Finite Group Databasebeta

← #7681881

Subgroups — #7681881

Order 512.

4465 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60015C214yesmaximal, complemented
2#59539C214yesmaximal, complemented
3#59519C214yesmaximal, complemented
4#59511C214yesmaximal, complemented
5#43850C214yesmaximal, complemented
6#43801C214yesmaximal
7#43435C214yesmaximal, complemented
8#43401C214yesmaximal, complemented
9#39757C211yesmaximal, characteristic, complemented
10#39638C211yesmaximal, characteristic, complemented
11#39081C212yesmaximal, complemented
12#39078C212yesmaximal, complemented
13#38915C212yesmaximal
14#37888C211yesmaximal, characteristic, complemented
15#37882C211yesmaximal, characteristic, complemented
16#37709C211yesmaximal, characteristic, complemented
17#37705C211yesmaximal, characteristic, complemented
18#36512C212yesmaximal, complemented
19#36181C211yesmaximal, characteristic, complemented
20#36131C211yesmaximal, characteristic, complemented
21#35653C212yesmaximal, complemented
22#35596C212yesmaximal, complemented
23#35336C211yesmaximal, characteristic, complemented
24#35323C211yesmaximal, characteristic, complemented
25#35323C211yesmaximal, characteristic, complemented
26#34920C212yesmaximal, complemented
27#34318C212yesmaximal, complemented
28#34217C211yesmaximal, characteristic, complemented
29#34214C211yesmaximal, characteristic, complemented
30#34151C211yesmaximal, characteristic
31C4×#541C211yesmaximal, characteristic, complemented
32C2×#552C2212yes—
33C2×#541C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C22×#125C2211yescharacteristic
37#2863C2212yes—
38#2863C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2851C2211yescharacteristic
44#2851C2212yes—
45#2851C2211yescharacteristic
46#2810C2214yes—
47#2805C2214yes—
48#2802C2214yes—
49#2794C2214yes—
50#2794C2214yes—
51#2781C2214yes—
52#2774C2214yes—
53#2770C2214yes—
54#2770C2214yes—
55#2769C2214yes—
56#2767C2214yes—
57#2758C2214yes—
58#2744C2214yes—
59#2738C2214yes—
60#2725C2214yes—
61#2721C2214yes—
62#2720C2214yes—
63#2719C2214yes—
64#2719C2214yes—
65#2717C2214yes—
66#2708C2214yes—
67#2702C2214yes—
68#2690C2214yes—
69#2690C2214yes—
70#2647C2211yescharacteristic
71#2647C2212yes—
72#2647C2211yescharacteristic
73#2642C2211yescharacteristic
74#2642C2211yescharacteristic
75#2629C2211yescharacteristic
76#2629C2211yescharacteristic
77#2625C2212yes—
78#2625C2212yes—
79#2599C2214yes—
80#2597C2214yes—
81#2596C2214yes—
82#2596C2214yes—
83#2590C2214yes—
84#2590C2214yes—
85#2590C2214yes—
86#2590C2214yes—
87#2590C2214yes—
88#2590C2214yes—
89#2588C2214yes—
90#2588C2214yes—
91#2588C2214yes—
92#2587C2214yes—
93#2587C2214yes—
94#2585C2214yes—
95#2585C2214yes—
96#2584C2212yes—
97#2581C2212yes—
98#2577C2214yes—
99#2577C2214yes—
100#2577C2214yes—
101#2575C2214yes—
102#2575C2214yes—
103#2573C2214yes—
104#2570C2214yes—
105#2565C2212yes—
106#2560C2214yes—
107#2556C2214yes—
108#2553C2214yes—
109#2550C2212yes—
110#2533C2214yes—
111#2533C2214yes—
112#2533C2214yes—
113#2533C2214yes—
114#2533C2214yes—
115#2533C2214yes—
116#2530C2214yes—
117#2530C2214yes—
118#2530C2214yes—
119#2529C2214yes—
120#2526C2214yes—
121#2525C2214yes—
122#2524C2214yes—
123#2524C2214yes—
124#2524C2214yes—
125#2523C2214yes—
126#2520C2214yes—
127#2516C2214yes—
128#2515C2214yes—
129#2511C2212yes—
130#2511C2212yes—
131#2509C2214yes—
132#2509C2212yes—
133#2509C2214yes—
134#2508C2212yes—
135#2508C2212yes—
136#2506C2214yes—
137#2506C2212yes—
138#2503C2212yes—
139#2499C2212yes—
140#2496C2214yes—
141#2496C2212yes—
