Finite Group Databasebeta

← #8115463

Subgroups — #8115463

Order 512.

4771 conjugacy classes of subgroups.

The subgroup lattice has 1556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58028C214yesmaximal, complemented
2#57254C214yesmaximal, complemented
3#57120C214yesmaximal, complemented
4#56932C214yesmaximal, complemented
5#56804C214yesmaximal, complemented
6#55748C214yesmaximal, complemented
7#54303C214yesmaximal, complemented
8#54193C214yesmaximal, complemented
9#53066C212yesmaximal, complemented
10#52960C212yesmaximal, complemented
11#45268C211yesmaximal, characteristic, complemented
12#45221C211yesmaximal, characteristic, complemented
13#45070C211yesmaximal, characteristic, complemented
14#44935C211yesmaximal, characteristic, complemented
15#42876C211yesmaximal, characteristic, complemented
16#42872C212yesmaximal, complemented
17#42788C211yesmaximal, characteristic, complemented
18#42649C211yesmaximal, characteristic, complemented
19#42560C212yesmaximal, complemented
20#42429C211yesmaximal, characteristic, complemented
21#39757C211yesmaximal, characteristic, complemented
22#39747C211yesmaximal, characteristic, complemented
23#39372C211yesmaximal, characteristic, complemented
24#39363C211yesmaximal, characteristic, complemented
25#37775C212yesmaximal, complemented
26#37750C212yesmaximal, complemented
27#37422C212yesmaximal, complemented
28#37327C212yesmaximal, complemented
29#35343C211yesmaximal, characteristic, complemented
30#35277C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#542C2211yescharacteristic
38C2×#540C2212yes—
39C2×#536C2212yes—
40C2×#529C2212yes—
41#2868C2211yescharacteristic
42#2861C2212yes—
43#2859C2211yescharacteristic
44#2858C2211yescharacteristic
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2832C2214yes—
49#2830C2214yes—
50#2829C2214yes—
51#2828C2214yes—
52#2827C2214yes—
53#2826C2214yes—
54#2824C2214yes—
55#2824C2214yes—
56#2824C2214yes—
57#2821C2212yes—
58#2818C2212yes—
59#2814C2212yes—
60#2813C2214yes—
61#2813C2212yes—
62#2810C2214yes—
63#2805C2214yes—
64#2804C2214yes—
65#2797C2214yes—
66#2797C2214yes—
67#2795C2214yes—
68#2793C2214yes—
69#2790C2214yes—
70#2784C2214yes—
71#2780C2214yes—
72#2770C2214yes—
73#2751C2214yes—
74#2751C2214yes—
75#2750C2214yes—
76#2749C2214yes—
77#2747C2214yes—
78#2731C2214yes—
79#2729C2214yes—
80#2724C2214yes—
81#2722C2214yes—
82#2718C2214yes—
83#2716C2214yes—
84#2716C2214yes—
85#2715C2214yes—
86#2714C2214yes—
87#2714C2214yes—
88#2714C2214yes—
89#2709C2214yes—
90#2709C2214yes—
91#2708C2214yes—
92#2705C2214yes—
93#2705C2214yes—
94#2703C2214yes—
95#2703C2214yes—
96#2703C2214yes—
97#2703C2214yes—
98#2696C2214yes—
99#2696C2214yes—
100#2696C2214yes—
101#2696C2214yes—
102#2696C2214yes—
103#2696C2214yes—
104#2695C2214yes—
105#2693C2214yes—
106#2693C2214yes—
107#2692C2214yes—
108#2692C2214yes—
109#2691C2214yes—
110#2691C2214yes—
111#2691C2214yes—
112#2689C2214yes—
113#2688C2214yes—
114#2687C2214yes—
115#2686C2214yes—
116#2682C2214yes—
117#2682C2214yes—
118#2681C2214yes—
119#2681C2214yes—
120#2676C2214yes—
121#2676C2214yes—
122#2674C2214yes—
123#2673C2214yes—
124#2673C2214yes—
125#2673C2214yes—
126#2659C2212yes—
127#2657C2212yes—
128#2657C2212yes—
129#2655C2212yes—
130#2654C2212yes—
131#2653C2212yes—
132#2653C2214yes—
133#2652C2212yes—
134#2651C2212yes—
135#2650C2212yes—
136#2649C2212yes—
137#2648C2212yes—
138#2648C2214yes—
139#2643C2214yes—
140#2642C2212yes—
141#2640C2212yes—
142#2640C2211yescharacteristic
143#2640C2211yescharacteristic
144#2639C2212yes—
145#2631C2212yes—
146#2631C2212yes—
