Finite Group Databasebeta

← #8383469

Subgroups — #8383469

Order 512.

4325 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59275C212yesmaximal, complemented
2#58847C214yesmaximal, complemented
3#56922C214yesmaximal, complemented
4#56649C214yesmaximal, complemented
5#54039C214yesmaximal, complemented
6#53144C212yesmaximal, complemented
7#51277C214yesmaximal, complemented
8#50607C214yesmaximal, complemented
9#45669C212yesmaximal, complemented
10#45431C211yesmaximal, characteristic, complemented
11#45428C211yesmaximal, characteristic, complemented
12#45338C211yesmaximal, characteristic, complemented
13#45167C212yesmaximal, complemented
14#45141C211yesmaximal, characteristic, complemented
15#42880C211yesmaximal, characteristic
16#42793C211yesmaximal, characteristic, complemented
17#42729C212yesmaximal, complemented
18#42715C212yesmaximal, complemented
19#41509C214yesmaximal, complemented
20#41161C214yesmaximal, complemented
21#40031C212yesmaximal, complemented
22#39903C212yesmaximal, complemented
23#39757C211yesmaximal, characteristic, complemented
24#39168C211yesmaximal, characteristic, complemented
25#37321C211yesmaximal, characteristic, complemented
26#36419C211yesmaximal, characteristic, complemented
27#36209C211yesmaximal, characteristic, complemented
28#36041C211yesmaximal, characteristic, complemented
29#36030C211yesmaximal, characteristic, complemented
30#35670C211yesmaximal, characteristic, complemented
31#34596C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#541C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2859C2211yescharacteristic
39#2858C2211yescharacteristic
40#2857C2212yes—
41#2850C2212yes—
42#2838C2214yes—
43#2837C2214yes—
44#2835C2214yes—
45#2832C2214yes—
46#2832C2214yes—
47#2827C2214yes—
48#2824C2214yes—
49#2821C2212yes—
50#2818C2212yes—
51#2810C2214yes—
52#2808C2214yes—
53#2805C2214yes—
54#2804C2214yes—
55#2803C2214yes—
56#2800C2214yes—
57#2797C2214yes—
58#2796C2214yes—
59#2784C2214yes—
60#2782C2214yes—
61#2781C2214yes—
62#2779C2214yes—
63#2779C2214yes—
64#2778C2214yes—
65#2771C2214yes—
66#2765C2214yes—
67#2763C2214yes—
68#2762C2214yes—
69#2758C2214yes—
70#2757C2214yes—
71#2754C2214yes—
72#2754C2214yes—
73#2753C2214yes—
74#2751C2214yes—
75#2743C2214yes—
76#2742C2214yes—
77#2741C2214yes—
78#2741C2214yes—
79#2741C2214yes—
80#2738C2214yes—
81#2737C2214yes—
82#2737C2214yes—
83#2737C2214yes—
84#2737C2214yes—
85#2731C2214yes—
86#2716C2214yes—
87#2716C2214yes—
88#2715C2214yes—
89#2714C2214yes—
90#2713C2214yes—
91#2711C2214yes—
92#2710C2214yes—
93#2709C2214yes—
94#2705C2214yes—
95#2702C2214yes—
96#2698C2214yes—
97#2696C2214yes—
98#2693C2214yes—
99#2692C2214yes—
100#2686C2214yes—
101#2674C2214yes—
102#2674C2214yes—
103#2665C2212yes—
104#2663C2212yes—
105#2655C2212yes—
106#2654C2214yes—
107#2653C2212yes—
108#2653C2214yes—
109#2652C2212yes—
110#2652C2214yes—
111#2650C2214yes—
112#2650C2212yes—
113#2649C2214yes—
114#2646C2214yes—
115#2642C2212yes—
116#2642C2212yes—
117#2641C2212yes—
118#2640C2212yes—
119#2638C2212yes—
120#2634C2212yes—
121#2633C2212yes—
122#2632C2212yes—
123#2632C2212yes—
124#2630C2212yes—
125#2628C2211yescharacteristic
126#2619C2211yescharacteristic
127#2610C2212yes—
128#2610C2212yes—
129#2605C2214yes—
130#2604C2212yes—
131#2603C2212yes—
132#2599C2212yes—
133#2598C2212yes—
134#2597C2214yes—
135#2596C2214yes—
136#2592C2212yes—
137#2592C2212yes—
138#2589C2214yes—
139#2587C2214yes—
140#2581C2211yescharacteristic
141#2581C2211yescharacteristic
142#2575C2214yes—
143#2575C2214yes—
144#2568C2211yescharacteristic
145#2568C2212yes—
146#2567C2211yescharacteristic
147#2565C2211yescharacteristic
148#2565C2211yescharacteristic
149#2559C2214yes—
