Finite Group Databasebeta

← #8746266

Subgroups — #8746266

Order 512.

4557 conjugacy classes of subgroups.

The subgroup lattice has 1469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59935C211yesmaximal, characteristic, complemented
2#59934C212yesmaximal, complemented
3#57273C214yesmaximal, complemented
4#55547C214yesmaximal, complemented
5#55252C214yesmaximal, complemented
6#54162C214yesmaximal, complemented
7#53491C212yesmaximal, complemented
8#53099C211yesmaximal, characteristic, complemented
9#53087C212yesmaximal, complemented
10#52960C212yesmaximal, complemented
11#52622C214yesmaximal, complemented
12#47814C212yesmaximal, complemented
13#45369C211yesmaximal, characteristic, complemented
14#45028C212yesmaximal, complemented
15#44995C212yesmaximal, complemented
16#44891C212yesmaximal, complemented
17#44883C212yesmaximal, complemented
18#42799C212yesmaximal, complemented
19#42603C212yesmaximal, complemented
20#42560C212yesmaximal, complemented
21#42519C212yesmaximal, complemented
22#42481C211yesmaximal, characteristic, complemented
23#42227C212yesmaximal, complemented
24#42058C214yesmaximal, complemented
25#39770C212yesmaximal, complemented
26#39745C211yesmaximal, characteristic
27#36698C211yesmaximal, characteristic, complemented
28#35959C211yesmaximal, characteristic, complemented
29#35916C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#542C2212yes—
35#2867C2211yescharacteristic
36#2844C2211yescharacteristic
37#2838C2212yes—
38#2838C2212yes—
39#2836C2212yes—
40#2836C2212yes—
41#2833C2212yes—
42#2830C2211yescharacteristic
43#2830C2211yescharacteristic
44#2830C2212yes—
45#2829C2214yes—
46#2829C2214yes—
47#2829C2214yes—
48#2827C2214yes—
49#2826C2214yes—
50#2824C2214yes—
51#2824C2214yes—
52#2823C2214yes—
53#2823C2212yes—
54#2822C2211yescharacteristic
55#2820C2212yes—
56#2814C2214yes—
57#2814C2212yes—
58#2809C2212yes—
59#2801C2214yes—
60#2797C2214yes—
61#2796C2214yes—
62#2791C2214yes—
63#2786C2214yes—
64#2785C2212yes—
65#2784C2214yes—
66#2784C2212yes—
67#2784C2212yes—
68#2781C2214yes—
69#2780C2214yes—
70#2780C2214yes—
71#2780C2214yes—
72#2779C2214yes—
73#2774C2214yes—
74#2752C2214yes—
75#2751C2214yes—
76#2750C2214yes—
77#2746C2214yes—
78#2743C2214yes—
79#2740C2214yes—
80#2730C2214yes—
81#2728C2214yes—
82#2718C2214yes—
83#2715C2214yes—
84#2709C2214yes—
85#2709C2214yes—
86#2709C2214yes—
87#2709C2214yes—
88#2709C2214yes—
89#2709C2214yes—
90#2706C2214yes—
91#2706C2214yes—
92#2705C2214yes—
93#2702C2214yes—
94#2702C2214yes—
95#2701C2214yes—
96#2700C2214yes—
97#2696C2214yes—
98#2696C2214yes—
99#2695C2214yes—
100#2693C2214yes—
101#2691C2214yes—
102#2686C2214yes—
103#2683C2214yes—
104#2683C2212yes—
105#2681C2214yes—
106#2681C2214yes—
107#2680C2212yes—
108#2680C2214yes—
109#2673C2214yes—
110#2673C2214yes—
111#2672C2214yes—
112#2663C2212yes—
113#2662C2214yes—
114#2658C2211yescharacteristic
115#2657C2212yes—
116#2653C2214yes—
117#2651C2214yes—
118#2648C2214yes—
119#2644C2212yes—
120#2643C2214yes—
121#2641C2214yes—
122#2640C2211yescharacteristic
123#2638C2212yes—
124#2630C2214yes—
125#2630C2214yes—
126#2630C2214yes—
127#2620C2212yes—
128#2620C2214yes—
129#2614C2212yes—
130#2612C2214yes—
131#2612C2212yes—
132#2609C2212yes—
133#2602C2214yes—
134#2601C2214yes—
135#2595C2214yes—
136#2593C2212yes—
137#2592C2211yescharacteristic
138#2592C2212yes—
139#2592C2211yescharacteristic
140#2590C2214yes—
141#2585C2214yes—
142#2574C2214yes—
143#2568C2211yescharacteristic
