Finite Group Databasebeta

← #7657660

Subgroups — #7657660

Order 512.

5210 conjugacy classes of subgroups.

The subgroup lattice has 1531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42056C214yesmaximal, complemented
2#42041C214yesmaximal, complemented
3#41978C212yesmaximal, complemented
4#41977C212yesmaximal, complemented
5#41975C214yesmaximal, complemented
6#40967C214yesmaximal, complemented
7#40951C214yesmaximal, complemented
8#39811C212yesmaximal, complemented
9#39808C212yesmaximal, complemented
10#37774C212yesmaximal, complemented
11#37772C212yesmaximal, complemented
12#37701C212yesmaximal, complemented
13#37699C212yesmaximal, complemented
14#37616C211yesmaximal, characteristic, complemented
15#37594C212yesmaximal, complemented
16#37587C212yesmaximal, complemented
17#37559C211yesmaximal, characteristic, complemented
18#36149C212yesmaximal, complemented
19#36141C212yesmaximal, complemented
20#35698C214yesmaximal, complemented
21#35690C212yesmaximal, complemented
22#35684C212yesmaximal, complemented
23#35318C212yesmaximal, complemented
24#35304C211yesmaximal, characteristic, complemented
25#34641C211yesmaximal, characteristic, complemented
26#34624C212yesmaximal, complemented
27#34232C211yesmaximal, characteristic, complemented
28#34226C211yesmaximal, characteristic, complemented
29#34149C211yesmaximal, characteristic, complemented
30C2×#542C2212yes—
31C2×#541C2212yes—
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#532C2212yes—
35C2×#532C2212yes—
36C2×#532C2212yes—
37C2×#529C2211yescharacteristic
38C2×#529C2212yes—
39#2862C2212yes—
40#2861C2212yes—
41#2857C2212yes—
42#2857C2212yes—
43#2851C2212yes—
44#2850C2212yes—
45#2837C2214yes—
46#2836C2214yes—
47#2829C2214yes—
48#2828C2214yes—
49#2816C2212yes—
50#2815C2212yes—
51#2813C2214yes—
52#2803C2214yes—
53#2803C2214yes—
54#2798C2214yes—
55#2797C2214yes—
56#2773C2214yes—
57#2754C2214yes—
58#2754C2214yes—
59#2733C2214yes—
60#2730C2214yes—
61#2727C2214yes—
62#2721C2214yes—
63#2714C2214yes—
64#2714C2214yes—
65#2714C2214yes—
66#2711C2214yes—
67#2711C2214yes—
68#2710C2214yes—
69#2705C2214yes—
70#2703C2214yes—
71#2694C2214yes—
72#2691C2214yes—
73#2681C2214yes—
74#2676C2214yes—
75#2673C2214yes—
76#2667C2214yes—
77#2662C2214yes—
78#2662C2214yes—
79#2661C2214yes—
80#2661C2214yes—
81#2661C2214yes—
82#2661C2214yes—
83#2660C2212yes—
84#2658C2212yes—
85#2658C2211yescharacteristic
86#2658C2211yescharacteristic
87#2657C2211yescharacteristic
88#2657C2212yes—
89#2657C2211yescharacteristic
90#2656C2214yes—
91#2656C2212yes—
92#2656C2212yes—
93#2654C2214yes—
94#2651C2214yes—
95#2649C2214yes—
96#2648C2214yes—
97#2647C2212yes—
98#2641C2212yes—
99#2640C2212yes—
100#2636C2214yes—
101#2635C2214yes—
102#2633C2212yes—
103#2631C2212yes—
104#2630C2214yes—
105#2621C2212yes—
106#2620C2212yes—
107#2620C2212yes—
108#2620C2212yes—
109#2620C2212yes—
110#2619C2212yes—
111#2619C2212yes—
112#2619C2212yes—
113#2612C2214yes—
114#2607C2214yes—
115#2606C2212yes—
116#2605C2212yes—
117#2603C2214yes—
118#2602C2214yes—
119#2600C2214yes—
120#2592C2212yes—
121#2589C2214yes—
122#2575C2214yes—
123#2569C2212yes—
124#2568C2211yescharacteristic
125#2566C2212yes—
126#2559C2214yes—
127#2556C2214yes—
128#2556C2214yes—
129#2553C2214yes—
130#2553C2214yes—
131#2549C2212yes—
132#2548C2211yescharacteristic
133#2544C2212yes—
134#2542C2211yescharacteristic
135#2541C2211yescharacteristic
136#2540C2212yes—
137#2535C2214yes—
138#2522C2214yes—
139#2521C2214yes—
140#2521C2214yes—
141#2519C2214yes—
142#2519C2214yes—
143#2517C2214yes—
