2214yes—
188#2429C2212yes—
189#2428C2212yes—
190#2427C2212yes—
191#2426C2212yes—
192#2423C2212yes—
193#2422C2212yes—
194#2421C2212yes—
195#2421C2214yes—
196#2420C2212yes—
197#2419C2214yes—
198#2379C2214yes—
199#2376C2214yes—
200#2369C2212yes—
201#2367C2214yes—
202#2367C2212yes—
203#2367C2212yes—
204#2365C2212yes—
205#2359C2214yes—
206#2355C2212yes—
207#2354C2212yes—
208#2351C2212yes—
209#2349C2212yes—
210#2334C2214yes—
211#2334C2214yes—
212#2331C2212yes—
213#2331C2211yescharacteristic
214#2331C2211yescharacteristic
215#2329C2214yes—
216#2328C2211yescharacteristic
217#2327C2211yescharacteristic
218#2326C2212yes—
219#2324C2212yes—
220#2324C2212yes—
221#2323C2212yes—
222#2323C2214yes—
223#2323C2212yes—
224#2320C2212yes—
225#2320C2212yes—
226#2320C2212yes—
227#2319C2212yes—
228#2319C2212yes—
229#2319C2212yes—
230#2318C2212yes—
231#2318C2212yes—
232#2318C2212yes—
233#2318C2212yes—
234#2314C2212yes—
235C4×C22⋊Q8C2212yes—
236C4×C22⋊Q8C2212yes—
237C4×#121C2212yes—
238C4×#121C2212yes—
239#2298C2212yes—
240#2298C2212yes—
241#2297C2211yescharacteristic
242#2297C2211yescharacteristic
243#2296C2211yescharacteristic
244#2296C2211yescharacteristic
245#2295C2212yes—
246#2293C2212yes—
247#2283C2212yes—
248#2283C2212yes—
249C4×#117C2211yescharacteristic
250C2×#376C2211yescharacteristic
251C22×#41C2311yescharacteristic
252#542—216no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2314yes—
260C2×#127C2311yescharacteristic
261C2×#126C2314yes—
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C4×#41—28no—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×#117C2312yes—
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2314yes—
299C2×#117C2314yes—
300C2×#117C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305#401C2314yes—
306#401C2314yes—
307#401C2314yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#399C2312yes—
330#399C2314yes—
331#399C2312yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2312yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2312yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#395C2314yes—
368#395C2312yes—
369#395C2312yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#394C2312yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2312yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2312yes—
399#393C2312yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2312yes—
408#392C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2314yes—
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2314yes—
443#390C2312yes—
444#390C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2312yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#386C2314yes—
564#386C2312yes—
565#386C2312yes—
566#386C2312yes—
567#386C2312yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#385C2312yes—
584#385C2312yes—
585#385C2311yescharacteristic
586#385C2311yescharacteristic
587#385C2311yescharacteristic
588#385C2311yescharacteristic
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2312yes—
602#384C2312yes—
603#383C2314yes—
604#383C2312yes—
605#383C2312yes—
606#383C2312yes—
607#383C2312yes—
608#383C2314yes—
609#383C2314yes—
610#382C2311yescharacteristic
611#382C2312yes—
612#382C2312yes—
613#382C2311yescharacteristic
614#382C2314yes—
615#382C2312yes—
616#382C2311yescharacteristic
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#381C2314yes—
625#381C2312yes—
626#381C2312yes—
627#381C2312yes—
628#381C2312yes—
629#381C2314yes—
630#381C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680#376C2312yes—
681#376C2312yes—
682#376C2312yes—
683#376C2312yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2314yes—
687C2×#95C2312yes—
688C2×#95C2312yes—
689C2×#95C2314yes—
690C43C2311yescharacteristic
691C43C2311yescharacteristic
692C2×#41—24no—
693C2×#41—42no—
694C2×#41—42no—
695C22×Q8C2412yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2414yes—
698C22×Q8C2414yes—
699C22×Q8C2412yes—
700C22×Q8C2412yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C22×D4C2411yescharacteristic
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2414yes—
707C22×D4C2412yes—
708C22×D4C2412yes—
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2414yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C23×C4C2412yes—
715C23×C4C2414yes—
716C23×C4C2414yes—
717C23×C4C2412yes—
718C23×C4C2411yescharacteristic
719C23×C4C2411yescharacteristic
720C4⋊Q8—28no—
721C4⋊Q8—44no—
722C4⋊Q8—42no—
723C4⋊Q8—42no—
