Finite Group Databasebeta

← #8751541

Subgroups — #8751541

Order 512.

5271 conjugacy classes of subgroups.

The subgroup lattice has 1521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59475C212yesmaximal, complemented
3#58802C212yesmaximal, complemented
4#58146C214yesmaximal, complemented
5#56774C214yesmaximal, complemented
6#55526C214yesmaximal, complemented
7#55284C214yesmaximal, complemented
8#53045C212yesmaximal, complemented
9#53005C211yesmaximal, characteristic, complemented
10#52414C212yesmaximal, complemented
11#52326C214yesmaximal, complemented
12#47750C212yesmaximal, complemented
13#45385C212yesmaximal, complemented
14#45332C212yesmaximal, complemented
15#45322C212yesmaximal, complemented
16#45308C211yesmaximal, characteristic, complemented
17#45243C212yesmaximal, complemented
18#42917C211yesmaximal, characteristic, complemented
19#42852C212yesmaximal, complemented
20#42807C212yesmaximal, complemented
21#42792C212yesmaximal, complemented
22#42706C212yesmaximal, complemented
23#41999C212yesmaximal, complemented
24#41122C214yesmaximal, complemented
25#39663C212yesmaximal, complemented
26#39491C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36085C211yesmaximal, characteristic, complemented
29#35687C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#555C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×#548C2212yes—
36C2×#547C2212yes—
37C2×#547C2211yescharacteristic
38C2×#541C2212yes—
39C2×#536C2211yescharacteristic
40#2862C2211yescharacteristic
41#2844C2212yes—
42#2843C2211yescharacteristic
43#2838C2214yes—
44#2837C2214yes—
45#2832C2214yes—
46#2831C2214yes—
47#2830C2211yescharacteristic
48#2830C2212yes—
49#2829C2212yes—
50#2829C2214yes—
51#2829C2214yes—
52#2829C2212yes—
53#2829C2212yes—
54#2828C2211yescharacteristic
55#2828C2212yes—
56#2827C2214yes—
57#2824C2212yes—
58#2823C2211yescharacteristic
59#2821C2214yes—
60#2818C2212yes—
61#2817C2214yes—
62#2814C2212yes—
63#2808C2214yes—
64#2806C2214yes—
65#2803C2214yes—
66#2801C2214yes—
67#2797C2214yes—
68#2795C2214yes—
69#2792C2214yes—
70#2789C2212yes—
71#2788C2214yes—
72#2785C2212yes—
73#2781C2214yes—
74#2781C2214yes—
75#2779C2214yes—
76#2774C2214yes—
77#2774C2214yes—
78#2768C2214yes—
79#2765C2214yes—
80#2763C2212yes—
81#2761C2214yes—
82#2759C2214yes—
83#2757C2214yes—
84#2753C2214yes—
85#2742C2212yes—
86#2739C2214yes—
87#2734C2214yes—
88#2729C2214yes—
89#2729C2214yes—
90#2728C2214yes—
91#2724C2214yes—
92#2723C2214yes—
93#2723C2214yes—
94#2720C2214yes—
95#2720C2214yes—
96#2714C2214yes—
97#2713C2214yes—
98#2712C2214yes—
99#2711C2214yes—
100#2710C2214yes—
101#2710C2214yes—
102#2707C2214yes—
103#2705C2214yes—
104#2701C2214yes—
105#2700C2214yes—
106#2699C2214yes—
107#2698C2214yes—
108#2690C2214yes—
109#2689C2214yes—
110#2686C2214yes—
111#2683C2212yes—
112#2683C2212yes—
113#2681C2214yes—
114#2680C2214yes—
115#2674C2214yes—
116#2672C2214yes—
117#2666C2214yes—
118#2663C2212yes—
119#2660C2214yes—
120#2650C2214yes—
121#2648C2214yes—
122#2648C2214yes—
123#2643C2214yes—
124#2638C2214yes—
125#2638C2214yes—
126#2633C2214yes—
127#2627C2212yes—
128#2625C2211yescharacteristic
129#2621C2212yes—
130#2619C2212yes—
131#2616C2212yes—
132#2616C2214yes—
133#2616C2211yescharacteristic
134#2614C2212yes—
135#2612C2212yes—
136#2603C2214yes—
137#2601C2214yes—
138#2600C2214yes—
139#2595C2214yes—
140#2589C2214yes—
141#2587C2214yes—
142#2586C2214yes—
143#2583C2212yes—
144#2573C2214yes—
145#2566C2212yes—
146#2563C2211yescharacteristic
147#2562C2212yes—
148#2558C2214yes—
149#2556C2214yes—
150#2554C2214yes—
151#2551C2212yes—
152#2550C2214yes—
153#2546C2212yes—
154#2546C2212yes—
155#2542C2212yes—
156#2542C2211yescharacteristic
