Finite Group Databasebeta

← #7642107

Subgroups — #7642107

Order 512.

4834 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37267C212yesmaximal, complemented
2#37263C214yesmaximal, complemented
3#37262C212yesmaximal, complemented
4#37236C212yesmaximal, complemented
5#37231C214yesmaximal, complemented
6#37227C212yesmaximal, complemented
7#37224C214yesmaximal, complemented
8#37221C214yesmaximal, complemented
9#37219C214yesmaximal, complemented
10#37216C212yesmaximal, complemented
11#37215C214yesmaximal, complemented
12#37198C212yesmaximal, complemented
13#37194C211yesmaximal, characteristic, complemented
14#37190C211yesmaximal, characteristic, complemented
15#37187C212yesmaximal, complemented
16#36792C214yesmaximal, complemented
17#36791C214yesmaximal, complemented
18#35100C214yesmaximal, complemented
19#35099C212yesmaximal, complemented
20#35095C214yesmaximal, complemented
21#35091C212yesmaximal, complemented
22C4×#536C212yesmaximal, complemented
23C2×#2326C211yesmaximal, characteristic, complemented
24C2×#538C2212yes—
25C2×#536C2212yes—
26C22×#124C2211yescharacteristic
27C2×C4×#41C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2866C2214yescomplemented
31#2865C2214yescomplemented
32#2861C2214yescomplemented
33#2860C2214yescomplemented
34#2855C2212yes—
35#2854C2212yes—
36#2854C2214yescomplemented
37#2853C2214yes—
38#2853C2214yescomplemented
39#2852C2214yescomplemented
40#2850C2214yescomplemented
41#2849C2214yes—
42#2848C2212yes—
43#2847C2212yes—
44#2811C2211yescharacteristic, complemented
45#2809C2212yescomplemented
46#2809C2211yescharacteristic, complemented
47#2808C2212yes—
48#2807C2214yescomplemented
49#2806C2214yescomplemented
50#2806C2212yescomplemented
51#2804C2214yescomplemented
52#2803C2214yes—
53#2803C2214yes—
54#2800C2214yes—
55#2799C2212yescomplemented
56#2799C2214yescomplemented
57#2797C2214yes—
58#2797C2214yescomplemented
59#2796C2214yescomplemented
60#2795C2212yescomplemented
61#2794C2212yescomplemented
62#2793C2214yescomplemented
63#2792C2212yescomplemented
64#2791C2214yescomplemented
65#2790C2214yescomplemented
66#2790C2214yescomplemented
67#2788C2214yescomplemented
68#2787C2214yescomplemented
69#2784C2214yescomplemented
70#2782C2214yescomplemented
71#2781C2214yescomplemented
72#2780C2214yescomplemented
73#2778C2214yescomplemented
74#2771C2214yescomplemented
75#2765C2214yescomplemented
76#2751C2214yescomplemented
77#2750C2214yescomplemented
78#2745C2214yescomplemented
79#2744C2214yescomplemented
80#2734C2211yescharacteristic, complemented
81#2733C2212yes—
82#2733C2212yes—
83#2733C2214yes—
84#2733C2212yes—
85#2733C2211yescharacteristic, complemented
86#2732C2212yescomplemented
87#2732C2214yescomplemented
88#2731C2212yes—
89#2731C2214yes—
90#2731C2212yes—
91#2731C2212yescomplemented
92#2730C2214yes—
93#2730C2214yes—
94#2730C2214yes—
95#2730C2214yes—
96#2730C2214yescomplemented
97#2729C2214yescomplemented
98#2728C2212yescomplemented
99#2727C2212yes—
100#2724C2214yescomplemented
101#2721C2214yescomplemented
102#2720C2214yescomplemented
103#2720C2214yescomplemented
104#2718C2214yescomplemented
105#2718C2214yescomplemented
106#2714C2214yes—
107#2714C2214yescomplemented
108#2710C2214yes—
109#2710C2214yescomplemented
110#2708C2214yescomplemented
111#2708C2214yescomplemented
112#2695C2214yescomplemented
113#2694C2214yescomplemented
114#2689C2214yescomplemented
115#2686C2214yescomplemented
116#2682C2212yes—
117#2682C2214yescomplemented
118#2680C2212yescomplemented
119#2680C2214yescomplemented
120#2654C2214yescomplemented
121#2651C2214yescomplemented
122#2651C2214yescomplemented
123#2650C2214yescomplemented
124#2646C2212yes—
125#2643C2214yes—
126#2639C2212yes—
127#2637C2214yescomplemented
128#2635C2214yescomplemented
129#2632C2214yescomplemented
130#2630C2214yescomplemented
