Finite Group Databasebeta

← #7658104

Subgroups — #7658104

Order 512.

4207 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42398C212yesmaximal, complemented
2#42335C214yesmaximal, complemented
3#42334C214yesmaximal, complemented
4#42332C212yesmaximal, complemented
5#41762C214yesmaximal, complemented
6#41757C214yesmaximal, complemented
7#41440C212yesmaximal, complemented
8#41438C212yesmaximal, complemented
9#39603C212yesmaximal, complemented
10#39081C212yesmaximal, complemented
11#39077C212yesmaximal, complemented
12#38927C212yesmaximal, complemented
13#37974C212yesmaximal
14#37971C212yesmaximal
15#37598C212yesmaximal, complemented
16#37592C212yesmaximal, complemented
17#37567C211yesmaximal, characteristic, complemented
18#37540C211yesmaximal, characteristic, complemented
19#36512C212yesmaximal, complemented
20#36199C212yesmaximal, complemented
21#36090C212yesmaximal, complemented
22#36081C212yesmaximal, complemented
23#36064C212yesmaximal, complemented
24#36052C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic
26#35321C212yesmaximal, complemented
27#34627C211yesmaximal, characteristic
28#34625C212yesmaximal, complemented
29#34239C211yesmaximal, characteristic, complemented
30#34225C211yesmaximal, characteristic, complemented
31#34121C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2863C2212yes—
36#2863C2212yes—
37#2855C2212yes—
38#2855C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2841C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2838C2214yes—
45#2836C2214yes—
46#2822C2214yes—
47#2794C2214yes—
48#2792C2214yes—
49#2791C2214yes—
50#2791C2214yes—
51#2788C2214yes—
52#2770C2214yes—
53#2769C2214yes—
54#2768C2214yes—
55#2768C2214yes—
56#2767C2214yes—
57#2767C2214yes—
58#2765C2214yes—
59#2764C2214yes—
60#2762C2214yes—
61#2761C2214yes—
62#2758C2214yes—
63#2755C2214yes—
64#2751C2214yes—
65#2744C2214yes—
66#2743C2214yes—
67#2743C2214yes—
68#2740C2214yes—
69#2738C2214yes—
70#2737C2214yes—
71#2667C2214yes—
72#2667C2212yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2665C2214yes—
79#2665C2212yes—
80#2660C2212yes—
81#2660C2212yes—
82#2655C2214yes—
83#2654C2214yes—
84#2650C2214yes—
85#2650C2214yes—
86#2647C2212yes—
87#2647C2212yes—
88#2647C2212yes—
89#2642C2212yes—
90#2638C2212yes—
91#2638C2212yes—
92#2637C2214yes—
93#2634C2212yes—
94#2634C2212yes—
95#2634C2214yes—
96#2634C2212yes—
97#2633C2212yes—
98#2629C2212yes—
99#2629C2212yes—
100#2629C2212yes—
101#2628C2211yescharacteristic
102#2628C2212yes—
103#2628C2211yescharacteristic
104#2627C2214yes—
105#2625C2212yes—
106#2621C2211yescharacteristic
107#2621C2211yescharacteristic
108#2616C2212yes—
109#2609C2214yes—
110#2606C2212yes—
111#2605C2214yes—
112#2605C2212yes—
113#2601C2214yes—
114#2599C2214yes—
115#2599C2214yes—
116#2588C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2579C2212yes—
120#2579C2212yes—
121#2579C2212yes—
122#2579C2212yes—
123#2575C2214yes—
124#2575C2214yes—
125#2574C2214yes—
126#2573C2214yes—
127#2573C2214yes—
128#2572C2214yes—
129#2570C2212yes—
130#2570C2214yes—
131#2566C2212yes—
132#2566C2212yes—
133#2565C2212yes—
134#2565C2212yes—
135#2565C2212yes—
136#2565C2214yes—
137#2565C2212yes—
138#2550C2212yes—
139#2533C2214yes—
140#2528C2214yes—
141#2526C2214yes—
142#2525C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2524C2214yes—
149#2524C2214yes—
150#2524C2214yes—
151#2524C2214yes—
152#2524C2214yes—
153#2523C2214yes—
154#2522C2214yes—
155#2520C2214yes—
156#2520C2214yes—
157#2520C2214yes—
158#2519C2214yes—
159#2516C2214yes—
160#2515C2214yes—
161#2515C2214yes—
162#2515C2214yes—
163#2515C2214yes—
164#2514C2212yes—
165#2511C2212yes—
166#2508C2214yes—
167#2508C2212yes—
168#2508C2212yes—
169#2507C2212yes—
170#2506C2212yes—
171#2503C2212yes—
172#2502C2212yes—
173#2497C2212yes—
174#2496C2212yes—
175#2495C2212yes—
176#2495C2212yes—
177#2493C2214yes—
178#2492C2212yes—
179#2489C2212yes—
180#2484C2214yes—
181#2484C2212yes—
182#2484C2212yes—
183#2479C2214yes—
184#2478C2214yes—
185#2475C2214yes—
186#2473C2214yes—
187#2453C2212yes—
188#2451C2212yes—
189#2441C2212yes—
190#2439C2212yes—
191#2423C2212yes—
192#2421C2212yes—
193#2402C2214yes—
194#2399C2214yes—
195#2399C2212yes—
196#2398C2212yes—
197#2396C2214yes—
198#2396C2214yes—
199#2395C2212yes—
200#2395C2212yes—
201#2373C2214yes—
202#2371C2212yes—
203#2371C2214yes—
