Finite Group Databasebeta

← #8115466

Subgroups — #8115466

Order 512.

4463 conjugacy classes of subgroups.

The subgroup lattice has 1481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58674C214yesmaximal, complemented
2#57247C214yesmaximal, complemented
3#57072C214yesmaximal, complemented
4#56979C214yesmaximal, complemented
5#56956C214yesmaximal, complemented
6#56777C214yesmaximal, complemented
7#55822C214yesmaximal, complemented
8#54163C214yesmaximal, complemented
9#53047C212yesmaximal, complemented
10#53022C212yesmaximal, complemented
11#45344C211yesmaximal, characteristic, complemented
12#45336C211yesmaximal, characteristic, complemented
13#45299C211yesmaximal, characteristic, complemented
14#45141C211yesmaximal, characteristic, complemented
15#42880C211yesmaximal, characteristic
16#42877C211yesmaximal, characteristic, complemented
17#42834C212yesmaximal, complemented
18#42792C211yesmaximal, characteristic, complemented
19#42791C211yesmaximal, characteristic, complemented
20#42715C212yesmaximal, complemented
21#39757C211yesmaximal, characteristic, complemented
22#39746C211yesmaximal, characteristic, complemented
23#39373C211yesmaximal, characteristic, complemented
24#39363C211yesmaximal, characteristic, complemented
25#37774C212yesmaximal, complemented
26#37750C212yesmaximal, complemented
27#37435C212yesmaximal, complemented
28#37390C212yesmaximal, complemented
29#35343C211yesmaximal, characteristic, complemented
30#35319C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#541C2212yes—
37C2×#541C2211yescharacteristic
38C2×#541C2211yescharacteristic
39C2×#536C2212yes—
40C2×#529C2212yes—
41#2868C2211yescharacteristic
42#2861C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2841C2214yes—
49#2838C2214yes—
50#2837C2214yes—
51#2837C2214yes—
52#2831C2214yes—
53#2830C2214yes—
54#2829C2214yes—
55#2827C2214yes—
56#2827C2214yes—
57#2826C2214yes—
58#2822C2212yes—
59#2821C2212yes—
60#2820C2212yes—
61#2818C2212yes—
62#2810C2214yes—
63#2805C2214yes—
64#2803C2214yes—
65#2801C2214yes—
66#2800C2214yes—
67#2796C2214yes—
68#2790C2214yes—
69#2790C2214yes—
70#2788C2214yes—
71#2780C2214yes—
72#2779C2214yes—
73#2779C2214yes—
74#2778C2214yes—
75#2777C2214yes—
76#2776C2214yes—
77#2772C2214yes—
78#2771C2214yes—
79#2766C2214yes—
80#2765C2214yes—
81#2765C2214yes—
82#2761C2214yes—
83#2757C2214yes—
84#2757C2214yes—
85#2757C2214yes—
86#2750C2214yes—
87#2748C2214yes—
88#2745C2214yes—
89#2741C2214yes—
90#2739C2214yes—
91#2737C2214yes—
92#2727C2214yes—
93#2727C2214yes—
94#2726C2214yes—
95#2726C2214yes—
96#2725C2214yes—
97#2723C2214yes—
98#2721C2214yes—
99#2720C2214yes—
100#2720C2214yes—
101#2720C2214yes—
102#2720C2214yes—
103#2720C2214yes—
104#2718C2214yes—
105#2718C2214yes—
106#2718C2214yes—
107#2718C2214yes—
108#2714C2214yes—
109#2713C2214yes—
110#2711C2214yes—
111#2709C2214yes—
112#2707C2214yes—
113#2705C2214yes—
114#2705C2214yes—
115#2695C2214yes—
116#2694C2214yes—
117#2694C2214yes—
118#2694C2214yes—
119#2693C2214yes—
120#2690C2214yes—
121#2689C2214yes—
122#2687C2214yes—
123#2686C2214yes—
124#2681C2214yes—
125#2681C2214yes—
126#2664C2212yes—
127#2662C2212yes—
128#2660C2212yes—
129#2658C2212yes—
130#2655C2212yes—
131#2654C2212yes—
132#2653C2212yes—
133#2652C2212yes—
134#2651C2212yes—
135#2650C2212yes—
136#2650C2214yes—
137#2649C2214yes—
138#2649C2214yes—
139#2649C2212yes—
140#2648C2212yes—
141#2646C2214yes—
142#2642C2212yes—
143#2642C2211yescharacteristic
144#2642C2211yescharacteristic
145#2641C2212yes—
146#2637C2212yes—
147#2636C2212yes—
148#2633C2212yes—
149#2633C2212yes—
150#2629C2212yes—
151#2621C2211yescharacteristic
152#2621C2211yescharacteristic
153#2621C2211yescharacteristic
154#2620C2212yes—
155#2620C2212yes—
156#2619C2211yescharacteristic
157#2606C2214yes—
158#2603C2212yes—
159#2603C2212yes—
160#2602C2214yes—
161#2602C2214yes—
162#2601C2214yes—
163#2601C2214yes—
164#2597C2214yes—
165#2597C2214yes—
166#2585C2214yes—
167#2584C2212yes—
168#2581C2211yescharacteristic
169#2581C2211yescharacteristic
170#2562C2212yes—
