Finite Group Databasebeta

← #8701659

Subgroups — #8701659

Order 512.

4506 conjugacy classes of subgroups.

The subgroup lattice has 1473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59938C212yesmaximal, complemented
2#59381C212yesmaximal, complemented
3#59307C212yesmaximal, complemented
4#59244C212yesmaximal, complemented
5#58347C214yesmaximal, complemented
6#57599C212yesmaximal, complemented
7#56164C212yesmaximal, complemented
8#53601C214yesmaximal, complemented
9#52299C211yesmaximal, characteristic, complemented
10#50347C214yesmaximal, complemented
11#50304C214yesmaximal, complemented
12#48701C214yesmaximal, complemented
13#45609C212yesmaximal, complemented
14#45502C211yesmaximal, characteristic, complemented
15#45433C211yesmaximal, characteristic, complemented
16#45258C212yesmaximal, complemented
17#45251C211yesmaximal, characteristic, complemented
18#45055C212yesmaximal, complemented
19#42920C212yesmaximal, complemented
20#42908C211yesmaximal, characteristic, complemented
21#42887C211yesmaximal, characteristic, complemented
22#42754C212yesmaximal, complemented
23#40175C212yesmaximal, complemented
24#39936C212yesmaximal, complemented
25#39666C212yesmaximal, complemented
26#37035C212yesmaximal, complemented
27#36927C214yesmaximal, complemented
28#36579C212yesmaximal, complemented
29#36483C211yesmaximal, characteristic, complemented
30C2×#556C2211yescharacteristic
31C2×#556C2212yes—
32C2×#548C2211yescharacteristic
33C2×#537C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2857C2212yes—
36#2855C2212yes—
37#2854C2211yescharacteristic
38#2854C2212yes—
39#2850C2214yes—
40#2841C2212yes—
41#2832C2214yes—
42#2832C2214yes—
43#2831C2214yes—
44#2819C2212yes—
45#2817C2212yes—
46#2804C2214yes—
47#2801C2212yes—
48#2800C2214yes—
49#2798C2214yes—
50#2797C2214yes—
51#2794C2214yes—
52#2789C2212yes—
53#2784C2214yes—
54#2783C2214yes—
55#2780C2214yes—
56#2779C2214yes—
57#2774C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2766C2214yes—
61#2761C2214yes—
62#2760C2211yescharacteristic
63#2760C2212yes—
64#2754C2214yes—
65#2752C2212yes—
66#2752C2211yescharacteristic
67#2752C2212yes—
68#2751C2214yes—
69#2745C2214yes—
70#2745C2214yes—
71#2745C2214yes—
72#2744C2214yes—
73#2743C2214yes—
74#2742C2211yescharacteristic
75#2742C2212yes—
76#2741C2214yes—
77#2740C2214yes—
78#2740C2214yes—
79#2731C2214yes—
80#2730C2214yes—
81#2729C2214yes—
82#2723C2214yes—
83#2715C2214yes—
84#2715C2214yes—
85#2714C2214yes—
86#2714C2214yes—
87#2712C2212yes—
88#2706C2214yes—
89#2703C2212yes—
90#2703C2212yes—
91#2703C2212yes—
92#2703C2214yes—
93#2702C2214yes—
94#2702C2214yes—
95#2700C2214yes—
96#2699C2214yes—
97#2698C2214yes—
98#2696C2214yes—
99#2692C2214yes—
100#2691C2214yes—
101#2688C2214yes—
102#2687C2214yes—
103#2686C2214yes—
104#2683C2212yes—
105#2681C2214yes—
106#2677C2212yes—
107#2676C2214yes—
108#2676C2214yes—
109#2675C2211yescharacteristic
110#2665C2214yes—
111#2662C2214yes—
112#2655C2214yes—
113#2651C2214yes—
114#2650C2214yes—
115#2649C2214yes—
116#2640C2211yescharacteristic
117#2639C2212yes—
118#2635C2212yes—
119#2632C2212yes—
120#2631C2212yes—
121#2630C2214yes—
122#2616C2211yescharacteristic
123#2609C2212yes—
124#2607C2212yes—
125#2607C2212yes—
126#2596C2214yes—
127#2595C2214yes—
128#2592C2214yes—
129#2589C2214yes—
130#2588C2214yes—
131#2586C2214yes—
132#2581C2214yes—
133#2580C2212yes—
134#2576C2214yes—
135#2575C2214yes—
136#2574C2214yes—
137#2570C2212yes—
138#2568C2212yes—
139#2564C2212yes—
140#2563C2212yes—
141#2563C2211yescharacteristic
142#2559C2214yes—
143#2557C2214yes—
144#2557C2214yes—
145#2555C2214yes—
146#2554C2214yes—