144#2516C2214yes—
145#2479C2214yes—
146#2476C2214yes—
147#2468C2214yes—
148#2467C2214yes—
149#2467C2214yes—
150#2467C2214yes—
151#2467C2214yes—
152#2466C2214yes—
153#2464C2214yes—
154#2464C2214yes—
155#2460C2214yes—
156#2460C2214yes—
157#2459C2214yes—
158#2459C2214yes—
159#2457C2214yes—
160#2457C2214yes—
161#2456C2214yes—
162#2456C2214yes—
163#2455C2214yes—
164#2454C2214yes—
165#2450C2214yes—
166#2448C2212yes—
167#2448C2212yes—
168#2447C2212yes—
169#2447C2212yes—
170#2447C2214yes—
171#2446C2212yes—
172#2446C2212yes—
173#2445C2212yes—
174#2445C2212yes—
175#2441C2214yes—
176#2438C2214yes—
177#2431C2214yes—
178#2429C2212yes—
179#2429C2212yes—
180#2428C2212yes—
181#2428C2212yes—
182#2427C2214yes—
183#2427C2212yes—
184#2427C2212yes—
185#2426C2212yes—
186#2426C2212yes—
187#2425C2214yes—
188#2420C2214yes—
189#2420C2214yes—
190#2407C2212yes—
191#2407C2212yes—
192#2407C2214yes—
193#2407C2212yes—
194#2407C2212yes—
195#2407C2214yes—
196#2397C2212yes—
197#2397C2212yes—
198#2397C2214yes—
199#2392C2214yes—
200#2392C2214yes—
201#2388C2214yes—
202#2388C2214yes—
203#2373C2212yes—
204#2373C2212yes—
205#2372C2211yescharacteristic
206#2372C2211yescharacteristic
207#2371C2211yescharacteristic
208#2371C2211yescharacteristic
209#2368C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2366C2212yes—
213#2365C2212yes—
214#2364C2214yes—
215#2364C2212yes—
216#2363C2214yes—
217#2363C2214yes—
218#2359C2214yes—
219#2359C2212yes—
220#2359C2212yes—
221#2357C2212yes—
222#2353C2212yes—
223#2353C2212yes—
224#2349C2214yes—
225#2349C2212yes—
226#2341C2211yescharacteristic
227#2341C2212yes—
228#2341C2211yescharacteristic
229#2339C2212yes—
230#2339C2211yescharacteristic
231#2339C2214yes—
232#2339C2211yescharacteristic
233#2333C2214yes—
234#2331C2212yes—
235#2330C2212yes—
236#2327C2212yes—
237#2326C2212yes—
238#2324C2214yes—
239#2319C2212yes—
240#2319C2212yes—
241C4×C4⋊Q8C2212yes—
242C4×#127C2212yes—
243C4×#127C2212yes—
244C4×#124C2212yes—
245C4×#124C2212yes—
246C4×#124C2212yes—
247#2298C2212yes—
248#2295C2212yes—
249#2290C2212yes—
250#2290C2212yes—
251#2285C2211yescharacteristic
252#2283C2211yescharacteristic
253#2275C2212yes—
254#2275C2212yes—
255C42×D4C2212yes—
256C4×#117C2212yes—
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262C22×#41C2314yes—
263#542—48no—
264#541—48no—
265#532—28no—
266#532—28no—
267#532—48no—
268#532—48no—
269#532—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#127C2312yes—
280#529—28no—
281#529—48no—
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2311yescharacteristic
295C2×#124C2312yes—
296C2×#124C2311yescharacteristic
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2311yescharacteristic
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2314yes—
362C2×#117C2312yes—
363C22×C42C2312yes—
364C22×C42C2312yes—
365C22×C42C2311yescharacteristic
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2312yes—
375#399C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2312yes—
383#399C2314yes—
384#399C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#395C2314yes—
419#395C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2312yes—
464#392C2314yes—
465#392C2312yes—
466#392C2314yes—
467#392C2312yes—
468#392C2314yes—
469#392C2312yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2314yes—
497#390C2314yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#390C2314yes—
503#390C2312yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#390C2314yes—
511#390C2312yes—
512#390C2314yes—
