Finite Group Databasebeta

← #7652539

Subgroups — #7652539

Order 512.

4152 conjugacy classes of subgroups.

The subgroup lattice has 1289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42980C211yesmaximal, characteristic
2#42933C211yesmaximal, characteristic, complemented
3#42756C212yesmaximal, complemented
4#42744C212yesmaximal, complemented
5#42695C211yesmaximal, characteristic, complemented
6#42686C211yesmaximal, characteristic
7#41868C214yesmaximal
8#41853C214yesmaximal, complemented
9#41763C214yesmaximal, complemented
10#41665C214yesmaximal, complemented
11#40460C214yesmaximal, complemented
12#40074C212yesmaximal, complemented
13#39890C212yesmaximal, complemented
14#39294C214yesmaximal, complemented
15#39250C212yesmaximal, complemented
16#39155C212yesmaximal, complemented
17#38794C214yesmaximal, complemented
18#38651C214yesmaximal, complemented
19#35652C212yesmaximal, complemented
20#35596C212yesmaximal, complemented
21#35577C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35217C212yesmaximal, complemented
24#34951C212yesmaximal, complemented
25#34881C211yesmaximal, characteristic
26#34318C212yesmaximal, complemented
27#34215C211yesmaximal, characteristic, complemented
28C2×#552C2212yes—
29C2×#533C2211yescharacteristic
30#2866C2214yes—
31#2864C2211yescharacteristic
32#2863C2214yes—
33#2862C2211yescharacteristic
34#2855C2212yes—
35#2843C2212yes—
36#2839C2214yes—
37#2834C2212yes—
38#2831C2214yes—
39#2824C2212yes—
40#2822C2212yes—
41#2807C2212yes—
42#2799C2214yes—
43#2795C2212yes—
44#2794C2214yes—
45#2794C2212yes—
46#2791C2214yes—
47#2789C2214yes—
48#2789C2214yes—
49#2789C2212yes—
50#2783C2214yes—
51#2776C2214yes—
52#2776C2214yes—
53#2775C2214yes—
54#2775C2214yes—
55#2775C2214yes—
56#2769C2214yes—
57#2769C2212yes—
58#2767C2214yes—
59#2767C2214yes—
60#2762C2214yes—
61#2758C2214yes—
62#2747C2214yes—
63#2747C2214yes—
64#2747C2214yes—
65#2729C2214yes—
66#2722C2212yes—
67#2716C2214yes—
68#2716C2214yes—
69#2702C2214yes—
70#2698C2214yes—
71#2695C2214yes—
72#2693C2212yes—
73#2689C2214yes—
74#2687C2214yes—
75#2680C2214yes—
76#2677C2212yes—
77#2666C2214yes—
78#2666C2214yes—
79#2655C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2653C2214yes—
83#2652C2214yes—
84#2650C2214yes—
85#2650C2214yes—
86#2649C2214yes—
87#2645C2212yes—
88#2645C2214yes—
89#2643C2214yes—
90#2634C2214yes—
91#2629C2214yes—
92#2628C2211yescharacteristic
93#2621C2211yescharacteristic
94#2609C2212yes—
95#2599C2214yes—
96#2597C2214yes—
97#2595C2214yes—
98#2594C2214yes—
99#2594C2214yes—
100#2593C2212yes—
101#2588C2214yes—
102#2588C2214yes—
103#2588C2214yes—
104#2588C2214yes—
105#2587C2214yes—
106#2586C2214yes—
107#2585C2214yes—
108#2585C2212yes—
109#2585C2214yes—
110#2585C2214yes—
111#2585C2214yes—
112#2582C2212yes—
113#2577C2214yes—
114#2575C2214yes—
115#2574C2214yes—
116#2573C2212yes—
117#2571C2212yes—
118#2570C2212yes—
119#2568C2212yes—
120#2565C2214yes—
121#2560C2214yes—
122#2554C2212yes—
123#2552C2212yes—
124#2551C2212yes—
125#2551C2212yes—
126#2550C2212yes—
127#2546C2212yes—
128#2533C2214yes—
129#2533C2214yes—
130#2532C2214yes—
131#2531C2214yes—
132#2530C2214yes—
133#2529C2214yes—
134#2529C2214yes—
135#2528C2214yes—
136#2528C2214yes—
137#2527C2214yes—
138#2525C2214yes—
139#2525C2212yes—
140#2524C2214yes—
141#2523C2212yes—
142#2523C2212yes—
143#2520C2214yes—
144#2520C2214yes—
145#2516C2212yes—
146#2514C2212yes—
147#2514C2212yes—
148#2511C2212yes—
149#2511C2214yes—
150#2509C2212yes—
151#2509C2212yes—
152#2509C2212yes—
153#2508C2212yes—
154#2507C2212yes—
155#2499C2212yes—
156#2499C2212yes—
157#2496C2212yes—
158#2496C2214yes—
159#2495C2212yes—
160#2494C2212yes—
161#2494C2214yes—
162#2493C2214yes—
163#2492C2212yes—
164#2492C2214yes—
165#2492C2212yes—
166#2492C2214yes—
167#2489C2212yes—
168#2488C2214yes—
169#2485C2212yes—
170#2485C2212yes—
171#2469C2214yes—
172#2469C2212yes—
173#2465C2214yes—
174#2458C2212yes—
175#2453C2212yes—
176#2453C2212yes—
177#2451C2212yes—
178#2446C2214yes—
179#2446C2214yes—
180#2446C2212yes—
181#2442C2212yes—
182#2442C2212yes—
183#2440C2212yes—
184#2440C2212yes—
185#2439C2212yes—
186#2439C2212yes—
187#2429C2212yes—
188#2421C2212yes—
189#2421C2214yes—
190#2417C2212yes—
191#2417C2212yes—
192#2402C2214yes—