142#2496C2214yes—
143#2495C2212yes—
144#2492C2212yes—
145#2489C2212yes—
146#2487C2212yes—
147#2486C2214yes—
148#2485C2212yes—
149#2481C2214yes—
150#2481C2214yes—
151#2478C2214yes—
152#2478C2214yes—
153#2473C2214yes—
154#2470C2214yes—
155#2469C2214yes—
156#2469C2214yes—
157#2462C2214yes—
158#2462C2214yes—
159#2462C2214yes—
160#2453C2212yes—
161#2453C2214yes—
162#2451C2212yes—
163#2449C2214yes—
164#2442C2214yes—
165#2441C2212yes—
166#2440C2212yes—
167#2421C2214yes—
168#2421C2214yes—
169#2417C2212yes—
170#2415C2212yes—
171#2402C2214yes—
172#2399C2214yes—
173#2374C2214yes—
174#2374C2212yes—
175#2374C2212yes—
176#2373C2214yes—
177#2373C2212yes—
178#2373C2212yes—
179#2373C2214yes—
180#2370C2214yes—
181#2370C2212yes—
182#2370C2212yes—
183#2370C2214yes—
184#2370C2214yes—
185#2367C2212yes—
186#2363C2212yes—
187#2362C2212yes—
188#2362C2212yes—
189#2360C2212yes—
190#2360C2214yes—
191#2360C2214yes—
192#2360C2214yes—
193#2356C2212yes—
194#2356C2214yes—
195#2355C2214yes—
196#2352C2212yes—
197Q8×C4⋊C4C2214yes—
198#2347C2212yes—
199#2347C2214yes—
200#2345C2212yes—
201#2345C2214yes—
202#2345C2214yes—
203#2344C2214yes—
204#2336C2214yes—
205#2336C2214yes—
206#2335C2214yes—
207#2334C2214yes—
208#2330C2211yescharacteristic
209#2330C2211yescharacteristic
210#2330C2211yescharacteristic
211#2330C2211yescharacteristic
212#2330C2211yescharacteristic
213#2330C2211yescharacteristic
214#2330C2211yescharacteristic
215#2327C2211yescharacteristic
216#2323C2212yes—
217#2323C2212yes—
218#2323C2212yes—
219#2320C2212yes—
220#2317C2212yes—
221#2316C2212yes—
222#2314C2211yescharacteristic
223#2314C2212yes—
224C4×C4⋊Q8C2212yes—
225C4×C4⋊Q8C2211yescharacteristic
226C4×C4⋊Q8C2212yes—
227C4×#125C2212yes—
228C4×#125C2211yescharacteristic
229C4×#125C2214yes—
230C4×#125C2212yes—
231C4×#125C2214yes—
232C4×#125C2212yes—
233C4×#126C2214yes—
234C4×#126C2214yes—
235C4×C22⋊Q8C2212yes—
236#2298C2214yes—
237#2298C2211yescharacteristic
238#2298C2211yescharacteristic
239#2295C2212yes—
240#2295C2212yes—
241#2295C2211yescharacteristic
242#2295C2214yes—
243#2293C2211yescharacteristic
244#2293C2211yescharacteristic
245#2293C2211yescharacteristic
246#2290C2211yescharacteristic
247#2290C2211yescharacteristic
248#2285C2211yescharacteristic
249C2×#384C2211yescharacteristic
250#2274C2212yes—
251#2274C2212yes—
252C42×Q8C2212yes—
253C42×Q8C2211yescharacteristic
254C42×D4C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259#552—216no—
260#541—28no—
261#533—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264#529—28no—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#126C2311yescharacteristic
268C2×#126C2311yescharacteristic
269C2×#126C2314yes—
270C2×#125—28no—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#125C2311yescharacteristic
275C2×#125C2311yescharacteristic
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2311yescharacteristic
279C2×#125C2314yes—
280C2×#125C2311yescharacteristic
281C2×#124C2311yescharacteristic
282C2×#123C2314yes—
283C2×#123C2311yescharacteristic
284C2×#123C2311yescharacteristic
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2314yes—
291C2×#121C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2314yes—
313C2×#117C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
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#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
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#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#394C2314yes—
391#394C2314yes—
