Finite Group Databasebeta

← #7652541

Subgroups — #7652541

Order 512.

4454 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42981C211yesmaximal, characteristic, complemented
2#42952C211yesmaximal, characteristic
3#42613C212yesmaximal, complemented
4#42569C212yesmaximal, complemented
5#42522C211yesmaximal, characteristic, complemented
6#42502C211yesmaximal, characteristic, complemented
7#41846C214yesmaximal, complemented
8#41740C214yesmaximal, complemented
9#41299C214yesmaximal, complemented
10#40984C214yesmaximal, complemented
11#40364C214yesmaximal, complemented
12#40050C212yesmaximal, complemented
13#39866C212yesmaximal, complemented
14#39258C214yesmaximal, complemented
15#39250C212yesmaximal, complemented
16#39145C212yesmaximal, complemented
17#38864C214yesmaximal, complemented
18#38715C214yesmaximal, complemented
19#35612C212yesmaximal, complemented
20#35588C212yesmaximal, complemented
21#35546C212yesmaximal, complemented
22#35296C211yesmaximal, characteristic, complemented
23#35235C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic, complemented
25#34788C212yesmaximal, complemented
26#34305C212yesmaximal, complemented
27#34215C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#533C2211yescharacteristic
30#2864C2211yescharacteristic
31#2858C2211yescharacteristic
32#2855C2214yes—
33#2855C2214yes—
34#2854C2212yes—
35#2844C2212yes—
36#2836C2214yes—
37#2835C2212yes—
38#2831C2214yes—
39#2826C2212yes—
40#2823C2212yes—
41#2807C2212yes—
42#2795C2212yes—
43#2794C2214yes—
44#2788C2214yes—
45#2783C2214yes—
46#2783C2214yes—
47#2782C2212yes—
48#2782C2214yes—
49#2781C2214yes—
50#2781C2214yes—
51#2776C2214yes—
52#2769C2212yes—
53#2765C2214yes—
54#2757C2214yes—
55#2754C2214yes—
56#2747C2214yes—
57#2747C2214yes—
58#2747C2214yes—
59#2742C2212yes—
60#2739C2214yes—
61#2730C2214yes—
62#2720C2214yes—
63#2717C2214yes—
64#2715C2214yes—
65#2693C2212yes—
66#2692C2214yes—
67#2691C2214yes—
68#2691C2214yes—
69#2690C2214yes—
70#2687C2214yes—
71#2681C2214yes—
72#2680C2212yes—
73#2680C2214yes—
74#2675C2212yes—
75#2672C2214yes—
76#2671C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2655C2214yes—
80#2651C2214yes—
81#2650C2214yes—
82#2649C2214yes—
83#2647C2214yes—
84#2644C2212yes—
85#2643C2214yes—
86#2638C2214yes—
87#2637C2214yes—
88#2636C2214yes—
89#2633C2214yes—
90#2630C2214yes—
91#2628C2211yescharacteristic
92#2625C2214yes—
93#2619C2211yescharacteristic
94#2612C2212yes—
95#2608C2214yes—
96#2606C2214yes—
97#2605C2214yes—
98#2604C2214yes—
99#2595C2214yes—
100#2595C2214yes—
101#2587C2214yes—
102#2584C2212yes—
103#2578C2214yes—
104#2578C2214yes—
105#2574C2212yes—
106#2573C2214yes—
107#2573C2212yes—
108#2572C2214yes—
109#2572C2212yes—
110#2570C2212yes—
111#2570C2212yes—
112#2569C2214yes—
113#2569C2214yes—
114#2566C2212yes—
115#2559C2214yes—
116#2557C2214yes—
117#2556C2214yes—
118#2553C2212yes—
119#2552C2212yes—
120#2550C2212yes—
121#2550C2212yes—
122#2549C2214yes—
123#2538C2212yes—
124#2537C2212yes—
125#2536C2214yes—
126#2531C2214yes—
127#2529C2214yes—
128#2525C2214yes—
129#2524C2212yes—
130#2524C2214yes—
131#2522C2214yes—
132#2518C2214yes—
133#2516C2214yes—
134#2515C2212yes—
135#2513C2212yes—
136#2513C2212yes—
137#2513C2212yes—
138#2510C2214yes—
139#2509C2212yes—
140#2509C2212yes—
141#2509C2212yes—
142#2508C2212yes—
143#2506C2212yes—
144#2504C2212yes—
145#2500C2212yes—
146#2497C2214yes—
147#2496C2212yes—
148#2496C2214yes—
149#2495C2212yes—
150#2494C2212yes—
151#2491C2212yes—
152#2490C2212yes—
153#2490C2212yes—
154#2488C2214yes—
155#2487C2212yes—
156#2485C2212yes—
157#2475C2214yes—
158#2474C2214yes—
159#2474C2214yes—
160#2471C2214yes—
161#2468C2214yes—
162#2468C2212yes—
163#2463C2212yes—
164#2463C2212yes—
165#2461C2214yes—
166#2459C2214yes—
167#2457C2214yes—
168#2457C2212yes—
169#2454C2212yes—
170#2454C2212yes—
171#2452C2212yes—
172#2445C2212yes—
173#2444C2214yes—
174#2444C2214yes—
175#2442C2212yes—
176#2442C2212yes—
177#2442C2212yes—
178#2442C2212yes—
179#2441C2214yes—
180#2440C2212yes—
181#2440C2212yes—
182#2438C2214yes—
183#2428C2212yes—
184#2427C2214yes—
185#2427C2214yes—
186#2425C2214yes—
187#2420C2214yes—
188#2420C2212yes—
189#2419C2214yes—
190#2416C2212yes—
191#2416C2212yes—
192#2402C2211yescharacteristic
193#2401C2214yes—
194#2398C2211yescharacteristic
195#2396C2211yescharacteristic
196#2395C2214yes—
197#2392C2211yescharacteristic
198#2373C2214yes—
199#2370C2212yes—
200#2368C2214yes—