157#2538C2212yes—
158#2538C2212yes—
159#2536C2212yes—
160#2531C2214yes—
161#2526C2214yes—
162#2523C2212yes—
163#2511C2212yes—
164#2505C2214yes—
165#2505C2214yes—
166#2504C2212yes—
167#2500C2212yes—
168#2497C2212yes—
169#2494C2212yes—
170#2492C2212yes—
171#2489C2212yes—
172#2489C2212yes—
173#2489C2212yes—
174#2485C2212yes—
175#2481C2214yes—
176#2474C2214yes—
177#2473C2214yes—
178#2468C2214yes—
179#2466C2214yes—
180#2464C2214yes—
181#2455C2214yes—
182#2453C2212yes—
183#2452C2214yes—
184#2452C2214yes—
185#2451C2212yes—
186#2449C2214yes—
187#2447C2212yes—
188#2447C2214yes—
189#2446C2212yes—
190#2446C2212yes—
191#2444C2214yes—
192#2440C2214yes—
193#2438C2214yes—
194#2434C2211yescharacteristic
195#2434C2212yes—
196#2434C2214yes—
197#2434C2212yes—
198#2434C2211yescharacteristic
199#2434C2212yes—
200#2432C2212yes—
201#2432C2214yes—
202#2432C2214yes—
203#2432C2212yes—
204#2430C2214yes—
205#2430C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2427C2212yes—
209#2423C2212yes—
210#2421C2212yes—
211#2421C2212yes—
212#2415C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2409C2212yes—
216#2409C2211yescharacteristic
217#2409C2212yes—
218#2409C2212yes—
219#2409C2212yes—
220#2409C2214yes—
221#2409C2211yescharacteristic
222#2407C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2407C2214yes—
226#2407C2214yes—
227#2406C2214yes—
228#2406C2212yes—
229#2395C2212yes—
230#2395C2211yescharacteristic
231#2392C2212yes—
232#2392C2212yes—
233#2392C2212yes—
234#2388C2211yescharacteristic
235#2388C2212yes—
236#2388C2214yes—
237C2×#395C2212yes—
238#2367C2212yes—
239#2366C2212yes—
240#2365C2212yes—
241#2362C2212yes—
242#2356C2212yes—
243#2343C2214yes—
244#2341C2212yes—
245#2341C2211yescharacteristic
246Q8×C22⋊C4C2212yes—
247Q8×C22⋊C4C2212yes—
248#2339C2212yes—
249#2339C2211yescharacteristic
250#2334C2214yes—
251#2324C2212yes—
252#2323C2212yes—
253#2317C2212yes—
254#2310C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2293C2211yescharacteristic
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C22×#41C2314yes—
266C22×#41C2312yes—
267C23×Q8C2311yescharacteristic
268C23×Q8C2312yes—
269C23×Q8C2312yes—
270C23×Q8C2312yes—
271C23×Q8C2311yescharacteristic
272#555—44no—
273D4×Q8—48no—
274D4×Q8—48no—
275D4×Q8—48no—
276#548—48no—
277#547—44no—
278#547—48no—
279#541—48no—
280#536—44no—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2312yes—
287C2×C4⋊Q8C2314yes—
288C2×C4⋊Q8C2312yes—
289C2×C4⋊Q8C2314yes—
290C2×#127C2311yescharacteristic
291C2×#126C2312yes—
292C2×#126C2314yes—
293C2×#126C2314yes—
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#123C2314yes—
301C2×#123C2312yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2311yescharacteristic
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2314yes—
355#401C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2311yescharacteristic
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2312yes—
375#399C2311yescharacteristic
376#399C2314yes—
377#399C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2311yescharacteristic
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2314yes—
412#397C2312yes—
413#397C2311yescharacteristic
414#397C2312yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2312yes—
425#396C2312yes—
426#396C2312yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#395C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2311yescharacteristic
444#395C2312yes—
445#395C2312yes—
446#395C2314yes—
447#395C2312yes—
448#395C2314yes—
449#395C2312yes—
450#395C2312yes—
451#395C2314yes—
452#395C2312yes—
453#395C2314yes—
454#395C2314yes—
455#395C2312yes—
456#395C2314yes—
457#395C2314yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2311yescharacteristic