144#2567C2211yescharacteristic
145#2564C2212yes—
146#2564C2214yes—
147#2560C2214yes—
148#2557C2214yes—
149#2554C2214yes—
150#2553C2214yes—
151#2548C2212yes—
152#2548C2211yescharacteristic
153#2548C2212yes—
154#2547C2212yes—
155#2545C2212yes—
156#2544C2212yes—
157#2544C2212yes—
158#2544C2212yes—
159#2544C2214yes—
160#2544C2212yes—
161#2544C2212yes—
162#2541C2211yescharacteristic
163#2541C2212yes—
164#2538C2212yes—
165#2521C2214yes—
166#2520C2214yes—
167#2516C2214yes—
168#2512C2212yes—
169#2511C2212yes—
170#2511C2212yes—
171#2511C2214yes—
172#2507C2212yes—
173#2507C2212yes—
174#2501C2212yes—
175#2498C2212yes—
176#2498C2214yes—
177#2497C2214yes—
178#2492C2212yes—
179#2491C2212yes—
180#2474C2214yes—
181#2471C2214yes—
182#2470C2214yes—
183#2468C2214yes—
184#2467C2214yes—
185#2461C2214yes—
186#2457C2214yes—
187#2452C2212yes—
188#2452C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2450C2214yes—
192#2450C2214yes—
193#2450C2214yes—
194#2447C2212yes—
195#2446C2212yes—
196#2446C2212yes—
197#2445C2212yes—
198#2445C2214yes—
199#2445C2212yes—
200#2445C2212yes—
201#2445C2214yes—
202#2445C2214yes—
203#2445C2212yes—
204#2436C2214yes—
205#2432C2212yes—
206#2432C2212yes—
207#2431C2212yes—
208#2431C2212yes—
209#2429C2212yes—
210#2428C2212yes—
211#2428C2212yes—
212#2427C2214yes—
213#2427C2212yes—
214#2426C2212yes—
215#2426C2212yes—
216#2426C2212yes—
217#2425C2214yes—
218#2425C2214yes—
219#2422C2212yes—
220#2422C2214yes—
221#2417C2212yes—
222#2409C2214yes—
223#2409C2212yes—
224#2401C2212yes—
225#2401C2212yes—
226#2399C2211yescharacteristic
227#2399C2211yescharacteristic
228#2396C2212yes—
229#2396C2212yes—
230#2395C2212yes—
231#2395C2212yes—
232#2392C2214yes—
233#2372C2212yes—
234#2371C2214yes—
235#2369C2212yes—
236#2367C2212yes—
237#2366C2212yes—
238#2366C2212yes—
239#2365C2212yes—
240#2361C2212yes—
241#2361C2212yes—
242#2360C2212yes—
243#2355C2212yes—
244#2354C2212yes—
245Q8×C4⋊C4C2212yes—
246#2345C2212yes—
247#2339C2212yes—
248#2328C2212yes—
249#2328C2214yes—
250#2326C2212yes—
251#2324C2212yes—
252#2319C2211yescharacteristic
253#2311C2212yes—
254C4×#125C2212yes—
255C4×#124C2211yescharacteristic
256#2295C2211yescharacteristic
257#2295C2212yes—
258#2275C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#559—44no—
262#556—44no—
263#550—44no—
264D4×Q8—44no—
265#542—48no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×#127C2312yes—
271C2×#127C2312yes—
272C2×#127C2312yes—
273C2×#127C2311yescharacteristic
274C2×#127C2311yescharacteristic
275C2×#127C2312yes—
276C2×#127C2314yes—
277C2×#127C2312yes—
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125C2312yes—
283C2×#124C2311yescharacteristic
284C2×#124C2312yes—
285C2×#124C2311yescharacteristic
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#123C2312yes—
295C2×#123C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C22×C4⋊C4C2312yes—
343#401C2312yes—
344#401C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#399C2312yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2312yes—
368#399C2314yes—
369#399C2312yes—
370#399C2314yes—
371#398C2312yes—
372#398C2311yescharacteristic
373#398C2311yescharacteristic
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2311yescharacteristic
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2312yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#395C2311yescharacteristic
437#395C2312yes—
438#395C2312yes—
439#395C2312yes—
440#395C2312yes—
441#395C2312yes—
