Finite Group Databasebeta

← #8115569

Subgroups — #8115569

Order 512.

3944 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58792C214yesmaximal, complemented
2#58730C214yesmaximal, complemented
3#58617C214yesmaximal, complemented
4#58360C214yesmaximal, complemented
5#58186C214yesmaximal, complemented
6#56970C214yesmaximal, complemented
7#55746C214yesmaximal, complemented
8#53916C214yesmaximal, complemented
9#53113C212yesmaximal, complemented
10#52994C212yesmaximal, complemented
11#45025C212yesmaximal, complemented
12#44961C212yesmaximal
13#42983C211yesmaximal, characteristic
14#42973C211yesmaximal, characteristic, complemented
15#42845C212yesmaximal, complemented
16#42697C211yesmaximal, characteristic, complemented
17#42614C212yesmaximal, complemented
18#42490C211yesmaximal, characteristic
19#38237C212yesmaximal, complemented
20#38231C212yesmaximal, complemented
21#38072C212yesmaximal, complemented
22#38054C212yesmaximal
23#37367C212yesmaximal, complemented
24#37352C212yesmaximal, complemented
25#35324C211yesmaximal, characteristic, complemented
26#35266C211yesmaximal, characteristic
27#34644C211yesmaximal, characteristic, complemented
28#2864C2211yescharacteristic, complemented
29#2862C2211yescharacteristic, complemented
30#2860C2212yes—
31#2860C2212yes—
32#2855C2212yes—
33#2844C2212yescomplemented
34#2842C2212yes—
35#2841C2214yescomplemented
36#2838C2214yescomplemented
37#2838C2214yescomplemented
38#2836C2214yescomplemented
39#2836C2214yescomplemented
40#2836C2214yescomplemented
41#2835C2212yes—
42#2831C2214yescomplemented
43#2831C2214yescomplemented
44#2831C2214yescomplemented
45#2830C2212yes—
46#2817C2214yescomplemented
47#2802C2214yescomplemented
48#2798C2214yescomplemented
49#2794C2212yescomplemented
50#2793C2214yescomplemented
51#2793C2214yescomplemented
52#2793C2214yescomplemented
53#2793C2214yescomplemented
54#2792C2212yescomplemented
55#2791C2214yescomplemented
56#2790C2214yescomplemented
57#2788C2214yes—
58#2788C2214yescomplemented
59#2787C2214yescomplemented
60#2784C2212yes—
61#2783C2214yescomplemented
62#2783C2214yescomplemented
63#2783C2214yescomplemented
64#2780C2214yes—
65#2775C2214yescomplemented
66#2772C2214yescomplemented
67#2772C2214yescomplemented
68#2772C2214yescomplemented
69#2771C2214yes—
70#2771C2214yescomplemented
71#2767C2214yescomplemented
72#2765C2214yes—
73#2765C2214yescomplemented
74#2763C2212yes—
75#2763C2214yescomplemented
76#2761C2214yes—
77#2761C2214yes—
78#2759C2214yescomplemented
79#2757C2214yes—
80#2747C2214yescomplemented
81#2745C2214yescomplemented
82#2745C2214yescomplemented
83#2739C2214yes—
84#2739C2214yescomplemented
85#2738C2214yes—
86#2738C2214yescomplemented
87#2737C2214yes—
88#2736C2212yes—
89#2735C2214yes—
90#2735C2214yes—
91#2735C2214yes—
92#2735C2212yes—
93#2729C2214yescomplemented
94#2725C2214yescomplemented
95#2725C2214yescomplemented
96#2723C2214yes—
97#2723C2214yes—
98#2721C2214yescomplemented
99#2720C2214yes—
100#2720C2214yescomplemented
101#2716C2214yescomplemented
102#2716C2214yescomplemented
103#2704C2214yes—
104#2698C2214yescomplemented
105#2698C2214yescomplemented
106#2698C2214yescomplemented
107#2690C2214yescomplemented
108#2690C2214yescomplemented
109#2690C2214yescomplemented
110#2689C2214yescomplemented
111#2689C2214yescomplemented
112#2689C2214yescomplemented
113#2683C2212yes—
114#2677C2212yes—
115#2667C2212yes—
116#2667C2212yes—
117#2666C2212yescomplemented
118#2666C2212yescomplemented
119#2666C2212yescomplemented
120#2666C2212yescomplemented
121#2665C2212yes—
122#2665C2212yes—
123#2660C2214yescomplemented
124#2654C2214yescomplemented
125#2652C2214yes—
126#2652C2214yescomplemented
127#2652C2214yescomplemented
128#2651C2214yes—
129#2647C2212yescomplemented
130#2645C2212yescomplemented
131#2645C2212yescomplemented
132#2644C2212yes—
133#2644C2212yes—
134#2644C2212yes—
135#2640C2212yes—
136#2637C2214yescomplemented
137#2628C2211yescharacteristic
138#2626C2214yes—
139#2621C2211yescharacteristic
140#2612C2212yescomplemented
