Finite Group Databasebeta

← #8757355

Subgroups — #8757355

Order 512.

4500 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58928C214yesmaximal, complemented
2#58909C214yesmaximal, complemented
3#56177C214yesmaximal, complemented
4#55779C214yesmaximal, complemented
5#54449C214yesmaximal, complemented
6#54204C214yesmaximal, complemented
7#51749C211yesmaximal, characteristic
8#51542C211yesmaximal, characteristic, complemented
9#51530C212yesmaximal, complemented
10#50887C212yesmaximal, complemented
11#50329C212yesmaximal, complemented
12#49032C212yesmaximal, complemented
13#48812C212yesmaximal, complemented
14#47567C212yesmaximal, complemented
15#47430C214yesmaximal, complemented
16#47361C214yesmaximal, complemented
17#47032C212yesmaximal, complemented
18#46325C212yesmaximal, complemented
19#46279C212yesmaximal, complemented
20#46138C214yesmaximal, complemented
21#45971C214yesmaximal, complemented
22#35316C211yesmaximal, characteristic, complemented
23#35143C212yesmaximal, complemented
24C2×#563C2211yescharacteristic
25C2×#563C2212yes—
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#551C2212yes—
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic, complemented
31C22×#126C2212yescomplemented
32C2×C4×#41C2211yescharacteristic
33#2857C2214yescomplemented
34#2852C2214yes—
35#2852C2214yescomplemented
36#2843C2212yescomplemented
37#2841C2212yescomplemented
38#2839C2214yescomplemented
39#2838C2214yescomplemented
40#2837C2214yes—
41#2836C2214yescomplemented
42#2836C2214yescomplemented
43#2836C2214yescomplemented
44#2823C2212yes—
45#2821C2214yescomplemented
46#2816C2212yes—
47#2806C2214yescomplemented
48#2790C2214yescomplemented
49#2789C2212yescomplemented
50#2788C2214yescomplemented
51#2787C2214yescomplemented
52#2786C2214yescomplemented
53#2783C2214yescomplemented
54#2782C2212yes—
55#2781C2214yes—
56#2780C2214yescomplemented
57#2778C2214yes—
58#2774C2214yescomplemented
59#2773C2214yescomplemented
60#2770C2214yescomplemented
61#2768C2214yescomplemented
62#2768C2214yescomplemented
63#2767C2214yescomplemented
64#2765C2214yescomplemented
65#2765C2214yescomplemented
66#2764C2212yescomplemented
67#2761C2214yescomplemented
68#2761C2214yescomplemented
69#2757C2214yes—
70#2755C2214yescomplemented
71#2755C2214yescomplemented
72#2754C2214yescomplemented
73#2752C2212yes—
74#2750C2214yescomplemented
75#2748C2214yes—
76#2747C2214yescomplemented
77#2741C2214yes—
78#2735C2214yescomplemented
79#2734C2212yescomplemented
80#2734C2212yescomplemented
81#2731C2212yes—
82#2731C2212yes—
83#2729C2214yescomplemented
84#2729C2214yescomplemented
85#2727C2214yes—
86#2725C2214yescomplemented
87#2723C2214yes—
88#2722C2214yescomplemented
89#2722C2214yescomplemented
90#2721C2214yescomplemented
91#2718C2214yes—
92#2717C2214yes—
93#2717C2212yes—
94#2717C2212yes—
95#2716C2214yescomplemented
96#2716C2214yescomplemented
97#2715C2214yes—
98#2715C2214yes—
99#2713C2214yescomplemented
100#2704C2214yescomplemented
101#2702C2214yes—
102#2700C2214yes—
103#2700C2214yes—
104#2698C2214yescomplemented
105#2698C2214yescomplemented
106#2698C2214yescomplemented
107#2697C2214yes—
108#2695C2214yes—
109#2695C2214yes—
110#2695C2214yescomplemented
111#2693C2214yes—
112#2689C2214yescomplemented
113#2689C2214yescomplemented
114#2687C2214yes—
115#2684C2212yes—
116#2684C2212yes—
117#2680C2214yescomplemented
118#2678C2214yes—
119#2677C2214yescomplemented
120#2674C2214yes—
121#2660C2212yescomplemented
122#2652C2214yescomplemented
123#2652C2214yescomplemented
124#2640C2212yes—
125#2638C2214yes—
126#2637C2214yescomplemented
127#2636C2214yes—
128#2628C2214yescomplemented
129#2622C2214yes—
130#2621C2214yescomplemented
131#2612C2214yescomplemented