193#2402C2211yescharacteristic
194#2402C2214yes—
195#2398C2211yescharacteristic
196#2396C2211yescharacteristic
197#2392C2211yescharacteristic
198#2374C2214yes—
199#2373C2214yes—
200#2370C2214yes—
201#2370C2212yes—
202#2368C2214yes—
203#2368C2214yes—
204#2362C2212yes—
205#2360C2212yes—
206#2356C2212yes—
207#2355C2214yes—
208#2355C2214yes—
209#2352C2212yes—
210#2347C2212yes—
211#2347C2214yes—
212#2345C2212yes—
213#2336C2214yes—
214#2335C2214yes—
215#2334C2214yes—
216#2331C2212yes—
217#2331C2214yes—
218#2331C2212yes—
219#2331C2211yescharacteristic
220#2329C2214yes—
221#2327C2211yescharacteristic
222#2323C2212yes—
223#2323C2212yes—
224#2323C2212yes—
225#2323C2214yes—
226#2317C2211yescharacteristic
227#2317C2211yescharacteristic
228#2314C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2214yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#126C2214yes—
235C4×#126C2212yes—
236C4×#123C2212yes—
237#2298C2214yes—
238#2298C2212yes—
239#2295C2212yes—
240#2295C2212yes—
241#2295C2214yes—
242#2293C2212yes—
243#2293C2211yescharacteristic
244C2×#382C2211yescharacteristic
245#2274C2211yescharacteristic
246#2274C2211yescharacteristic
247#2274C2212yes—
248C42×Q8C2212yes—
249C42×Q8C2211yescharacteristic
250C4×#117C2211yescharacteristic
251#552—216no—
252#533—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2314yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2314yes—
259C2×#126C2314yes—
260C2×#126C2312yes—
261C2×#126C2314yes—
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#123C2314yes—
266C2×#123C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×#117C2312yes—
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2314yes—
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C42C2311yescharacteristic
293#401C2314yes—
294#401C2314yes—
295#401C2314yes—
296#401C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2311yescharacteristic
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#399C2312yes—
333#399C2311yescharacteristic
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2311yescharacteristic
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2311yescharacteristic
365#397C2312yes—
366#397C2312yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#396C2312yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2312yes—
388#395C2314yes—
389#395C2314yes—
390#395C2311yescharacteristic
391#395C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2311yescharacteristic
395#394C2312yes—
396#394C2312yes—
397#393C2314yes—
398#393C2314yes—
399#393C2312yes—
400#393C2314yes—
401#393C2311yescharacteristic
402#393C2314yes—
403#393C2312yes—
404#392C2311yescharacteristic
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#388C2312yes—
471#388C2314yes—
472#388C2312yes—
473#388C2312yes—
474#388C2314yes—
475#388C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2312yes—
480#388C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2312yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#387C2314yes—
508#387C2312yes—
509#387C2314yes—
510#387C2312yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
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#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2312yes—
582#385C2312yes—
583#385C2312yes—
584#385C2312yes—
585#385C2312yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#384C2314yes—
594#384C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2312yes—
598#383C2312yes—
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#382C2312yes—
605#382C2312yes—
606#382C2314yes—
607#382C2312yes—
608#382C2312yes—
609#382C2311yescharacteristic
610#382C2314yes—
611#382C2312yes—
612#382C2312yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2314yes—
616#382C2314yes—
617#381C2312yes—
618#381C2314yes—
619#380C2312yes—
620#380C2312yes—
621#380C2314yes—
622#380C2314yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2311yescharacteristic
683#376C2311yescharacteristic
684#376C2314yes—
685#376C2314yes—
686#376C2314yes—
687C2×#95C2314yes—
688C43C2311yescharacteristic
689C43C2314yes—
690C43C2311yescharacteristic
691C43C2312yes—
692C22×Q8C2412yes—
693C22×Q8C2411yescharacteristic
694C22×Q8C2414yes—
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×D4C2412yes—
