Finite Group Databasebeta

← #9062267

Subgroups — #9062267

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60048C211yesmaximal, characteristic
2#60047C212yesmaximal, complemented
3#60046C211yesmaximal, characteristic, complemented
4#58959C212yesmaximal, complemented
5#55578C214yesmaximal, complemented
6#53900C212yesmaximal, complemented
7#51317C212yesmaximal, complemented
8#49610C214yesmaximal, complemented
9#47808C214yesmaximal, complemented
10#47661C214yesmaximal, complemented
11#47174C212yesmaximal, complemented
12#46361C212yesmaximal, complemented
13#45364C212yesmaximal, complemented
14#44860C212yesmaximal, complemented
15#44372C214yesmaximal, complemented
16#44364C214yesmaximal, complemented
17#44277C214yesmaximal, complemented
18#44268C214yesmaximal, complemented
19#44068C214yesmaximal, complemented
20#36030C212yesmaximal, complemented
21#35778C214yesmaximal, complemented
22#35667C211yesmaximal, characteristic, complemented
23#35574C212yesmaximal, complemented
24C2×#559C2212yes—
25C2×#556C2212yes—
26C2×#539C2212yes—
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2212yes—
31C2×#519C2211yescharacteristic
32#2832C2212yes—
33#2829C2214yes—
34#2820C2214yes—
35#2816C2212yes—
36#2811C2211yescharacteristic
37#2811C2212yes—
38#2809C2212yes—
39#2807C2214yes—
40#2806C2214yes—
41#2806C2214yes—
42#2805C2212yes—
43#2803C2214yes—
44#2801C2214yes—
45#2800C2214yes—
46#2792C2214yes—
47#2790C2214yes—
48#2788C2214yes—
49#2777C2214yes—
50#2775C2214yes—
51#2772C2214yes—
52#2765C2214yes—
53#2759C2214yes—
54#2759C2214yes—
55#2745C2214yes—
56#2737C2214yes—
57#2734C2212yes—
58#2733C2212yes—
59#2733C2211yescharacteristic
60#2732C2214yes—
61#2731C2214yes—
62#2728C2212yes—
63#2727C2212yes—
64#2727C2212yes—
65#2725C2214yes—
66#2724C2211yescharacteristic
67#2724C2212yes—
68#2723C2214yes—
69#2721C2214yes—
70#2720C2214yes—
71#2715C2214yes—
72#2712C2214yes—
73#2710C2214yes—
74#2710C2214yes—
75#2710C2214yes—
76#2709C2212yes—
77#2706C2214yes—
78#2702C2214yes—
79#2700C2214yes—
80#2700C2214yes—
81#2694C2214yes—
82#2692C2214yes—
83#2691C2214yes—
84#2683C2211yescharacteristic
85#2681C2214yes—
86#2674C2214yes—
87#2674C2214yes—
88#2674C2214yes—
89#2672C2214yes—
90#2632C2212yes—
91#2632C2212yes—
92#2630C2214yes—
93#2630C2214yes—
94#2628C2212yes—
95#2620C2214yes—
96#2612C2214yes—
97#2611C2214yes—
98#2611C2214yes—
99#2610C2212yes—
100#2610C2212yes—
101#2610C2214yes—
102#2606C2214yes—
103#2605C2214yes—
104#2599C2212yes—
105#2599C2212yes—
106#2594C2214yes—
107#2593C2214yes—
108#2589C2214yes—
109#2587C2214yes—
110#2586C2212yes—
111#2586C2212yes—
112#2584C2214yes—
113#2583C2212yes—
114#2582C2214yes—
115#2579C2214yes—
116#2579C2214yes—
117#2579C2214yes—
118#2577C2214yes—
119#2573C2214yes—
120#2567C2212yes—
121#2556C2214yes—
122#2556C2214yes—
123#2555C2214yes—
124#2555C2212yes—
125#2554C2214yes—
126#2553C2214yes—
127#2550C2214yes—
128#2550C2214yes—
129#2546C2212yes—
130#2546C2212yes—
131#2545C2212yes—
132#2545C2214yes—
133#2545C2212yes—
134#2536C2212yes—
135#2531C2214yes—
136#2529C2214yes—
137#2528C2214yes—
138#2525C2214yes—
139#2522C2214yes—
140#2479C2214yes—
141#2479C2214yes—
142#2479C2214yes—
143#2477C2214yes—
144#2474C2214yes—
145#2474C2214yes—
146#2474C2214yes—
147#2470C2214yes—
148#2470C2214yes—
149#2470C2214yes—
150#2469C2214yes—
151#2469C2214yes—
152#2466C2214yes—
153#2465C2214yes—
154#2465C2214yes—
155#2461C2214yes—
156#2461C2214yes—
157#2459C2214yes—
158#2459C2214yes—
159#2455C2214yes—
160#2455C2214yes—
161#2452C2214yes—
162#2452C2214yes—
163#2451C2214yes—
164#2451C2214yes—
165#2451C2214yes—
166#2449C2214yes—
167#2447C2214yes—
168#2445C2214yes—
169#2440C2214yes—
170#2440C2214yes—
171#2439C2214yes—
172#2439C2214yes—
173#2432C2214yes—
174#2431C2212yes—
175#2431C2214yes—
176#2429C2214yes—
177#2429C2214yes—
178#2423C2214yes—
179#2413C2214yes—
180#2413C2214yes—
181#2413C2214yes—
182#2409C2214yes—
183#2409C2214yes—
184#2406C2212yes—
185#2399C2212yes—
186#2399C2212yes—
187#2396C2214yes—
188#2392C2214yes—
189#2392C2212yes—
190#2376C2212yes—