147#2630C2214yes—
148#2629C2212yes—
149#2625C2212yes—
150#2621C2211yescharacteristic
151#2620C2212yes—
152#2620C2211yescharacteristic
153#2620C2212yes—
154#2620C2211yescharacteristic
155#2619C2211yescharacteristic
156#2616C2212yes—
157#2603C2214yes—
158#2603C2212yes—
159#2603C2212yes—
160#2602C2214yes—
161#2602C2214yes—
162#2601C2214yes—
163#2601C2214yes—
164#2581C2211yescharacteristic
165#2581C2211yescharacteristic
166#2569C2214yes—
167#2557C2214yes—
168#2548C2211yescharacteristic
169#2548C2212yes—
170#2547C2211yescharacteristic
171#2547C2212yes—
172#2547C2212yes—
173#2546C2211yescharacteristic
174#2544C2212yes—
175#2544C2212yes—
176#2544C2212yes—
177#2541C2211yescharacteristic
178#2541C2212yes—
179#2540C2212yes—
180#2535C2211yescharacteristic
181#2535C2211yescharacteristic
182#2533C2214yes—
183#2533C2214yes—
184#2530C2214yes—
185#2512C2212yes—
186#2512C2214yes—
187#2511C2212yes—
188#2511C2212yes—
189#2511C2212yes—
190#2498C2212yes—
191#2492C2212yes—
192#2491C2214yes—
193#2491C2212yes—
194#2477C2214yes—
195#2471C2214yes—
196#2470C2214yes—
197#2467C2214yes—
198#2457C2214yes—
199#2456C2214yes—
200#2452C2214yes—
201#2452C2212yes—
202#2452C2214yes—
203#2451C2212yes—
204#2450C2214yes—
205#2450C2214yes—
206#2447C2212yes—
207#2446C2212yes—
208#2445C2214yes—
209#2444C2214yes—
210#2444C2214yes—
211#2438C2214yes—
212#2436C2212yes—
213#2436C2212yes—
214#2436C2212yes—
215#2432C2212yes—
216#2431C2212yes—
217#2431C2212yes—
218#2430C2214yes—
219#2430C2212yes—
220#2429C2212yes—
221#2428C2214yes—
222#2428C2212yes—
223#2428C2212yes—
224#2427C2212yes—
225#2427C2212yes—
226#2426C2212yes—
227#2425C2214yes—
228#2425C2214yes—
229#2423C2212yes—
230#2422C2212yes—
231#2422C2212yes—
232#2422C2212yes—
233#2422C2214yes—
234#2414C2214yes—
235#2414C2214yes—
236#2409C2212yes—
237#2407C2214yes—
238#2407C2212yes—
239#2402C2211yescharacteristic
240#2401C2212yes—
241#2398C2211yescharacteristic
242#2396C2211yescharacteristic
243#2395C2212yes—
244#2392C2211yescharacteristic
245#2367C2212yes—
246#2366C2212yes—
247#2356C2211yescharacteristic
248#2356C2211yescharacteristic
249#2349C2211yescharacteristic
250#2349C2211yescharacteristic
251Q8×C22⋊C4C2212yes—
252#2339C2212yes—
253#2330C2212yes—
254#2328C2211yescharacteristic
255#2327C2211yescharacteristic
256#2326C2211yescharacteristic
257#2326C2212yes—
258#2326C2212yes—
259#2326C2211yescharacteristic
260C4×C4⋊Q8C2211yescharacteristic
261C4×#127C2211yescharacteristic
262#2298C2212yes—
263#2295C2211yescharacteristic
264#2293C2211yescharacteristic
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2312yes—
269C23×Q8C2312yes—
270#556—44no—
271#550—44no—
272#550—44no—
273D4×Q8—44no—
274#542—44no—
275#542—44no—
276#540—48no—
277#536—48no—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2314yes—
285C2×#127C2311yescharacteristic
286C2×#127C2311yescharacteristic
287C2×#127C2312yes—
288C2×#127C2312yes—
289C2×#127C2312yes—
290C2×#127C2314yes—
291#529—48no—
292C2×#126C2312yes—
293C2×#126C2312yes—
294C2×#126C2314yes—
295C2×#126C2314yes—
296C2×#126C2314yes—
297C2×#125C2312yes—
298C2×#124C2312yes—
299C2×#124C2311yescharacteristic
300C2×#124C2312yes—
301C2×#124C2311yescharacteristic
302C2×#124C2311yescharacteristic
303C2×#124C2311yescharacteristic
304C2×#124C2312yes—
305C2×#124C2312yes—
306C2×#124C2312yes—
307C2×#124C2312yes—
308C2×#124C2312yes—
309C2×#124C2314yes—
310C2×#123C2314yes—
311C2×#123C2312yes—
312C2×#123C2312yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×#121C2311yescharacteristic
332C2×#121C2311yescharacteristic
333C2×#121C2312yes—
