Finite Group Databasebeta

← #8751612

Subgroups — #8751612

Order 512.

5331 conjugacy classes of subgroups.

The subgroup lattice has 1549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic, complemented
2#59752C212yesmaximal, complemented
3#58943C212yesmaximal, complemented
4#58919C214yesmaximal, complemented
5#58242C214yesmaximal, complemented
6#57019C214yesmaximal, complemented
7#56675C214yesmaximal, complemented
8#53064C212yesmaximal, complemented
9#53007C211yesmaximal, characteristic, complemented
10#52424C214yesmaximal, complemented
11#52420C212yesmaximal, complemented
12#47541C212yesmaximal, complemented
13#45336C212yesmaximal, complemented
14#45321C211yesmaximal, characteristic, complemented
15#45307C212yesmaximal, complemented
16#45268C212yesmaximal, complemented
17#45245C212yesmaximal, complemented
18#42985C211yesmaximal, characteristic, complemented
19#42900C212yesmaximal, complemented
20#42893C212yesmaximal, complemented
21#42858C212yesmaximal, complemented
22#42796C212yesmaximal, complemented
23#42109C214yesmaximal, complemented
24#42043C212yesmaximal, complemented
25#39954C212yesmaximal, complemented
26#39174C211yesmaximal, characteristic, complemented
27#36694C211yesmaximal, characteristic, complemented
28#35757C211yesmaximal, characteristic, complemented
29#35687C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2212yes—
33C2×#550C2211yescharacteristic
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#537C2211yescharacteristic
39C2×#536C2212yes—
40#2858C2211yescharacteristic
41#2844C2211yescharacteristic
42#2841C2212yes—
43#2838C2214yes—
44#2837C2214yes—
45#2832C2212yes—
46#2832C2211yescharacteristic
47#2832C2212yes—
48#2832C2211yescharacteristic
49#2830C2214yes—
50#2829C2214yes—
51#2828C2214yes—
52#2828C2214yes—
53#2828C2212yes—
54#2828C2212yes—
55#2828C2212yes—
56#2828C2214yes—
57#2825C2214yes—
58#2823C2212yes—
59#2819C2212yes—
60#2819C2211yescharacteristic
61#2815C2212yes—
62#2813C2214yes—
63#2808C2214yes—
64#2803C2214yes—
65#2803C2214yes—
66#2800C2214yes—
67#2798C2214yes—
68#2797C2214yes—
69#2797C2214yes—
70#2792C2212yes—
71#2789C2212yes—
72#2787C2214yes—
73#2786C2214yes—
74#2784C2214yes—
75#2770C2214yes—
76#2756C2214yes—
77#2752C2212yes—
78#2752C2214yes—
79#2750C2214yes—
80#2747C2214yes—
81#2737C2214yes—
82#2733C2214yes—
83#2731C2214yes—
84#2730C2214yes—
85#2729C2214yes—
86#2723C2214yes—
87#2717C2212yes—
88#2716C2214yes—
89#2716C2214yes—
90#2715C2214yes—
91#2714C2214yes—
92#2714C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2711C2214yes—
96#2711C2214yes—
97#2705C2214yes—
98#2700C2214yes—
99#2692C2214yes—
100#2692C2214yes—
101#2692C2214yes—
102#2691C2214yes—
103#2690C2214yes—
104#2690C2214yes—
105#2689C2214yes—
106#2688C2214yes—
107#2686C2214yes—
108#2681C2214yes—
109#2680C2212yes—
110#2677C2212yes—
111#2677C2214yes—
112#2676C2214yes—
113#2676C2214yes—
114#2674C2214yes—
115#2673C2214yes—
116#2672C2214yes—
117#2662C2214yes—
118#2662C2214yes—
119#2661C2214yes—
120#2653C2214yes—
121#2652C2214yes—
122#2651C2214yes—
123#2648C2214yes—
124#2648C2214yes—
125#2644C2212yes—
126#2641C2212yes—
127#2639C2212yes—
128#2638C2212yes—
129#2630C2214yes—
130#2616C2212yes—
131#2616C2214yes—
132#2615C2211yescharacteristic
133#2615C2211yescharacteristic