191#2374C2212yes—
192#2373C2214yes—
193#2373C2214yes—
194#2372C2212yes—
195#2372C2214yes—
196#2369C2214yes—
197#2367C2214yes—
198#2365C2214yes—
199#2362C2214yes—
200#2361C2214yes—
201#2360C2214yes—
202#2360C2214yes—
203#2356C2212yes—
204#2354C2214yes—
205#2337C2214yes—
206#2332C2212yes—
207#2332C2214yes—
208#2331C2214yes—
209#2330C2214yes—
210#2326C2214yes—
211#2317C2212yes—
212#2316C2212yes—
213#2311C2212yes—
214#2310C2211yescharacteristic
215#2297C2211yescharacteristic
216#2297C2212yes—
217#2296C2211yescharacteristic
218#2296C2212yes—
219C22×#41C2312yes—
220C22×#41C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×Q8C2311yescharacteristic
223#559—48no—
224#556—48no—
225#539—48no—
226#536—44no—
227#536—44no—
228C2×C4⋊Q8—44no—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2312yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2314yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2314yes—
251C2×#123C2312yes—
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270#520—48no—
271#519—44no—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C42C2311yescharacteristic
301#401C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2312yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2312yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2312yes—
362#395C2314yes—
363#395C2312yes—
364#395C2312yes—
365#395C2312yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2312yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2312yes—
400#393C2312yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#392C2314yes—
405#392C2312yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2311yescharacteristic
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2311yescharacteristic
431#391C2312yes—
432#390C2314yes—
433#390C2314yes—
434#390C2312yes—
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
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#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#386C2312yes—
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#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#384C2314yes—
578#384C2314yes—
579#383C2312yes—
580#383C2314yes—
581#383C2312yes—
582#382C2314yes—
583#382C2314yes—
584#382C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2314yes—
619#376C2314yes—
620#376C2312yes—
621#376C2312yes—
622C2×#41—28no—
623C2×#41—44no—
624C2×#41—42no—
625C2×#41—44no—
626C2×#41—42no—
627C2×#41—42no—
628C22×Q8—24no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8—42no—
633C22×Q8—42no—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2414yes—
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×Q8C2412yes—
641C22×Q8C2412yes—
642C22×Q8C2412yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2411yescharacteristic
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2412yes—
651C23×C4C2412yes—
652C23×C4C2411yescharacteristic
653C23×C4C2414yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2412yes—
661C23×C4C2411yescharacteristic
662C4⋊Q8—216no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665C4⋊Q8—44no—
666C4⋊Q8—48no—
667C4⋊Q8—44no—
668C4⋊Q8—44no—
669#127—44no—
670#126—216no—
671#126—48no—
672#126—48no—
673#125—48no—
674#125—48no—
675#124—216no—
676#124—48no—
677#124—44no—
678#124—44no—
679#124—44no—
680#124—48no—
681#124—48no—
682#124—44no—
683#124—44no—
684#123—28no—
685#123—48no—
686#123—48no—
687#123—48no—
688#123—44no—
689#123—48no—
690#123—44no—
691#123—44no—
692C22⋊Q8—28no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—44no—
701#121—48no—
702#121—44no—
703C4×Q8—28no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—44no—
707C4×Q8—48no—
708C4×Q8—44no—
709C4×Q8—48no—
710C4×Q8—44no—
711C4×D4—216no—
712C4×D4—48no—
713C4×D4—44no—
714C4×D4—48no—
715C4×D4—48no—
716C4×D4—48no—
717#117—24no—
718#117—44no—
719#117—42no—
720#117—44no—
721#117—44no—
722#117—48no—
723#117—48no—
724#117—44no—
725#117—42no—
726#117—44no—
727C2×C4⋊C4—28no—
728C2×C4⋊C4—48no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C42—42no—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849#95C2412yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2412yes—