147#2551C2212yes—
148#2547C2212yes—
149#2540C2211yescharacteristic
150#2538C2212yes—
151#2538C2212yes—
152#2535C2212yes—
153#2522C2214yes—
154#2520C2214yes—
155#2517C2212yes—
156#2516C2214yes—
157#2515C2214yes—
158#2512C2214yes—
159#2511C2212yes—
160#2508C2212yes—
161#2507C2212yes—
162#2503C2211yescharacteristic
163#2501C2212yes—
164#2501C2211yescharacteristic
165#2500C2212yes—
166#2499C2214yes—
167#2497C2212yes—
168#2497C2212yes—
169#2496C2214yes—
170#2496C2212yes—
171#2494C2212yes—
172#2492C2214yes—
173#2492C2212yes—
174#2491C2212yes—
175#2491C2214yes—
176#2487C2212yes—
177#2487C2211yescharacteristic
178#2486C2212yes—
179#2486C2211yescharacteristic
180#2485C2212yes—
181#2485C2212yes—
182#2481C2214yes—
183#2481C2214yes—
184#2478C2214yes—
185#2471C2214yes—
186#2471C2214yes—
187#2469C2214yes—
188#2469C2214yes—
189#2469C2214yes—
190#2469C2214yes—
191#2467C2214yes—
192#2465C2214yes—
193#2461C2214yes—
194#2457C2214yes—
195#2452C2212yes—
196#2451C2212yes—
197#2448C2212yes—
198#2448C2214yes—
199#2440C2212yes—
200#2440C2212yes—
201#2439C2212yes—
202#2439C2212yes—
203#2427C2212yes—
204#2426C2214yes—
205#2423C2212yes—
206#2423C2214yes—
207#2422C2212yes—
208#2421C2212yes—
209#2421C2212yes—
210#2421C2212yes—
211#2419C2214yes—
212#2417C2212yes—
213#2416C2212yes—
214#2415C2212yes—
215#2414C2212yes—
216#2414C2212yes—
217#2409C2212yes—
218#2409C2212yes—
219#2407C2212yes—
220#2401C2212yes—
221#2397C2211yescharacteristic
222#2388C2211yescharacteristic
223#2388C2212yes—
224#2379C2214yes—
225#2376C2212yes—
226#2374C2214yes—
227#2368C2214yes—
228#2365C2214yes—
229#2362C2212yes—
230#2362C2212yes—
231#2360C2212yes—
232#2357C2212yes—
233#2355C2212yes—
234#2354C2212yes—
235#2352C2212yes—
236#2352C2212yes—
237#2352C2212yes—
238Q8×C4⋊C4C2212yes—
239#2344C2212yes—
240#2341C2212yes—
241Q8×C22⋊C4C2211yescharacteristic
242#2339C2211yescharacteristic
243#2333C2214yes—
244#2332C2214yes—
245#2331C2212yes—
246#2324C2214yes—
247#2320C2211yescharacteristic
248#2311C2212yes—
249C4×C22⋊Q8C2214yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#123C2212yes—
253C4×#123C2211yescharacteristic
254C4×#121C2212yes—
255C4×#121C2212yes—
256C4×#121C2212yes—
257C4×#121C2212yes—
258#2285C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262#556—48no—
263#556—44no—
264#548—44no—
265#537—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#124C2311yescharacteristic
279C2×#124C2314yes—
280C2×#123C2312yes—
281C2×#123C2311yescharacteristic
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2311yescharacteristic
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×C4×Q8—44no—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C42C2312yes—
335C22×C42C2311yescharacteristic
336C22×C42C2312yes—
337#401C2314yes—
338#401C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2311yescharacteristic
362#399C2312yes—
363#399C2314yes—
364#399C2314yes—
365#399C2311yescharacteristic
366#399C2314yes—
367#399C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2312yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2311yescharacteristic
410#395C2312yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2311yescharacteristic
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2312yes—
434#394C2312yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#393C2312yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2312yes—
443#393C2314yes—
444#393C2311yescharacteristic
445#393C2314yes—
446#393C2312yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2312yes—
453#392C2311yescharacteristic
454#392C2312yes—
455#392C2314yes—
456#392C2311yescharacteristic
457#392C2314yes—