204#2371C2212yes—
205#2370C2212yes—
206#2370C2214yes—
207#2370C2212yes—
208#2362C2212yes—
209#2362C2212yes—
210#2357C2211yescharacteristic
211#2357C2211yescharacteristic
212#2356C2211yescharacteristic
213#2356C2211yescharacteristic
214#2356C2212yes—
215#2356C2214yes—
216#2355C2212yes—
217#2354C2212yes—
218#2353C2211yescharacteristic
219#2353C2211yescharacteristic
220#2353C2211yescharacteristic
221#2353C2211yescharacteristic
222#2352C2212yes—
223#2352C2212yes—
224#2351C2212yes—
225#2347C2212yes—
226#2346C2212yes—
227#2345C2212yes—
228#2344C2212yes—
229#2344C2214yes—
230#2343C2214yes—
231#2336C2214yes—
232#2323C2212yes—
233#2323C2212yes—
234#2323C2214yes—
235#2320C2212yes—
236#2320C2212yes—
237#2320C2212yes—
238#2317C2211yescharacteristic
239#2317C2211yescharacteristic
240#2313C2212yes—
241#2311C2211yescharacteristic
242#2311C2211yescharacteristic
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#125C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2298C2212yes—
252#2298C2212yes—
253#2297C2212yes—
254#2285C2211yescharacteristic
255#2285C2212yes—
256#2285C2211yescharacteristic
257#2283C2211yescharacteristic
258#2283C2212yes—
259#2283C2211yescharacteristic
260#2283C2211yescharacteristic
261#2276C2212yes—
262#2274C2212yes—
263C4×#117C2212yes—
264C4×#117C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2311yescharacteristic
268#533—28no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×#126C2314yes—
273C2×#125—28no—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C4×#41—28no—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2314yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2314yes—
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2312yes—
355#399C2312yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2312yes—
422#395C2312yes—
423#395C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
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#387C2312yes—
528#387C2314yes—
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#387C2314yes—
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#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#386C2312yes—
577#386C2312yes—
578#386C2312yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2312yes—
583#386C2312yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#384C2312yes—
603#384C2312yes—
604#384C2312yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2312yes—
613#383C2314yes—
614#383C2311yescharacteristic
615#383C2311yescharacteristic
616#383C2311yescharacteristic
617#383C2311yescharacteristic
618#383C2314yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#382C2314yes—
630#382C2312yes—
631#382C2314yes—
632#382C2314yes—
633#382C2312yes—
634#382C2314yes—
635#382C2311yescharacteristic
636#382C2311yescharacteristic
637#382C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2311yescharacteristic
643#381C2314yes—
644#381C2312yes—
645#381C2311yescharacteristic
646#381C2311yescharacteristic
647#381C2311yescharacteristic
648#381C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2314yes—
654#380C2311yescharacteristic
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2311yescharacteristic
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2311yescharacteristic
720C4×C22⋊C4C2311yescharacteristic
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724#376C2311yescharacteristic
725#376C2312yes—
726#376C2314yes—
727#376C2312yes—
728#376C2314yes—
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731#376C2311yescharacteristic
732#376C2312yes—
733C2×#95C2311yescharacteristic
734C2×#95C2311yescharacteristic
735C43C2312yes—
736C43C2312yes—
737C2×#41—24no—
738C2×#41—24no—
739C2×#41—42no—
740C22×Q8C2412yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2414yes—
744C22×D4C2411yescharacteristic
745C22×D4C2411yescharacteristic
746C22×D4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—44no—
763#126—48no—
764#125—28no—
765#125—28no—
766#125—28no—
767#125—28no—
768#125—28no—
769#125—44no—
770#125—48no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—44no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—28no—
778C4×Q8—28no—
779C4×Q8—48no—
780C4×Q8—48no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×D4—24no—
784C4×D4—24no—
785C4×D4—24no—
786C4×D4—24no—
787C4×D4—24no—
788C4×D4—24no—
789#117—24no—