132#2612C2214yescomplemented
133#2611C2212yescomplemented
134#2610C2212yes—
135#2609C2214yescomplemented
136#2608C2212yescomplemented
137#2606C2214yescomplemented
138#2604C2214yescomplemented
139#2603C2214yes—
140#2601C2214yes—
141#2601C2214yescomplemented
142#2600C2212yes—
143#2595C2214yes—
144#2589C2214yescomplemented
145#2586C2214yescomplemented
146#2579C2212yes—
147#2579C2212yescomplemented
148#2577C2214yescomplemented
149#2557C2214yes—
150#2553C2214yes—
151#2553C2214yescomplemented
152#2547C2212yes—
153#2547C2212yes—
154#2546C2212yescomplemented
155#2546C2212yescomplemented
156#2534C2212yes—
157#2534C2212yescomplemented
158#2532C2214yescomplemented
159#2532C2214yescomplemented
160#2531C2214yes—
161#2530C2214yescomplemented
162#2530C2214yescomplemented
163#2530C2214yescomplemented
164#2529C2214yescomplemented
165#2529C2214yescomplemented
166#2528C2214yescomplemented
167#2521C2214yes—
168#2520C2214yescomplemented
169#2507C2214yescomplemented
170#2486C2214yescomplemented
171#2486C2214yescomplemented
172#2484C2212yescomplemented
173#2482C2212yescomplemented
174#2481C2214yes—
175#2481C2214yescomplemented
176#2480C2214yescomplemented
177#2480C2214yescomplemented
178#2475C2214yescomplemented
179#2474C2214yes—
180#2474C2214yes—
181#2473C2214yescomplemented
182#2473C2214yescomplemented
183#2472C2214yes—
184#2455C2214yes—
185#2449C2214yes—
186#2449C2214yescomplemented
187#2447C2214yes—
188#2443C2214yes—
189#2442C2214yescomplemented
190#2440C2214yescomplemented
191#2439C2214yescomplemented
192#2437C2214yescomplemented
193#2437C2214yescomplemented
194#2436C2212yes—
195#2434C2212yescomplemented
196#2418C2214yes—
197#2418C2214yescomplemented
198#2417C2214yes—
199#2412C2214yes—
200#2409C2214yescomplemented
201#2406C2212yes—
202#2404C2212yes—
203#2383C2214yescomplemented
204#2381C2212yescomplemented
205#2379C2212yes—
206#2372C2211yescharacteristic
207#2372C2211yescharacteristic
208#2333C2212yes—
209#2332C2212yescomplemented
210#2322C2212yes—
211#2322C2212yescomplemented
212#2321C2212yes—
213#2321C2212yescomplemented
214#2319C2214yescomplemented
215#2310C2211yescharacteristic, complemented
216#2310C2211yescharacteristic, complemented
217#2285C2211yescharacteristic, complemented
218#2283C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#563—44no—
223#563—48no—
224H(3,𝔽4)—44no—
225#551—48no—
226#536—44no—
227#536—44no—
228C2×C4⋊Q8—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×#126—48no—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2312yes—
247C2×#125C2314yes—
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#120C2312yes—
270C2×#120C2312yes—
271C2×#120C2314yes—
272C4×#41—44no—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294#401C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2312yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2312yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#392C2312yes—
417#392C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#386C2312yes—
527#386C2314yes—
528#386C2312yes—
529#386C2314yes—
530#386C2312yes—
531#386C2312yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#385C2312yes—
545#385C2312yes—
546#385C2314yes—
547#385C2312yes—
548#385C2314yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#384C2312yes—
571#384C2314yes—
572#383C2314yes—
573#383C2314yes—
574#382C2314yes—
575#382C2314yes—
576#382C2314yes—
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2314yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#379C2312yes—
604#379C2312yes—
605#379C2314yes—
606#379C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620#376C2314yes—
621#376C2312yes—
622#376C2312yes—
623C25C2412yes—
624C2×#41—24no—
625C2×#41—42no—