458#392C2311yescharacteristic
459#392C2314yes—
460#392C2312yes—
461#392C2312yes—
462#392C2312yes—
463#392C2312yes—
464#392C2312yes—
465#392C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#388C2312yes—
523#388C2314yes—
524#388C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
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#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2311yescharacteristic
616#386C2314yes—
617#386C2312yes—
618#386C2312yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2312yes—
623#386C2312yes—
624#386C2312yes—
625#386C2312yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2311yescharacteristic
639#385C2312yes—
640#384C2312yes—
641#384C2312yes—
642#384C2314yes—
643#384C2312yes—
644#383C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#381C2312yes—
654#381C2314yes—
655#381C2311yescharacteristic
656#381C2314yes—
657#381C2314yes—
658#381C2312yes—
659#381C2314yes—
660#381C2312yes—
661#380C2311yescharacteristic
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2311yescharacteristic
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2312yes—
682#380C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2311yescharacteristic
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2311yescharacteristic
716C2×#95C2312yes—
717C2×#41—24no—
718C2×#41—42no—
719C2×#41—44no—
720C2×#41—44no—
721C22×Q8—24no—
722C22×Q8—44no—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2411yescharacteristic
740C22×D4C2412yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C4⋊Q8—44no—
759C4⋊Q8—44no—
760C4⋊Q8—42no—
761C4⋊Q8—48no—
762#126—48no—
763#126—48no—
764#126—48no—
765#126—84no—
766#124—48no—
767#124—44no—
768#124—42no—
769#124—44no—
770#124—48no—
771#124—84no—
772#123—28no—
773#123—24no—
774#123—44no—
775#123—82no—
776#123—82no—
777#123—84no—
778#123—82no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—42no—
788C22⋊Q8—44no—
789C22⋊Q8—84no—
790#121—28no—
791#121—44no—
792#121—44no—
793#121—44no—
794#121—48no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—42no—
799#121—44no—
800C4×Q8—28no—
801C4×Q8—24no—
802C4×Q8—48no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—48no—
806C4×Q8—44no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—42no—
816C4×D4—84no—
817#117—44no—
818#117—44no—
819#117—44no—
820#117—84no—
821C2×C4⋊C4—44no—
822C2×C4⋊C4—42no—
823C2×C4⋊C4—44no—
824C2×C4⋊C4—42no—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2411yescharacteristic
934C2×C42—42no—
935C2×C42—44no—
936C2×C42—44no—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2412yes—
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022C24C2512yes—
1023C24C2512yes—
1024C24C2512yes—
1025C24C2511yescharacteristic
1026C24C2511yescharacteristic
1027#41—88no—
1028#41—88no—
1029C2×Q8—24no—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—28no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—416no—
1045C2×Q8H(5,𝔽2)14yes—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—42no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—42no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C22×C4—24no—
1085C22×C4—22no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—41no—
1101C22×C4—44no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—41no—
1114C22×C4—44no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—22no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—28no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—41no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—41no—
1219C22⋊C4—42no—
1220C22⋊C4—41no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
