Finite Group Databasebeta

← #8121424

Subgroups — #8121424

Order 512.

4014 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57566C214yesmaximal, complemented
2#56992C214yesmaximal, complemented
3#56480C214yesmaximal, complemented
4#56468C214yesmaximal, complemented
5#52431C214yesmaximal, complemented
6#47782C214yesmaximal, complemented
7#47331C214yesmaximal, complemented
8#47183C214yesmaximal, complemented
9#47106C214yesmaximal, complemented
10#43196C214yesmaximal, complemented
11#39767C212yesmaximal
12#39755C212yesmaximal, complemented
13#39677C212yesmaximal, complemented
14#39671C212yesmaximal, complemented
15#38573C214yesmaximal, complemented
16#38147C214yesmaximal, complemented
17#36980C212yesmaximal, complemented
18#35099C212yesmaximal, complemented
19#35087C211yesmaximal, characteristic, complemented
20#35082C211yesmaximal, characteristic
21C2×#2606C211yesmaximal, characteristic, complemented
22#2857C2211yescharacteristic
23#2856C2211yescharacteristic
24#2855C2212yes—
25#2854C2212yes—
26#2853C2214yes—
27#2851C2211yescharacteristic
28#2851C2211yescharacteristic
29#2836C2214yes—
30#2836C2214yes—
31#2834C2214yes—
32#2834C2214yes—
33#2831C2214yes—
34#2831C2214yes—
35#2830C2214yes—
36#2822C2214yes—
37#2808C2214yes—
38#2806C2214yes—
39#2802C2214yes—
40#2802C2214yes—
41#2800C2214yes—
42#2800C2214yes—
43#2798C2214yes—
44#2796C2214yes—
45#2796C2214yes—
46#2793C2214yes—
47#2791C2214yes—
48#2791C2214yes—
49#2790C2214yes—
50#2790C2214yes—
51#2789C2214yes—
52#2788C2214yes—
53#2787C2214yes—
54#2784C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2775C2214yes—
58#2774C2214yes—
59#2772C2214yes—
60#2771C2214yes—
61#2770C2214yes—
62#2770C2214yes—
63#2770C2214yes—
64#2768C2214yes—
65#2767C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2766C2214yes—
69#2766C2214yes—
70#2765C2214yes—
71#2764C2214yes—
72#2764C2214yes—
73#2759C2214yes—
74#2759C2214yes—
75#2758C2214yes—
76#2757C2214yes—
77#2757C2214yes—
78#2747C2214yes—
79#2739C2214yes—
80#2738C2214yes—
81#2738C2214yes—
82#2737C2214yes—
83#2737C2214yes—
84#2726C2214yes—
85#2724C2214yes—
86#2724C2214yes—
87#2721C2214yes—
88#2716C2214yes—
89#2707C2214yes—
90#2707C2214yes—
91#2707C2214yes—
92#2707C2214yes—
93#2664C2214yes—
94#2659C2212yes—
95#2655C2214yes—
96#2652C2214yes—
97#2652C2214yes—
98#2651C2214yes—
99#2650C2214yes—
100#2646C2212yes—
101#2643C2214yes—
102#2639C2212yes—
103#2639C2212yes—
104#2606C2214yes—
105#2606C2214yes—
106#2606C2214yes—
107#2606C2214yes—
108#2606C2214yes—
109#2594C2214yes—
110#2590C2214yes—
111#2588C2214yes—
112#2585C2214yes—
113#2584C2214yes—
114#2583C2214yes—
115#2580C2214yes—
116#2579C2214yes—
117#2579C2214yes—
118#2579C2214yes—
119#2574C2214yes—
120#2570C2214yes—
121#2565C2214yes—
122#2533C2214yes—
123#2533C2214yes—
124#2532C2214yes—
125#2532C2214yes—
126#2531C2214yes—
127#2530C2214yes—
128#2530C2214yes—
129#2529C2214yes—
130#2528C2214yes—
131#2527C2214yes—
132#2527C2214yes—
133#2526C2214yes—
134#2524C2214yes—
135#2523C2214yes—
136#2520C2214yes—
137#2514C2212yes—
138#2513C2212yes—
139#2513C2214yes—
140#2510C2214yes—
141#2510C2214yes—
142#2507C2212yes—
143#2506C2212yes—
144#2504C2214yes—
145#2494C2214yes—
146#2493C2214yes—
147#2488C2214yes—
148#2486C2214yes—
149#2481C2214yes—
150#2473C2214yes—
151#2473C2214yes—
152#2473C2214yes—
153#2473C2214yes—
154#2473C2214yes—
155#2473C2214yes—
156#2468C2214yes—
157#2466C2214yes—
158#2466C2214yes—
159#2462C2214yes—
160#2458C2214yes—
161#2458C2214yes—
162#2454C2212yes—
163#2453C2212yes—
164#2453C2214yes—
165#2450C2214yes—
166#2450C2214yes—
167#2450C2214yes—
168#2446C2212yes—
169#2445C2212yes—
170#2445C2214yes—
171#2443C2214yes—
172#2443C2214yes—
173#2443C2214yes—
174#2425C2214yes—
175#2419C2214yes—
176C2×#398C2212yes—
177C2×#398C2212yes—
178#2361C2214yes—
179#2360C2214yes—
180#2353C2214yes—
181D4×C4⋊C4C2214yes—
182#2336C2214yes—
183#2336C2214yes—
184#2335C2214yes—
185#2335C2214yes—
186#2329C2212yes—
187#2329C2212yes—
188#2325C2212yes—
189#2325C2212yes—
190#2322C2214yes—
191#2320C2214yes—
192#2318C2214yes—
193C4×C22⋊Q8C2212yes—
194C4×#123C2214yes—
195C4×#121C2212yes—
196C2×#389C2212yes—
197C2×#389C2212yes—
198C2×#387C2212yes—
199C2×#387C2212yes—
200C2×#383C2211yescharacteristic
201C2×C4×C4⋊C4C2211yescharacteristic
202C2×#376C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#127C2311yescharacteristic
205C2×#126C2314yes—
206C2×#125C2314yes—
207C2×#125C2314yes—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2314yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2314yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#401C2314yes—
239#401C2314yes—
240#401C2314yes—
241#401C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#399C2314yes—
266#399C2314yes—
267#399C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#393C2314yes—
345#393C2314yes—
346#393C2314yes—
347#393C2314yes—
348#393C2314yes—