724C4⋊Q8—42no—
725C4⋊Q8—84no—
726C4⋊Q8—84no—
727#127—42no—
728#126—216no—
729#124—216no—
730#124—28no—
731#124—44no—
732#124—84no—
733#124—84no—
734#124—84no—
735#123—216no—
736#123—84no—
737#123—84no—
738C22⋊Q8—28no—
739C22⋊Q8—216no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744#121—28no—
745#121—44no—
746#121—44no—
747#121—84no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8—44no—
751C4×Q8—44no—
752C4×Q8—84no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—44no—
758C4×D4—44no—
759C4×D4—84no—
760C4×D4—84no—
761#117—28no—
762#117—42no—
763#117—42no—
764#117—84no—
765#117—84no—
766#117#4118yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C42—24no—
862C2×C42—28no—
863C2×C42—42no—
864C2×C42—42no—
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969C24C2514yes—
970C24C2512yes—
971C24C2511yescharacteristic
972#41—416no—
973C2×Q8—22no—
974C2×Q8—24no—
975C2×Q8—28no—
976C2×Q8—24no—
977C2×Q8—24no—
978C2×Q8—41no—
979C2×Q8—41no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—44no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—44no—
989C2×D4—24no—
990C2×D4—28no—
991C2×D4—22no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—41no—
996C2×D4—41no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—28no—
1020C22×C4—42no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4C2×#4114yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2514yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4C2×#4118yes—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4C2×#4114yes—
1159C22⋊C4C2×#4114yes—
1160C42—22no—
1161C42—22no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—28no—
1166C42—24no—
1167C42—24no—
1168C42—22no—
1169C42—22no—
1170C42—22no—
1171C42—22no—
1172C42—41no—
1173C42—42no—
1174C42—41no—
1175C42—42no—
1176C42—42no—
1177C42—42no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—42no—
1187C42C2×#4118yes—
1188C23—21no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—24no—
1193C23—22no—
1194C23—24no—
1195C23—24no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23—24no—
1206C23C22×#4112yes—
1207C23C2611yescharacteristic
1208Q8—44no—
1209Q8—48no—
1210Q8—88no—
1211Q8—164no—
1212Q8—162no—
1213Q8—162no—
1214D4—44no—
1215D4—48no—
1216D4—48no—
1217D4—88no—
1218D4—88no—
1219D4—164no—
1220D4—162no—
1221D4—162no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—28no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—48no—
1286C2×C4—84no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—88no—
1291C2×C4—84no—
1292C2×C4—82no—
1293C2×C4—82no—
1294C2×C4—164no—
1295C2×C4C22×#4114yes—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4114yes—
1298C2×C4C22×#4112yes—
1299C2×C4#58512yes—
1300C2×C4#58512yes—
1301C22—22no—
1302C22—24no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—42no—
1307C22—44no—
1308C22—44no—
1309C22—42no—
1310C22—42no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—42no—
1320C22C23×#4111yescharacteristic
1321C22C2×#58511yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22H(7,𝔽2)12yes—
1324C222−1+612yes—
1325C4—22no—
1326C4—24no—
1327C4—24no—
1328C4—42no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—44no—
1342C4—41no—
1343C4—41no—
1344C4—44no—
1345C4—41no—
1346C4—42no—
1347C4—41no—
1348C4#349314yes—
1349C2—42no—
1350C2—82no—
1351C2—84no—
1352C2C2×#349311yescharacteristic
1353C2#6285712yes—
1354C2#6288212yes—
1355C2#6288511yescharacteristic
1356C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37513C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48979C2semidirect
2. #48921C2semidirect
3. #48124C2semidirect
4. #48056C2semidirect
5. #47333C2semidirect
6. #47329C2semidirect
7. #47326C2semidirect
8. #47322C2semidirect
9. #39159C2semidirect
10. #39158C2semidirect
11. #39143C2semidirect
12. #39142C2semidirect
13. #38285C2semidirect
14. #38284C2semidirect
15. #38277C2semidirect
16. #38276C2semidirect
17. #37514C2semidirect
19. #37421C2semidirect
20. #37325C2semidirect
21. #37308C2semidirect
22. #35324C2semidirect
23. #35296C2semidirect
24. #35270C2semidirect
25. #35258C2semidirect
26. #34419C2semidirect
27. #34056C2semidirect

Maximal subgroups

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

subgroupindex
#489792
#489212
#481242
#480562
#473332
#473292
#473262
#473222
#391592
#391582
#391432
#391422
#382852
#382842
#382772
#382762
#375142
#375132
#374212
#373252
#373082
#353242
#352962
#352702
#352582
#344192
#340562