134#2615C2212yes—
135#2610C2214yes—
136#2605C2214yes—
137#2603C2214yes—
138#2602C2214yes—
139#2597C2214yes—
140#2592C2212yes—
141#2587C2214yes—
142#2586C2212yes—
143#2582C2212yes—
144#2581C2212yes—
145#2581C2212yes—
146#2578C2214yes—
147#2566C2212yes—
148#2551C2212yes—
149#2548C2212yes—
150#2548C2211yescharacteristic
151#2543C2212yes—
152#2542C2211yescharacteristic
153#2540C2212yes—
154#2538C2212yes—
155#2536C2212yes—
156#2535C2212yes—
157#2532C2214yes—
158#2531C2214yes—
159#2530C2214yes—
160#2527C2214yes—
161#2521C2214yes—
162#2520C2214yes—
163#2504C2211yescharacteristic
164#2500C2212yes—
165#2496C2212yes—
166#2495C2212yes—
167#2494C2212yes—
168#2491C2214yes—
169#2486C2211yescharacteristic
170#2485C2212yes—
171#2477C2214yes—
172#2477C2214yes—
173#2476C2214yes—
174#2467C2214yes—
175#2467C2214yes—
176#2466C2214yes—
177#2465C2214yes—
178#2465C2214yes—
179#2464C2214yes—
180#2461C2214yes—
181#2460C2214yes—
182#2460C2214yes—
183#2456C2214yes—
184#2455C2212yes—
185#2452C2214yes—
186#2450C2214yes—
187#2438C2214yes—
188#2436C2212yes—
189#2436C2212yes—
190#2436C2211yescharacteristic
191#2434C2212yes—
192#2434C2212yes—
193#2434C2214yes—
194#2432C2212yes—
195#2432C2212yes—
196#2432C2212yes—
197#2432C2214yes—
198#2432C2214yes—
199#2431C2212yes—
200#2431C2214yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2428C2212yes—
205#2427C2212yes—
206#2426C2212yes—
207#2426C2212yes—
208#2426C2212yes—
209#2426C2212yes—
210#2423C2212yes—
211#2423C2212yes—
212#2421C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2420C2212yes—
216#2417C2212yes—
217#2415C2212yes—
218#2414C2212yes—
219#2409C2211yescharacteristic
220#2409C2214yes—
221#2409C2212yes—
222#2409C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2407C2214yes—
226#2407C2214yes—
227#2407C2212yes—
228#2407C2214yes—
229#2398C2212yes—
230#2398C2212yes—
231#2398C2212yes—
232#2388C2211yescharacteristic
233#2388C2211yescharacteristic
234#2388C2212yes—
235#2388C2212yes—
236#2388C2212yes—
237#2388C2214yes—
238#2374C2212yes—
239#2373C2214yes—
240#2362C2212yes—
241#2362C2212yes—
242#2360C2212yes—
243#2341C2212yes—
244#2341C2211yescharacteristic
245Q8×C22⋊C4C2212yes—
246Q8×C22⋊C4C2212yes—
247Q8×C22⋊C4C2212yes—
248Q8×C22⋊C4C2212yes—
249#2339C2211yescharacteristic
250#2327C2212yes—
251#2327C2212yes—
252#2326C2212yes—
253#2326C2212yes—
254#2324C2214yes—
255C4×#124C2211yescharacteristic
256C4×#124C2212yes—
257#2295C2211yescharacteristic
258#2295C2212yes—
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C22×#41C2312yes—
266C22×#41C2314yes—
267C22×#41C2311yescharacteristic
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270C23×Q8C2312yes—
271C23×Q8C2312yes—
272#557—44no—
273#556—48no—
274#550—44no—
275D4×Q8—48no—
276D4×Q8—48no—
277#548—48no—
278#548—48no—
279#537—44no—
280#536—48no—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×C4⋊Q8C2314yes—
287C2×#127C2311yescharacteristic
288C2×#127C2312yes—
289C2×#126C2314yes—
290C2×#126C2314yes—
291C2×#126C2314yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2311yescharacteristic
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2314yes—
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#123C2314yes—
304C2×#123C2312yes—
305C2×#123C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×#121C2314yes—