131#2627C2212yes—
132#2618C2212yes—
133#2613C2214yes—
134#2533C2214yescomplemented
135#2532C2214yescomplemented
136#2532C2214yescomplemented
137#2531C2214yescomplemented
138#2531C2214yescomplemented
139#2530C2214yescomplemented
140#2529C2214yescomplemented
141#2529C2214yescomplemented
142#2528C2214yescomplemented
143#2527C2214yescomplemented
144#2526C2214yescomplemented
145#2526C2214yescomplemented
146#2525C2214yescomplemented
147#2521C2214yescomplemented
148#2519C2214yescomplemented
149#2516C2214yescomplemented
150#2498C2214yes—
151#2482C2214yes—
152#2481C2214yes—
153#2480C2214yes—
154#2479C2214yescomplemented
155#2476C2214yescomplemented
156#2474C2214yescomplemented
157#2473C2214yes—
158#2472C2214yes—
159#2471C2214yescomplemented
160#2469C2214yescomplemented
161#2468C2214yes—
162#2468C2214yes—
163#2464C2214yes—
164#2464C2214yes—
165#2464C2214yescomplemented
166#2461C2214yes—
167#2461C2214yes—
168#2461C2214yescomplemented
169#2458C2214yescomplemented
170#2457C2214yes—
171#2457C2214yes—
172#2449C2214yes—
173#2443C2214yes—
174#2438C2214yes—
175#2438C2214yes—
176#2430C2214yes—
177#2424C2214yes—
178#2418C2214yes—
179#2411C2214yes—
180#2411C2214yes—
181#2404C2214yes—
182#2329C2212yes—
183#2327C2212yescomplemented
184#2327C2212yescomplemented
185#2326C2212yes—
186#2326C2212yes—
187#2326C2214yes—
188#2326C2214yes—
189#2326C2212yes—
190#2326C2212yes—
191#2326C2212yescomplemented
192#2326C2212yescomplemented
193#2325C2212yes—
194#2323C2214yescomplemented
195#2323C2214yescomplemented
196#2322C2214yes—
197#2322C2214yes—
198#2321C2214yes—
199#2318C2214yes—
200#2317C2212yes—
201#2312C2212yes—
202#2311C2212yes—
203#2310C2212yes—
204C4×C4⋊Q8C2212yescomplemented
205C4×C4⋊Q8C2212yescomplemented
206C4×#124C2212yescomplemented
207C4×#124C2212yescomplemented
208C4×C22⋊Q8C2214yescomplemented
209C4×C22⋊Q8C2214yescomplemented
210C4×#123C2214yes—
211C4×#123C2214yes—
212C2×#391C2211yescharacteristic
213C2×#390C2211yescharacteristic
214C2×#388C2214yes—
215C2×#385C2214yes—
216C2×#384C2211yescharacteristic
217C4×#117C2212yes—
218C2×#376C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C24×C4C2312yes—
223#538—48no—
224#536—216no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2314yes—
231C2×#124—28no—
232C2×#124C2312yes—
233C2×#124C2314yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#120C2314yes—
258C2×#120C2314yes—
259C4×#41—48no—
260C2×C4×Q8—44no—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×D4—44no—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2314yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2314yes—
285C22×C22⋊C4C2314yes—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289C22×C42C2314yes—
290C22×C42C2311yescharacteristic
291#401C2314yes—
292#400C2312yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#398C2312yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2312yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2312yes—
364#394C2312yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2311yescharacteristic
400#391C2314yes—
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#390C2314yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2314yes—
418#390C2312yes—
419#390C2312yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
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#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#384C2312yes—
574#384C2312yes—
575#384C2312yes—
576#384C2312yes—
577#384C2312yes—
578#383C2314yes—
579#382C2312yes—
580#382C2312yes—
581#382C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#379C2314yes—
597#379C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610#376C2312yes—
611#376C2314yes—
612#376C2312yes—
613#376C2312yes—
614#376C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2314yes—
618C43C2312yes—
619C43C2312yes—
620C25C2412yes—