626C2×#41—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8—42no—
633C22×Q8C2411yescharacteristic
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2411yescharacteristic
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2411yescharacteristic
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C4⋊Q8—28no—
660C4⋊Q8—44no—
661C4⋊Q8—44no—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—42no—
665C4⋊Q8—42no—
666C4⋊Q8—44no—
667C4⋊Q8—44no—
668#126—216no—
669#126—48no—
670#126—48no—
671#126—48no—
672#126—48no—
673#126—48no—
674#126—48no—
675#125—44no—
676#125—48no—
677#124—28no—
678#124—24no—
679#124—24no—
680#124—44no—
681#124—48no—
682#124—44no—
683#124—44no—
684#123—28no—
685#123—48no—
686#123—44no—
687#123—48no—
688#123—48no—
689#123—48no—
690C22⋊Q8—44no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697#121—44no—
698#120—28no—
699#120—48no—
700#120—44no—
701C4×Q8—44no—
702C4×D4—44no—
703C4×D4—44no—
704C4×D4—44no—
705C4×D4—48no—
706C4×D4—48no—
707#117—42no—
708#117—44no—
709#117—42no—
710#117—42no—
711#117—48no—
712C2×C4⋊C4—44no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—48no—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C22⋊C4—44no—
766C2×C22⋊C4—44no—
767C2×C22⋊C4—44no—
768C2×C22⋊C4—48no—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C42—28no—
814C2×C42—24no—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2411yescharacteristic
834#95C2412yes—
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890C24—24no—
891C24—42no—
892C24—44no—
893C24—44no—
894C24—42no—
895C24C2514yes—
896C24C2512yes—
897C24C2511yescharacteristic
898#41—416no—
899C2×Q8—22no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—22no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—41no—
906C2×Q8—41no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—41no—
910C2×Q8—41no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—44no—
922C2×Q8—88no—
923C2×Q8—88no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—41no—
929C2×D4—42no—
930C2×D4—41no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4H(5,𝔽2)14yes—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—44no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—44no—
1077C22⋊C4—42no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—42no—
1085C42—24no—
1086C42—22no—
1087C42—24no—
1088C42—24no—
1089C42—24no—
1090C42—24no—
1091C42—22no—
1092C42—22no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42H(5,𝔽2)14yes—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—88no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—164no—
1123C23C2×H(5,𝔽2)14yes—
1124C23#58512yes—
1125C23C2611yescharacteristic
1126Q8—44no—
1127Q8—84no—
1128Q8—84no—
1129Q8—84no—
1130Q8—82no—
1131Q8—82no—
1132Q8—162no—
1133Q8—162no—
1134D4—44no—
1135D4—48no—
1136D4—88no—
1137D4—88no—
1138D4—162no—
1139D4—162no—
1140C2×C4—28no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—84no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—88no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—164no—
1203C2×C4C2×H(5,𝔽2)12yes—
1204C2×C4C2×H(5,𝔽2)14yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C22—28no—
1207C22—24no—
1208C22—22no—
1209C22—24no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—168no—
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C22×H(5,𝔽2)11yescharacteristic
1225C22C2×#58511yescharacteristic
1226C222−1+614yes—
1227C4—22no—
1228C4—22no—
1229C4—24no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—44no—
1236C4—44no—
1237C4—42no—
1238C4—44no—
1239C4—44no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—44no—
1246C4—44no—
1247C2—42no—
1248C2—44no—
1249C2—84no—
1250C2#6281811yescharacteristic
1251C2#6288612yes—
