Finite Group Databasebeta

← #7681187

Subgroups — #7681187

Order 512.

4635 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59955C214yesmaximal
2#59708C214yesmaximal, complemented
3#59664C214yesmaximal, complemented
4#59491C214yesmaximal, complemented
5#44712C214yesmaximal, complemented
6#44614C214yesmaximal, complemented
7#44372C214yesmaximal, complemented
8#44218C214yesmaximal, complemented
9#39757C211yesmaximal, characteristic, complemented
10#39641C211yesmaximal, characteristic, complemented
11#39293C212yesmaximal, complemented
12#38261C212yesmaximal, complemented
13#38040C212yesmaximal
14#37883C211yesmaximal, characteristic, complemented
15#37882C211yesmaximal, characteristic, complemented
16#37709C211yesmaximal, characteristic, complemented
17#37705C211yesmaximal, characteristic, complemented
18#36280C212yesmaximal, complemented
19#36180C211yesmaximal, characteristic, complemented
20#36131C211yesmaximal, characteristic, complemented
21#35613C212yesmaximal, complemented
22#35583C212yesmaximal, complemented
23#35323C211yesmaximal, characteristic, complemented
24#35315C211yesmaximal, characteristic, complemented
25#35294C211yesmaximal, characteristic, complemented
26#34772C212yesmaximal, complemented
27#34299C212yesmaximal, complemented
28#34281C211yesmaximal, characteristic, complemented
29#34214C211yesmaximal, characteristic, complemented
30#34149C211yesmaximal, characteristic
31C2×#2330C211yesmaximal, characteristic, complemented
32C2×#554C2212yes—
33C2×#541C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C22×#125C2211yescharacteristic
37#2868C2211yescharacteristic
38#2863C2212yes—
39#2859C2211yescharacteristic
40#2859C2212yes—
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2855C2212yes—
44#2851C2211yescharacteristic
45#2851C2211yescharacteristic
46#2810C2214yes—
47#2805C2214yes—
48#2805C2214yes—
49#2794C2214yes—
50#2793C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2777C2214yes—
56#2771C2214yes—
57#2767C2214yes—
58#2765C2214yes—
59#2759C2214yes—
60#2758C2214yes—
61#2725C2214yes—
62#2721C2214yes—
63#2721C2214yes—
64#2719C2214yes—
65#2719C2214yes—
66#2702C2214yes—
67#2690C2214yes—
68#2689C2214yes—
69#2674C2214yes—
70#2647C2211yescharacteristic
71#2647C2211yescharacteristic
72#2645C2212yes—
73#2642C2211yescharacteristic
74#2642C2211yescharacteristic
75#2629C2211yescharacteristic
76#2629C2211yescharacteristic
77#2628C2212yes—
78#2625C2212yes—
79#2612C2214yes—
80#2612C2214yes—
81#2611C2214yes—
82#2606C2214yes—
83#2606C2214yes—
84#2605C2214yes—
85#2604C2214yes—
86#2590C2214yes—
87#2590C2214yes—
88#2588C2214yes—
89#2585C2214yes—
90#2585C2214yes—
91#2581C2214yes—
92#2581C2212yes—
93#2577C2214yes—
94#2577C2214yes—
95#2575C2214yes—
96#2570C2214yes—
97#2567C2212yes—
98#2556C2214yes—
99#2553C2214yes—
100#2552C2214yes—
101#2550C2214yes—
102#2550C2214yes—
103#2550C2212yes—
104#2546C2214yes—
105#2546C2212yes—
106#2533C2214yes—
107#2533C2214yes—
108#2533C2214yes—
109#2533C2214yes—
110#2530C2214yes—
111#2528C2214yes—
112#2528C2214yes—
113#2528C2214yes—
114#2522C2214yes—
115#2520C2214yes—
116#2515C2214yes—
117#2511C2212yes—
118#2511C2212yes—
119#2508C2214yes—
120#2507C2212yes—
121#2507C2212yes—
122#2507C2212yes—
123#2506C2214yes—
124#2506C2212yes—
125#2505C2214yes—
126#2505C2214yes—
127#2502C2212yes—
128#2502C2212yes—
129#2497C2212yes—
130#2496C2212yes—
131#2493C2214yes—
132#2492C2212yes—
133#2489C2212yes—
134#2488C2214yes—
135#2487C2212yes—
136#2486C2212yes—
137#2484C2214yes—
138#2481C2214yes—
139#2481C2214yes—
140#2478C2214yes—
141#2475C2214yes—
142#2473C2214yes—
143#2473C2214yes—
144#2470C2214yes—
145#2469C2214yes—
146#2469C2214yes—
147#2462C2214yes—
148#2462C2214yes—
149#2462C2214yes—
150#2453C2214yes—
151#2453C2212yes—