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2312yes—
340C2×#121C2312yes—
341C2×#121C2314yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×#117C2311yescharacteristic
365C2×#117C2312yes—
366C2×#117C2314yes—
367C2×#117C2311yescharacteristic
368C2×#117C2312yes—
369C22×C42C2311yescharacteristic
370#401C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#400C2314yes—
380#400C2312yes—
381#400C2312yes—
382#400C2312yes—
383#400C2311yescharacteristic
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2312yes—
390#400C2312yes—
391#400C2312yes—
392#400C2312yes—
393#399C2314yes—
394#399C2312yes—
395#399C2314yes—
396#399C2311yescharacteristic
397#398C2311yescharacteristic
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2314yes—
411#398C2312yes—
412#397C2312yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2312yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2312yes—
430#397C2312yes—
431#397C2312yes—
432#397C2314yes—
433#397C2311yescharacteristic
434#397C2314yes—
435#397C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2312yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2312yes—
449#396C2314yes—
450#396C2314yes—
451#396C2312yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2312yes—
458#395C2312yes—
459#395C2311yescharacteristic
460#394C2311yescharacteristic
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2312yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2312yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2312yes—
491#394C2312yes—
492#394C2312yes—
493#394C2312yes—
494#394C2314yes—
495#393C2314yes—
496#393C2314yes—
497#393C2314yes—
498#393C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2311yescharacteristic
509#392C2314yes—
510#392C2312yes—
511#392C2314yes—
512#392C2312yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2312yes—
521#392C2312yes—
522#392C2312yes—
523#392C2312yes—
524#392C2311yescharacteristic
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#391C2311yescharacteristic
531#391C2311yescharacteristic
532#391C2314yes—
533#391C2312yes—
534#391C2312yes—
535#391C2311yescharacteristic
536#391C2311yescharacteristic
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2314yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2314yes—
545#391C2314yes—
546#391C2312yes—
547#390C2311yescharacteristic
548#390C2311yescharacteristic
549#390C2314yes—
550#390C2314yes—
551#390C2314yes—
552#390C2314yes—
553#390C2311yescharacteristic
554#390C2311yescharacteristic
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2314yes—
561#390C2314yes—
562#390C2314yes—
563#390C2314yes—
564#390C2314yes—
565#390C2312yes—
566#390C2314yes—
567#390C2312yes—
568#390C2314yes—
569#390C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2312yes—
582#389C2312yes—
583#389C2314yes—
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#388C2314yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2314yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2312yes—
659#386C2312yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2312yes—
686#385C2312yes—
687#385C2314yes—
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#384C2312yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#384C2314yes—
694#383C2312yes—
695#383C2312yes—
696#382C2311yescharacteristic
697#382C2311yescharacteristic
698#381C2314yes—
699#381C2314yes—
700#380C2314yes—
701#380C2314yes—
702#380C2314yes—
703#380C2312yes—
704#380C2312yes—
705#380C2314yes—
706#380C2314yes—
707#380C2312yes—
708#380C2312yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2311yescharacteristic