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—44no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—41no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C42−1+414yes—
1253C42—24no—
1254C42—28no—
1255C42—22no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—42no—
1261C42—42no—
1262C42—44no—
1263C42—42no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—42no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C23—21no—
1274C23—22no—
1275C23—22no—
1276C23—21no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—21no—
1281C23—21no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—24no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—21no—
1299C23—22no—
1300C23—22no—
1301C23C2×2−1+412yes—
1302C23C2611yescharacteristic
1303Q8—28no—
1304Q8—48no—
1305Q8—44no—
1306Q8—88no—
1307Q8—84no—
1308Q8—82no—
1309Q8—164no—
1310D4—44no—
1311D4—84no—
1312D4—84no—
1313D4—84no—
1314D4—84no—
1315D4—84no—
1316D4—84no—
1317D4—82no—
1318D4—82no—
1319D4—88no—
1320D4—84no—
1321D4—82no—
1322D4—84no—
1323D4—164no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—21no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
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—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—44no—
1386C2×C4—48no—
1387C2×C4—48no—
1388C2×C4—44no—
1389C2×C4—48no—
1390C2×C4—44no—
1391C2×C4—84no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—82no—
1395C2×C4—84no—
1396C2×C4—88no—
1397C2×C4—162no—
1398C2×C4—164no—
1399C2×C4C2×H(5,𝔽2)14yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×2−1+414yes—
1402C2×C4#58514yes—
1403C2×C4#58514yes—
1404C22—24no—
1405C22—22no—
1406C22—41no—
1407C22—41no—
1408C22—42no—
1409C22—41no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—41no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—44no—
1423C22—42no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—44no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22C22×H(5,𝔽2)11yescharacteristic
1434C22C22×2−1+411yescharacteristic
1435C22C2×#58512yes—
1436C22C2×#58512yes—
1437C22H(7,𝔽2)11yescharacteristic
1438C4—24no—
1439C4—24no—
1440C4—24no—
1441C4—42no—
1442C4—41no—
1443C4—42no—
1444C4—41no—
1445C4—42no—
1446C4—44no—
1447C4—41no—
1448C4—44no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—42no—
1454C4—41no—
1455C4—42no—
1456C4—42no—
1457C4—44no—
1458C4—44no—
1459C4—44no—
1460C4—42no—
1461C4#353314yes—
1462C2—42no—
1463C2—81no—
1464C2—82no—
1465C2—82no—
1466C2—82no—
1467C2C2×#353311yescharacteristic
1468C2#6291711yescharacteristic
1469C2#6293812yes—
1470C2#6302011yescharacteristic
1471C2#6302512yes—
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. #59938C2semidirect
2. #59381C2semidirect
3. #59307C2semidirect
4. #59244C2semidirect
5. #58347C2semidirect
6. #57599C2semidirect
7. #56164C2semidirect
8. #53601C2semidirect
9. #52299C2semidirect
10. #50347C2semidirect
11. #50304C2semidirect
12. #48701C2semidirect
13. #45609C2semidirect
14. #45502C2semidirect
15. #45433C2semidirect
16. #45258C2semidirect
17. #45251C2semidirect
18. #45055C2semidirect
19. #42920C2semidirect
20. #42908C2semidirect
21. #42887C2semidirect
22. #42754C2semidirect
23. #40175C2semidirect
24. #39936C2semidirect
25. #39666C2semidirect
26. #37035C2semidirect
27. #36927C2semidirect
28. #36579C2semidirect
29. #36483C2semidirect

Maximal subgroups

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

subgroupindex
#599382
#593812
#593072
#592442
#583472
#575992
#561642
#536012
#522992
#503472
#503042
#487012
#456092
#455022
#454332
#452582
#452512
#450552
#429202
#429082
#428872
#427542
#401752
#399362
#396662
#370352
#369272
#365792
#364832