323C2×#121C2311yescharacteristic
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2314yes—
327C2×#121C2311yescharacteristic
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×#117C2314yes—
356C2×#117C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358#401C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#399C2314yes—
373#399C2312yes—
374#399C2314yes—
375#399C2312yes—
376#399C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2311yescharacteristic
425#395C2311yescharacteristic
426#395C2312yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2311yescharacteristic
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2311yescharacteristic
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2312yes—
446#394C2314yes—
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#394C2314yes—
451#394C2312yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2312yes—
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#393C2312yes—
478#393C2312yes—
479#393C2312yes—
480#393C2312yes—
481#393C2312yes—
482#393C2312yes—
483#393C2314yes—
484#393C2311yescharacteristic
485#393C2311yescharacteristic
486#393C2312yes—
487#393C2312yes—
488#393C2312yes—
489#393C2314yes—
490#393C2312yes—
491#393C2312yes—
492#393C2312yes—
493#393C2314yes—
494#393C2312yes—
495#393C2314yes—
496#392C2312yes—
497#392C2312yes—
498#392C2312yes—
499#392C2312yes—
500#392C2312yes—
501#392C2312yes—
502#392C2312yes—
503#392C2314yes—
504#392C2314yes—
505#392C2312yes—
506#392C2311yescharacteristic
507#392C2314yes—
508#392C2311yescharacteristic
509#392C2312yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2312yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2314yes—
528#391C2312yes—
529#391C2312yes—
530#391C2314yes—
531#391C2314yes—
532#391C2314yes—
533#391C2314yes—
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2314yes—
538#390C2312yes—
539#390C2312yes—
540#390C2311yescharacteristic
541#390C2312yes—
542#390C2314yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2314yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2312yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#384C2312yes—
671#384C2312yes—
672#383C2314yes—
673#382C2311yescharacteristic
674#382C2312yes—
675#382C2312yes—
676#382C2312yes—
677#381C2312yes—
678#381C2312yes—
679#381C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2311yescharacteristic
683#380C2312yes—
684#380C2314yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2311yescharacteristic
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718#376C2312yes—
719#376C2312yes—
720#376C2314yes—
721C2×#95C2312yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—24no—
727C2×#41—44no—
728C2×#41—48no—
729C2×#41—42no—
730C2×#41—44no—
731C2×#41—44no—
732C2×#41—42no—
733C2×#41—44no—
734C2×#41—48no—
735C2×#41—44no—
736C2×#41—48no—
737C2×#41—44no—
738C2×#41—48no—
739C2×#41—44no—
740C22×Q8—28no—
741C22×Q8—28no—
742C22×Q8—28no—
743C22×Q8—28no—
744C22×Q8—42no—
745C22×Q8—44no—
746C22×Q8—44no—
747C22×Q8—48no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2411yescharacteristic
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×Q8C2411yescharacteristic
759C22×Q8C2411yescharacteristic
760C22×D4C2411yescharacteristic
761C22×D4C2411yescharacteristic