698C22×D4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C4⋊Q8—28no—
706C4⋊Q8—42no—
707C4⋊Q8—44no—
708C4⋊Q8—42no—
709C4⋊Q8—48no—
710C4⋊Q8—48no—
711#126—216no—
712#126—48no—
713#126—44no—
714#125—28no—
715#125—28no—
716#125—216no—
717#123—216no—
718#123—44no—
719C22⋊Q8—28no—
720C22⋊Q8—28no—
721C22⋊Q8—216no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—44no—
725C4×Q8—28no—
726C4×Q8—216no—
727C4×Q8—28no—
728C4×Q8—42no—
729C4×Q8—48no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×D4—28no—
733C4×D4—42no—
734#117—24no—
735#117—216no—
736#117—24no—
737#117—28no—
738#117—42no—
739#117—44no—
740#117#4118yes—
741C2×C4⋊C4—28no—
742C2×C4⋊C4—42no—
743C2×C4⋊C4—42no—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C42—24no—
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2412yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2411yescharacteristic
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955C24C2512yes—
956C24C2511yescharacteristic
957C2×Q8—24no—
958C2×Q8—28no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—28no—
963C2×Q8—41no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×D4—24no—
971C2×D4—41no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—42no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—28no—
982C22×C4—44no—
983C22×C4—42no—
984C22×C4—44no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4C2×#4114yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4C2×#4118yes—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—24no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4C2×#4118yes—
1109C42—24no—
1110C42—22no—
1111C42—22no—
1112C42—24no—
1113C42—28no—
1114C42—24no—
1115C42—22no—
1116C42—24no—
1117C42—28no—
1118C42—22no—
1119C42—22no—
1120C42—24no—
1121C42—24no—
1122C42—44no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—44no—
1127C42—42no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—42no—
1132C42—42no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—42no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42C2×#4118yes—
1141C422−1+414yes—
1142C23—21no—
1143C23—22no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23C22×#4112yes—
1154C23C2611yescharacteristic
1155Q8—44no—
1156Q8—48no—
1157Q8—88no—
1158Q8—88no—
1159Q8—162no—
1160D4—84no—
1161D4—82no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—28no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—48no—
1228C2×C4—88no—
1229C2×C4—84no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4C22×#4112yes—
1233C2×C4C22×#4118yes—
1234C2×C4C22×#4112yes—
1235C2×C4C2×2−1+414yes—
1236C2×C4C2×2−1+412yes—
1237C2×C4#58514yes—
1238C2×C4#58512yes—
1239C22—24no—
1240C22—22no—
1241C22—41no—
1242C22—41no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22C23×#4111yescharacteristic
1252C22C22×2−1+411yescharacteristic
1253C22C2×#58512yes—
1254C22C2×#58511yescharacteristic
1255C222−1+612yes—
1256C4—28no—
1257C4—24no—
1258C4—22no—
1259C4—24no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—42no—
1264C4—42no—
1265C4—44no—
1266C4—44no—
1267C4—41no—
1268C4—44no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—44no—
1273C4—41no—
1274C4—42no—
1275C4—44no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4#346114yes—
1281C2—42no—
1282C2—82no—
1283C2C2×#346111yescharacteristic
1284C2#6282911yescharacteristic
1285C2#6289111yescharacteristic
1286C2#6295612yes—
1287C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42933C2semidirect
3. #42756C2semidirect
4. #42744C2semidirect
5. #42695C2semidirect
8. #41853C2semidirect
9. #41763C2semidirect
10. #41665C2semidirect
11. #40460C2semidirect
12. #40074C2semidirect
13. #39890C2semidirect
14. #39294C2semidirect
15. #39250C2semidirect
16. #39155C2semidirect
17. #38794C2semidirect
18. #38651C2semidirect
19. #35652C2semidirect
20. #35596C2semidirect
21. #35577C2semidirect
22. #35324C2semidirect
23. #35217C2semidirect
24. #34951C2semidirect
26. #34318C2semidirect
27. #34215C2semidirect

Maximal subgroups

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

subgroupindex
#429802
#429332
#427562
#427442
#426952
#426862
#418682
#418532
#417632
#416652
#404602
#400742
#398902
#392942
#392502
#391552
#387942
#386512
#356522
#355962
#355772
#353242
#352172
#349512
#348812
#343182
#342152