Finite Group Databasebeta

← #7732384

Subgroups — #7732384

Order 512.

4428 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51242C214yesmaximal, complemented
2#50934C214yesmaximal, complemented
3#47765C214yesmaximal, complemented
4#47748C214yesmaximal, complemented
5#44476C214yesmaximal, complemented
6#44000C214yesmaximal, complemented
7#39822C212yesmaximal, complemented
8#39799C212yesmaximal, complemented
9#39798C212yesmaximal, complemented
10#39764C212yesmaximal, complemented
11#39764C212yesmaximal, complemented
12#39286C212yesmaximal, complemented
13#38276C212yesmaximal, complemented
14#38125C212yesmaximal, complemented
15#37984C212yesmaximal, complemented
16#37892C212yesmaximal, complemented
17#37555C211yesmaximal, characteristic, complemented
18#37404C212yesmaximal, complemented
19#37362C212yesmaximal, complemented
20#36292C212yesmaximal, complemented
21#36172C212yesmaximal, complemented
22#35655C212yesmaximal, complemented
23#35605C212yesmaximal, complemented
24#35238C211yesmaximal, characteristic
25#35180C211yesmaximal, characteristic, complemented
26C2×#2570C211yesmaximal, characteristic, complemented
27#34398C211yesmaximal, characteristic, complemented
28#34235C211yesmaximal, characteristic, complemented
29#34083C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#529C2211yescharacteristic
33#2864C2212yes—
34#2863C2212yes—
35#2856C2212yes—
36#2854C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2822C2212yes—
42#2820C2212yes—
43#2801C2214yes—
44#2796C2214yes—
45#2796C2214yes—
46#2795C2214yes—
47#2794C2214yes—
48#2794C2214yes—
49#2793C2214yes—
50#2790C2214yes—
51#2789C2214yes—
52#2787C2214yes—
53#2786C2214yes—
54#2779C2214yes—
55#2777C2214yes—
56#2777C2214yes—
57#2775C2214yes—
58#2762C2214yes—
59#2762C2214yes—
60#2758C2214yes—
61#2758C2214yes—
62#2756C2214yes—
63#2755C2214yes—
64#2753C2214yes—
65#2751C2214yes—
66#2751C2214yes—
67#2749C2214yes—
68#2747C2214yes—
69#2747C2214yes—
70#2746C2214yes—
71#2745C2214yes—
72#2743C2214yes—
73#2741C2214yes—
74#2741C2214yes—
75#2740C2214yes—
76#2739C2214yes—
77#2739C2214yes—
78#2738C2214yes—
79#2718C2214yes—
80#2709C2214yes—
81#2709C2214yes—
82#2706C2214yes—
83#2662C2214yes—
84#2659C2212yes—
85#2647C2212yes—
86#2645C2212yes—
87#2639C2212yes—
88#2639C2212yes—
89#2639C2212yes—
90#2637C2214yes—
91#2628C2212yes—
92#2624C2212yes—
93#2621C2212yes—
94#2620C2212yes—
95#2604C2214yes—
96#2599C2214yes—
97#2597C2214yes—
98#2597C2214yes—
99#2597C2214yes—
100#2595C2214yes—
101#2595C2214yes—
102#2594C2214yes—
103#2594C2214yes—
104#2592C2214yes—
105#2591C2214yes—
106#2591C2214yes—
107#2589C2214yes—
108#2581C2212yes—
109#2579C2214yes—
110#2578C2214yes—
111#2577C2214yes—
112#2576C2214yes—
113#2570C2212yes—
114#2570C2212yes—
115#2570C2214yes—
116#2570C2212yes—
117#2570C2212yes—
118#2570C2214yes—
119#2569C2214yes—
120#2568C2212yes—
121#2567C2211yescharacteristic
122#2566C2212yes—
123#2563C2211yescharacteristic
124#2563C2212yes—
125#2562C2214yes—
126#2553C2214yes—
127#2548C2211yescharacteristic
128#2548C2212yes—
129#2547C2212yes—
130#2544C2212yes—
131#2541C2211yescharacteristic
132#2536C2212yes—
133#2532C2214yes—
134#2532C2214yes—
135#2531C2214yes—
136#2530C2214yes—
137#2529C2214yes—
138#2528C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2524C2214yes—
142#2522C2214yes—
143#2522C2214yes—
144#2521C2214yes—
145#2518C2214yes—
146#2518C2214yes—
147#2516C2214yes—
148#2516C2214yes—
149#2515C2214yes—
150#2514C2212yes—
151#2513C2212yes—
152#2512C2212yes—
153#2511C2212yes—
154#2510C2214yes—
155#2510C2214yes—
156#2510C2214yes—
157#2510C2214yes—
158#2509C2212yes—
159#2508C2212yes—
160#2498C2214yes—
161#2498C2214yes—
162#2495C2212yes—
163#2494C2212yes—
164#2493C2214yes—
165#2487C2214yes—
166#2481C2214yes—
167#2479C2214yes—
168#2474C2214yes—
169#2470C2214yes—
170#2458C2214yes—
171#2458C2214yes—
172#2448C2212yes—
173#2448C2212yes—
174#2444C2214yes—
175#2444C2214yes—
176#2443C2214yes—
177#2443C2214yes—
178#2430C2214yes—
179#2427C2212yes—
180#2427C2212yes—
181#2423C2212yes—
182#2422C2212yes—
183#2421C2212yes—
184#2420C2212yes—
185#2417C2212yes—
186#2417C2212yes—
187#2416C2212yes—
188#2416C2212yes—
189C2×#400C2212yes—
190C2×#398C2212yes—
191#2379C2212yes—
192#2379C2212yes—
193#2365C2211yescharacteristic
194#2365C2211yescharacteristic
195#2365C2211yescharacteristic
196#2365C2211yescharacteristic
197#2364C2214yes—
198#2364C2214yes—