719C4×C4⋊C4C2311yescharacteristic
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2312yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733#376C2311yescharacteristic
734#376C2311yescharacteristic
735#376C2312yes—
736#376C2312yes—
737#376C2312yes—
738C2×#95C2312yes—
739C2×#95C2314yes—
740C2×#95C2312yes—
741C43C2311yescharacteristic
742C43C2311yescharacteristic
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—44no—
746C2×#41—44no—
747C2×#41—84no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8—44no—
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2412yes—
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2414yes—
771C22×D4C2412yes—
772C22×D4C2414yes—
773C22×D4C2414yes—
774C22×D4C2414yes—
775C22×D4C2414yes—
776C22×D4C2414yes—
777C23×C4C2411yescharacteristic
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2412yes—
781C23×C4C2412yes—
782C23×C4C2414yes—
783C23×C4C2414yes—
784C23×C4C2414yes—
785C23×C4C2414yes—
786C23×C4C2414yes—
787C23×C4C2414yes—
788C4⋊Q8—24no—
789C4⋊Q8—24no—
790C4⋊Q8—42no—
791C4⋊Q8—42no—
792C4⋊Q8—44no—
793C4⋊Q8—44no—
794C4⋊Q8—84no—
795#127—24no—
796#127—24no—
797#127—44no—
798#127—44no—
799#127—44no—
800#127—84no—
801#126—48no—
802#126—44no—
803#126—44no—
804#126—48no—
805#126—84no—
806#125—28no—
807#124—28no—
808#124—44no—
809#124—44no—
810#124—42no—
811#124—42no—
812#124—44no—
813#124—44no—
814#124—44no—
815#124—42no—
816#124—42no—
817#124—44no—
818#124—84no—
819#123—48no—
820#123—48no—
821#123—48no—
822#123—44no—
823#123—44no—
824#123—48no—
825#123—48no—
826#123—84no—
827#123—84no—
828#123—84no—
829C22⋊Q8—48no—
830C22⋊Q8—48no—
831C22⋊Q8—48no—
832C22⋊Q8—44no—
833C22⋊Q8—44no—
834C22⋊Q8—44no—
835C22⋊Q8—42no—
836C22⋊Q8—42no—
837C22⋊Q8—44no—
838C22⋊Q8—44no—
839C22⋊Q8—84no—
840#121—48no—
841#121—48no—
842#121—48no—
843#121—48no—
844#121—44no—
845#121—44no—
846#121—44no—
847#121—42no—
848#121—42no—
849#121—44no—
850#121—44no—
851#121—84no—
852#121—84no—
853#121—84no—
854#121—84no—
855C4×Q8—24no—
856C4×Q8—24no—
857C4×Q8—24no—
858C4×Q8—44no—
859C4×Q8—44no—
860C4×D4—24no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—44no—
864C4×D4—44no—
865C4×D4—44no—
866C4×D4—44no—
867C4×D4—44no—
868C4×D4—44no—
869C4×D4—44no—
870C4×D4—48no—
871C4×D4—84no—
872C4×D4—84no—
873#117—28no—
874#117—24no—
875#117—42no—
876#117—48no—
877#117—44no—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2411yescharacteristic
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2411yescharacteristic
934C2×C22⋊C4C2411yescharacteristic
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2414yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2412yes—
991C2×C22⋊C4C2412yes—
992C2×C22⋊C4C2414yes—
993C2×C22⋊C4C2414yes—
994C2×C42—24no—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2411yescharacteristic
1000C2×C42C2411yescharacteristic
1001C2×C42C2412yes—
1002C2×C42C2412yes—
1003C2×C42C2412yes—
1004C2×C42C2412yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2412yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2412yes—
1011C2×C42C2412yes—
1012C2×C42C2412yes—
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015#95C2412yes—
1016#95C2411yescharacteristic
1017#95C2411yescharacteristic
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2411yescharacteristic
1026#95C2411yescharacteristic
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2412yes—
1050#95C2414yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2412yes—
1056#95C2414yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2414yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077C24C2511yescharacteristic