171#2548C2211yescharacteristic
172#2548C2211yescharacteristic
173#2547C2212yes—
174#2546C2212yes—
175#2546C2212yes—
176#2546C2211yescharacteristic
177#2546C2211yescharacteristic
178#2545C2212yes—
179#2545C2212yes—
180#2545C2212yes—
181#2542C2212yes—
182#2540C2212yes—
183#2536C2211yescharacteristic
184#2536C2211yescharacteristic
185#2533C2214yes—
186#2533C2214yes—
187#2526C2214yes—
188#2519C2214yes—
189#2519C2214yes—
190#2514C2212yes—
191#2513C2212yes—
192#2511C2212yes—
193#2511C2212yes—
194#2506C2214yes—
195#2506C2214yes—
196#2505C2214yes—
197#2496C2214yes—
198#2496C2214yes—
199#2490C2212yes—
200#2489C2212yes—
201#2479C2214yes—
202#2470C2214yes—
203#2467C2214yes—
204#2465C2214yes—
205#2460C2214yes—
206#2457C2214yes—
207#2454C2214yes—
208#2454C2212yes—
209#2454C2214yes—
210#2453C2212yes—
211#2452C2214yes—
212#2450C2214yes—
213#2448C2214yes—
214#2447C2212yes—
215#2446C2212yes—
216#2445C2214yes—
217#2444C2214yes—
218#2441C2214yes—
219#2438C2214yes—
220#2436C2212yes—
221#2434C2212yes—
222#2434C2212yes—
223#2432C2212yes—
224#2432C2212yes—
225#2432C2212yes—
226#2429C2212yes—
227#2429C2212yes—
228#2429C2212yes—
229#2427C2212yes—
230#2427C2212yes—
231#2426C2212yes—
232#2423C2212yes—
233#2423C2212yes—
234#2421C2212yes—
235#2420C2212yes—
236#2419C2214yes—
237#2409C2212yes—
238#2407C2212yes—
239#2402C2211yescharacteristic
240#2401C2212yes—
241#2398C2211yescharacteristic
242#2396C2211yescharacteristic
243#2395C2212yes—
244#2392C2211yescharacteristic
245#2367C2212yes—
246#2365C2212yes—
247#2356C2211yescharacteristic
248#2356C2211yescharacteristic
249#2351C2211yescharacteristic
250#2351C2211yescharacteristic
251Q8×C22⋊C4C2212yes—
252#2339C2212yes—
253#2330C2212yes—
254#2328C2211yescharacteristic
255#2327C2211yescharacteristic
256#2327C2211yescharacteristic
257#2327C2211yescharacteristic
258#2326C2212yes—
259#2326C2212yes—
260C4×C4⋊Q8C2211yescharacteristic
261C4×C4⋊Q8C2211yescharacteristic
262#2298C2212yes—
263#2295C2211yescharacteristic
264#2293C2211yescharacteristic
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2312yes—
269#559—44no—
270#557—44no—
271#550—44no—
272D4×Q8—44no—
273#541—44no—
274#541—44no—
275#541—48no—
276#536—48no—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2311yescharacteristic
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2312yes—
287C2×C4⋊Q8C2312yes—
288C2×#127C2311yescharacteristic
289C2×#127C2312yes—
290#529—48no—
291C2×#126C2312yes—
292C2×#126C2312yes—
293C2×#126C2314yes—
294C2×#126C2312yes—
295C2×#126C2312yes—
296C2×#126C2314yes—
297C2×#126C2314yes—
298C2×#125C2312yes—
299C2×#125C2312yes—
300C2×#125C2312yes—
301C2×#125C2312yes—
302C2×#125C2311yescharacteristic
303C2×#125C2311yescharacteristic
304C2×#125C2312yes—
305C2×#125C2312yes—
306C2×#125C2314yes—
307C2×#125C2314yes—
308C2×#125C2314yes—
309C2×#124C2312yes—
310C2×#124C2312yes—
311C2×#124C2312yes—
312C2×#124C2312yes—
313C2×#124C2312yes—
314C2×#124C2312yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×C22⋊Q8C2311yescharacteristic
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2311yescharacteristic
355C22×C42C2311yescharacteristic
356#401C2314yes—
357#401C2312yes—
358#400C2311yescharacteristic
359#400C2312yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2312yes—
381#400C2312yes—
382#400C2314yes—
383#400C2312yes—
384#400C2312yes—
385#399C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2312yes—
391#399C2314yes—
392#399C2311yescharacteristic
393#399C2314yes—
394#399C2314yes—
395#399C2314yes—
396#399C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2312yes—
414#398C2312yes—
415#398C2312yes—
416#398C2312yes—
417#398C2312yes—
418#398C2312yes—
419#398C2312yes—
420#398C2314yes—
421#398C2314yes—
422#398C2311yescharacteristic
423#398C2314yes—
424#398C2312yes—
425#397C2314yes—
426#397C2311yescharacteristic
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2312yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2312yes—
446#397C2312yes—
447#397C2312yes—
448#397C2312yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2312yes—