141#2604C2214yescomplemented
142#2593C2212yes—
143#2592C2212yes—
144#2592C2212yes—
145#2588C2214yescomplemented
146#2586C2214yescomplemented
147#2584C2212yescomplemented
148#2584C2214yescomplemented
149#2582C2212yescomplemented
150#2581C2212yescomplemented
151#2575C2214yes—
152#2575C2214yescomplemented
153#2571C2212yescomplemented
154#2567C2212yescomplemented
155#2566C2212yes—
156#2561C2214yes—
157#2561C2214yes—
158#2556C2214yescomplemented
159#2551C2212yescomplemented
160#2545C2212yes—
161#2538C2212yes—
162#2538C2212yes—
163#2533C2214yescomplemented
164#2531C2214yes—
165#2530C2214yescomplemented
166#2529C2214yescomplemented
167#2528C2214yescomplemented
168#2528C2214yescomplemented
169#2527C2214yes—
170#2527C2214yescomplemented
171#2526C2214yes—
172#2525C2214yescomplemented
173#2524C2214yescomplemented
174#2522C2214yes—
175#2517C2212yes—
176#2513C2212yes—
177#2513C2212yes—
178#2513C2214yes—
179#2512C2212yes—
180#2512C2212yes—
181#2512C2214yes—
182#2511C2212yescomplemented
183#2511C2212yescomplemented
184#2509C2212yescomplemented
185#2508C2212yescomplemented
186#2508C2214yescomplemented
187#2507C2212yescomplemented
188#2507C2212yescomplemented
189#2506C2212yescomplemented
190#2506C2212yescomplemented
191#2499C2212yes—
192#2496C2214yescomplemented
193#2483C2214yes—
194#2480C2214yes—
195#2480C2214yes—
196#2480C2214yes—
197#2480C2214yes—
198#2469C2214yescomplemented
199#2454C2212yes—
200#2453C2212yescomplemented
201#2453C2212yescomplemented
202#2452C2212yes—
203#2452C2212yes—
204#2451C2212yescomplemented
205#2448C2212yes—
206#2448C2212yes—
207#2448C2212yes—
208#2447C2212yes—
209#2447C2212yes—
210#2446C2212yescomplemented
211#2441C2212yes—
212#2440C2212yes—
213#2437C2214yes—
214#2437C2212yes—
215#2435C2212yes—
216#2429C2214yescomplemented
217#2423C2214yes—
218#2402C2212yescomplemented
219#2399C2211yescharacteristic, complemented
220#2399C2211yescharacteristic, complemented
221#2396C2212yes—
222#2396C2211yescharacteristic
223#2396C2211yescharacteristic
224#2367C2212yes—
225#2365C2212yescomplemented
226#2362C2212yes—
227#2360C2212yes—
228#2357C2212yes—
229Q8×C4⋊C4C2212yescomplemented
230#2346C2212yes—
231D4×C22⋊C4C2212yes—
232#2331C2211yescharacteristic, complemented
233#2330C2212yescomplemented
234#2327C2211yescharacteristic, complemented
235#2326C2212yes—
236#2323C2212yes—
237#2320C2212yescomplemented
238#2319C2212yes—
239#2317C2211yescharacteristic
240#2316C2211yescharacteristic
241#2309C2211yescharacteristic
242#2309C2211yescharacteristic
243#2296C2211yescharacteristic
244#2295C2211yescharacteristic, complemented
245#2295C2211yescharacteristic, complemented
246#2295C2212yescomplemented
247#2295C2212yescomplemented
248C2×#390C2211yescharacteristic
249#2283C2212yes—
250C4×#117C2211yescharacteristic
251C23×D4C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4C2314yes—
286C22×C22⋊C4C2314yes—
287C22×C42C2311yescharacteristic
288#401C2314yes—
289#401C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2311yescharacteristic
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2311yescharacteristic
318#400C2312yes—
319#400C2312yes—
320#400C2312yes—
321#399C2312yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2311yescharacteristic
327#399C2314yes—
328#399C2311yescharacteristic
329#399C2312yes—
330#398C2312yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2312yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2312yes—
350#398C2312yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2312yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#396C2312yes—
411#396C2312yes—
412#395C2312yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2311yescharacteristic
418#395C2312yes—
419#395C2314yes—
420#395C2312yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#395C2314yes—
427#395C2311yescharacteristic
428#394C2314yes—
429#394C2314yes—
430#393C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2311yescharacteristic
437#393C2314yes—
438#393C2312yes—
439#393C2311yescharacteristic