762C22×D4C2412yes—
763C22×D4C2411yescharacteristic
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C22×D4C2412yes—
768C22×D4C2412yes—
769C22×D4C2414yes—
770C22×D4C2412yes—
771C22×D4C2412yes—
772C22×D4C2414yes—
773C22×D4C2414yes—
774C22×D4C2411yescharacteristic
775C22×D4C2412yes—
776C22×D4C2412yes—
777C22×D4C2412yes—
778C22×D4C2412yes—
779C22×D4C2411yescharacteristic
780C22×D4C2412yes—
781C23×C4C2411yescharacteristic
782C23×C4C2412yes—
783C23×C4C2412yes—
784C23×C4C2411yescharacteristic
785C23×C4C2414yes—
786C23×C4C2412yes—
787C23×C4C2412yes—
788C23×C4C2414yes—
789C23×C4C2412yes—
790C23×C4C2414yes—
791C23×C4C2412yes—
792C23×C4C2414yes—
793C4⋊Q8—28no—
794C4⋊Q8—28no—
795C4⋊Q8—42no—
796C4⋊Q8—48no—
797C4⋊Q8—48no—
798C4⋊Q8—48no—
799#127—44no—
800#127—42no—
801#126—48no—
802#126—48no—
803#126—48no—
804#125—44no—
805#125—48no—
806#124—28no—
807#124—44no—
808#124—42no—
809#124—44no—
810#124—48no—
811#124—44no—
812#124—44no—
813#124—48no—
814#124—48no—
815#123—48no—
816#123—48no—
817#123—44no—
818C22⋊Q8—28no—
819C22⋊Q8—28no—
820C22⋊Q8—28no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—48no—
824C22⋊Q8—48no—
825C22⋊Q8—44no—
826C22⋊Q8—48no—
827C22⋊Q8—48no—
828C22⋊Q8—44no—
829C22⋊Q8—44no—
830C22⋊Q8—44no—
831C22⋊Q8—48no—
832C22⋊Q8—44no—
833C22⋊Q8—44no—
834#121—44no—
835#121—48no—
836#121—48no—
837#121—48no—
838#121—44no—
839#121—44no—
840#121—44no—
841#121—48no—
842#121—42no—
843#121—42no—
844#121—44no—
845#121—44no—
846C4×Q8—28no—
847C4×Q8—24no—
848C4×Q8—44no—
849C4×Q8—42no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×D4—44no—
857C4×D4—48no—
858C4×D4—44no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—44no—
863C4×D4—42no—
864C4×D4—48no—
865C4×D4—48no—
866C4×D4—48no—
867#117—48no—
868#117—44no—
869C2×C4⋊C4—42no—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2411yescharacteristic
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2412yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2414yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996C2×C42C2414yes—
997#95C2411yescharacteristic
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2411yescharacteristic
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2411yescharacteristic
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2411yescharacteristic
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056C24C2512yes—
1057C24C2512yes—
1058C24C2511yescharacteristic
1059C24C2511yescharacteristic
1060C24C2512yes—
1061C24C2512yes—
1062#41—432no—
1063#41—416no—
1064#41—432no—
1065#41—464no—
1066#41—416no—
1067#41—88no—
1068#41—88no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—28no—
1076C2×Q8—28no—
1077C2×Q8—28no—
1078C2×Q8—28no—
1079C2×Q8—22no—
1080C2×Q8—41no—
1081C2×Q8—44no—
1082C2×Q8—42no—
1083C2×Q8—41no—
1084C2×Q8—42no—
1085C2×Q8—41no—
1086C2×Q8—42no—
1087C2×Q8—41no—
1088C2×Q8—44no—
1089C2×Q8—44no—
1090C2×Q8—42no—
1091C2×Q8—42no—
1092C2×Q8—42no—
1093C2×Q8—416no—
1094C2×Q8—432no—
1095C2×Q8—432no—
1096C2×Q8—816no—
1097C2×Q8H(5,𝔽2)18yes—
1098C2×Q8H(5,𝔽2)14yes—
1099C2×D4—24no—
1100C2×D4—22no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—22no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—22no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—42no—
1112C2×D4—42no—