513#390C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2312yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#386C2314yes—
615#386C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2312yes—
635#383C2312yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#381C2312yes—
643#381C2312yes—
644#381C2312yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652#380C2312yes—
653#380C2311yescharacteristic
654#380C2312yes—
655#380C2314yes—
656#380C2311yescharacteristic
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2311yescharacteristic
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703#376C2311yescharacteristic
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2311yescharacteristic
708#376C2311yescharacteristic
709#376C2311yescharacteristic
710#376C2312yes—
711#376C2311yescharacteristic
712#376C2311yescharacteristic
713C2×#95C2311yescharacteristic
714C2×#95C2312yes—
715C2×#95C2314yes—
716C2×#95C2312yes—
717C2×#95C2311yescharacteristic
718C2×#95C2312yes—
719C43C2312yes—
720C43C2312yes—
721C2×#41—28no—
722C2×#41—24no—
723C2×#41—24no—
724C2×#41—48no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—44no—
728C2×#41—44no—
729C2×#41—48no—
730C2×#41—84no—
731C22×Q8C2411yescharacteristic
732C22×Q8C2412yes—
733C22×Q8C2411yescharacteristic
734C22×Q8C2411yescharacteristic
735C22×Q8C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2412yes—
744C22×D4C2414yes—
745C22×D4C2411yescharacteristic
746C22×D4C2412yes—
747C22×D4C2414yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2414yes—
751C22×D4C2414yes—
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2414yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2411yescharacteristic
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C4⋊Q8—24no—
772C4⋊Q8—24no—
773C4⋊Q8—28no—
774C4⋊Q8—28no—
775C4⋊Q8—44no—
776#127—24no—
777#127—24no—
778#127—28no—
779#127—44no—
780#127—82no—
781#126—28no—
782#126—48no—
783#126—48no—
784#126—48no—
785#126—48no—
786#125—24no—
787#125—28no—
788#125—48no—
789#125—48no—
790#124—24no—
791#124—24no—
792#124—24no—
793#124—28no—
794#124—28no—
795#124—28no—
796#124—48no—
797#124—44no—
798#124—44no—
799#124—48no—
800#124—82no—
801#123—28no—
802#123—48no—
803#123—48no—
804#123—48no—
805#123—84no—
806C22⋊Q8—24no—
807C22⋊Q8—48no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812C22⋊Q8—84no—
813#121—24no—
814#121—28no—
815#121—28no—
816#121—28no—
817#121—28no—
818#121—48no—
819#121—48no—
820#121—48no—
821#121—44no—
822#121—44no—
823#121—44no—
824#121—48no—
825#121—48no—
826#121—48no—
827#121—44no—
828#121—84no—
829C4×Q8—24no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—44no—
834C4×D4—28no—
835C4×D4—24no—
836C4×D4—28no—
837C4×D4—28no—
838C4×D4—28no—
839C4×D4—28no—
840C4×D4—44no—
841C4×D4—48no—
842C4×D4—48no—
843C4×D4—44no—
844C4×D4—48no—
845C4×D4—48no—
846C4×D4—48no—
847C4×D4—44no—
848C4×D4—44no—
849C4×D4—44no—
850C4×D4—48no—
851C4×D4—48no—
852C4×D4—44no—
853C4×D4—48no—
854C4×D4—48no—
855C4×D4—84no—
856C4×D4—84no—
857#117—28no—
858#117—28no—
859#117—44no—
860#117—48no—
861#117—82no—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2414yes—
965C2×C42—28no—
966C2×C42—28no—
967C2×C42#4118yescomplemented
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996#95C2411yescharacteristic
997#95C2411yescharacteristic
998#95C2412yes—
999#95C2411yescharacteristic
1000#95C2412yes—
1001#95C2411yescharacteristic
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2411yescharacteristic
1007#95C2412yes—
1008#95C2411yescharacteristic
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2411yescharacteristic