467#396C2312yes—
468#396C2312yes—
469#395C2311yescharacteristic
470#395C2312yes—
471#395C2314yes—
472#395C2314yes—
473#395C2314yes—
474#395C2312yes—
475#395C2314yes—
476#395C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2312yes—
480#394C2312yes—
481#394C2314yes—
482#394C2314yes—
483#394C2312yes—
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2312yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2312yes—
499#394C2312yes—
500#394C2312yes—
501#394C2314yes—
502#394C2314yes—
503#394C2311yescharacteristic
504#394C2312yes—
505#394C2312yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2311yescharacteristic
510#393C2312yes—
511#392C2311yescharacteristic
512#392C2314yes—
513#392C2314yes—
514#392C2312yes—
515#392C2312yes—
516#391C2311yescharacteristic
517#391C2311yescharacteristic
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2314yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2311yescharacteristic
526#391C2311yescharacteristic
527#391C2311yescharacteristic
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2314yes—
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2314yes—
541#390C2314yes—
542#390C2314yes—
543#390C2314yes—
544#390C2312yes—
545#390C2314yes—
546#390C2312yes—
547#390C2314yes—
548#390C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2312yes—
640#387C2312yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2312yes—
657#386C2312yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2312yes—
679#385C2312yes—
680#385C2314yes—
681#385C2314yes—
682#384C2311yescharacteristic
683#384C2311yescharacteristic
684#384C2312yes—
685#384C2314yes—
686#384C2314yes—
687#384C2314yes—
688#383C2312yes—
689#383C2312yes—
690#383C2314yes—
691#382C2312yes—
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2311yescharacteristic
696#382C2311yescharacteristic
697#382C2314yes—
698#381C2314yes—
699#381C2314yes—
700#381C2314yes—
701#380C2314yes—
702#380C2314yes—
703#380C2314yes—
704#380C2312yes—
705#380C2312yes—
706#380C2314yes—
707#380C2314yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2311yescharacteristic
721C4×C4⋊C4C2311yescharacteristic
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2312yes—
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2312yes—
735#376C2311yescharacteristic
736#376C2312yes—
737#376C2311yescharacteristic
738#376C2312yes—
739#376C2312yes—
740C2×#95C2314yes—
741C43C2311yescharacteristic
742C43C2311yescharacteristic
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—44no—
746C22×Q8—44no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2414yes—
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2412yes—
762C22×D4C2414yes—
763C22×D4C2414yes—
764C23×C4C2411yescharacteristic
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C4⋊Q8—24no—
772C4⋊Q8—24no—
773C4⋊Q8—24no—
774C4⋊Q8—44no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777C4⋊Q8—44no—
778C4⋊Q8—44no—
779C4⋊Q8—42no—
780C4⋊Q8—42no—
781C4⋊Q8—44no—
782#127—24no—
783#127—44no—
784#126—48no—
785#126—44no—
786#126—44no—
787#126—44no—
788#126—44no—
789#126—48no—
790#126—48no—
791#125—28no—
792#125—42no—
793#125—42no—
794#125—44no—
795#125—44no—
796#125—44no—
797#125—44no—
798#125—44no—
799#125—48no—
800#125—48no—
801#125—48no—
802#124—28no—
803#124—44no—
804#124—44no—
805#124—44no—
806#124—44no—
807#124—44no—
808#123—48no—
809#123—48no—
810#123—48no—
811#123—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—48no—
815C22⋊Q8—44no—
816C22⋊Q8—42no—
817C22⋊Q8—44no—
818C22⋊Q8—42no—
819C22⋊Q8—42no—
820C22⋊Q8—42no—
821C22⋊Q8—44no—
822C22⋊Q8—44no—
823#121—48no—
824#121—44no—
825#121—44no—
826C4×Q8—24no—
827C4×Q8—24no—
828C4×Q8—24no—
829C4×Q8—24no—
830C4×Q8—24no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—44no—
834C4×Q8—44no—
835C4×Q8—44no—
836C4×D4—24no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—44no—
841C4×D4—44no—
842C4×D4—44no—
843C4×D4—48no—
844#117—28no—
845#117—24no—
846#117—42no—
847#117—48no—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C42—24no—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2411yescharacteristic