201#2368C2214yes—
202#2364C2214yes—
203#2361C2212yes—
204#2361C2212yes—
205#2359C2214yes—
206#2355C2214yes—
207#2355C2214yes—
208#2354C2212yes—
209#2349C2214yes—
210D4×C4⋊C4C2212yes—
211#2346C2212yes—
212#2345C2212yes—
213#2335C2214yes—
214#2334C2214yes—
215#2334C2214yes—
216#2331C2212yes—
217#2331C2211yescharacteristic
218#2331C2212yes—
219#2330C2212yes—
220#2330C2212yes—
221#2328C2211yescharacteristic
222#2326C2214yes—
223#2325C2214yes—
224#2324C2212yes—
225#2324C2214yes—
226#2319C2212yes—
227#2317C2211yescharacteristic
228#2317C2211yescharacteristic
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#126C2212yes—
232C4×#123C2212yes—
233C4×#121C2214yes—
234C4×#121C2212yes—
235C4×#121C2212yes—
236C4×#121C2214yes—
237#2295C2211yescharacteristic
238#2293C2212yes—
239#2290C2212yes—
240#2290C2214yes—
241#2290C2214yes—
242#2283C2212yes—
243#2283C2212yes—
244C2×#382C2211yescharacteristic
245#2275C2212yes—
246#2274C2211yescharacteristic
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×C4×C4⋊C4C2212yes—
251#553—216no—
252#533—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×#127C2311yescharacteristic
256C2×#126C2314yes—
257C2×#126C2312yes—
258C2×#126C2314yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#123C2314yes—
266C2×#123C2312yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2314yes—
299C2×#117C2314yes—
300C2×#117C2311yescharacteristic
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C42C2311yescharacteristic
306C22×C42C2312yes—
307C22×C42C2314yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2312yes—
314#400C2314yes—
315#400C2311yescharacteristic
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#399C2311yescharacteristic
332#399C2314yes—
333#399C2314yes—
334#399C2312yes—
335#399C2314yes—
336#398C2311yescharacteristic
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#397C2314yes—
356#397C2314yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2311yescharacteristic
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2312yes—
387#395C2311yescharacteristic
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#394C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2311yescharacteristic
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2312yes—
411#393C2311yescharacteristic
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#392C2312yes—
417#392C2312yes—
418#392C2314yes—
419#392C2311yescharacteristic
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#388C2312yes—
472#388C2312yes—
473#388C2312yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2312yes—
478#388C2314yes—
479#388C2314yes—
480#388C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
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#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2314yes—
527#387C2312yes—
528#387C2314yes—
529#387C2312yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2312yes—
550#386C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2312yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2312yes—
572#385C2312yes—
573#385C2312yes—
574#385C2312yes—
575#385C2314yes—
576#385C2312yes—
577#385C2312yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2314yes—
595#383C2312yes—
596#383C2312yes—
597#383C2314yes—
598#383C2312yes—
599#383C2314yes—
600#382C2312yes—
601#382C2311yescharacteristic
602#382C2312yes—
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2311yescharacteristic
609#382C2314yes—
610#382C2314yes—
611#382C2314yes—
612#382C2312yes—
613#381C2314yes—
614#381C2312yes—
615#381C2314yes—
616#381C2312yes—
617#381C2312yes—
618#381C2314yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2312yes—
683#376C2314yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2314yes—
687C2×#95C2314yes—
688C2×#95C2314yes—
689C2×#95C2314yes—
690C43C2311yescharacteristic
691C43C2311yescharacteristic
692C22×Q8C2414yes—
693C22×Q8C2411yescharacteristic
694C22×Q8C2412yes—
695C22×D4C2412yes—
696C22×D4C2412yes—
697C22×D4C2414yes—
698C22×D4C2411yescharacteristic
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2412yes—
714C23×C4C2414yes—
715C4⋊Q8—28no—
716C4⋊Q8—42no—
717#127—42no—
718#126—216no—
719#126—44no—
720#126—48no—
721#125—28no—
722#125—28no—
723#125—44no—
724#125—84no—
725#124—48no—
726#124—84no—
727#123—216no—
728#123—44no—
729#123—84no—
730#123—84no—
731C22⋊Q8—216no—
732C22⋊Q8—84no—
733C22⋊Q8—84no—
734C22⋊Q8—84no—
735C22⋊Q8—84no—
736#121—28no—