150#2559C2214yes—
151#2550C2212yes—
152#2548C2211yescharacteristic
153#2548C2211yescharacteristic
154#2547C2212yes—
155#2546C2211yescharacteristic
156#2546C2211yescharacteristic
157#2545C2212yes—
158#2544C2214yes—
159#2542C2212yes—
160#2540C2212yes—
161#2536C2211yescharacteristic
162#2536C2211yescharacteristic
163#2533C2214yes—
164#2533C2214yes—
165#2531C2214yes—
166#2531C2214yes—
167#2528C2214yes—
168#2516C2214yes—
169#2514C2212yes—
170#2513C2214yes—
171#2512C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2508C2214yes—
176#2505C2214yes—
177#2500C2212yes—
178#2499C2211yescharacteristic
179#2499C2211yescharacteristic
180#2495C2214yes—
181#2494C2214yes—
182#2492C2212yes—
183#2492C2212yes—
184#2490C2212yes—
185#2490C2212yes—
186#2489C2212yes—
187#2489C2212yes—
188#2488C2214yes—
189#2485C2214yes—
190#2479C2214yes—
191#2479C2214yes—
192#2478C2214yes—
193#2478C2214yes—
194#2477C2214yes—
195#2477C2214yes—
196#2471C2214yes—
197#2471C2214yes—
198#2469C2214yes—
199#2469C2214yes—
200#2462C2214yes—
201#2462C2214yes—
202#2458C2214yes—
203#2454C2212yes—
204#2452C2214yes—
205#2448C2214yes—
206#2448C2212yes—
207#2446C2214yes—
208#2446C2212yes—
209#2444C2214yes—
210#2439C2212yes—
211#2436C2212yes—
212#2434C2211yescharacteristic
213#2434C2211yescharacteristic
214#2432C2212yes—
215#2432C2212yes—
216#2432C2212yes—
217#2429C2212yes—
218#2427C2212yes—
219#2423C2212yes—
220#2422C2212yes—
221#2421C2212yes—
222#2420C2212yes—
223#2419C2214yes—
224#2409C2212yes—
225#2407C2212yes—
226#2401C2212yes—
227#2399C2211yescharacteristic
228#2399C2212yes—
229#2398C2211yescharacteristic
230#2398C2212yes—
231#2398C2212yes—
232#2396C2211yescharacteristic
233#2392C2211yescharacteristic
234#2376C2214yes—
235#2368C2214yes—
236#2367C2214yes—
237#2367C2212yes—
238#2363C2212yes—
239#2362C2212yes—
240#2362C2212yes—
241#2357C2212yes—
242#2356C2211yescharacteristic
243#2356C2211yescharacteristic
244#2356C2211yescharacteristic
245#2356C2211yescharacteristic
246#2355C2212yes—
247#2354C2212yes—
248#2346C2214yes—
249#2339C2212yes—
250#2334C2214yes—
251#2332C2214yes—
252#2331C2211yescharacteristic
253#2330C2212yes—
254#2328C2211yescharacteristic
255#2327C2211yescharacteristic
256#2327C2211yescharacteristic
257#2326C2212yes—
258C4×C4⋊Q8C2211yescharacteristic
259C4×C4⋊Q8C2211yescharacteristic
260C4×C22⋊Q8C2212yes—
261C4×#123C2212yes—
262#2298C2211yescharacteristic
263#2297C2212yes—
264#2295C2211yescharacteristic
265#2285C2212yes—
266C42×D4C2211yescharacteristic
267C22×#41C2312yes—
268C23×Q8C2311yescharacteristic
269#559—44no—
270Q82—44no—
271#556—44no—
272#550—44no—
273#541—44no—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#127C2312yes—
285C2×#126C2312yes—
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#126C2314yes—
289C2×#125C2311yescharacteristic
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#123C2312yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2311yescharacteristic
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313#519—44no—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2311yescharacteristic
339C2×#117C2312yes—
340C22×C42C2312yes—
341#401C2314yes—
342#401C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2311yescharacteristic
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#399C2311yescharacteristic
375#399C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2311yescharacteristic
393#398C2312yes—
394#398C2314yes—
395#398C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2311yescharacteristic
412#397C2312yes—
413#397C2314yes—
414#397C2312yes—
415#397C2312yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2312yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2312yes—