1078C24C2514yes—
1079C24C2512yes—
1080C24C2512yes—
1081C24C2512yes—
1082#41—816no—
1083#41—816no—
1084C2×Q8—22no—
1085C2×Q8—22no—
1086C2×Q8—22no—
1087C2×Q8—24no—
1088C2×Q8—24no—
1089C2×Q8—22no—
1090C2×Q8—22no—
1091C2×Q8—24no—
1092C2×Q8—22no—
1093C2×Q8—22no—
1094C2×Q8—42no—
1095C2×Q8—44no—
1096C2×Q8—44no—
1097C2×Q8—44no—
1098C2×Q8—42no—
1099C2×Q8—42no—
1100C2×Q8—44no—
1101C2×Q8—44no—
1102C2×Q8—816no—
1103C2×D4—22no—
1104C2×D4—22no—
1105C2×D4—22no—
1106C2×D4—22no—
1107C2×D4—22no—
1108C2×D4—24no—
1109C2×D4—24no—
1110C2×D4—24no—
1111C2×D4—24no—
1112C2×D4—28no—
1113C2×D4—22no—
1114C2×D4—22no—
1115C2×D4—24no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—42no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—44no—
1133C2×D4—44no—
1134C2×D4—42no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—42no—
1141C2×D4—42no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—44no—
1146C2×D4—44no—
1147C2×D4—44no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—44no—
1152C2×D4—44no—
1153C2×D4—44no—
1154C2×D4—44no—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—24no—
1158C22×C4—24no—
1159C22×C4—22no—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—24no—
1163C22×C4—24no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4—44no—
1170C22×C4—44no—
1171C22×C4—42no—
1172C22×C4—44no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—42no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2512yes—
1194C22×C4C2512yes—
1195C22×C4C2512yes—
1196C22×C4C2511yescharacteristic
1197C22×C4C2512yes—
1198C22×C4C2512yes—
1199C22×C4C2511yescharacteristic
1200C22×C4C2512yes—
1201C22×C4C2512yes—
1202C22×C4C2512yes—
1203C22×C4C2512yes—
1204C22×C4C2514yes—
1205C22×C4C2512yes—
1206C22×C4C2512yes—
1207C22×C4C2511yescharacteristic
1208C22×C4C2511yescharacteristic
1209C22×C4C2511yescharacteristic
1210C22×C4C2512yes—
1211C22×C4C2511yescharacteristic
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—22no—
1217C4⋊C4—28no—
1218C4⋊C4—24no—
1219C4⋊C4—22no—
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—22no—
1227C4⋊C4—24no—
1228C4⋊C4—24no—
1229C4⋊C4—22no—
1230C4⋊C4—24no—
1231C4⋊C4—28no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—42no—
1237C4⋊C4—44no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—42no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—44no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—22no—
1267C22⋊C4—22no—
1268C22⋊C4—28no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—24no—
1272C22⋊C4—28no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—42no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—42no—
1309C22⋊C4—42no—
1310C22⋊C4—42no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—42no—
1314C22⋊C4—42no—
1315C22⋊C4—42no—
1316C22⋊C4—42no—
1317C22⋊C4—42no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—44no—
1321C22⋊C4—44no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—44no—
1325C22⋊C4—44no—
1326C22⋊C4—44no—
1327C22⋊C4—42no—
1328C42—24no—
1329C42—22no—
1330C42—24no—
1331C42—22no—
1332C42—24no—
1333C42—24no—
1334C42—24no—
1335C42—22no—
1336C42—22no—
1337C42—24no—
1338C42—42no—
1339C42—42no—
1340C42—44no—
1341C42—44no—
1342C42—42no—
1343C42—44no—
1344C42—44no—
1345C42—42no—
1346C42H(5,𝔽2)14yes—
1347C42H(5,𝔽2)14yes—
1348C23—21no—
1349C23—24no—
1350C23—22no—
1351C23—22no—
1352C23—22no—
1353C23—22no—
1354C23—21no—
1355C23—22no—
1356C23—22no—
1357C23—24no—
1358C23—22no—
1359C23—21no—
1360C23—24no—
1361C23—22no—
1362C23—22no—
1363C23—22no—
1364C23—22no—