1113C2×D4—42no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—41no—
1118C2×D4—42no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—44no—
1124C2×D4—42no—
1125C2×D4—44no—
1126C2×D4—42no—
1127C2×D4—41no—
1128C2×D4—42no—
1129C2×D4—41no—
1130C2×D4—44no—
1131C2×D4—44no—
1132C2×D4—42no—
1133C2×D4—42no—
1134C2×D4—42no—
1135C2×D4—42no—
1136C2×D4—42no—
1137C2×D4—41no—
1138C2×D4—44no—
1139C2×D4—42no—
1140C2×D4—42no—
1141C2×D4—42no—
1142C2×D4—44no—
1143C2×D4—44no—
1144C2×D4—44no—
1145C2×D4—42no—
1146C2×D4—42no—
1147C2×D4—42no—
1148C2×D4—44no—
1149C2×D4—44no—
1150C2×D4—44no—
1151C2×D4—44no—
1152C2×D4—44no—
1153C22×C4—22no—
1154C22×C4—24no—
1155C22×C4—24no—
1156C22×C4—28no—
1157C22×C4—24no—
1158C22×C4—24no—
1159C22×C4—22no—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—28no—
1163C22×C4—28no—
1164C22×C4—24no—
1165C22×C4—24no—
1166C22×C4—28no—
1167C22×C4—24no—
1168C22×C4—24no—
1169C22×C4—28no—
1170C22×C4—44no—
1171C22×C4—44no—
1172C22×C4—42no—
1173C22×C4—44no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—44no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—44no—
1180C22×C4—44no—
1181C22×C4—42no—
1182C22×C4—42no—
1183C22×C4—42no—
1184C22×C4C2512yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2512yes—
1187C22×C4C2512yes—
1188C22×C4C2512yes—
1189C22×C4C2512yes—
1190C22×C4C2514yes—
1191C22×C4C2512yes—
1192C22×C4C2514yes—
1193C22×C4C2514yes—
1194C22×C4C2511yescharacteristic
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2512yes—
1198C22×C4C2512yes—
1199C22×C4C2514yes—
1200C22×C4C2512yes—
1201C22×C4C2511yescharacteristic
1202C22×C4C2514yes—
1203C22×C4C2514yes—
1204C22×C4C2512yes—
1205C22×C4C2511yescharacteristic
1206C22×C4C2511yescharacteristic
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—28no—
1211C4⋊C4—24no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—28no—
1215C4⋊C4—22no—
1216C4⋊C4—24no—
1217C4⋊C4—28no—
1218C4⋊C4—28no—
1219C4⋊C4—28no—
1220C4⋊C4—28no—
1221C4⋊C4—28no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—42no—
1229C4⋊C4—41no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
1243C4⋊C4—42no—
1244C4⋊C4—42no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—42no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—44no—
1268C22⋊C4—42no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—44no—
1275C22⋊C4—42no—
1276C22⋊C4—44no—
1277C22⋊C4—42no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—42no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—42no—
1311C22⋊C4—42no—
1312C22⋊C4—42no—
1313C22⋊C4—42no—
1314C22⋊C4—44no—
1315C22⋊C4—44no—
1316C42—28no—
1317C42—24no—
1318C42—24no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—22no—
1324C42—24no—
1325C42—41no—
1326C42—44no—
1327C42—42no—
1328C42—44no—
1329C42—44no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C23—24no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—24no—
1343C23—22no—
1344C23—22no—
1345C23—21no—
1346C23—21no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—21no—
1351C23—21no—
1352C23—22no—
1353C23—22no—
1354C23—22no—
1355C23—22no—
1356C23—22no—
1357C23—21no—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—22no—
1362C23—24no—
1363C23—24no—
1364C23—21no—
1365C23—22no—
1366C23—22no—
1367C23—22no—
1368C23C2611yescharacteristic