621C2×#41—28no—
622C2×#41—44no—
623C2×#41—44no—
624C22×Q8—42no—
625C22×Q8—42no—
626C22×Q8#4118yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2411yescharacteristic
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×D4—24no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C23×C4—44no—
647C23×C4—84no—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2411yescharacteristic
661C4⋊Q8—28no—
662C4⋊Q8—28no—
663#126—48no—
664#126—84no—
665#126—84no—
666#125—84no—
667#124—28no—
668#124—216no—
669#124—28no—
670#124—28no—
671#124—28no—
672#124—48no—
673#124—84no—
674#123—216no—
675#123—216no—
676#123—48no—
677#123—84no—
678#123—84no—
679#123—84no—
680#123—84no—
681C22⋊Q8—216no—
682C22⋊Q8—216no—
683C22⋊Q8—44no—
684C22⋊Q8—44no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687#121—48no—
688#121—44no—
689#121—44no—
690#121—84no—
691#121—84no—
692#120—48no—
693#120—48no—
694C4×Q8—44no—
695C4×Q8—44no—
696C4×Q8—44no—
697C4×Q8—44no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×D4—216no—
701C4×D4—44no—
702C4×D4—48no—
703C4×D4—44no—
704C4×D4—44no—
705C4×D4—44no—
706C4×D4—48no—
707#117—28no—
708#117—48no—
709#117—44no—
710#117—44no—
711C2×C4⋊C4—42no—
712C2×C4⋊C4—42no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4—84no—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C22⋊C4—216no—
764C2×C22⋊C4—28no—
765C2×C22⋊C4—84no—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C42—24no—
812C2×C42—24no—
813C2×C42—28no—
814C2×C42—48no—
815C2×C42—42no—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888C24—24no—
889C24—24no—
890C24—24no—
891C24—44no—
892C24—44no—
893C24C2514yes—
894C24C2514yes—
895C24C2511yescharacteristic
896#41—432no—
897C2×Q8—24no—
898C2×Q8—41no—
899C2×Q8—42no—
900C2×Q8—41no—
901C2×Q8—42no—
902C2×Q8—416no—
903C2×Q8—41no—
904C2×Q8—42no—
905C2×Q8—41no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—44no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8C2×#4114yes—
913C2×Q8C2×#4118yes—
914C2×Q8C2×#4114yes—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—416no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—44no—
945C22×C4—22no—
946C22×C4—24no—
947C22×C4—22no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—28no—
955C22×C4—28no—
956C22×C4—44no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—816no—
978C22×C4C2×#4114yes—
979C22×C4C2×#4118yes—
980C22×C4H(5,𝔽2)14yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—41no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C42—24no—
1095C42—24no—
1096C42—24no—
1097C42—24no—
1098C42—24no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—41no—
1106C42—42no—
1107C42—41no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—42no—
1113C42—42no—
1114C42—44no—
1115C42—44no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—24no—
1130C23—24no—
1131C23—24no—
1132C23—416no—
1133C23—48no—
1134C23—84no—
1135C23—84no—
1136C23—88no—
1137C23C22×#4112yes—
1138C23C2×H(5,𝔽2)12yes—
1139C23#58512yes—
1140C23C2611yescharacteristic
1141Q8—44no—
1142Q8—48no—
1143Q8—44no—
1144Q8—48no—
1145Q8—162no—
1146Q8—162no—
1147D4—48no—
1148D4—48no—
1149D4—48no—
1150D4—416no—
1151D4—164no—
1152D4—162no—
1153D4—164no—
1154D4—164no—
1155D4—162no—
1156D4—164no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—216no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—44no—
1209C2×C4—416no—
1210C2×C4—48no—
1211C2×C4—44no—
1212C2×C4—88no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4C22×#4114yes—
1220C2×C4C22×#4112yes—
1221C2×C4C22×#4112yes—
1222C2×C4C22×#4114yes—
1223C2×C4C2×H(5,𝔽2)14yes—
1224C22—24no—
1225C22—22no—
1226C22—24no—
1227C22—22no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—816no—
1243C22#345914yes—
1244C22C23×#4111yescharacteristic
1245C22C22×H(5,𝔽2)11yescharacteristic
1246C22C2×#58511yescharacteristic
