Finite Group Databasebeta

← #8115478

Subgroups — #8115478

Order 512.

3991 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58677C214yesmaximal, complemented
2#57566C214yesmaximal, complemented
3#57077C214yesmaximal, complemented
4#56984C214yesmaximal
5#56961C214yesmaximal, complemented
6#56825C214yesmaximal, complemented
7#55771C214yesmaximal, complemented
8#54225C214yesmaximal, complemented
9#53050C212yesmaximal, complemented
10#53024C212yesmaximal, complemented
11#45300C212yesmaximal, complemented
12#45154C212yesmaximal, complemented
13#42803C212yesmaximal
14#42801C212yesmaximal, complemented
15#42772C212yesmaximal, complemented
16#42717C212yesmaximal, complemented
17#39635C211yesmaximal, characteristic, complemented
18#39612C211yesmaximal, characteristic, complemented
19#39506C211yesmaximal, characteristic, complemented
20#39484C211yesmaximal, characteristic, complemented
21#37955C212yesmaximal, complemented
22#37947C212yesmaximal, complemented
23#37429C212yesmaximal, complemented
24#37395C212yesmaximal, complemented
25#35345C211yesmaximal, characteristic, complemented
26#35319C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#552C2212yes—
30C2×#541C2212yes—
31#2868C2211yescharacteristic
32#2864C2212yes—
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2845C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2838C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2831C2214yes—
45#2831C2214yes—
46#2830C2214yes—
47#2827C2214yes—
48#2823C2214yes—
49#2822C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2800C2214yes—
56#2794C2214yes—
57#2793C2214yes—
58#2793C2214yes—
59#2793C2214yes—
60#2793C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2790C2214yes—
68#2790C2214yes—
69#2788C2214yes—
70#2783C2214yes—
71#2783C2214yes—
72#2783C2214yes—
73#2781C2214yes—
74#2777C2214yes—
75#2776C2214yes—
76#2775C2214yes—
77#2774C2214yes—
78#2772C2214yes—
79#2772C2214yes—
80#2770C2214yes—
81#2770C2214yes—
82#2769C2214yes—
83#2769C2214yes—
84#2768C2214yes—
85#2768C2214yes—
86#2767C2214yes—
87#2767C2214yes—
88#2766C2214yes—
89#2762C2214yes—
90#2755C2214yes—
91#2755C2214yes—
92#2747C2214yes—
93#2746C2214yes—
94#2744C2214yes—
95#2742C2214yes—
96#2739C2214yes—
97#2737C2214yes—
98#2734C2214yes—
99#2726C2214yes—
100#2726C2214yes—
101#2726C2214yes—
102#2725C2214yes—
103#2725C2214yes—
104#2724C2214yes—
105#2721C2214yes—
106#2719C2214yes—
107#2719C2214yes—
108#2716C2214yes—
109#2716C2214yes—
110#2713C2214yes—
111#2707C2214yes—
112#2707C2214yes—
113#2705C2214yes—
114#2664C2214yes—
115#2664C2214yes—
116#2660C2212yes—
117#2655C2212yes—
118#2655C2214yes—
119#2654C2212yes—
120#2653C2212yes—
121#2652C2214yes—
122#2652C2212yes—
123#2651C2212yes—
124#2650C2212yes—
125#2650C2214yes—
126#2649C2212yes—
127#2648C2212yes—
128#2647C2214yes—
129#2647C2212yes—
130#2642C2212yes—
131#2637C2214yes—
132#2629C2211yescharacteristic
133#2629C2212yes—
134#2629C2211yescharacteristic
135#2629C2214yes—
136#2621C2212yes—
137#2621C2212yes—
138#2621C2212yes—
139#2612C2214yes—
140#2608C2214yes—
141#2608C2214yes—
142#2606C2214yes—
143#2606C2214yes—
144#2606C2214yes—
145#2601C2214yes—
146#2585C2214yes—
147#2582C2212yes—
148#2578C2214yes—
149#2574C2214yes—
150#2571C2212yes—
151#2570C2212yes—
152#2567C2212yes—
153#2565C2212yes—
154#2565C2212yes—
155#2565C2214yes—
156#2565C2212yes—
157#2552C2212yes—
158#2550C2212yes—
159#2538C2212yes—
160#2538C2212yes—
161#2536C2212yes—
162#2531C2214yes—
163#2530C2214yes—
164#2530C2214yes—
165#2529C2214yes—
166#2528C2214yes—
167#2528C2214yes—
168#2524C2214yes—
169#2522C2214yes—
170#2514C2212yes—
171#2513C2214yes—
172#2511C2212yes—
173#2511C2214yes—
174#2509C2214yes—
175#2508C2214yes—
176#2507C2214yes—
177#2506C2214yes—
178#2506C2214yes—
179#2502C2212yes—
180#2499C2212yes—
181#2496C2214yes—
182#2496C2214yes—