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2312yes—
475#394C2312yes—
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#394C2312yes—
481#394C2312yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#393C2312yes—
495#393C2312yes—
496#393C2314yes—
497#393C2314yes—
498#393C2314yes—
499#393C2312yes—
500#393C2311yescharacteristic
501#393C2312yes—
502#393C2314yes—
503#393C2314yes—
504#393C2312yes—
505#392C2312yes—
506#392C2312yes—
507#392C2312yes—
508#392C2312yes—
509#392C2312yes—
510#392C2312yes—
511#392C2311yescharacteristic
512#392C2312yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2314yes—
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#391C2312yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#391C2314yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#390C2311yescharacteristic
538#390C2312yes—
539#390C2311yescharacteristic
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2314yes—
550#390C2312yes—
551#390C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2312yes—
569#389C2314yes—
570#389C2312yes—
571#389C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
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#388C2314yes—
601#388C2314yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
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#387C2314yes—
624#387C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2312yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
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#385C2314yes—
661#385C2314yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#384C2311yescharacteristic
666#384C2312yes—
667#384C2312yes—
668#384C2314yes—
669#383C2312yes—
670#383C2314yes—
671#382C2312yes—
672#382C2312yes—
673#382C2312yes—
674#382C2314yes—
675#382C2312yes—
676#382C2314yes—
677#382C2314yes—
678#381C2314yes—
679#381C2314yes—
680#381C2314yes—
681#381C2312yes—
682#381C2314yes—
683#380C2311yescharacteristic
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2311yescharacteristic
691#380C2314yes—
692#380C2314yes—
693#380C2314yes—
694#380C2312yes—
695#380C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2311yescharacteristic
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719#376C2314yes—
720C2×#95C2314yes—
721C2×#95C2312yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—28no—
727C2×#41—24no—
728C2×#41—48no—
729C2×#41—44no—
730C2×#41—42no—
731C2×#41—44no—
732C2×#41—48no—
733C2×#41—44no—
734C2×#41—44no—
735C2×#41—48no—
736C2×#41—48no—
737C2×#41—44no—
738C22×Q8—28no—
739C22×Q8—28no—
740C22×Q8—28no—
741C22×Q8—44no—
742C22×Q8—48no—
743C22×Q8—44no—
744C22×Q8—42no—
745C22×Q8—44no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2412yes—
754C22×Q8C2412yes—
755C22×Q8C2414yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×Q8C2412yes—
759C22×Q8C2411yescharacteristic
760C22×D4C2414yes—
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2414yes—
765C22×D4C2411yescharacteristic
766C22×D4C2411yescharacteristic
767C22×D4C2412yes—
768C22×D4C2412yes—
769C22×D4C2412yes—
770C22×D4C2412yes—
771C22×D4C2412yes—
772C22×D4C2412yes—
773C22×D4C2411yescharacteristic
774C23×C4C2412yes—
775C23×C4C2411yescharacteristic
776C23×C4C2411yescharacteristic
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2414yes—
780C23×C4C2412yes—
781C23×C4C2412yes—
782C23×C4C2412yes—
783C23×C4C2414yes—
784C23×C4C2414yes—
785C23×C4C2414yes—
786C23×C4C2412yes—
787C4⋊Q8—28no—
788C4⋊Q8—28no—
789C4⋊Q8—42no—
790C4⋊Q8—44no—
791C4⋊Q8—42no—
792C4⋊Q8—44no—
793C4⋊Q8—48no—
794C4⋊Q8—48no—
795C4⋊Q8—48no—
796#127—24no—
797#126—28no—
798#126—48no—
799#126—48no—
800#125—44no—
801#125—48no—