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2414yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062C24C2511yescharacteristic
1063C24C2512yes—
1064C24C2514yes—
1065#41—816no—
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—22no—
1076C2×Q8—22no—
1077C2×Q8—22no—
1078C2×Q8—24no—
1079C2×Q8—22no—
1080C2×Q8—22no—
1081C2×Q8—22no—
1082C2×Q8—42no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×Q8—816no—
1087C2×D4—22no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—42no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—44no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C22×C4—22no—
1109C22×C4—22no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—22no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—28no—
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—42no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—28no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C42—24no—
1279C42—22no—
1280C42—24no—
1281C42—22no—
1282C42—24no—
1283C42—24no—
1284C42—24no—
1285C42—24no—
1286C42—24no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—42no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—44no—
1299C42—44no—
1300C42H(5,𝔽2)14yes—
1301C42H(5,𝔽2)14yes—
1302C23—21no—
1303C23—22no—
1304C23—24no—
1305C23—22no—
1306C23—21no—
1307C23—24no—
1308C23—21no—
1309C23—24no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—24no—
1315C23—24no—
1316C23—24no—
1317C23—24no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23C2611yescharacteristic
1322Q8—44no—
1323Q8—44no—
1324Q8—44no—
1325Q8—48no—
1326Q8—44no—
1327Q8—44no—
1328Q8—88no—
1329D4—44no—
1330D4—48no—
1331D4—84no—
1332D4—84no—
1333D4—88no—
1334D4—84no—
1335D4—88no—
1336D4—164no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—44no—
1408C2×C4—48no—
1409C2×C4—84no—
1410C2×C4—88no—
1411C2×C4—88no—
1412C2×C4—88no—
1413C2×C4—164no—
1414C2×C4C2×H(5,𝔽2)12yes—
1415C2×C4C2×H(5,𝔽2)12yes—
1416C2×C4C2×H(5,𝔽2)14yes—
1417C2×C4C2×H(5,𝔽2)12yes—
1418C2×C4C2×H(5,𝔽2)12yes—
1419C2×C4#58512yes—
1420C22—42no—
1421C22—41no—
1422C22—44no—
1423C22—44no—
1424C22—42no—
1425C22—44no—
1426C22—42no—
1427C22—41no—
1428C22—41no—
1429C22—42no—
1430C22—44no—
1431C22—44no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—44no—
1437C22—44no—
1438C22—42no—
1439C22C22×H(5,𝔽2)11yescharacteristic
1440C22C22×H(5,𝔽2)11yescharacteristic
1441C22C2×#58511yescharacteristic
1442C222−1+612yes—
1443C222−1+612yes—
1444C4—22no—
1445C4—22no—
1446C4—24no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—41no—
1456C4—41no—
1457C4—42no—
1458C4—42no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—42no—
1463C4—42no—
1464C4—44no—
1465C4—42no—
1466C4—44no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4#354614yes—
1472C2—82no—
1473C2—81no—
1474C2—84no—
1475C2C2×#354611yescharacteristic
1476C2#6288711yescharacteristic
1477C2#6288711yescharacteristic
1478C2#6288812yes—
1479C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42880C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58674C2semidirect
2. #57247C2semidirect
3. #57072C2semidirect
4. #56979C2semidirect
5. #56956C2semidirect
6. #56777C2semidirect
7. #55822C2semidirect
8. #54163C2semidirect
9. #53047C2semidirect
10. #53022C2semidirect
11. #45344C2semidirect
12. #45336C2semidirect
13. #45299C2semidirect
14. #45141C2semidirect
16. #42877C2semidirect
17. #42834C2semidirect
18. #42792C2semidirect
19. #42791C2semidirect
20. #42715C2semidirect
21. #39757C2semidirect
22. #39746C2semidirect
23. #39373C2semidirect
24. #39363C2semidirect
25. #37774C2semidirect
26. #37750C2semidirect
27. #37435C2semidirect
28. #37390C2semidirect
29. #35343C2semidirect
30. #35319C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#586742
#572472
#570722
#569792
#569562
#567772
#558222
#541632
#530472
#530222
#453442
#453362
#452992
#451412
#428802
#428772
#428342
#427922
#427912
#427152
#397572
#397462
#393732
#393632
#377742
#377502
#374352
#373902
#353432
#353192
#346402