183#2492C2212yes—
184#2492C2212yes—
185#2489C2212yes—
186#2489C2212yes—
187#2489C2212yes—
188#2489C2212yes—
189#2478C2214yes—
190#2478C2214yes—
191#2475C2214yes—
192#2462C2214yes—
193#2462C2214yes—
194#2458C2214yes—
195#2453C2212yes—
196#2453C2212yes—
197#2453C2214yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2442C2212yes—
203#2442C2212yes—
204#2441C2212yes—
205#2439C2212yes—
206#2439C2214yes—
207#2429C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2423C2212yes—
212#2421C2212yes—
213#2417C2212yes—
214#2415C2212yes—
215#2402C2211yescharacteristic
216#2401C2212yes—
217#2398C2211yescharacteristic
218#2396C2211yescharacteristic
219#2395C2212yes—
220#2392C2211yescharacteristic
221#2362C2212yes—
222#2360C2212yes—
223#2356C2212yes—
224#2355C2212yes—
225#2355C2212yes—
226Q8×C4⋊C4C2212yes—
227#2330C2211yescharacteristic
228#2330C2212yes—
229#2330C2211yescharacteristic
230#2327C2212yes—
231#2327C2212yes—
232#2327C2212yes—
233#2317C2212yes—
234#2314C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237#2298C2212yes—
238#2295C2211yescharacteristic
239#2293C2211yescharacteristic
240#2290C2212yes—
241#2283C2212yes—
242C4×#117C2211yescharacteristic
243#557—48no—
244#552—48no—
245#541—48no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2311yescharacteristic
260C2×#125C2311yescharacteristic
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2312yes—
282C2×#117C2312yes—
283C2×#117C2311yescharacteristic
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2311yescharacteristic
287C22×C4⋊C4C2312yes—
288C22×C42C2311yescharacteristic
289#401C2314yes—
290#401C2312yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2312yes—
321#400C2312yes—
322#400C2314yes—
323#400C2311yescharacteristic
324#400C2312yes—
325#400C2314yes—
326#399C2314yes—
327#399C2312yes—
328#399C2314yes—
329#399C2311yescharacteristic
330#398C2312yes—
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#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2311yescharacteristic
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2312yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2311yescharacteristic
396#397C2312yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2311yescharacteristic
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2312yes—
429#394C2311yescharacteristic
430#394C2312yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2312yes—
435#393C2311yescharacteristic
436#392C2311yescharacteristic
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#390C2314yes—
456#390C2312yes—
457#390C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
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#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#388C2312yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
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#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
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#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2314yes—
607#384C2311yescharacteristic
608#384C2311yescharacteristic
609#384C2311yescharacteristic
610#384C2312yes—
611#384C2312yes—
612#384C2314yes—
613#384C2311yescharacteristic
614#384C2314yes—
615#384C2312yes—
616#384C2314yes—
617#384C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#382C2314yes—
633#381C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670#376C2311yescharacteristic
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2314yes—
674#376C2314yes—
675C43C2311yescharacteristic
676C43C2311yescharacteristic
677C22×Q8C2412yes—
678C22×Q8C2412yes—
679C22×Q8C2411yescharacteristic
680C22×Q8C2414yes—
681C22×D4C2411yescharacteristic
682C22×D4C2412yes—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2414yes—
687C4⋊Q8—24no—
688C4⋊Q8—24no—
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—44no—