737#121—28no—
738#121—216no—
739#121—48no—
740#121—48no—
741#121—48no—
742#121—44no—
743C4×Q8—216no—
744C4×Q8—42no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—216no—
748C4×D4—28no—
749C4×D4—44no—
750C4×D4—42no—
751C4×D4—44no—
752C4×D4—48no—
753C4×D4—84no—
754C4×D4—84no—
755C4×D4—84no—
756C4×D4—84no—
757#117—24no—
758#117—24no—
759#117—42no—
760#117—84no—
761#117—84no—
762#117#4118yes—
763C2×C4⋊C4—28no—
764C2×C4⋊C4—42no—
765C2×C4⋊C4—44no—
766C2×C4⋊C4—42no—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C42—24no—
869C2×C42—28no—
870C2×C42—84no—
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2411yescharacteristic
927#95C2411yescharacteristic
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2411yescharacteristic
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970C24C2514yes—
971C24C2511yescharacteristic
972C24C2512yes—
973C2×Q8—28no—
974C2×Q8—41no—
975C2×Q8—44no—
976C2×Q8—42no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—42no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—28no—
984C2×D4—28no—
985C2×D4—28no—
986C2×D4—28no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—41no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—42no—
1000C2×D4—42no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—28no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—28no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4C2×#4114yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—41no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4C2×#4118yes—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4C2×#4118yes—
1160C42—24no—
1161C42—22no—
1162C42—22no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—22no—
1169C42—22no—
1170C42—22no—
1171C42—24no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42—42no—
1183C42—44no—
1184C42—42no—
1185C42C2×#4118yes—
1186C422−1+414yes—
1187C23—22no—
1188C23—21no—
1189C23—22no—
1190C23—21no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23C22×#4112yes—
1205C23#58514yes—
1206C23C2611yescharacteristic
1207Q8—88no—
1208Q8—82no—
1209Q8—162no—
1210D4—416no—
1211D4—48no—
1212D4—44no—
1213D4—48no—
1214D4—88no—
1215D4—88no—
1216D4—162no—
1217D4—162no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—28no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—48no—
1282C2×C4—48no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—84no—
1286C2×C4—88no—
1287C2×C4—84no—
1288C2×C4—88no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—164no—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4118yes—
1294C2×C4C22×#4112yes—
1295C2×C4C2×2−1+414yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4#58512yes—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—22no—
1302C22—24no—
1303C22—42no—
1304C22—41no—
1305C22—42no—
1306C22—41no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22C23×#4111yescharacteristic
1318C22C22×2−1+411yescharacteristic
1319C22C2×#58512yes—
1320C22C2×#58511yescharacteristic
1321C22H(7,𝔽2)12yes—
1322C4—28no—
1323C4—22no—
1324C4—24no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—41no—
1334C4—41no—
1335C4—44no—
1336C4—44no—
1337C4—42no—
1338C4—41no—
1339C4—41no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4#346114yes—
1346C2—42no—
1347C2—44no—
1348C2—84no—
1349C2C2×#346111yescharacteristic
1350C2#6282911yescharacteristic
1351C2#6288511yescharacteristic
1352C2#6295812yes—
1353C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42952C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42981C2semidirect
3. #42613C2semidirect
4. #42569C2semidirect
5. #42522C2semidirect
6. #42502C2semidirect
7. #41846C2semidirect
8. #41740C2semidirect
9. #41299C2semidirect
10. #40984C2semidirect
11. #40364C2semidirect
12. #40050C2semidirect
13. #39866C2semidirect
14. #39258C2semidirect
15. #39250C2semidirect
16. #39145C2semidirect
17. #38864C2semidirect
18. #38715C2semidirect
19. #35612C2semidirect
20. #35588C2semidirect
21. #35546C2semidirect
22. #35296C2semidirect
23. #35235C2semidirect
24. #34879C2semidirect
25. #34788C2semidirect
26. #34305C2semidirect
27. #34215C2semidirect

Maximal subgroups

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

subgroupindex
#429812
#429522
#426132
#425692
#425222
#425022
#418462
#417402
#412992
#409842
#403642
#400502
#398662
#392582
#392502
#391452
#388642
#387152
#356122
#355882
#355462
#352962
#352352
#348792
#347882
#343052
#342152