152#2451C2214yes—
153#2451C2212yes—
154#2450C2214yes—
155#2449C2214yes—
156#2446C2214yes—
157#2443C2214yes—
158#2442C2214yes—
159#2441C2212yes—
160#2441C2214yes—
161#2440C2214yes—
162#2440C2214yes—
163#2440C2212yes—
164#2440C2214yes—
165#2439C2214yes—
166#2438C2214yes—
167#2419C2214yes—
168#2417C2212yes—
169#2415C2212yes—
170#2413C2214yes—
171#2402C2214yes—
172#2396C2214yes—
173#2373C2214yes—
174#2373C2214yes—
175#2373C2212yes—
176#2373C2212yes—
177#2372C2212yes—
178#2371C2214yes—
179#2371C2212yes—
180#2371C2214yes—
181#2370C2214yes—
182#2368C2212yes—
183#2368C2214yes—
184#2365C2212yes—
185#2364C2212yes—
186#2362C2214yes—
187#2362C2212yes—
188#2360C2214yes—
189#2360C2214yes—
190#2360C2214yes—
191#2360C2212yes—
192#2360C2214yes—
193#2359C2212yes—
194#2359C2212yes—
195#2356C2212yes—
196#2355C2214yes—
197#2353C2214yes—
198#2352C2212yes—
199Q8×C4⋊C4C2214yes—
200D4×C4⋊C4C2214yes—
201#2345C2212yes—
202#2344C2212yes—
203#2343C2214yes—
204#2336C2214yes—
205#2332C2214yes—
206#2331C2212yes—
207#2330C2212yes—
208#2330C2214yes—
209#2330C2211yescharacteristic
210#2330C2211yescharacteristic
211#2330C2214yes—
212#2330C2212yes—
213#2330C2211yescharacteristic
214#2330C2211yescharacteristic
215#2330C2211yescharacteristic
216#2330C2211yescharacteristic
217#2330C2211yescharacteristic
218#2327C2211yescharacteristic
219#2323C2212yes—
220#2323C2212yes—
221#2320C2212yes—
222#2317C2212yes—
223#2314C2211yescharacteristic
224C4×C4⋊Q8C2211yescharacteristic
225C4×C4⋊Q8C2212yes—
226C4×C4⋊Q8C2212yes—
227C4×#125C2211yescharacteristic
228C4×C22⋊Q8C2214yes—
229C4×C22⋊Q8C2214yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232#2298C2211yescharacteristic
233#2298C2211yescharacteristic
234#2295C2211yescharacteristic
235#2295C2211yescharacteristic
236#2295C2212yes—
237#2295C2212yes—
238C2×#389C2214yes—
239C2×#389C2212yes—
240#2290C2211yescharacteristic
241#2290C2214yes—
242#2290C2214yes—
243#2290C2211yescharacteristic
244#2290C2211yescharacteristic
245#2290C2211yescharacteristic
246C2×#387C2214yes—
247#2285C2212yes—
248C2×#384C2211yescharacteristic
249C2×#384C2211yescharacteristic
250#2276C2212yes—
251#2274C2212yes—
252C42×D4C2211yescharacteristic
253C42×D4C2211yescharacteristic
254C4×#117C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×#376C2211yescharacteristic
259#554—216no—
260#541—28no—
261#533—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2314yes—
267#529—28no—
268C2×#126C2311yescharacteristic
269C2×#126C2311yescharacteristic
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125—28no—
273C2×#125C2311yescharacteristic
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2311yescharacteristic
283C2×#124C2311yescharacteristic
284C2×#123C2311yescharacteristic
285C2×#123C2311yescharacteristic
286C2×#123C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×#121C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2314yes—
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2314yes—
331#401C2314yes—
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#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
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#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#388C2314yes—
475#388C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2314yes—
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#387C2312yes—
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#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2314yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#386C2314yes—
567#386C2312yes—
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#386C2314yes—
572#386C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2312yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#385C2312yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#384C2312yes—
