Finite Group Databasebeta

← #7681595

Subgroups — #7681595

Order 512.

5223 conjugacy classes of subgroups.

The subgroup lattice has 1512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60007C214yesmaximal, complemented
2#59977C214yesmaximal, complemented
3#59798C214yesmaximal, complemented
4#59633C214yesmaximal, complemented
5#44670C214yesmaximal, complemented
6#44605C214yesmaximal, complemented
7#44265C214yesmaximal, complemented
8#44200C214yesmaximal, complemented
9#39507C211yesmaximal, characteristic, complemented
10#39501C211yesmaximal, characteristic, complemented
11#39500C211yesmaximal, characteristic, complemented
12#39386C211yesmaximal, characteristic, complemented
13#39382C211yesmaximal, characteristic, complemented
14#39382C211yesmaximal, characteristic, complemented
15#39130C212yesmaximal, complemented
16#38290C212yesmaximal, complemented
17#38285C212yesmaximal, complemented
18#36595C211yesmaximal, characteristic, complemented
19#36565C211yesmaximal, characteristic, complemented
20#36373C212yesmaximal, complemented
21#35607C212yesmaximal, complemented
22#35572C212yesmaximal, complemented
23#35343C211yesmaximal, characteristic, complemented
24#35331C211yesmaximal, characteristic, complemented
25#35293C211yesmaximal, characteristic, complemented
26#34889C212yesmaximal, complemented
27#34329C212yesmaximal, complemented
28#34281C211yesmaximal, characteristic, complemented
29#34280C211yesmaximal, characteristic, complemented
30#34151C211yesmaximal, characteristic, complemented
31C4×#540C211yesmaximal, characteristic, complemented
32C2×#559C2212yes—
33C2×#542C2212yes—
34C2×#541C2211yescharacteristic
35C2×#540C2211yescharacteristic
36C2×#540C2211yescharacteristic
37C2×#532C2212yes—
38C2×#529C2211yescharacteristic
39C2×#529C2212yes—
40#2867C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2861C2212yes—
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2858C2211yescharacteristic
47#2858C2212yes—
48#2850C2212yes—
49#2809C2214yes—
50#2808C2214yes—
51#2808C2214yes—
52#2808C2214yes—
53#2803C2214yes—
54#2803C2214yes—
55#2803C2214yes—
56#2803C2214yes—
57#2784C2214yes—
58#2756C2214yes—
59#2737C2214yes—
60#2733C2214yes—
61#2733C2214yes—
62#2731C2214yes—
63#2730C2214yes—
64#2714C2214yes—
65#2714C2214yes—
66#2694C2214yes—
67#2694C2214yes—
68#2694C2214yes—
69#2686C2214yes—
70#2673C2214yes—
71#2673C2214yes—
72#2673C2214yes—
73#2640C2212yes—
74#2621C2211yescharacteristic
75#2621C2211yescharacteristic
76#2620C2212yes—
77#2619C2211yescharacteristic
78#2619C2211yescharacteristic
79#2619C2211yescharacteristic
80#2619C2211yescharacteristic
81#2619C2212yes—
82#2610C2214yes—
83#2610C2214yes—
84#2610C2214yes—
85#2610C2214yes—
86#2603C2214yes—
87#2602C2214yes—
88#2602C2214yes—
89#2602C2214yes—
90#2601C2214yes—
91#2601C2214yes—
92#2601C2214yes—
93#2593C2214yes—
94#2586C2214yes—
95#2586C2214yes—
96#2564C2214yes—
97#2560C2214yes—
98#2560C2214yes—
99#2560C2214yes—
100#2559C2214yes—
101#2559C2214yes—
102#2557C2214yes—
103#2557C2214yes—
104#2557C2214yes—
105#2555C2214yes—
106#2554C2214yes—
107#2554C2214yes—
108#2554C2214yes—
109#2554C2214yes—
110#2551C2212yes—
111#2550C2212yes—
112#2550C2212yes—
113#2548C2214yes—
114#2548C2212yes—
115#2544C2212yes—
116#2544C2212yes—
117#2544C2214yes—
118#2544C2214yes—
119#2544C2214yes—
120#2541C2214yes—
121#2541C2212yes—
122#2540C2212yes—
123#2540C2212yes—
124#2537C2212yes—
125#2536C2212yes—
126#2535C2212yes—
127#2532C2214yes—
128#2532C2214yes—
129#2531C2214yes—
130#2526C2214yes—
131#2526C2214yes—
132#2521C2214yes—
133#2521C2214yes—
134#2492C2212yes—
135#2492C2212yes—
136#2491C2214yes—
137#2491C2212yes—
138#2491C2212yes—
139#2491C2214yes—
140#2490C2212yes—
141#2490C2214yes—
142#2490C2212yes—
143#2490C2214yes—
144#2485C2214yes—
145#2485C2214yes—
146#2476C2214yes—
147#2474C2214yes—
148#2474C2214yes—
149#2467C2214yes—
150#2464C2214yes—
151#2461C2214yes—
152#2459C2214yes—
153#2459C2214yes—
154#2459C2214yes—
