Finite Group Databasebeta

← #8701454

Subgroups — #8701454

Order 512.

4379 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60003C212yesmaximal, complemented
2#59933C211yesmaximal, characteristic, complemented
3#59766C212yesmaximal, complemented
4#59632C211yesmaximal, characteristic
5#59134C212yesmaximal, complemented
6#57860C214yesmaximal, complemented
7#56729C214yesmaximal, complemented
8#56428C214yesmaximal, complemented
9#52304C211yesmaximal, characteristic, complemented
10#52039C212yesmaximal, complemented
11#51134C214yesmaximal, complemented
12#49103C212yesmaximal, complemented
13#48943C214yesmaximal, complemented
14#45703C212yesmaximal, complemented
15#45683C211yesmaximal, characteristic
16#45283C212yesmaximal, complemented
17#45220C212yesmaximal, complemented
18#44964C212yesmaximal, complemented
19#42834C212yesmaximal, complemented
20#42834C212yesmaximal, complemented
21#42701C212yesmaximal, complemented
22#40025C212yesmaximal, complemented
23#39593C211yesmaximal, characteristic, complemented
24#39171C211yesmaximal, characteristic
25#39031C212yesmaximal, complemented
26#37080C212yesmaximal, complemented
27#36788C214yesmaximal, complemented
28Q8×#123C211yesmaximal, characteristic, complemented
29#36233C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2858C2211yescharacteristic
36#2855C2211yescharacteristic
37#2855C2211yescharacteristic
38#2855C2212yes—
39#2852C2214yes—
40#2850C2212yes—
41#2839C2214yes—
42#2836C2214yes—
43#2831C2214yes—
44#2831C2214yes—
45#2824C2212yes—
46#2805C2212yes—
47#2800C2214yes—
48#2799C2212yes—
49#2798C2214yes—
50#2794C2214yes—
51#2789C2212yes—
52#2788C2214yes—
53#2788C2214yes—
54#2787C2214yes—
55#2782C2214yes—
56#2780C2214yes—
57#2780C2214yes—
58#2780C2214yes—
59#2779C2214yes—
60#2778C2214yes—
61#2776C2214yes—
62#2774C2214yes—
63#2772C2214yes—
64#2770C2214yes—
65#2767C2214yes—
66#2766C2214yes—
67#2765C2212yes—
68#2765C2212yes—
69#2764C2214yes—
70#2761C2214yes—
71#2761C2214yes—
72#2760C2212yes—
73#2758C2214yes—
74#2754C2214yes—
75#2752C2212yes—
76#2750C2214yes—
77#2750C2214yes—
78#2750C2214yes—
79#2748C2214yes—
80#2748C2212yes—
81#2747C2214yes—
82#2747C2214yes—
83#2745C2214yes—
84#2745C2214yes—
85#2743C2214yes—
86#2743C2214yes—
87#2739C2214yes—
88#2737C2214yes—
89#2734C2214yes—
90#2732C2214yes—
91#2729C2214yes—
92#2724C2211yescharacteristic
93#2718C2214yes—
94#2717C2211yescharacteristic
95#2717C2211yescharacteristic
96#2716C2214yes—
97#2716C2214yes—
98#2715C2214yes—
99#2709C2212yes—
100#2709C2212yes—
101#2707C2214yes—
102#2696C2214yes—
103#2696C2214yes—
104#2695C2214yes—
105#2690C2214yes—
106#2690C2212yes—
107#2690C2212yes—
108#2683C2211yescharacteristic
109#2680C2214yes—
110#2666C2214yes—
111#2655C2214yes—
112#2652C2214yes—
113#2651C2214yes—
114#2650C2214yes—
115#2650C2214yes—
116#2649C2214yes—
117#2649C2214yes—
118#2642C2212yes—
119#2640C2212yes—
120#2627C2212yes—
121#2612C2212yes—
122#2606C2214yes—
123#2604C2214yes—
124#2602C2214yes—
125#2599C2214yes—
126#2597C2214yes—
127#2597C2214yes—
128#2597C2214yes—
129#2589C2214yes—
130#2583C2212yes—
131#2582C2212yes—
132#2581C2212yes—
133#2579C2212yes—
134#2579C2214yes—
135#2578C2214yes—
136#2578C2214yes—
137#2568C2211yescharacteristic
138#2568C2212yes—
139#2565C2212yes—
140#2563C2212yes—
141#2547C2212yes—
142#2546C2212yes—
143#2545C2212yes—
144#2545C2212yes—
145#2545C2212yes—
146#2545C2212yes—
147#2544C2212yes—
148#2544C2212yes—
149#2541C2211yescharacteristic
150#2538C2212yes—
151#2533C2214yes—
152#2533C2214yes—
153#2531C2214yes—
154#2531C2214yes—
155#2528C2214yes—
156#2527C2214yes—
157#2526C2214yes—
158#2522C2214yes—
159#2520C2214yes—
160#2518C2214yes—
161#2514C2212yes—
162#2511C2212yes—
163#2511C2212yes—
164#2509C2212yes—
165#2506C2212yes—
166#2506C2214yes—
167#2502C2212yes—
168#2502C2211yescharacteristic
169#2497C2212yes—
170#2492C2214yes—
171#2490C2212yes—
172#2490C2212yes—
173#2487C2211yescharacteristic
174#2487C2212yes—
175#2481C2214yes—
176#2481C2214yes—
177#2481C2214yes—
178#2474C2214yes—
179#2469C2214yes—
180#2468C2214yes—
181#2465C2214yes—
182#2460C2214yes—
183#2460C2214yes—
184#2455C2212yes—
185#2453C2212yes—
186#2453C2212yes—
187#2449C2214yes—
188#2449C2214yes—
189#2449C2214yes—
190#2448C2212yes—