592#384C2311yescharacteristic
593#384C2312yes—
594#384C2314yes—
595#384C2314yes—
596#384C2311yescharacteristic
597#384C2311yescharacteristic
598#384C2314yes—
599#384C2312yes—
600#384C2312yes—
601#384C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#382C2311yescharacteristic
606#382C2314yes—
607#382C2314yes—
608#382C2314yes—
609#382C2314yes—
610#382C2314yes—
611#382C2312yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2312yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2311yescharacteristic
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2311yescharacteristic
671C4×C22⋊C4C2311yescharacteristic
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2311yescharacteristic
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2311yescharacteristic
686#376C2311yescharacteristic
687#376C2311yescharacteristic
688#376C2312yes—
689#376C2312yes—
690#376C2311yescharacteristic
691#376C2311yescharacteristic
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694#376C2314yes—
695#376C2314yes—
696#376C2314yes—
697#376C2312yes—
698#376C2314yes—
699C2×#95C2314yes—
700C2×#95C2314yes—
701C2×#95C2312yes—
702C2×#95C2312yes—
703C43C2311yescharacteristic
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C22×Q8C2412yes—
708C22×Q8C2414yes—
709C22×Q8C2414yes—
710C22×Q8C2411yescharacteristic
711C22×D4C2411yescharacteristic
712C22×D4C2411yescharacteristic
713C22×D4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C23×C4C2412yes—
717C23×C4C2414yes—
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2414yes—
724C23×C4C2411yescharacteristic
725C23×C4C2414yes—
726C4⋊Q8—28no—
727C4⋊Q8—24no—
728C4⋊Q8—28no—
729C4⋊Q8—84no—
730C4⋊Q8—84no—
731#126—24no—
732#126—216no—
733#126—24no—
734#126—84no—
735#125—28no—
736#125—216no—
737#125—24no—
738#125—216no—
739#125—216no—
740#125—24no—
741#125—24no—
742#125—84no—
743#125—84no—
744#125#4118yes—
745#124—24no—
746#123—24no—
747#123—24no—
748#123—84no—
749C22⋊Q8—28no—
750C22⋊Q8—28no—
751C22⋊Q8—216no—
752C22⋊Q8—28no—
753C22⋊Q8—24no—
754C22⋊Q8—216no—
755C22⋊Q8—216no—
756C22⋊Q8—216no—
757#121—24no—
758C4×Q8—216no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—84no—
764C4×Q8—84no—
765C4×Q8—84no—
766C4×D4—216no—
767C4×D4—24no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4#4118yes—
772#117—24no—
773#117—28no—
774#117—28no—
775#117—24no—
776#117—24no—
777#117—24no—
778#117—84no—
779#117—84no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—216no—
784C2×C4⋊C4—84no—
785C2×C4⋊C4—84no—
786C2×C4⋊C4—84no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2411yescharacteristic
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2411yescharacteristic
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C42—24no—
884C2×C42—24no—
885C2×C42—24no—
886C2×C42—24no—
887C2×C42—24no—
888C2×C42—84no—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001C24C2511yescharacteristic
1002C24C2511yescharacteristic
1003C24C2511yescharacteristic
1004C2×Q8—24no—
1005C2×Q8—28no—
1006C2×Q8—24no—
1007C2×Q8—22no—
1008C2×Q8—28no—
1009C2×Q8—24no—
1010C2×Q8—28no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×D4—24no—
1016C2×D4—22no—
1017C2×D4—24no—
1018C2×D4—22no—
1019C2×D4—42no—
1020C2×D4C2×#4114yes—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—28no—
1030C22×C4—22no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4C2×#4114yes—
1054C22×C4C2×#4114yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—28no—
1102C4⋊C4—22no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
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—44no—
1148C4⋊C4—44no—
1149C4⋊C4C2×#4118yes—
1150C4⋊C4C2×#41116yes—
1151C4⋊C4C2×#4114yes—
1152C22⋊C4—22no—