155#2459C2214yes—
156#2456C2214yes—
157#2451C2214yes—
158#2445C2214yes—
159#2445C2214yes—
160#2445C2214yes—
161#2445C2214yes—
162#2445C2214yes—
163#2432C2214yes—
164#2431C2214yes—
165#2431C2214yes—
166#2430C2214yes—
167#2428C2212yes—
168#2428C2212yes—
169#2427C2212yes—
170#2427C2212yes—
171#2426C2212yes—
172#2426C2212yes—
173#2414C2214yes—
174#2395C2214yes—
175#2388C2214yes—
176#2374C2214yes—
177#2374C2214yes—
178#2374C2212yes—
179#2374C2212yes—
180#2373C2214yes—
181#2373C2212yes—
182#2373C2212yes—
183#2373C2214yes—
184#2372C2214yes—
185#2372C2214yes—
186#2371C2214yes—
187#2370C2212yes—
188#2370C2214yes—
189#2369C2214yes—
190#2367C2212yes—
191#2367C2212yes—
192#2367C2212yes—
193#2366C2212yes—
194#2366C2214yes—
195#2364C2214yes—
196#2363C2214yes—
197#2363C2212yes—
198#2363C2214yes—
199#2362C2212yes—
200#2359C2214yes—
201#2359C2214yes—
202#2357C2212yes—
203#2356C2212yes—
204#2355C2212yes—
205#2354C2212yes—
206#2353C2214yes—
207#2337C2214yes—
208#2335C2214yes—
209#2335C2214yes—
210#2333C2214yes—
211#2330C2211yescharacteristic
212#2328C2211yescharacteristic
213#2328C2211yescharacteristic
214#2328C2212yes—
215#2327C2211yescharacteristic
216#2326C2212yes—
217#2324C2212yes—
218#2324C2212yes—
219#2323C2212yes—
220#2319C2212yes—
221#2314C2211yescharacteristic
222#2314C2211yescharacteristic
223#2314C2211yescharacteristic
224C4×C4⋊Q8C2211yescharacteristic
225C4×#127C2211yescharacteristic
226C4×#127C2211yescharacteristic
227C4×#125C2211yescharacteristic
228C4×#125C2211yescharacteristic
229C4×#125C2211yescharacteristic
230C4×#124C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×#123C2214yes—
233C4×#123C2214yes—
234C4×#121C2212yes—
235C4×#121C2214yes—
236C4×#121C2214yes—
237C4×#121C2212yes—
238#2298C2211yescharacteristic
239#2298C2211yescharacteristic
240#2297C2214yes—
241#2295C2212yes—
242#2295C2211yescharacteristic
243#2293C2212yes—
244#2293C2211yescharacteristic
245#2293C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2211yescharacteristic
248#2290C2214yes—
249#2290C2211yescharacteristic
250#2276C2212yes—
251#2275C2212yes—
252C42×Q8C2211yescharacteristic
253C42×D4C2212yes—
254C42×D4C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C22×#41C2314yes—
260#559—216no—
261#542—48no—
262#541—28no—
263#540—28no—
264#540—28no—
265#532—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#127C2312yes—
274C2×#127C2314yes—
275C2×#127C2314yes—
276C2×#127C2314yes—
277#529—28no—
278#529—48no—
279C2×#126C2311yescharacteristic
280C2×#126C2311yescharacteristic
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#125C2311yescharacteristic
285C2×#125C2314yes—
286C2×#125C2312yes—
287C2×#125C2311yescharacteristic
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2311yescharacteristic
304C2×#123C2311yescharacteristic
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2311yescharacteristic
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2311yescharacteristic
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×#117C2311yescharacteristic
350C2×#117C2311yescharacteristic
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2311yescharacteristic
355C2×#117C2314yes—
356C2×#117C2312yes—
357C2×#117C2314yes—
358C2×#117C2314yes—
359C22×C42C2311yescharacteristic
360C22×C42C2311yescharacteristic
361C22×C42C2311yescharacteristic
362C22×C42C2314yes—
363#400C2314yes—
364#400C2314yes—
365#399C2314yes—
366#399C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
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#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2312yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#388C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#384C2311yescharacteristic
614#384C2312yes—
615#383C2314yes—
616#382C2311yescharacteristic
617#382C2311yescharacteristic
618#382C2311yescharacteristic
619#382C2312yes—
620#382C2312yes—
621#381C2314yes—
622#381C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2311yescharacteristic