392#393C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2314yes—
407#390C2312yes—
408#390C2312yes—
409#390C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#388C2312yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2312yes—
469#388C2314yes—
470#388C2312yes—
471#388C2314yes—
472#388C2314yes—
473#388C2312yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2312yes—
486#388C2312yes—
487#388C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
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#387C2312yes—
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#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2312yes—
569#386C2312yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2312yes—
583#384C2312yes—
584#384C2311yescharacteristic
585#384C2312yes—
586#384C2314yes—
587#384C2311yescharacteristic
588#384C2311yescharacteristic
589#384C2314yes—
590#383C2314yes—
591#383C2314yes—
592#383C2314yes—
593#383C2314yes—
594#383C2314yes—
595#383C2314yes—
596#382C2312yes—
597#382C2311yescharacteristic
598#382C2314yes—
599#382C2314yes—
600#382C2312yes—
601#382C2312yes—
602#382C2314yes—
603#382C2314yes—
604#382C2314yes—
605#381C2314yes—
606#381C2314yes—
607#380C2312yes—
608#380C2312yes—
609#380C2312yes—
610#380C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2314yes—
614#380C2312yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2311yescharacteristic
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2312yes—
697#376C2314yes—
698#376C2314yes—
699#376C2314yes—
700C43C2314yes—
701C43C2311yescharacteristic
702C43C2311yescharacteristic
703C43C2311yescharacteristic
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C22×Q8C2412yes—
708C22×Q8C2414yes—
709C22×Q8C2411yescharacteristic
710C22×D4C2411yescharacteristic
711C22×D4C2411yescharacteristic
712C22×D4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2412yes—
715C23×C4C2411yescharacteristic
716C23×C4C2411yescharacteristic
717C23×C4C2414yes—
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C4⋊Q8—28no—
723C4⋊Q8—24no—
724#126—216no—
725#126—24no—
726#126—24no—
727#126—216no—
728#126—48no—
729#125—28no—
730#125—216no—
731#125—24no—
732#125—216no—
733#125—216no—
734#125—24no—
735#125—24no—
736#125—28no—
737#125—48no—
738#125#4118yes—
739#124—24no—
740#123—216no—
741#123—24no—
742#123—24no—
743C22⋊Q8—28no—
744C22⋊Q8—28no—
745C22⋊Q8—24no—
746C22⋊Q8—216no—
747C22⋊Q8—28no—
748C22⋊Q8—48no—
749#121—24no—
750C4×Q8—216no—
751C4×Q8—28no—
752C4×Q8—24no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—44no—
756C4×Q8—48no—
757C4×Q8—48no—
758C4×D4—24no—
759C4×D4—24no—
760C4×D4—44no—
761C4×D4#4118yes—
762#117—24no—
763#117—24no—
764#117—28no—
765#117—28no—
766#117—216no—
767#117—24no—
768#117—24no—
769#117—24no—
770#117—24no—
771#117—44no—
772C2×C4⋊C4—28no—
773C2×C4⋊C4—28no—
774C2×C4⋊C4—216no—
775C2×C4⋊C4—48no—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C42—24no—
874C2×C42—24no—
875C2×C42—24no—
876C2×C42C2414yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991C24C2511yescharacteristic
992C24C2511yescharacteristic
993C24C2511yescharacteristic
994C2×Q8—24no—
995C2×Q8—22no—
996C2×Q8—28no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—28no—
1000C2×Q8—42no—
1001C2×Q8—44no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4C2×#4114yes—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—28no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—22no—
1021C22×C4—28no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4C2×#4114yes—