442#395C2311yescharacteristic
443#395C2311yescharacteristic
444#395C2311yescharacteristic
445#395C2312yes—
446#395C2314yes—
447#395C2314yes—
448#394C2314yes—
449#394C2312yes—
450#394C2312yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2312yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2312yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#393C2314yes—
487#393C2312yes—
488#393C2312yes—
489#393C2312yes—
490#393C2312yes—
491#393C2314yes—
492#393C2314yes—
493#393C2312yes—
494#393C2312yes—
495#393C2314yes—
496#393C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2312yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#391C2312yes—
520#390C2314yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2311yescharacteristic
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2312yes—
531#390C2314yes—
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2314yes—
536#390C2314yes—
537#390C2312yes—
538#390C2312yes—
539#390C2314yes—
540#390C2312yes—
541#390C2312yes—
542#390C2314yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#384C2312yes—
659#384C2314yes—
660#384C2312yes—
661#384C2312yes—
662#382C2312yes—
663#382C2311yescharacteristic
664#382C2312yes—
665#382C2314yes—
666#381C2312yes—
667#381C2314yes—
668#381C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710#376C2311yescharacteristic
711#376C2312yes—
712#376C2314yes—
713#376C2311yescharacteristic
714C2×#95C2314yes—
715C2×#95C2312yes—
716C43C2311yescharacteristic
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—44no—
721C22×Q8—84no—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2414yes—
754C4⋊Q8—28no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757C4⋊Q8—42no—
758#127—28no—
759#127—44no—
760#127—44no—
761#127—44no—
762#127—42no—
763#127—42no—
764#127—82no—
765#127—84no—
766#127—82no—
767#126—48no—
768#126—48no—
769#126—84no—
770#125—28no—
771#124—24no—
772#124—44no—
773#124—44no—
774#124—44no—
775#124—44no—
776#124—48no—
777#124—44no—
778#124—42no—
779#124—42no—
780#124—84no—
781#124—82no—
782#123—44no—
783#123—44no—
784#123—48no—
785#123—84no—
786#123—84no—
787#123—84no—
788#123—84no—
789#123—84no—
790#123—84no—
791#123—84no—
792C22⋊Q8—48no—
793C22⋊Q8—48no—
794C22⋊Q8—44no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—84no—
799C22⋊Q8—84no—
800C22⋊Q8—84no—
801#121—28no—
802#121—48no—
803#121—44no—
804#121—44no—
805#121—84no—
806#121—84no—
807C4×Q8—28no—
808C4×Q8—24no—
809C4×Q8—42no—
810C4×Q8—42no—
811C4×Q8—42no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×D4—24no—
815C4×D4—24no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—44no—
821C4×D4—42no—
822C4×D4—44no—
823C4×D4—84no—
824C4×D4—84no—
825C4×D4—84no—
826C4×D4—84no—
827#117—44no—
828#117—44no—
829#117—84no—
830C2×C4⋊C4—44no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2411yescharacteristic
975#95C2414yes—
976#95C2414yes—
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028C24C2512yes—
1029C24C2512yes—
1030C24C2514yes—
1031C24C2512yes—
1032#41—816no—
1033C2×Q8—24no—
1034C2×Q8—22no—
1035C2×Q8—28no—
1036C2×Q8—22no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—41no—
1041C2×Q8—42no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—816no—
1051C2×D4—22no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—28no—
1055C2×D4—22no—
1056C2×D4—28no—