699#376C2314yes—
700#376C2314yes—
701#376C2314yes—
702#376C2312yes—
703C2×#95C2314yes—
704C43C2311yescharacteristic
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C43C2311yescharacteristic
708C43C2311yescharacteristic
709C43C2311yescharacteristic
710C2×#41—48no—
711C2×#41—48no—
712C2×#41—84no—
713C22×Q8C2412yes—
714C22×Q8C2414yes—
715C22×Q8C2414yes—
716C22×Q8C2411yescharacteristic
717C22×D4C2412yes—
718C22×D4C2412yes—
719C22×D4C2411yescharacteristic
720C22×D4C2411yescharacteristic
721C22×D4C2414yes—
722C22×D4C2414yes—
723C22×D4C2414yes—
724C22×D4C2411yescharacteristic
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2411yescharacteristic
745C23×C4C2414yes—
746C23×C4C2414yes—
747C4⋊Q8—24no—
748C4⋊Q8—44no—
749C4⋊Q8—44no—
750C4⋊Q8—48no—
751#127—24no—
752#127—24no—
753#127—28no—
754#127—48no—
755#127—44no—
756#127—84no—
757#127—84no—
758#126—24no—
759#126—24no—
760#126—216no—
761#126—48no—
762#126—48no—
763#125—24no—
764#125—216no—
765#125—44no—
766#125#4118yescomplemented
767#124—24no—
768#124—216no—
769#124—28no—
770#124—28no—
771#124—48no—
772#124—48no—
773#124—48no—
774#124—44no—
775#124—44no—
776#124—84no—
777#124—84no—
778#124—84no—
779#123—24no—
780#123—24no—
781#123—216no—
782#123—216no—
783#123—216no—
784#123—216no—
785#123—48no—
786#123—48no—
787C22⋊Q8—24no—
788C22⋊Q8—28no—
789C22⋊Q8—48no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792#121—24no—
793#121—216no—
794#121—216no—
795#121—28no—
796#121—28no—
797#121—48no—
798#121—48no—
799#121—48no—
800#121—44no—
801#121—44no—
802#121—44no—
803#121—44no—
804#121—84no—
805C4×Q8—28no—
806C4×Q8—28no—
807C4×Q8—28no—
808C4×Q8—44no—
809C4×Q8#4118yescomplemented
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—216no—
813C4×D4—24no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—48no—
821C4×D4—48no—
822C4×D4—44no—
823C4×D4—84no—
824C4×D4—84no—
825C4×D4—84no—
826C4×D4—84no—
827C4×D4—84no—
828#117—24no—
829#117—24no—
830#117—24no—
831#117—24no—
832#117—24no—
833#117—24no—
834#117—48no—
835#117—44no—
836#117—84no—
837#117—84no—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2411yescharacteristic
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2411yescharacteristic
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C42—24no—
945C2×C42—24no—
946C2×C42—24no—
947C2×C42—84no—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2414yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035C24C2511yescharacteristic
1036C24C2511yescharacteristic
1037C24C2514yes—
1038C24C2514yes—
1039C24C2511yescharacteristic
1040#41—832no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—28no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8C2×#4114yes—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—28no—
1060C2×D4—28no—
1061C2×D4—28no—
1062C2×D4—28no—
1063C2×D4—28no—
1064C2×D4—28no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—28no—
1068C2×D4—28no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—42no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—28no—
1112C22×C4—24no—
1113C22×C4—22no—
1114C22×C4—28no—
1115C22×C4—28no—
1116C22×C4—28no—
1117C22×C4—28no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—42no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2514yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2514yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4C2×#4114yes—
1203C4⋊C4C2×#4118yes—
1204C4⋊C4C2×#4114yes—
1205C4⋊C4C2×#4114yes—
1206C4⋊C4C2×#41116yes—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—22no—
1210C22⋊C4—22no—
1211C22⋊C4—22no—
1212C22⋊C4—22no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—22no—
1217C22⋊C4—22no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—22no—
1223C22⋊C4—22no—
1224C22⋊C4—22no—
1225C22⋊C4—22no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—42no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—28no—
1276C42—28no—
1277C42—24no—
1278C42—24no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—28no—