1032C22×C4C2×#4114yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2514yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4C2×#4118yes—
1126C4⋊C4C2×#41116yes—
1127C4⋊C4C2×#4114yes—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—28no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—28no—
1134C22⋊C4—22no—
1135C22⋊C4—22no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—24no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4C2×#4114yes—
1157C22⋊C4C2×#4114yes—
1158C42—22no—
1159C42—24no—
1160C42—22no—
1161C42—24no—
1162C42—22no—
1163C42—22no—
1164C42—22no—
1165C42—28no—
1166C42—22no—
1167C42—22no—
1168C42—28no—
1169C42—22no—
1170C42—28no—
1171C42—28no—
1172C42—22no—
1173C42—22no—
1174C42—22no—
1175C42—28no—
1176C42—24no—
1177C42—24no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—42no—
1182C42—44no—
1183C42—42no—
1184C42—44no—
1185C42—42no—
1186C42—42no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—44no—
1191C42—42no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42C2×#4114yes—
1198C42C2×#4114yes—
1199C422−1+414yes—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—21no—
1209C23—21no—
1210C23—21no—
1211C23—22no—
1212C23—22no—
1213C23C22×#4112yes—
1214C23C22×#4112yes—
1215C23C2611yescharacteristic
1216Q8—416no—
1217Q8—44no—
1218Q8—48no—
1219D4—44no—
1220D4—82no—
1221D4—82no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—28no—
1237C2×C4—28no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—48no—
1290C2×C4—44no—
1291C2×C4—44no—
1292C2×C4—84no—
1293C2×C4—88no—
1294C2×C4—82no—
1295C2×C4—88no—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4112yes—
1298C2×C4C22×#4114yes—
1299C2×C4C22×#4118yes—
1300C2×C4C22×#4112yes—
1301C2×C4C22×#4112yes—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C2×2−1+414yes—
1305C2×C4C2×2−1+412yes—
1306C2×C4#58514yes—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22C23×#4111yescharacteristic
1323C22C23×#4111yescharacteristic
1324C22C22×2−1+411yescharacteristic
1325C22C2×#58512yes—
1326C222−1+612yes—
1327C4—24no—
1328C4—24no—
1329C4—28no—
1330C4—22no—
1331C4—22no—
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—42no—
1336C4—42no—
1337C4—44no—
1338C4—44no—
1339C4—41no—
1340C4—44no—
1341C4—44no—
1342C4—41no—
1343C4—41no—
1344C4—44no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—44no—
1352C4—41no—
1353C4—44no—
1354C4#348214yes—
1355C2—42no—
1356C2—42no—
1357C2—81no—
1358C2C2×#348211yescharacteristic
1359C2#6281511yescharacteristic
1360C2#6286111yescharacteristic
1361C2#6295612yes—
1362C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60015C2semidirect
2. #59539C2semidirect
3. #59519C2semidirect
4. #59511C2semidirect
5. #43850C2semidirect
7. #43435C2semidirect
8. #43401C2semidirect
9. #39757C2semidirect
10. #39638C2semidirect
11. #39081C2semidirect
12. #39078C2semidirect
14. #37888C2semidirect
15. #37882C2semidirect
16. #37709C2semidirect
17. #37705C2semidirect
18. #36512C2semidirect
19. #36181C2semidirect
20. #36131C2semidirect
21. #35653C2semidirect
22. #35596C2semidirect
23. #35336C2semidirect
24. #35323C2semidirect
25. #35323C2semidirect
26. #34920C2semidirect
27. #34318C2semidirect
28. #34217C2semidirect
29. #34214C2semidirect
31. C4×#541C2semidirect

Maximal subgroups

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

subgroupindex
#600152
#595392
#595192
#595112
#438502
#438012
#434352
#434012
#397572
#396382
#390812
#390782
#389152
#378882
#378822
#377092
#377052
#365122
#361812
#361312
#356532
#355962
#353362
#353232
#349202
#343182
#342172
#342142
#341512
C4×#5412