199#2361C2212yes—
200#2361C2212yes—
201#2360C2212yes—
202#2360C2212yes—
203#2357C2212yes—
204#2356C2212yes—
205#2353C2214yes—
206#2352C2214yes—
207#2351C2212yes—
208#2349C2212yes—
209#2343C2214yes—
210#2339C2214yes—
211#2337C2212yes—
212#2336C2212yes—
213#2336C2214yes—
214#2334C2212yes—
215#2334C2212yes—
216#2331C2212yes—
217#2329C2211yescharacteristic
218#2329C2211yescharacteristic
219#2328C2212yes—
220#2326C2212yes—
221#2325C2211yescharacteristic
222#2325C2211yescharacteristic
223#2325C2212yes—
224#2325C2212yes—
225#2324C2212yes—
226#2324C2212yes—
227#2323C2212yes—
228#2322C2212yes—
229#2322C2212yes—
230#2320C2212yes—
231#2319C2212yes—
232#2318C2214yes—
233#2314C2212yes—
234#2311C2212yes—
235#2311C2212yes—
236C4×#124C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240#2298C2212yes—
241#2296C2212yes—
242#2295C2212yes—
243#2293C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2211yescharacteristic
246#2290C2212yes—
247#2290C2212yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250C2×#384C2211yescharacteristic
251#2283C2211yescharacteristic
252#2283C2212yes—
253C2×#382C2211yescharacteristic
254C2×#382C2211yescharacteristic
255#2276C2212yes—
256C42×D4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2312yes—
260#533—28no—
261#532—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#125C2312yes—
271C2×#125C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#123C2312yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×#121C2312yes—
286C2×#121C2311yescharacteristic
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2311yescharacteristic
328#401C2314yes—
329#401C2314yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#392C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2312yes—
485#388C2312yes—
486#388C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2312yes—
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#388C2314yes—
516#388C2314yes—
517#387C2312yes—
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#387C2312yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
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#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2312yes—
577#386C2312yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2312yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2312yes—
602#385C2312yes—
603#385C2312yes—
604#385C2312yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2312yes—
616#384C2312yes—
617#384C2314yes—
618#383C2312yes—
619#383C2314yes—
620#383C2314yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2314yes—
635#382C2311yescharacteristic
636#382C2311yescharacteristic
637#382C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2312yes—
642#381C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657#380C2314yes—
658#380C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700#376C2312yes—
701#376C2312yes—
702#376C2314yes—
703#376C2314yes—
704C2×#95C2314yes—
705C2×#95C2312yes—
706C2×#95C2311yescharacteristic
707C2×#95C2311yescharacteristic
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C2×#41—28no—
716C2×#41—44no—
717C2×#41—44no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2414yes—
725C22×D4C2411yescharacteristic
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C4⋊Q8—24no—
748C4⋊Q8—24no—
749C4⋊Q8—24no—
750#127—24no—
751#127—82no—
752#126—28no—
753#126—84no—
754#125—24no—
755#125—28no—
756#124—24no—
757#124—28no—
758#124—44no—
759#124—44no—
760#124—82no—
761#123—28no—
762#123—84no—
763#123—84no—
764C22⋊Q8—24no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769#121—24no—
770#121—28no—
771#121—28no—
772#121—44no—
773#121—44no—
774#121—48no—
775#121—48no—
776C4×Q8—24no—
777C4×Q8—28no—
778C4×Q8—28no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—82no—
782C4×Q8—82no—
783C4×D4—28no—
784C4×D4—24no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—44no—
788C4×D4—44no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—48no—
792C4×D4—48no—
793#117—28no—
794#117—28no—
795#117—44no—
796#117—84no—
797C2×C4⋊C4—42no—
798C2×C4⋊C4—42no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4—42no—
801C2×C4⋊C4—42no—
802C2×C4⋊C4—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—82no—
806C2×C4⋊C4—82no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C42—42no—
908C2×C42—44no—
909C2×C42—42no—
910C2×C42—82no—