1283C42—24no—
1284C42—24no—
1285C42—42no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—42no—
1290C42—42no—
1291C42—44no—
1292C42—44no—
1293C42—42no—
1294C42—42no—
1295C42—42no—
1296C42—44no—
1297C42—42no—
1298C42—42no—
1299C42—42no—
1300C42—42no—
1301C42—44no—
1302C42C2×#4114yes—
1303C42C2×#4114yes—
1304C42C2×#4114yes—
1305C42C2×#4114yes—
1306C42H(5,𝔽2)14yes—
1307C23—21no—
1308C23—21no—
1309C23—21no—
1310C23—24no—
1311C23—24no—
1312C23—21no—
1313C23—24no—
1314C23—24no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—24no—
1319C23—24no—
1320C23—21no—
1321C23—21no—
1322C23—22no—
1323C23—22no—
1324C23—24no—
1325C23—24no—
1326C23—22no—
1327C23—24no—
1328C23—24no—
1329C23—24no—
1330C23—24no—
1331C23—22no—
1332C23—22no—
1333C23—24no—
1334C23—22no—
1335C23—24no—
1336C23C2611yescharacteristic
1337Q8—44no—
1338Q8—48no—
1339Q8—88no—
1340Q8—164no—
1341D4—44no—
1342D4—48no—
1343D4—48no—
1344D4—88no—
1345D4—88no—
1346D4—88no—
1347D4—88no—
1348D4—88no—
1349D4—82no—
1350D4—82no—
1351D4—88no—
1352D4—88no—
1353D4—88no—
1354D4—88no—
1355D4—88no—
1356D4—88no—
1357D4—164no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—21no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—48no—
1416C2×C4—44no—
1417C2×C4—416no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—88no—
1422C2×C4—88no—
1423C2×C4—82no—
1424C2×C4—88no—
1425C2×C4—88no—
1426C2×C4—84no—
1427C2×C4—88no—
1428C2×C4C22×#4112yes—
1429C2×C4C22×#4112yes—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4118yes—
1432C2×C4C22×#4112yes—
1433C2×C4C22×#4112yes—
1434C2×C4C22×#4114yes—
1435C2×C4C22×#4112yes—
1436C2×C4C22×#4112yes—
1437C2×C4C22×#4112yes—
1438C2×C4C2×H(5,𝔽2)14yes—
1439C2×C4C2×H(5,𝔽2)12yes—
1440C2×C4#58514yes—
1441C22—44no—
1442C22—44no—
1443C22—42no—
1444C22—42no—
1445C22—44no—
1446C22—44no—
1447C22—42no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—44no—
1452C22—44no—
1453C22—41no—
1454C22—44no—
1455C22—44no—
1456C22—41no—
1457C22—41no—
1458C22—42no—
1459C22—44no—
1460C22—44no—
1461C22—42no—
1462C22—44no—
1463C22—44no—
1464C22—42no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—44no—
1469C22—44no—
1470C22C23×#4111yescharacteristic
1471C22C23×#4111yescharacteristic
1472C22C22×H(5,𝔽2)11yescharacteristic
1473C22C2×#58512yes—
1474C22H(7,𝔽2)12yes—
1475C4—28no—
1476C4—24no—
1477C4—22no—
1478C4—22no—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—22no—
1483C4—24no—
1484C4—24no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—41no—
1489C4—41no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—44no—
1494C4—44no—
1495C4—42no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—44no—
1500C4#348314yes—
1501C2—84no—
1502C2—84no—
1503C2—81no—
1504C2—81no—
1505C2—81no—
1506C2C2×#348311yescharacteristic
1507C2#6281511yescharacteristic
1508C2#6285811yescharacteristic
1509C2#6292412yes—
1510C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60007C2semidirect
2. #59977C2semidirect
3. #59798C2semidirect
4. #59633C2semidirect
5. #44670C2semidirect
6. #44605C2semidirect
7. #44265C2semidirect
8. #44200C2semidirect
9. #39507C2semidirect
10. #39501C2semidirect
11. #39500C2semidirect
12. #39386C2semidirect
13. #39382C2semidirect
14. #39382C2semidirect
15. #39130C2semidirect
16. #38290C2semidirect
17. #38285C2semidirect
18. #36595C2semidirect
19. #36565C2semidirect
20. #36373C2semidirect
21. #35607C2semidirect
22. #35572C2semidirect
23. #35343C2semidirect
24. #35331C2semidirect
25. #35293C2semidirect
26. #34889C2semidirect
27. #34329C2semidirect
28. #34281C2semidirect
29. #34280C2semidirect
30. #34151C2semidirect
31. C4×#540C2semidirect
766. #125#41semidirect
809. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600072
#599772
#597982
#596332
#446702
#446052
#442652
#442002
#395072
#395012
#395002
#393862
#393822
#391302
#382902
#382852
#365952
#365652
#363732
#356072
#355722
#353432
#353312
#352932
#348892
#343292
#342812
#342802
#341512
C4×#5402