428#396C2312yes—
429#396C2314yes—
430#395C2314yes—
431#395C2312yes—
432#395C2312yes—
433#395C2314yes—
434#395C2314yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2312yes—
439#395C2312yes—
440#395C2311yescharacteristic
441#395C2312yes—
442#394C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2311yescharacteristic
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2312yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2311yescharacteristic
481#393C2312yes—
482#393C2312yes—
483#393C2314yes—
484#392C2311yescharacteristic
485#392C2314yes—
486#392C2312yes—
487#392C2314yes—
488#392C2312yes—
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2311yescharacteristic
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2312yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2312yes—
627#387C2314yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2312yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2312yes—
663#385C2312yes—
664#385C2314yes—
665#384C2311yescharacteristic
666#384C2311yescharacteristic
667#384C2312yes—
668#384C2312yes—
669#383C2312yes—
670#383C2312yes—
671#383C2312yes—
672#383C2312yes—
673#383C2314yes—
674#382C2311yescharacteristic
675#382C2311yescharacteristic
676#382C2314yes—
677#382C2312yes—
678#382C2314yes—
679#382C2314yes—
680#382C2311yescharacteristic
681#382C2311yescharacteristic
682#382C2314yes—
683#381C2314yes—
684#381C2314yes—
685#381C2314yes—
686#381C2312yes—
687#380C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2312yes—
691#380C2312yes—
692#380C2314yes—
693#380C2314yes—
694#380C2314yes—
695#380C2314yes—
696#380C2312yes—
697#380C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2311yescharacteristic
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2311yescharacteristic
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735#376C2312yes—
736#376C2312yes—
737#376C2312yes—
738C2×#95C2314yes—
739C43C2311yescharacteristic
740C2×#41—44no—
741C2×#41—44no—
742C2×#41—44no—
743C22×Q8—42no—
744C22×Q8—42no—
745C22×Q8—42no—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2414yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2414yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C4⋊Q8—24no—
772C4⋊Q8—44no—
773C4⋊Q8—44no—
774C4⋊Q8—42no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777C4⋊Q8—42no—
778C4⋊Q8—42no—
779C4⋊Q8—48no—
780#127—24no—
781#127—44no—
782#126—44no—
783#126—44no—
784#126—48no—
785#126—48no—
786#125—44no—
787#125—42no—
788#125—44no—
789#125—44no—
790#124—48no—
791#124—44no—
792#124—44no—
793#124—44no—
794#124—44no—
795#124—44no—
796#123—48no—
797#123—44no—
798#123—48no—
799C22⋊Q8—48no—
800C22⋊Q8—48no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804C22⋊Q8—42no—
805C22⋊Q8—42no—
806C22⋊Q8—44no—
807#121—48no—
808#121—44no—
809#121—44no—
810C4×Q8—24no—
811C4×Q8—24no—
812C4×Q8—24no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—44no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×Q8—42no—
819C4×Q8—42no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—44no—
823C4×D4—24no—
824C4×D4—44no—
825C4×D4—44no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—44no—
830#117—24no—
831#117—44no—
832#117—44no—
833#117—48no—
834#117—42no—
835#117—44no—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C42—44no—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2411yescharacteristic
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2511yescharacteristic
1048C24C2512yes—
1049C24C2514yes—
1050#41—816no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—22no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—42no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—42no—