790#117—28no—
791#117—24no—
792#117—24no—
793#117—48no—
794#117—44no—
795#117—48no—
796#117—44no—
797#117—44no—
798#117—42no—
799#117—42no—
800C2×C4⋊C4—24no—
801C2×C4⋊C4—28no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—24no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C42—28no—
899C2×C42—24no—
900C2×C42—24no—
901C2×C42#4118yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938#95C2411yescharacteristic
939#95C2411yescharacteristic
940#95C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024C24C2511yescharacteristic
1025C24C2511yescharacteristic
1026C24C2511yescharacteristic
1027#41—416no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—44no—
1035C2×Q8—41no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—22no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4C2×#4114yes—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C42−1+414yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C22⋊C4—22no—
1173C22⋊C4—22no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—22no—
1177C22⋊C4—22no—
1178C22⋊C4—22no—
1179C22⋊C4—22no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C42—22no—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—22no—
1205C42—22no—
1206C42—28no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—28no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—28no—
1216C42—24no—
1217C42—28no—
1218C42—42no—
1219C42—42no—
1220C42—44no—
1221C42—42no—
1222C42—44no—
1223C42—44no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—42no—
1230C42—44no—
1231C42—44no—
1232C42C2×#4114yes—
1233C42C2×#4114yes—
1234C42C2×#4114yes—
1235C42C2×#4114yes—
1236C23—21no—
1237C23—21no—
1238C23—22no—
1239C23—22no—
1240C23—21no—
1241C23—21no—
1242C23—22no—
1243C23—22no—
1244C23—21no—
1245C23—21no—
1246C23—22no—
1247C23—21no—
1248C23—22no—
1249C23C22×#4112yes—
1250C23C2×2−1+412yes—
1251C23C2611yescharacteristic
1252Q8—44no—
1253Q8—48no—
1254Q8—48no—
1255Q8—88no—
1256D4—44no—
1257D4—44no—
1258D4—44no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—28no—
1270C2×C4—28no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
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—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—44no—
1328C2×C4—44no—
1329C2×C4—48no—
1330C2×C4—44no—
1331C2×C4—44no—
1332C2×C4—48no—
1333C2×C4—44no—
1334C2×C4—82no—
1335C2×C4—82no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4112yes—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C2×2−1+412yes—
1345C2×C4C2×2−1+412yes—
1346C2×C4#58514yes—
1347C2×C4#58512yes—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—24no—
1352C22—22no—
1353C22—41no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—42no—
1361C22—42no—
1362C22—41no—
1363C22C23×#4111yescharacteristic
1364C22C22×2−1+411yescharacteristic
1365C22C2×#58511yescharacteristic
1366C22C2×#58512yes—
1367C222−1+612yes—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—24no—
1373C4—22no—
1374C4—22no—
1375C4—41no—
1376C4—44no—
1377C4—41no—
1378C4—41no—
1379C4—44no—
1380C4—44no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—42no—
1391C4—41no—
1392C4—41no—
1393C4—44no—
1394C4—44no—
1395C4#349514yes—
1396C2—42no—
1397C2—42no—
1398C2—81no—
1399C2#6268611yescharacteristic
1400C2C2×#349511yescharacteristic
1401C2#6286011yescharacteristic
1402C2#6292812yes—
1403C2#6293912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42398C2semidirect
2. #42335C2semidirect
3. #42334C2semidirect
4. #42332C2semidirect
5. #41762C2semidirect
6. #41757C2semidirect
7. #41440C2semidirect
8. #41438C2semidirect
9. #39603C2semidirect
10. #39081C2semidirect
11. #39077C2semidirect
12. #38927C2semidirect
15. #37598C2semidirect
16. #37592C2semidirect
17. #37567C2semidirect
18. #37540C2semidirect
19. #36512C2semidirect
20. #36199C2semidirect
21. #36090C2semidirect
22. #36081C2semidirect
23. #36064C2semidirect
24. #36052C2semidirect
26. #35321C2semidirect
28. #34625C2semidirect
29. #34239C2semidirect
30. #34225C2semidirect

Maximal subgroups

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

subgroupindex
#423982
#423352
#423342
#423322
#417622
#417572
#414402
#414382
#396032
#390812
#390772
#389272
#379742
#379712
#375982
#375922
#375672
#375402
#365122
#361992
#360902
#360812
#360642
#360522
#353332
#353212
#346272
#346252
#342392
#342252
#341212