802#125—48no—
803#124—28no—
804#124—48no—
805#124—48no—
806#123—48no—
807#123—48no—
808#123—44no—
809#123—44no—
810#123—48no—
811C22⋊Q8—28no—
812C22⋊Q8—28no—
813C22⋊Q8—44no—
814C22⋊Q8—44no—
815C22⋊Q8—48no—
816C22⋊Q8—48no—
817C22⋊Q8—48no—
818C22⋊Q8—48no—
819C22⋊Q8—48no—
820C22⋊Q8—44no—
821C22⋊Q8—42no—
822C22⋊Q8—42no—
823C22⋊Q8—44no—
824C22⋊Q8—44no—
825C22⋊Q8—44no—
826C22⋊Q8—44no—
827C22⋊Q8—44no—
828C22⋊Q8—48no—
829C22⋊Q8—48no—
830C22⋊Q8—44no—
831#121—28no—
832#121—48no—
833#121—48no—
834#121—44no—
835#121—44no—
836C4×Q8—28no—
837C4×Q8—44no—
838C4×Q8—44no—
839C4×Q8—44no—
840C4×Q8—44no—
841C4×D4—24no—
842C4×D4—44no—
843C4×D4—44no—
844C4×D4—42no—
845C4×D4—44no—
846C4×D4—44no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—48no—
850C4×D4—42no—
851C4×D4—48no—
852C4×D4—48no—
853C4×D4—48no—
854#117—28no—
855#117—42no—
856#117—44no—
857#117—44no—
858#117—44no—
859C2×C4⋊C4—48no—
860C2×C4⋊C4—44no—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2411yescharacteristic
947C2×C22⋊C4C2411yescharacteristic
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2412yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2411yescharacteristic
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2411yescharacteristic
988C2×C42C2412yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2411yescharacteristic
992#95C2412yes—
993#95C2411yescharacteristic
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2411yescharacteristic
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2411yescharacteristic
1010#95C2412yes—
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053C24C2512yes—
1054C24C2511yescharacteristic
1055C24C2511yescharacteristic
1056C24C2512yes—
1057C24C2512yes—
1058#41—432no—
1059#41—416no—
1060#41—464no—
1061#41—432no—
1062#41—416no—
1063#41—88no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—24no—
1070C2×Q8—22no—
1071C2×Q8—28no—
1072C2×Q8—28no—
1073C2×Q8—24no—
1074C2×Q8—22no—
1075C2×Q8—28no—
1076C2×Q8—42no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—41no—
1080C2×Q8—42no—
1081C2×Q8—42no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—44no—
1087C2×Q8—416no—
1088C2×Q8—432no—
1089C2×Q8—432no—
1090C2×Q8—816no—
1091C2×Q8—88no—
1092C2×Q8H(5,𝔽2)18yes—
1093C2×D4—24no—
1094C2×D4—28no—
1095C2×D4—28no—
1096C2×D4—24no—
1097C2×D4—24no—
1098C2×D4—28no—
1099C2×D4—24no—
1100C2×D4—24no—
1101C2×D4—22no—
1102C2×D4—22no—
1103C2×D4—42no—
1104C2×D4—42no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C2×D4—41no—
1114C2×D4—44no—
1115C2×D4—42no—
1116C2×D4—42no—
1117C2×D4—41no—
1118C2×D4—41no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—44no—
1122C2×D4—41no—
1123C2×D4—41no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—44no—
1128C2×D4—42no—
1129C2×D4—42no—
1130C2×D4H(5,𝔽2)14yes—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—28no—
1134C22×C4—24no—
1135C22×C4—28no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—22no—
1139C22×C4—24no—
1140C22×C4—24no—
1141C22×C4—28no—
1142C22×C4—28no—
1143C22×C4—24no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—22no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—28no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—44no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—42no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2512yes—
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2514yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2512yes—
1183C22×C4C2512yes—
1184C22×C4C2514yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2512yes—
1187C22×C4C2511yescharacteristic
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—41no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—41no—