1069C2×Q8—42no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—416no—
1077C2×D4—22no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C22×C4—22no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—42no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2511yescharacteristic
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—22no—
1160C4⋊C4—24no—
1161C4⋊C4—22no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C22⋊C4—22no—
1211C22⋊C4—22no—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C42—22no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—24no—
1264C42—24no—
1265C42—22no—
1266C42—24no—
1267C42—22no—
1268C42—24no—
1269C42—24no—
1270C42—22no—
1271C42—22no—
1272C42—42no—
1273C42—42no—
1274C42—42no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42—42no—
1281C42—42no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42H(5,𝔽2)14yes—
1286C23—21no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—22no—
1291C23—24no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—21no—
1297C23—24no—
1298C23—22no—
1299C23—21no—
1300C23—24no—
1301C23—22no—
1302C23—22no—
1303C23—24no—
1304C23—22no—
1305C23C2611yescharacteristic
1306Q8—44no—
1307Q8—48no—
1308Q8—44no—
1309Q8—44no—
1310Q8—44no—
1311Q8—44no—
1312Q8—84no—
1313Q8—84no—
1314Q8—164no—
1315D4—44no—
1316D4—48no—
1317D4—84no—
1318D4—84no—
1319D4—84no—
1320D4—88no—
1321D4—164no—
1322D4—164no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—48no—
1394C2×C4—48no—
1395C2×C4—44no—
1396C2×C4—48no—
1397C2×C4—84no—
1398C2×C4—88no—
1399C2×C4—164no—
1400C2×C4—164no—
1401C2×C4C2×H(5,𝔽2)12yes—
1402C2×C4C2×H(5,𝔽2)12yes—
1403C2×C4C2×H(5,𝔽2)12yes—
1404C2×C4#58514yes—
1405C2×C4#58512yes—
1406C2×C4#58512yes—
1407C22—41no—
1408C22—42no—
1409C22—44no—
1410C22—44no—
1411C22—42no—
1412C22—41no—
1413C22—44no—
1414C22—42no—
1415C22—41no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—44no—
1420C22—44no—
1421C22—44no—
1422C22—42no—
1423C22—44no—
1424C22—42no—
1425C22—42no—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22C2×#58511yescharacteristic
1429C22C2×#58512yes—
1430C222−1+612yes—
1431C4—22no—
1432C4—22no—
1433C4—24no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—42no—
1439C4—42no—
1440C4—41no—
1441C4—42no—
1442C4—42no—
1443C4—44no—
1444C4—42no—
1445C4—42no—
1446C4—41no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—44no—
1456C4—42no—
1457C4—44no—
1458C4#354014yes—
1459C2—81no—
1460C2—82no—
1461C2—84no—
1462C2C2×#354011yescharacteristic
1463C2#6283611yescharacteristic
1464C2#6288711yescharacteristic
1465C2#6290712yes—
1466C2#6296812yes—
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. #59275C2semidirect
2. #58847C2semidirect
3. #56922C2semidirect
4. #56649C2semidirect
5. #54039C2semidirect
6. #53144C2semidirect
7. #51277C2semidirect
8. #50607C2semidirect
9. #45669C2semidirect
10. #45431C2semidirect
11. #45428C2semidirect
12. #45338C2semidirect
13. #45167C2semidirect
14. #45141C2semidirect
16. #42793C2semidirect
17. #42729C2semidirect
18. #42715C2semidirect
19. #41509C2semidirect
20. #41161C2semidirect
21. #40031C2semidirect
22. #39903C2semidirect
23. #39757C2semidirect
24. #39168C2semidirect
25. #37321C2semidirect
26. #36419C2semidirect
27. #36209C2semidirect
28. #36041C2semidirect
29. #36030C2semidirect
30. #35670C2semidirect
31. #34596C2semidirect

Maximal subgroups

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

subgroupindex
#592752
#588472
#569222
#566492
#540392
#531442
#512772
#506072
#456692
#454312
#454282
#453382
#451672
#451412
#428802
#427932
#427292
#427152
#415092
#411612
#400312
#399032
#397572
#391682
#373212
#364192
#362092
#360412
#360302
#356702
#345962