191#2448C2212yes—
192#2447C2212yes—
193#2447C2212yes—
194#2446C2214yes—
195#2446C2212yes—
196#2446C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2445C2212yes—
200#2442C2214yes—
201#2439C2214yes—
202#2436C2212yes—
203#2436C2212yes—
204#2436C2212yes—
205#2434C2211yescharacteristic
206#2434C2212yes—
207#2429C2212yes—
208#2427C2212yes—
209#2427C2212yes—
210#2427C2212yes—
211#2423C2214yes—
212#2423C2212yes—
213#2423C2212yes—
214#2420C2212yes—
215#2417C2214yes—
216#2413C2214yes—
217#2409C2211yescharacteristic
218#2401C2212yes—
219#2401C2212yes—
220#2399C2212yes—
221#2380C2212yes—
222#2378C2214yes—
223#2372C2212yes—
224#2371C2214yes—
225#2370C2212yes—
226#2367C2212yes—
227#2367C2212yes—
228#2366C2212yes—
229#2365C2212yes—
230#2365C2212yes—
231#2361C2212yes—
232#2360C2212yes—
233#2356C2212yes—
234#2352C2214yes—
235Q8×C4⋊C4C2212yes—
236D4×C4⋊C4C2212yes—
237Q8×C22⋊C4C2212yes—
238Q8×C22⋊C4C2211yescharacteristic
239Q8×C22⋊C4C2211yescharacteristic
240Q8×C22⋊C4C2212yes—
241#2335C2214yes—
242#2328C2212yes—
243#2326C2212yes—
244#2326C2212yes—
245#2322C2212yes—
246#2320C2212yes—
247#2313C2214yes—
248C4×#125C2212yes—
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2211yescharacteristic
253C4×#123C2211yescharacteristic
254C4×#123C2212yes—
255C4×#121C2212yes—
256#2295C2211yescharacteristic
257#2295C2212yes—
258#2290C2214yes—
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#559—44no—
263#556—48no—
264D4×Q8—44no—
265C2×C4⋊Q8—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2312yes—
280C2×#124C2311yescharacteristic
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#123C2311yescharacteristic
287C2×#123C2311yescharacteristic
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×C4×Q8—44no—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×#117C2314yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2311yescharacteristic
325C22×C4⋊C4C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2312yes—
328C22×C42C2311yescharacteristic
329#401C2314yes—
330#401C2312yes—
331#401C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2314yes—
361#400C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2312yes—
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#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2312yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#392C2312yes—
449#392C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2312yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#390C2314yes—
483#390C2312yes—
484#390C2314yes—
485#390C2314yes—
486#390C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#386C2314yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2311yescharacteristic
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2311yescharacteristic
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#385C2311yescharacteristic
618#385C2312yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2314yes—
625#385C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2311yescharacteristic
631#385C2312yes—
632#385C2312yes—
633#385C2314yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2312yes—
644#385C2312yes—
645#384C2312yes—
646#384C2312yes—
647#384C2314yes—
648#383C2314yes—
649#383C2314yes—
650#383C2314yes—
651#382C2312yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#382C2314yes—
656#382C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2312yes—
661#381C2311yescharacteristic
662#381C2311yescharacteristic
663#381C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2314yes—
716C43C2311yescharacteristic
717C22×Q8—24no—
718C22×Q8—24no—
719C22×Q8—44no—
720C22×Q8—42no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C4⋊Q8—28no—
752C4⋊Q8—44no—
753C4⋊Q8—44no—
754C4⋊Q8—44no—
755C4⋊Q8—42no—
756C4⋊Q8—48no—
757#127—28no—
758#127—42no—
759#126—48no—
760#126—48no—
761#125—44no—
762#125—48no—
763#125—44no—
764#124—28no—
765#124—24no—
766#124—44no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—44no—
771#123—24no—
772#123—24no—
773#123—48no—
774#123—48no—
775C22⋊Q8—48no—
776C22⋊Q8—44no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—42no—
781C22⋊Q8—42no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784#121—44no—
785#121—44no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—44no—