911C2×C42#4118yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012C24C2512yes—
1013C24C2514yes—
1014C24C2511yescharacteristic
1015#41—816no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×D4—24no—
1029C2×D4—28no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—28no—
1033C2×D4—28no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—24no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—42no—
1041C2×D4—41no—
1042C2×D4—41no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—42no—
1075C22×C4—41no—
1076C22×C4—41no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—41no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—41no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4C2×#4114yes—
1101C22×C4C2×#4114yes—
1102C22×C4C2×#4114yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—22no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—22no—
1146C4⋊C4—22no—
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—41no—
1179C4⋊C4—41no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C42—24no—
1230C42—28no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—42no—
1236C42—42no—
1237C42—42no—
1238C42—42no—
1239C42—42no—
1240C42—42no—
1241C42—42no—
1242C42—42no—
1243C42—42no—
1244C42—42no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—42no—
1249C42—42no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42C2×#4114yes—
1254C42C2×#4114yes—
1255C42C2×#4114yes—
1256C42C2×#4114yes—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—22no—
1265C23—24no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—24no—
1270C23—24no—
1271C23—24no—
1272C23—22no—
1273C23—22no—
1274C23—24no—
1275C23C22×#4112yes—
1276C23#58512yes—
1277C23#58512yes—
1278C23C2611yescharacteristic
1279Q8—48no—
1280Q8—48no—
1281Q8—82no—
1282Q8—84no—
1283D4—48no—
1284D4—416no—
1285D4—48no—
1286D4—82no—
1287D4—84no—
1288D4—84no—
1289D4—164no—
1290D4—164no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—28no—
1302C2×C4—28no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—44no—
1364C2×C4—44no—
1365C2×C4—44no—
1366C2×C4—48no—
1367C2×C4—88no—
1368C2×C4—82no—
1369C2×C4—84no—
1370C2×C4—82no—
1371C2×C4—84no—
1372C2×C4—84no—
1373C2×C4—84no—
1374C2×C4—84no—
1375C2×C4—84no—
1376C2×C4—88no—
1377C2×C4—164no—
1378C2×C4C22×#4112yes—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4112yes—
1381C2×C4C22×#4112yes—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4#58512yes—
1385C2×C4#58512yes—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—44no—
1393C22—42no—
1394C22—42no—
1395C22—44no—
1396C22—42no—
1397C22—44no—
1398C22—42no—
1399C22—44no—
1400C22—42no—
1401C22—44no—
1402C22—44no—
1403C22—42no—
1404C22—44no—
1405C22—42no—
1406C22#351014yes—
1407C22C23×#4111yescharacteristic
1408C22C2×#58511yescharacteristic
1409C22C2×#58511yescharacteristic
1410C22C2×#58511yescharacteristic
1411C22C2×#58511yescharacteristic
1412C22H(7,𝔽2)11yescharacteristic
1413C222−1+611yescharacteristic
1414C4—22no—
1415C4—22no—
1416C4—22no—
1417C4—22no—
1418C4—22no—
1419C4—44no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4#351214yes—
1440C2—24no—
1441C2—84no—
1442C2—82no—
1443C2C2×#351011yescharacteristic
1444C2C2×#351211yescharacteristic
1445C2#6285611yescharacteristic
1446C2#6290711yescharacteristic
1447C2#6290811yescharacteristic
1448C2#6296411yescharacteristic
1449C2#6296511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35238C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51242C2semidirect
2. #50934C2semidirect
3. #47765C2semidirect
4. #47748C2semidirect
5. #44476C2semidirect
6. #44000C2semidirect
7. #39822C2semidirect
8. #39799C2semidirect
9. #39798C2semidirect
10. #39764C2semidirect
11. #39764C2semidirect
12. #39286C2semidirect
13. #38276C2semidirect
14. #38125C2semidirect
15. #37984C2semidirect
16. #37892C2semidirect
17. #37555C2semidirect
18. #37404C2semidirect
19. #37362C2semidirect
20. #36292C2semidirect
21. #36172C2semidirect
22. #35655C2semidirect
23. #35605C2semidirect
25. #35180C2semidirect
26. C2×#2570C2semidirect
27. #34398C2semidirect
28. #34235C2semidirect
29. #34083C2semidirect

Maximal subgroups

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

subgroupindex
#512422
#509342
#477652
#477482
#444762
#440002
#398222
#397992
#397982
#397642
#392862
#382762
#381252
#379842
#378922
#375552
#374042
#373622
#362922
#361722
#356552
#356052
#352382
#351802
C2×#25702
#343982
#342352
#340832