1247C22H(7,𝔽2)12yes—
1248C222−1+612yes—
1249C4—24no—
1250C4—24no—
1251C4—22no—
1252C4—22no—
1253C4—24no—
1254C4—44no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4—44no—
1261C4—44no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C2—24no—
1270C2—84no—
1271C2—84no—
1272C2C2×#345911yescharacteristic
1273C2#6285112yes—
1274C2#6287111yescharacteristic
1275C2#6287212yes—
1276C2#6287411yescharacteristic
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. #37267C2semidirect
2. #37263C2semidirect
3. #37262C2semidirect
4. #37236C2semidirect
5. #37231C2semidirect
6. #37227C2semidirect
7. #37224C2semidirect
8. #37221C2semidirect
9. #37219C2semidirect
10. #37216C2semidirect
11. #37215C2semidirect
12. #37198C2semidirect
13. #37194C2semidirect
14. #37190C2semidirect
15. #37187C2semidirect
16. #36792C2semidirect
17. #36791C2semidirect
18. #35100C2semidirect
19. #35099C2semidirect
20. #35095C2semidirect
21. #35091C2semidirect
22. C4×#536C2semidirect
23. C2×#2326C2semidirect
30. #2866C22semidirect
31. #2865C22semidirect
32. #2861C22semidirect
33. #2860C22semidirect
36. #2854C22semidirect
38. #2853C22semidirect
39. #2852C22semidirect
40. #2850C22semidirect
44. #2811C22semidirect
45. #2809C22semidirect
46. #2809C22semidirect
48. #2807C22semidirect
49. #2806C22semidirect
50. #2806C22semidirect
51. #2804C22semidirect
55. #2799C22semidirect
56. #2799C22semidirect
58. #2797C22semidirect
59. #2796C22semidirect
60. #2795C22semidirect
61. #2794C22semidirect
62. #2793C22semidirect
63. #2792C22semidirect
64. #2791C22semidirect
65. #2790C22semidirect
66. #2790C22semidirect
67. #2788C22semidirect
68. #2787C22semidirect
69. #2784C22semidirect
70. #2782C22semidirect
71. #2781C22semidirect
72. #2780C22semidirect
73. #2778C22semidirect
74. #2771C22semidirect
75. #2765C22semidirect
76. #2751C22semidirect
77. #2750C22semidirect
78. #2745C22semidirect
79. #2744C22semidirect
80. #2734C22semidirect
85. #2733C22semidirect
86. #2732C22semidirect
87. #2732C22semidirect
91. #2731C22semidirect
96. #2730C22semidirect
97. #2729C22semidirect
98. #2728C22semidirect
100. #2724C22semidirect
101. #2721C22semidirect
102. #2720C22semidirect
103. #2720C22semidirect
104. #2718C22semidirect
105. #2718C22semidirect
107. #2714C22semidirect
109. #2710C22semidirect
110. #2708C22semidirect
111. #2708C22semidirect
112. #2695C22semidirect
113. #2694C22semidirect
114. #2689C22semidirect
115. #2686C22semidirect
117. #2682C22semidirect
118. #2680C22semidirect
119. #2680C22semidirect
120. #2654C22semidirect
121. #2651C22semidirect
122. #2651C22semidirect
123. #2650C22semidirect
127. #2637C22semidirect
128. #2635C22semidirect
129. #2632C22semidirect
130. #2630C22semidirect
134. #2533C22semidirect
135. #2532C22semidirect
136. #2532C22semidirect
137. #2531C22semidirect
138. #2531C22semidirect
139. #2530C22semidirect
140. #2529C22semidirect
141. #2529C22semidirect
142. #2528C22semidirect
143. #2527C22semidirect
144. #2526C22semidirect
145. #2526C22semidirect
146. #2525C22semidirect
147. #2521C22semidirect
148. #2519C22semidirect
149. #2516C22semidirect
154. #2479C22semidirect
155. #2476C22semidirect
156. #2474C22semidirect
159. #2471C22semidirect
160. #2469C22semidirect
165. #2464C22semidirect
168. #2461C22semidirect
169. #2458C22semidirect
183. #2327C22semidirect
184. #2327C22semidirect
191. #2326C22semidirect
192. #2326C22semidirect
194. #2323C22semidirect
195. #2323C22semidirect
204. C4×C4⋊Q8C22semidirect
205. C4×C4⋊Q8C22semidirect
206. C4×#124C22semidirect
207. C4×#124C22semidirect
208. C4×C22⋊Q8C22semidirect
209. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#372672
#372632
#372622
#372362
#372312
#372272
#372242
#372212
#372192
#372162
#372152
#371982
#371942
#371902
#371872
#367922
#367912
#351002
#350992
#350952
#350912
C4×#5362
C2×#23262