789C4×Q8—42no—
790C4×Q8—48no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—42no—
802C4×D4—48no—
803C4×D4—48no—
804#117—48no—
805C2×C4⋊C4—48no—
806C2×C4⋊C4—42no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—44no—
809C2×C4⋊C4—44no—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C42—44no—
914C2×C42—42no—
915C2×C42—42no—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2514yes—
1015C24C2511yescharacteristic
1016C24C2511yescharacteristic
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—44no—
1030C2×Q8—42no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—41no—
1037C2×Q8—416no—
1038C2×Q8—88no—
1039C2×Q8—88no—
1040C2×Q8H(5,𝔽2)14yes—
1041C2×D4—28no—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—41no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—44no—
1057C2×D42−1+414yes—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—41no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4C2514yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C22⋊C4—22no—
1176C22⋊C4—22no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—42no—
1186C22⋊C4—41no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—41no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—41no—
1199C22⋊C4—41no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C42—28no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—22no—
1223C42—24no—
1224C42—22no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—41no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—42no—
1240C42—44no—
1241C23—21no—
1242C23—21no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—21no—
1248C23—21no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—24no—
1253C23—24no—
1254C23—24no—
1255C23—24no—
1256C23C2×2−1+412yes—
1257C23C2×2−1+412yes—
1258C23C2611yescharacteristic
1259Q8—28no—
1260Q8—48no—
1261Q8—44no—
1262Q8—48no—
1263Q8—44no—
1264Q8—84no—
1265Q8—82no—
1266Q8—84no—
1267Q8—84no—
1268D4—44no—
1269D4—48no—
1270D4—84no—
1271D4—88no—
1272D4—88no—
1273D4—162no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—21no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—44no—
1340C2×C4—48no—
1341C2×C4—44no—
1342C2×C4—44no—
1343C2×C4—44no—
1344C2×C4—44no—
1345C2×C4—88no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—82no—
1349C2×C4—88no—
1350C2×C4—84no—
1351C2×C4—164no—
1352C2×C4C2×H(5,𝔽2)14yes—
1353C2×C4C2×H(5,𝔽2)12yes—
1354C2×C4C2×2−1+412yes—
1355C2×C4#58514yes—
1356C2×C4#58514yes—
1357C22—24no—
1358C22—24no—
1359C22—22no—
1360C22—22no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—42no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—44no—
1371C22—44no—
1372C22—44no—
1373C22—44no—
1374C22C22×H(5,𝔽2)11yescharacteristic
1375C22C22×2−1+411yescharacteristic
1376C22C2×#58512yes—
1377C22C2×#58512yes—
1378C222−1+611yescharacteristic
1379C4—24no—
1380C4—24no—
1381C4—22no—
1382C4—41no—
1383C4—42no—
1384C4—41no—
1385C4—44no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—41no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—44no—
1403C4—42no—
1404C4#353314yes—
1405C2—42no—
1406C2—42no—
1407C2—84no—
1408C2C2×#353311yescharacteristic
1409C2#6289311yescharacteristic
1410C2#6296712yes—
1411C2#6302011yescharacteristic
1412C2#6302512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60003C2semidirect
2. #59933C2semidirect
3. #59766C2semidirect
5. #59134C2semidirect
6. #57860C2semidirect
7. #56729C2semidirect
8. #56428C2semidirect
9. #52304C2semidirect
10. #52039C2semidirect
11. #51134C2semidirect
12. #49103C2semidirect
13. #48943C2semidirect
14. #45703C2semidirect
16. #45283C2semidirect
17. #45220C2semidirect
18. #44964C2semidirect
19. #42834C2semidirect
20. #42834C2semidirect
21. #42701C2semidirect
22. #40025C2semidirect
23. #39593C2semidirect
25. #39031C2semidirect
26. #37080C2semidirect
27. #36788C2semidirect
28. Q8×#123C2semidirect
29. #36233C2semidirect

Maximal subgroups

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

subgroupindex
#600032
#599332
#597662
#596322
#591342
#578602
#567292
#564282
#523042
#520392
#511342
#491032
#489432
#457032
#456832
#452832
#452202
#449642
#428342
#427012
#400252
#395932
#391712
#390312
#370802
#367882
Q8×#1232
#362332