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
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#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2314yes—
597#386C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2314yes—
616#384C2312yes—
617#384C2312yes—
618#384C2312yes—
619#384C2314yes—
620#383C2314yes—
621#383C2312yes—
622#383C2312yes—
623#382C2311yescharacteristic
624#382C2311yescharacteristic
625#382C2312yes—
626#382C2314yes—
627#382C2312yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#382C2312yes—
633#382C2312yes—
634#381C2312yes—
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#379C2314yes—
650#379C2314yes—
651#379C2314yes—
652#379C2314yes—
653#379C2312yes—
654#379C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682#376C2312yes—
683#376C2312yes—
684#376C2311yescharacteristic
685#376C2314yes—
686#376C2314yes—
687#376C2311yescharacteristic
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C25C2412yes—
691C22×Q8C2412yes—
692C22×Q8C2411yescharacteristic
693C22×Q8C2414yes—
694C22×Q8C2412yes—
695C22×Q8C2411yescharacteristic
696C22×Q8C2412yes—
697C22×D4—24no—
698C22×D4—42no—
699C22×D4—42no—
700C22×D4C2412yes—
701C22×D4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C4⋊Q8—42no—
708C4⋊Q8—44no—
709C4⋊Q8—42no—
710C4⋊Q8—84no—
711#126—84no—
712#126—84no—
713#126—84no—
714#126—84no—
715#125—44no—
716#125—84no—
717#125—84no—
718#124—44no—
719#124—44no—
720C22⋊Q8—28no—
721C22⋊Q8—84no—
722C22⋊Q8—84no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725C22⋊Q8—84no—
726C4×Q8—42no—
727C4×Q8—44no—
728C4×Q8—42no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×Q8—84no—
733C4×D4—44no—
734C4×D4—44no—
735#117—24no—
736#117—42no—
737#117—42no—
738#117—42no—
739C2×C4⋊C4—42no—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C22⋊C4—84no—
808C2×C22⋊C4—84no—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C42—24no—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2411yescharacteristic
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2411yescharacteristic
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952C24—24no—
953C24—42no—
954C24—44no—
955C24—44no—
956C24—42no—
957C24C2514yes—
958C24C2511yescharacteristic
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—42no—
963C2×Q8—41no—
964C2×Q8—41no—
965C2×Q8—44no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—42no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—88no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C42−1+414yes—
995C22×C4C2512yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2514yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—41no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C22⋊C4—24no—
1088C22⋊C4—28no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—42no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
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⋊C4—44no—
1123C22⋊C4—44no—
1124C42—24no—
1125C42—22no—
1126C42—22no—
1127C42—24no—
1128C42—22no—
1129C42—22no—
1130C42—22no—
1131C42—22no—
1132C42—24no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—44no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—44no—
1147C42—42no—
1148C42—42no—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—84no—
1161C23—88no—
1162C23—88no—
1163C23—162no—
1164C23—162no—
1165C23C2×2−1+412yes—
1166C23C2611yescharacteristic
1167Q8—48no—
1168Q8—84no—
1169Q8—82no—
1170Q8—88no—
1171Q8—82no—
1172Q8—162no—
1173D4—48no—
1174D4—84no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—28no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—84no—
1244C2×C4—164no—
1245C2×C4—164no—
1246C2×C4—162no—
1247C2×C4C2×2−1+412yes—
1248C2×C4C2×2−1+412yes—
1249C2×C4#58512yes—
1250C2×C4#58512yes—
1251C22—22no—
1252C22—24no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—168no—
1264C22C22×2−1+411yescharacteristic
1265C22C2×#58511yescharacteristic
1266C22C2×#58511yescharacteristic
1267C22H(7,𝔽2)12yes—
1268C222−1+612yes—
1269C4—22no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—44no—