1369Q8—216no—
1370Q8—28no—
1371Q8—416no—
1372Q8—48no—
1373Q8—44no—
1374Q8—44no—
1375Q8—48no—
1376Q8—88no—
1377Q8—84no—
1378Q8—82no—
1379D4—48no—
1380D4—416no—
1381D4—48no—
1382D4—48no—
1383D4—44no—
1384D4—48no—
1385D4—44no—
1386D4—44no—
1387D4—82no—
1388D4—84no—
1389D4—84no—
1390D4—84no—
1391D4—88no—
1392D4—88no—
1393D4—84no—
1394D4—82no—
1395D4—84no—
1396D4—162no—
1397D4—162no—
1398D4—162no—
1399D4—164no—
1400C2×C4—21no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—24no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—24no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—24no—
1439C2×C4—22no—
1440C2×C4—22no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—24no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—24no—
1454C2×C4—22no—
1455C2×C4—24no—
1456C2×C4—22no—
1457C2×C4—24no—
1458C2×C4—416no—
1459C2×C4—48no—
1460C2×C4—48no—
1461C2×C4—416no—
1462C2×C4—48no—
1463C2×C4—44no—
1464C2×C4—48no—
1465C2×C4—44no—
1466C2×C4—88no—
1467C2×C4—84no—
1468C2×C4—88no—
1469C2×C4—162no—
1470C2×C4C2×H(5,𝔽2)18yes—
1471C2×C4C2×H(5,𝔽2)14yes—
1472C2×C4C2×H(5,𝔽2)14yes—
1473C2×C4C2×H(5,𝔽2)12yes—
1474C2×C4#58512yes—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—44no—
1479C22—42no—
1480C22—42no—
1481C22—42no—
1482C22—44no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22—41no—
1487C22—41no—
1488C22—42no—
1489C22—41no—
1490C22—42no—
1491C22—41no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—44no—
1496C22—42no—
1497C22—42no—
1498C22—44no—
1499C22—42no—
1500C22—42no—
1501C22—42no—
1502C22—42no—
1503C22—41no—
1504C22—42no—
1505C22—42no—
1506C22—42no—
1507C22—41no—
1508C22—42no—
1509C22C22×H(5,𝔽2)12yes—
1510C22C22×H(5,𝔽2)11yescharacteristic
1511C22C2×#58511yescharacteristic
1512C222−1+611yescharacteristic
1513C222−1+612yes—
1514C4—22no—
1515C4—24no—
1516C4—28no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—44no—
1521C4—42no—
1522C4—42no—
1523C4—41no—
1524C4—44no—
1525C4—42no—
1526C4—44no—
1527C4—42no—
1528C4—44no—
1529C4—42no—
1530C4—42no—
1531C4—41no—
1532C4—42no—
1533C4—41no—
1534C4—42no—
1535C4—44no—
1536C4#353214yes—
1537C2—81no—
1538C2—82no—
1539C2—82no—
1540C2—81no—
1541C2—82no—
1542C2—82no—
1543C2C2×#353211yescharacteristic
1544C2#6291911yescharacteristic
1545C2#6292212yes—
1546C2#6304412yes—
1547C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59946C2semidirect
2. #59752C2semidirect
3. #58943C2semidirect
4. #58919C2semidirect
5. #58242C2semidirect
6. #57019C2semidirect
7. #56675C2semidirect
8. #53064C2semidirect
9. #53007C2semidirect
10. #52424C2semidirect
11. #52420C2semidirect
12. #47541C2semidirect
13. #45336C2semidirect
14. #45321C2semidirect
15. #45307C2semidirect
16. #45268C2semidirect
17. #45245C2semidirect
18. #42985C2semidirect
19. #42900C2semidirect
20. #42893C2semidirect
21. #42858C2semidirect
22. #42796C2semidirect
23. #42109C2semidirect
24. #42043C2semidirect
25. #39954C2semidirect
26. #39174C2semidirect
27. #36694C2semidirect
28. #35757C2semidirect
29. #35687C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#597522
#589432
#589192
#582422
#570192
#566752
#530642
#530072
#524242
#524202
#475412
#453362
#453212
#453072
#452682
#452452
#429852
#429002
#428932
#428582
#427962
#421092
#420432
#399542
#391742
#366942
#357572
#356872