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#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899C24C2514yes—
900C24C2512yes—
901C24C2511yescharacteristic
902#41—432no—
903#41—88no—
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—24no—
907C2×Q8—24no—
908C2×Q8—28no—
909C2×Q8—24no—
910C2×Q8—24no—
911C2×Q8—22no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×Q8—44no—
921C2×Q8—42no—
922C2×Q8—44no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—41no—
926C2×Q8—41no—
927C2×Q8—42no—
928C2×Q8—416no—
929C2×Q8—88no—
930C2×Q82−1+418yes—
931C2×D4—28no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—24no—
935C2×D4—28no—
936C2×D4—22no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—44no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—42no—
954C22×C4—24no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—24no—
962C22×C4—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—24no—
966C22×C4—44no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4H(5,𝔽2)14yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4H(5,𝔽2)14yes—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—44no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C42—24no—
1101C42—28no—
1102C42—24no—
1103C42—28no—
1104C42—24no—
1105C42—24no—
1106C42—28no—
1107C42—28no—
1108C42—28no—
1109C42—41no—
1110C42—42no—
1111C42—41no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—42no—
1116C42—42no—
1117C42—44no—
1118C42—42no—
1119C42—44no—
1120C42—42no—
1121C42—42no—
1122C42—44no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—21no—
1127C23—24no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—22no—
1138C23—24no—
1139C23C2×H(5,𝔽2)12yes—
1140C23C2611yescharacteristic
1141Q8—48no—
1142Q8—48no—
1143Q8—48no—
1144Q8—88no—
1145Q8—84no—
1146Q8—84no—
1147Q8—82no—
1148Q8—84no—
1149Q8—84no—
1150D4—416no—
1151D4—48no—
1152D4—88no—
1153D4—82no—
1154D4—84no—
1155D4—88no—
1156D4—84no—
1157D4—162no—
1158C2×C4—28no—
1159C2×C4—216no—
1160C2×C4—21no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—44no—
1210C2×C4—416no—
1211C2×C4—44no—
1212C2×C4—88no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—162no—
1217C2×C4—164no—
1218C2×C4C2×H(5,𝔽2)14yes—
1219C2×C4C2×H(5,𝔽2)14yes—
1220C2×C4C2×H(5,𝔽2)12yes—
1221C2×C4C2×2−1+418yes—
1222C2×C4C2×2−1+414yes—
1223C2×C4#58514yes—
1224C2×C4#58512yes—
1225C22—22no—
1226C22—24no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—42no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—42no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C22×H(5,𝔽2)11yescharacteristic
1244C22C22×2−1+412yes—
1245C22C2×#58512yes—
1246C22C2×#58511yescharacteristic
1247C4—24no—
1248C4—22no—
1249C4—22no—
1250C4—24no—
1251C4—24no—
1252C4—24no—
1253C4—28no—
1254C4—42no—
1255C4—44no—
1256C4—44no—
1257C4—42no—
1258C4—44no—
1259C4—44no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—44no—
1266C4—44no—
1267C2—42no—
1268C2—82no—
1269C2—84no—
1270C2#6281811yescharacteristic
1271C2#6281912yes—
1272C2#6302211yescharacteristic
1273C2#6303412yes—
1274C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#60048C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60047C2semidirect
3. #60046C2semidirect
4. #58959C2semidirect
5. #55578C2semidirect
6. #53900C2semidirect
7. #51317C2semidirect
8. #49610C2semidirect
9. #47808C2semidirect
10. #47661C2semidirect
11. #47174C2semidirect
12. #46361C2semidirect
13. #45364C2semidirect
14. #44860C2semidirect
15. #44372C2semidirect
16. #44364C2semidirect
17. #44277C2semidirect
18. #44268C2semidirect
19. #44068C2semidirect
20. #36030C2semidirect
21. #35778C2semidirect
22. #35667C2semidirect
23. #35574C2semidirect

Maximal subgroups

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

subgroupindex
#600482
#600472
#600462
#589592
#555782
#539002
#513172
#496102
#478082
#476612
#471742
#463612
#453642
#448602
#443722
#443642
#442772
#442682
#440682
#360302
#357782
#356672
#355742