692C4⋊Q8—48no—
693#126—48no—
694#126—48no—
695#126—48no—
696#125—28no—
697#125—42no—
698#125—42no—
699#125—44no—
700#125—48no—
701#125—48no—
702#125—44no—
703#125—48no—
704#125—48no—
705#125—48no—
706#123—48no—
707C22⋊Q8—44no—
708C22⋊Q8—44no—
709C22⋊Q8—44no—
710C22⋊Q8—44no—
711C22⋊Q8—44no—
712C22⋊Q8—44no—
713C4×Q8—28no—
714C4×Q8—28no—
715C4×Q8—24no—
716C4×Q8—48no—
717C4×Q8—44no—
718C4×Q8—44no—
719C4×Q8—44no—
720C4×Q8—44no—
721C4×D4—24no—
722C4×D4—44no—
723#117—24no—
724#117—28no—
725#117—42no—
726#117—48no—
727#117—44no—
728C2×C4⋊C4—44no—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C42—24no—
830C2×C42C2414yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2414yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935C24C2511yescharacteristic
936C24C2512yes—
937C2×Q8—24no—
938C2×Q8—24no—
939C2×Q8—22no—
940C2×Q8—24no—
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—24no—
944C2×Q8—44no—
945C2×Q8—42no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×D4—22no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—42no—
953C22×C4—24no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—24no—
957C22×C4—22no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2511yescharacteristic
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—22no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—22no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
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⋊C4—44no—
1060C4⋊C4—44no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—44no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C42—22no—
1091C42—28no—
1092C42—24no—
1093C42—28no—
1094C42—24no—
1095C42—22no—
1096C42—24no—
1097C42—22no—
1098C42—22no—
1099C42—24no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42H(5,𝔽2)14yes—
1114C422−1+414yes—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23C2611yescharacteristic
1128Q8—48no—
1129Q8—48no—
1130Q8—82no—
1131Q8—88no—
1132D4—82no—
1133D4—84no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—21no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—48no—
1200C2×C4—44no—
1201C2×C4—84no—
1202C2×C4—88no—
1203C2×C4C2×H(5,𝔽2)12yes—
1204C2×C4C2×H(5,𝔽2)12yes—
1205C2×C4C2×H(5,𝔽2)12yes—
1206C2×C4C2×2−1+414yes—
1207C2×C4C2×2−1+412yes—
1208C2×C4#58512yes—
1209C22—41no—
1210C22—42no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C22×2−1+411yescharacteristic
1223C22C2×#58511yescharacteristic
1224C222−1+612yes—
1225C222−1+612yes—
1226C4—22no—
1227C4—22no—
1228C4—24no—
1229C4—42no—
1230C4—41no—
1231C4—44no—
1232C4—44no—
1233C4—42no—
1234C4—41no—
1235C4—41no—
1236C4—44no—
1237C4—44no—
1238C4—44no—
1239C4—44no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—44no—
1248C4—44no—
1249C4—42no—
1250C4#354714yes—
1251C2—82no—
1252C2—81no—
1253C2C2×#354711yescharacteristic
1254C2#6288811yescharacteristic
1255C2#6288811yescharacteristic
1256C2#6288912yes—
1257C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58677C2semidirect
2. #57566C2semidirect
3. #57077C2semidirect
5. #56961C2semidirect
6. #56825C2semidirect
7. #55771C2semidirect
8. #54225C2semidirect
9. #53050C2semidirect
10. #53024C2semidirect
11. #45300C2semidirect
12. #45154C2semidirect
14. #42801C2semidirect
15. #42772C2semidirect
16. #42717C2semidirect
17. #39635C2semidirect
18. #39612C2semidirect
19. #39506C2semidirect
20. #39484C2semidirect
21. #37955C2semidirect
22. #37947C2semidirect
23. #37429C2semidirect
24. #37395C2semidirect
25. #35345C2semidirect
26. #35319C2semidirect

Maximal subgroups

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

subgroupindex
#586772
#575662
#570772
#569842
#569612
#568252
#557712
#542252
#530502
#530242
#453002
#451542
#428032
#428012
#427722
#427172
#396352
#396122
#395062
#394842
#379552
#379472
#374292
#373952
#353452
#353192
#346402