1219C4⋊C4—42no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—42no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C22⋊C4—28no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—42no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—42no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—42no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—22no—
1306C42—24no—
1307C42—28no—
1308C42—24no—
1309C42—42no—
1310C42—41no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—44no—
1318C422−1+414yescomplemented
1319C23—24no—
1320C23—22no—
1321C23—22no—
1322C23—24no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—21no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—21no—
1333C23—22no—
1334C23—22no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—21no—
1345C23—22no—
1346C23—22no—
1347C23C2×H(5,𝔽2)14yes—
1348C23C2611yescharacteristic
1349Q8—216no—
1350Q8—48no—
1351Q8—416no—
1352Q8—44no—
1353Q8—44no—
1354Q8—48no—
1355Q8—44no—
1356Q8—88no—
1357Q8—84no—
1358Q8—162no—
1359D4—28no—
1360D4—416no—
1361D4—48no—
1362D4—48no—
1363D4—48no—
1364D4—48no—
1365D4—48no—
1366D4—44no—
1367D4—82no—
1368D4—82no—
1369D4—88no—
1370D4—84no—
1371D4—84no—
1372D4—84no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—22no—
1425C2×C4—24no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—24no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—48no—
1435C2×C4—48no—
1436C2×C4—416no—
1437C2×C4—416no—
1438C2×C4—48no—
1439C2×C4—44no—
1440C2×C4—48no—
1441C2×C4—48no—
1442C2×C4—44no—
1443C2×C4—88no—
1444C2×C4—84no—
1445C2×C4—88no—
1446C2×C4—84no—
1447C2×C4C2×H(5,𝔽2)18yes—
1448C2×C4C2×H(5,𝔽2)14yes—
1449C2×C4C2×H(5,𝔽2)12yes—
1450C2×C4C2×2−1+412yes—
1451C2×C4C2×2−1+414yes—
1452C22—24no—
1453C22—24no—
1454C22—24no—
1455C22—44no—
1456C22—44no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—41no—
1466C22—41no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—41no—
1474C22—42no—
1475C22—41no—
1476C22—42no—
1477C22—41no—
1478C22—42no—
1479C22—41no—
1480C22—42no—
1481C22C22×H(5,𝔽2)12yes—
1482C22C22×H(5,𝔽2)11yescharacteristic
1483C22C22×2−1+411yescharacteristic
1484C222−1+611yescharacteristic
1485C222−1+612yes—
1486C4—24no—
1487C4—22no—
1488C4—28no—
1489C4—42no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4—41no—
1497C4—42no—
1498C4—42no—
1499C4—44no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—41no—
1504C4—42no—
1505C4—41no—
1506C4—42no—
1507C4—44no—
1508C4—42no—
1509C4#353214yes—
1510C2—44no—
1511C2—82no—
1512C2—82no—
1513C2—81no—
1514C2—81no—
1515C2C2×#353211yescharacteristic
1516C2#6291312yes—
1517C2#6291511yescharacteristic
1518C2#6304412yes—
1519C2#6306311yescharacteristic
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. #59817C2semidirect
2. #59475C2semidirect
3. #58802C2semidirect
4. #58146C2semidirect
5. #56774C2semidirect
6. #55526C2semidirect
7. #55284C2semidirect
8. #53045C2semidirect
9. #53005C2semidirect
10. #52414C2semidirect
11. #52326C2semidirect
12. #47750C2semidirect
13. #45385C2semidirect
14. #45332C2semidirect
15. #45322C2semidirect
16. #45308C2semidirect
17. #45243C2semidirect
18. #42917C2semidirect
19. #42852C2semidirect
20. #42807C2semidirect
21. #42792C2semidirect
22. #42706C2semidirect
23. #41999C2semidirect
24. #41122C2semidirect
25. #39663C2semidirect
26. #39491C2semidirect
27. #36696C2semidirect
28. #36085C2semidirect
29. #35687C2semidirect
1318. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#598172
#594752
#588022
#581462
#567742
#555262
#552842
#530452
#530052
#524142
#523262
#477502
#453852
#453322
#453222
#453082
#452432
#429172
#428522
#428072
#427922
#427062
#419992
#411222
#396632
#394912
#366962
#360852
#356872