349#393C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2314yes—
360#391C2312yes—
361#390C2314yes—
362#390C2314yes—
363#390C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2314yes—
367#390C2314yes—
368#390C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#389C2312yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#384C2314yes—
523#384C2311yescharacteristic
524#384C2311yescharacteristic
525#383C2314yes—
526#383C2314yes—
527#383C2314yes—
528#383C2314yes—
529#383C2314yes—
530#383C2314yes—
531#383C2314yes—
532#382C2314yes—
533#382C2314yes—
534#382C2314yes—
535#382C2311yescharacteristic
536#382C2314yes—
537#382C2311yescharacteristic
538#381C2314yes—
539#381C2314yes—
540#381C2314yes—
541#381C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2314yes—
546#380C2312yes—
547#380C2312yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2312yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2312yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2312yes—
562C4×C4⋊C4C2312yes—
563C4×C4⋊C4C2312yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571#376C2314yes—
572#376C2314yes—
573#376C2314yes—
574C2×#95C2311yescharacteristic
575C2×#95C2312yes—
576C2×#95C2312yes—
577C2×#95C2312yes—
578C2×#95C2311yescharacteristic
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2311yescharacteristic
582C2×#95C2312yes—
583C2×#95C2311yescharacteristic
584C22×Q8C2412yes—
585C22×Q8C2414yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2412yes—
589C23×C4C2411yescharacteristic
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2411yescharacteristic
601C4⋊Q8—81no—
602#127—81no—
603#126—84no—
604#125—48no—
605#125—48no—
606#125—81no—
607#125—81no—
608#125—84no—
609#123—48no—
610#123—48no—
611#123—48no—
612#123—48no—
613C22⋊Q8—28no—
614C22⋊Q8—48no—
615#121—28no—
616#121—48no—
617C4×Q8—48no—
618C4×Q8—82no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—82no—
623C4×D4—84no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4—44no—
629C2×C4⋊C4—82no—
630C2×C4⋊C4—84no—
631C2×C4⋊C4—82no—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C42—24no—
712C2×C42—44no—
713C2×C42—81no—
714C2×C42—81no—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800C24C2514yes—
801C24C2511yescharacteristic
802C2×Q8—24no—
803C2×Q8—44no—
804C2×Q8—42no—
805C2×Q8—44no—
806C2×Q8—42no—
807C2×Q8—44no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—24no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—42no—
815C2×D4—44no—
816C2×D4—42no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—41no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—41no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C42−1+414yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—44no—
953C42—44no—
954C42—42no—
955C42—42no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—44no—
961C42—44no—
962C42—44no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—44no—
967C42—44no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23C2×2−1+412yes—
979C23#58514yes—
980C23C2611yescharacteristic
981Q8—84no—
982Q8—88no—
983D4—416no—
984D4—84no—
985D4—88no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—44no—
1041C2×C4—48no—
1042C2×C4—44no—
1043C2×C4—48no—
1044C2×C4—44no—
1045C2×C4—84no—
1046C2×C4—84no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4—88no—
1050C2×C4—164no—
1051C2×C4—164no—
1052C2×C4C2×2−1+412yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4#58514yes—
1055C22—22no—
1056C22—22no—
1057C22—24no—
1058C22—24no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22#355714yes—
1067C22C22×2−1+411yescharacteristic
1068C22C2×#58512yes—
1069C22C2×#58512yes—
1070C22H(7,𝔽2)11yescharacteristic
1071C222−1+611yescharacteristic
1072C4—22no—
1073C4—22no—
1074C4—24no—
1075C4—42no—
1076C4—44no—
1077C4—44no—
1078C4—42no—
1079C4—44no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4—42no—
1085C4—42no—
1086C4—44no—
1087C4—44no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C2—24no—
1092C2—84no—
1093C2C2×#355711yescharacteristic
1094C2#6283811yescharacteristic
1095C2#6286511yescharacteristic
1096C2#6290712yes—
1097C2#6296312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57566C2semidirect
2. #56992C2semidirect
3. #56480C2semidirect
4. #56468C2semidirect
5. #52431C2semidirect
6. #47782C2semidirect
7. #47331C2semidirect
8. #47183C2semidirect
9. #47106C2semidirect
10. #43196C2semidirect
12. #39755C2semidirect
13. #39677C2semidirect
14. #39671C2semidirect
15. #38573C2semidirect
16. #38147C2semidirect
17. #36980C2semidirect
18. #35099C2semidirect
19. #35087C2semidirect
21. C2×#2606C2semidirect

Maximal subgroups

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

subgroupindex
#575662
#569922
#564802
#564682
#524312
#477822
#473312
#471832
#471062
#431962
#397672
#397552
#396772
#396712
#385732
#381472
#369802
#350992
#350872
#350822
C2×#26062