1365C23—24no—
1366C23—24no—
1367C23—24no—
1368C23—24no—
1369C23—22no—
1370C23—22no—
1371C23—22no—
1372C23—24no—
1373C23—24no—
1374C23—22no—
1375C23—24no—
1376C23—24no—
1377C23C2611yescharacteristic
1378Q8—44no—
1379Q8—48no—
1380Q8—44no—
1381Q8—44no—
1382Q8—88no—
1383Q8—162no—
1384Q8—162no—
1385D4—44no—
1386D4—44no—
1387D4—44no—
1388D4—48no—
1389D4—88no—
1390D4—84no—
1391D4—84no—
1392D4—88no—
1393D4—88no—
1394D4—84no—
1395D4—88no—
1396D4—88no—
1397D4—164no—
1398D4—162no—
1399D4—162no—
1400D4—164no—
1401D4—164no—
1402D4—164no—
1403D4—164no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—21no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—24no—
1436C2×C4—21no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—22no—
1446C2×C4—24no—
1447C2×C4—24no—
1448C2×C4—24no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—22no—
1453C2×C4—24no—
1454C2×C4—22no—
1455C2×C4—22no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—22no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—22no—
1464C2×C4—24no—
1465C2×C4—24no—
1466C2×C4—22no—
1467C2×C4—22no—
1468C2×C4—44no—
1469C2×C4—48no—
1470C2×C4—84no—
1471C2×C4—84no—
1472C2×C4—84no—
1473C2×C4—88no—
1474C2×C4—88no—
1475C2×C4—88no—
1476C2×C4—88no—
1477C2×C4—164no—
1478C2×C4—164no—
1479C2×C4C2×H(5,𝔽2)12yes—
1480C2×C4C2×H(5,𝔽2)14yes—
1481C2×C4C2×H(5,𝔽2)12yes—
1482C2×C4C2×H(5,𝔽2)12yes—
1483C2×C4C2×H(5,𝔽2)12yes—
1484C2×C4#58512yes—
1485C22—42no—
1486C22—41no—
1487C22—44no—
1488C22—42no—
1489C22—42no—
1490C22—42no—
1491C22—44no—
1492C22—42no—
1493C22—41no—
1494C22—42no—
1495C22—42no—
1496C22—44no—
1497C22—44no—
1498C22—44no—
1499C22—44no—
1500C22—42no—
1501C22—42no—
1502C22—44no—
1503C22—42no—
1504C22—44no—
1505C22—42no—
1506C22—44no—
1507C22—44no—
1508C22—42no—
1509C22—42no—
1510C22—44no—
1511C22—42no—
1512C22—41no—
1513C22—42no—
1514C22C22×H(5,𝔽2)11yescharacteristic
1515C22C22×H(5,𝔽2)11yescharacteristic
1516C22C2×#58511yescharacteristic
1517C22H(7,𝔽2)12yes—
1518C222−1+612yes—
1519C4—22no—
1520C4—24no—
1521C4—22no—
1522C4—41no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—44no—
1527C4—42no—
1528C4—42no—
1529C4—42no—
1530C4—42no—
1531C4—42no—
1532C4—41no—
1533C4—42no—
1534C4—44no—
1535C4—42no—
1536C4—42no—
1537C4—44no—
1538C4—42no—
1539C4—42no—
1540C4—42no—
1541C4—42no—
1542C4—41no—
1543C4—42no—
1544C4#354614yes—
1545C2—82no—
1546C2—81no—
1547C2—84no—
1548C2—82no—
1549C2—82no—
1550C2C2×#354611yescharacteristic
1551C2#6287611yescharacteristic
1552C2#6287812yes—
1553C2#6288412yes—
1554C2#6288711yescharacteristic
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. #58028C2semidirect
2. #57254C2semidirect
3. #57120C2semidirect
4. #56932C2semidirect
5. #56804C2semidirect
6. #55748C2semidirect
7. #54303C2semidirect
8. #54193C2semidirect
9. #53066C2semidirect
10. #52960C2semidirect
11. #45268C2semidirect
12. #45221C2semidirect
13. #45070C2semidirect
14. #44935C2semidirect
15. #42876C2semidirect
16. #42872C2semidirect
17. #42788C2semidirect
18. #42649C2semidirect
19. #42560C2semidirect
20. #42429C2semidirect
21. #39757C2semidirect
22. #39747C2semidirect
23. #39372C2semidirect
24. #39363C2semidirect
25. #37775C2semidirect
26. #37750C2semidirect
27. #37422C2semidirect
28. #37327C2semidirect
29. #35343C2semidirect
30. #35277C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#580282
#572542
#571202
#569322
#568042
#557482
#543032
#541932
#530662
#529602
#452682
#452212
#450702
#449352
#428762
#428722
#427882
#426492
#425602
#424292
#397572
#397472
#393722
#393632
#377752
#377502
#374222
#373272
#353432
#352772
#346402