1057C2×D4—28no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—41no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2514yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—41no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4H(5,𝔽2)14yes—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—44no—
1258C42—24no—
1259C42—24no—
1260C42—28no—
1261C42—22no—
1262C42—22no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—42no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—42no—
1275C42—42no—
1276C42—42no—
1277C42—41no—
1278C422−1+414yes—
1279C23—22no—
1280C23—22no—
1281C23—24no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—24no—
1287C23—24no—
1288C23—22no—
1289C23—24no—
1290C23—24no—
1291C23—24no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23—24no—
1298C23—24no—
1299C23—22no—
1300C23—24no—
1301C23—22no—
1302C23—22no—
1303C23C2611yescharacteristic
1304Q8—44no—
1305Q8—48no—
1306Q8—44no—
1307Q8—82no—
1308Q8—88no—
1309Q8—82no—
1310Q8—84no—
1311D4—44no—
1312D4—44no—
1313D4—48no—
1314D4—88no—
1315D4—82no—
1316D4—84no—
1317D4—84no—
1318D4—88no—
1319D4—88no—
1320D4—88no—
1321D4—88no—
1322D4—162no—
1323D4—162no—
1324D4—164no—
1325D4—164no—
1326D4—164no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—48no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—88no—
1395C2×C4—88no—
1396C2×C4—88no—
1397C2×C4—164no—
1398C2×C4—164no—
1399C2×C4—164no—
1400C2×C4C2×H(5,𝔽2)14yes—
1401C2×C4C2×H(5,𝔽2)12yes—
1402C2×C4C2×2−1+414yes—
1403C2×C4C2×2−1+412yes—
1404C2×C4#58514yes—
1405C22—42no—
1406C22—44no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—44no—
1412C22—42no—
1413C22—44no—
1414C22—42no—
1415C22—44no—
1416C22—42no—
1417C22—44no—
1418C22—44no—
1419C22—42no—
1420C22—42no—
1421C22—44no—
1422C22—42no—
1423C22—44no—
1424C22—44no—
1425C22—44no—
1426C22—44no—
1427C22—42no—
1428C22—42no—
1429C22C22×H(5,𝔽2)11yescharacteristic
1430C22C22×2−1+411yescharacteristic
1431C22C2×#58512yes—
1432C22H(7,𝔽2)12yes—
1433C22H(7,𝔽2)11yescharacteristic
1434C4—24no—
1435C4—22no—
1436C4—24no—
1437C4—42no—
1438C4—42no—
1439C4—44no—
1440C4—42no—
1441C4—41no—
1442C4—41no—
1443C4—44no—
1444C4—42no—
1445C4—41no—
1446C4—42no—
1447C4—44no—
1448C4—44no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—41no—
1455C4—41no—
1456C4—42no—
1457C4—42no—
1458C4#355114yes—
1459C2—82no—
1460C2—84no—
1461C2—82no—
1462C2—82no—
1463C2C2×#355111yescharacteristic
1464C2#6291711yescharacteristic
1465C2#6296212yes—
1466C2#6304111yescharacteristic
1467C2#6306012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39745C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59935C2semidirect
2. #59934C2semidirect
3. #57273C2semidirect
4. #55547C2semidirect
5. #55252C2semidirect
6. #54162C2semidirect
7. #53491C2semidirect
8. #53099C2semidirect
9. #53087C2semidirect
10. #52960C2semidirect
11. #52622C2semidirect
12. #47814C2semidirect
13. #45369C2semidirect
14. #45028C2semidirect
15. #44995C2semidirect
16. #44891C2semidirect
17. #44883C2semidirect
18. #42799C2semidirect
19. #42603C2semidirect
20. #42560C2semidirect
21. #42519C2semidirect
22. #42481C2semidirect
23. #42227C2semidirect
24. #42058C2semidirect
25. #39770C2semidirect
27. #36698C2semidirect
28. #35959C2semidirect
29. #35916C2semidirect

Maximal subgroups

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

subgroupindex
#599352
#599342
#572732
#555472
#552522
#541622
#534912
#530992
#530872
#529602
#526222
#478142
#453692
#450282
#449952
#448912
#448832
#427992
#426032
#425602
#425192
#424812
#422272
#420582
#397702
#397452
#366982
#359592
#359162