1153C22⋊C4—22no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—22no—
1157C22⋊C4—22no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—22no—
1161C22⋊C4—28no—
1162C22⋊C4—22no—
1163C22⋊C4—24no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4C2×#4114yes—
1177C22⋊C4C2×#4114yes—
1178C22⋊C42−1+418yes—
1179C42—22no—
1180C42—22no—
1181C42—24no—
1182C42—22no—
1183C42—24no—
1184C42—22no—
1185C42—22no—
1186C42—22no—
1187C42—22no—
1188C42—28no—
1189C42—22no—
1190C42—28no—
1191C42—28no—
1192C42—22no—
1193C42—24no—
1194C42—24no—
1195C42—22no—
1196C42—24no—
1197C42—24no—
1198C42—22no—
1199C42—24no—
1200C42—24no—
1201C42—28no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—44no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42—42no—
1215C42C2×#4114yes—
1216C42C2×#4114yes—
1217C422−1+414yes—
1218C23—21no—
1219C23—21no—
1220C23—22no—
1221C23—21no—
1222C23—21no—
1223C23—22no—
1224C23—22no—
1225C23—21no—
1226C23—21no—
1227C23—22no—
1228C23—21no—
1229C23—22no—
1230C23C22×#4112yes—
1231C23C22×#4112yes—
1232C23C2×2−1+414yes—
1233C23C2611yescharacteristic
1234Q8—416no—
1235Q8—48no—
1236Q8—82no—
1237Q8—88no—
1238D4—28no—
1239D4—44no—
1240D4—82no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—28no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—24no—
1267C2×C4—21no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—21no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—48no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—416no—
1311C2×C4—48no—
1312C2×C4—44no—
1313C2×C4—44no—
1314C2×C4—82no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4114yes—
1319C2×C4C22×#4118yes—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4112yes—
1322C2×C4C22×#4112yes—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4112yes—
1325C2×C4C2×2−1+414yes—
1326C2×C4C2×2−1+414yes—
1327C2×C4C2×2−1+414yes—
1328C2×C4C2×2−1+412yes—
1329C22—24no—
1330C22—22no—
1331C22—24no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—41no—
1343C22#350914yes—
1344C22C23×#4111yescharacteristic
1345C22C23×#4111yescharacteristic
1346C22C22×2−1+412yes—
1347C22C22×2−1+411yescharacteristic
1348C22H(7,𝔽2)12yes—
1349C4—24no—
1350C4—28no—
1351C4—24no—
1352C4—22no—
1353C4—22no—
1354C4—24no—
1355C4—24no—
1356C4—22no—
1357C4—22no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—44no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—44no—
1367C4—41no—
1368C4—44no—
1369C4—44no—
1370C4—41no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—41no—
1375C4—44no—
1376C4#348214yes—
1377C2—24no—
1378C2—42no—
1379C2—81no—
1380C2C2×#348211yescharacteristic
1381C2C2×#350911yescharacteristic
1382C2#6285811yescharacteristic
1383C2#6294512yes—
1384C2#6300012yes—
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
2. #59708C2semidirect
3. #59664C2semidirect
4. #59491C2semidirect
5. #44712C2semidirect
6. #44614C2semidirect
7. #44372C2semidirect
8. #44218C2semidirect
9. #39757C2semidirect
10. #39641C2semidirect
11. #39293C2semidirect
12. #38261C2semidirect
14. #37883C2semidirect
15. #37882C2semidirect
16. #37709C2semidirect
17. #37705C2semidirect
18. #36280C2semidirect
19. #36180C2semidirect
20. #36131C2semidirect
21. #35613C2semidirect
22. #35583C2semidirect
23. #35323C2semidirect
24. #35315C2semidirect
25. #35294C2semidirect
26. #34772C2semidirect
27. #34299C2semidirect
28. #34281C2semidirect
29. #34214C2semidirect
31. C2×#2330C2semidirect

Maximal subgroups

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

subgroupindex
#599552
#597082
#596642
#594912
#447122
#446142
#443722
#442182
#397572
#396412
#392932
#382612
#380402
#378832
#378822
#377092
#377052
#362802
#361802
#361312
#356132
#355832
#353232
#353152
#352942
#347722
#342992
#342812
#342142
#341492
C2×#23302