1252C2#6306312yes—
1253C2#6306412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#51749C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58928C2semidirect
2. #58909C2semidirect
3. #56177C2semidirect
4. #55779C2semidirect
5. #54449C2semidirect
6. #54204C2semidirect
8. #51542C2semidirect
9. #51530C2semidirect
10. #50887C2semidirect
11. #50329C2semidirect
12. #49032C2semidirect
13. #48812C2semidirect
14. #47567C2semidirect
15. #47430C2semidirect
16. #47361C2semidirect
17. #47032C2semidirect
18. #46325C2semidirect
19. #46279C2semidirect
20. #46138C2semidirect
21. #45971C2semidirect
22. #35316C2semidirect
23. #35143C2semidirect
30. C22×C4⋊Q8C22semidirect
31. C22×#126C22semidirect
33. #2857C22semidirect
35. #2852C22semidirect
36. #2843C22semidirect
37. #2841C22semidirect
38. #2839C22semidirect
39. #2838C22semidirect
41. #2836C22semidirect
42. #2836C22semidirect
43. #2836C22semidirect
45. #2821C22semidirect
47. #2806C22semidirect
48. #2790C22semidirect
49. #2789C22semidirect
50. #2788C22semidirect
51. #2787C22semidirect
52. #2786C22semidirect
53. #2783C22semidirect
56. #2780C22semidirect
58. #2774C22semidirect
59. #2773C22semidirect
60. #2770C22semidirect
61. #2768C22semidirect
62. #2768C22semidirect
63. #2767C22semidirect
64. #2765C22semidirect
65. #2765C22semidirect
66. #2764C22semidirect
67. #2761C22semidirect
68. #2761C22semidirect
70. #2755C22semidirect
71. #2755C22semidirect
72. #2754C22semidirect
74. #2750C22semidirect
76. #2747C22semidirect
78. #2735C22semidirect
79. #2734C22semidirect
80. #2734C22semidirect
83. #2729C22semidirect
84. #2729C22semidirect
86. #2725C22semidirect
88. #2722C22semidirect
89. #2722C22semidirect
90. #2721C22semidirect
95. #2716C22semidirect
96. #2716C22semidirect
99. #2713C22semidirect
100. #2704C22semidirect
104. #2698C22semidirect
105. #2698C22semidirect
106. #2698C22semidirect
110. #2695C22semidirect
112. #2689C22semidirect
113. #2689C22semidirect
117. #2680C22semidirect
119. #2677C22semidirect
121. #2660C22semidirect
122. #2652C22semidirect
123. #2652C22semidirect
126. #2637C22semidirect
128. #2628C22semidirect
130. #2621C22semidirect
131. #2612C22semidirect
132. #2612C22semidirect
133. #2611C22semidirect
135. #2609C22semidirect
136. #2608C22semidirect
137. #2606C22semidirect
138. #2604C22semidirect
141. #2601C22semidirect
144. #2589C22semidirect
145. #2586C22semidirect
147. #2579C22semidirect
148. #2577C22semidirect
151. #2553C22semidirect
154. #2546C22semidirect
155. #2546C22semidirect
157. #2534C22semidirect
158. #2532C22semidirect
159. #2532C22semidirect
161. #2530C22semidirect
162. #2530C22semidirect
163. #2530C22semidirect
164. #2529C22semidirect
165. #2529C22semidirect
166. #2528C22semidirect
168. #2520C22semidirect
169. #2507C22semidirect
170. #2486C22semidirect
171. #2486C22semidirect
172. #2484C22semidirect
173. #2482C22semidirect
175. #2481C22semidirect
176. #2480C22semidirect
177. #2480C22semidirect
178. #2475C22semidirect
181. #2473C22semidirect
182. #2473C22semidirect
186. #2449C22semidirect
189. #2442C22semidirect
190. #2440C22semidirect
191. #2439C22semidirect
192. #2437C22semidirect
193. #2437C22semidirect
195. #2434C22semidirect
197. #2418C22semidirect
200. #2409C22semidirect
203. #2383C22semidirect
204. #2381C22semidirect
209. #2332C22semidirect
211. #2322C22semidirect
213. #2321C22semidirect
214. #2319C22semidirect
215. #2310C22semidirect
216. #2310C22semidirect
217. #2285C22semidirect
218. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#589282
#589092
#561772
#557792
#544492
#542042
#517492
#515422
#515302
#508872
#503292
#490322
#488122
#475672
#474302
#473612
#470322
#463252
#462792
#461382
#459712
#353162
#351432