1279C4—44no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—41no—
1287C4—42no—
1288C4—41no—
1289C4—42no—
1290C4—41no—
1291C4—42no—
1292C4—41no—
1293C4#356414yes—
1294C2—42no—
1295C2—84no—
1296C2C2×#356411yescharacteristic
1297C2#6287912yes—
1298C2#6288412yes—
1299C2#6288511yescharacteristic
1300C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58792C2semidirect
2. #58730C2semidirect
3. #58617C2semidirect
4. #58360C2semidirect
5. #58186C2semidirect
6. #56970C2semidirect
7. #55746C2semidirect
8. #53916C2semidirect
9. #53113C2semidirect
10. #52994C2semidirect
11. #45025C2semidirect
14. #42973C2semidirect
15. #42845C2semidirect
16. #42697C2semidirect
17. #42614C2semidirect
19. #38237C2semidirect
20. #38231C2semidirect
21. #38072C2semidirect
23. #37367C2semidirect
24. #37352C2semidirect
25. #35324C2semidirect
27. #34644C2semidirect
28. #2864C22semidirect
29. #2862C22semidirect
33. #2844C22semidirect
35. #2841C22semidirect
36. #2838C22semidirect
37. #2838C22semidirect
38. #2836C22semidirect
39. #2836C22semidirect
40. #2836C22semidirect
42. #2831C22semidirect
43. #2831C22semidirect
44. #2831C22semidirect
46. #2817C22semidirect
47. #2802C22semidirect
48. #2798C22semidirect
49. #2794C22semidirect
50. #2793C22semidirect
51. #2793C22semidirect
52. #2793C22semidirect
53. #2793C22semidirect
54. #2792C22semidirect
55. #2791C22semidirect
56. #2790C22semidirect
58. #2788C22semidirect
59. #2787C22semidirect
61. #2783C22semidirect
62. #2783C22semidirect
63. #2783C22semidirect
65. #2775C22semidirect
66. #2772C22semidirect
67. #2772C22semidirect
68. #2772C22semidirect
70. #2771C22semidirect
71. #2767C22semidirect
73. #2765C22semidirect
75. #2763C22semidirect
78. #2759C22semidirect
80. #2747C22semidirect
81. #2745C22semidirect
82. #2745C22semidirect
84. #2739C22semidirect
86. #2738C22semidirect
93. #2729C22semidirect
94. #2725C22semidirect
95. #2725C22semidirect
98. #2721C22semidirect
100. #2720C22semidirect
101. #2716C22semidirect
102. #2716C22semidirect
104. #2698C22semidirect
105. #2698C22semidirect
106. #2698C22semidirect
107. #2690C22semidirect
108. #2690C22semidirect
109. #2690C22semidirect
110. #2689C22semidirect
111. #2689C22semidirect
112. #2689C22semidirect
117. #2666C22semidirect
118. #2666C22semidirect
119. #2666C22semidirect
120. #2666C22semidirect
123. #2660C22semidirect
124. #2654C22semidirect
126. #2652C22semidirect
127. #2652C22semidirect
129. #2647C22semidirect
130. #2645C22semidirect
131. #2645C22semidirect
136. #2637C22semidirect
140. #2612C22semidirect
141. #2604C22semidirect
145. #2588C22semidirect
146. #2586C22semidirect
147. #2584C22semidirect
148. #2584C22semidirect
149. #2582C22semidirect
150. #2581C22semidirect
152. #2575C22semidirect
153. #2571C22semidirect
154. #2567C22semidirect
158. #2556C22semidirect
159. #2551C22semidirect
163. #2533C22semidirect
165. #2530C22semidirect
166. #2529C22semidirect
167. #2528C22semidirect
168. #2528C22semidirect
170. #2527C22semidirect
172. #2525C22semidirect
173. #2524C22semidirect
182. #2511C22semidirect
183. #2511C22semidirect
184. #2509C22semidirect
185. #2508C22semidirect
186. #2508C22semidirect
187. #2507C22semidirect
188. #2507C22semidirect
189. #2506C22semidirect
190. #2506C22semidirect
192. #2496C22semidirect
198. #2469C22semidirect
200. #2453C22semidirect
201. #2453C22semidirect
204. #2451C22semidirect
210. #2446C22semidirect
216. #2429C22semidirect
218. #2402C22semidirect
219. #2399C22semidirect
220. #2399C22semidirect
225. #2365C22semidirect
229. Q8×C4⋊C4C22semidirect
232. #2331C22semidirect
233. #2330C22semidirect
234. #2327C22semidirect
237. #2320C22semidirect
244. #2295C22semidirect
245. #2295C22semidirect
246. #2295C22semidirect
247. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#587922
#587302
#586172
#583602
#581862
#569702
#557462
#539162
#531132
#529942
#450252
#449612
#429832
#429732
#428452
#426972
#426142
#424902
#382372
#382312
#380722
#380542
#373672
#373522
#353242
#352662
#346442