1017#95C2412yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054C24C2512yes—
1055C24C2512yes—
1056C24C2514yes—
1057C24C2512yes—
1058C24C2511yescharacteristic
1059#41—88no—
1060#41—816no—
1061#41—88no—
1062#41—832no—
1063C2×Q8—22no—
1064C2×Q8—24no—
1065C2×Q8—22no—
1066C2×Q8—22no—
1067C2×Q8—24no—
1068C2×Q8—24no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—28no—
1072C2×Q8—44no—
1073C2×Q8—41no—
1074C2×Q8—41no—
1075C2×Q8—44no—
1076C2×D4—24no—
1077C2×D4—28no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—22no—
1084C2×D4—24no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—28no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—28no—
1092C2×D4—24no—
1093C2×D4—24no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—44no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4—42no—
1119C2×D4—41no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—41no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—44no—
1128C2×D4—44no—
1129C2×D4—44no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—24no—
1136C22×C4—28no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—24no—
1140C22×C4—24no—
1141C22×C4—24no—
1142C22×C4—28no—
1143C22×C4—28no—
1144C22×C4—28no—
1145C22×C4—42no—
1146C22×C4—41no—
1147C22×C4—41no—
1148C22×C4—42no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—42no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—42no—
1163C22×C4—42no—
1164C22×C4—42no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4C2×#4114yes—
1169C22×C4C2×#4114yes—
1170C22×C4C2×#4114yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2514yes—
1175C22×C4C2514yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2514yes—
1185C22×C4C2512yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2512yes—
1193C22×C4C2512yes—
1194C22×C4C2511yescharacteristic
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—22no—
1202C4⋊C4—24no—
1203C4⋊C4—22no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—28no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—28no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—28no—
1248C22⋊C4—28no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—28no—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—28no—
1257C22⋊C4—24no—
1258C22⋊C4—24no—
1259C22⋊C4—28no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—42no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—44no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—44no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—24no—
1305C42—24no—
1306C42—24no—
1307C42—24no—
1308C42—42no—
1309C42—42no—
1310C42—42no—
1311C42—44no—
1312C42—42no—
1313C42—42no—
1314C42—44no—
1315C42—42no—
1316C42—42no—
1317C42—42no—
1318C42—44no—
1319C42—44no—
1320C42—44no—
1321C42C2×#4114yes—
1322C42C2×#4114yes—
1323C42C2×#4114yes—
1324C42C2×#4114yes—
1325C42H(5,𝔽2)18yes—
1326C23—22no—
1327C23—22no—
1328C23—21no—
1329C23—21no—
1330C23—22no—
1331C23—24no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—24no—
1336C23—24no—
1337C23—24no—
1338C23—24no—
1339C23—22no—
1340C23—24no—
1341C23—22no—
1342C23—24no—
1343C23—24no—
1344C23—22no—
1345C23—24no—
1346C23—24no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23—22no—
1353C23—24no—
1354C23C22×#4112yes—
1355C23C2611yescharacteristic
1356Q8—44no—
1357Q8—48no—
1358Q8—44no—
1359Q8—82no—
1360Q8—88no—
1361D4—48no—
1362D4—416no—
1363D4—48no—
1364D4—48no—
1365D4—416no—
1366D4—48no—
1367D4—44no—
1368D4—48no—
1369D4—44no—
1370D4—82no—
1371D4—84no—
1372D4—84no—
1373D4—88no—
1374D4—84no—
1375D4—88no—
1376D4—88no—
1377D4—88no—
1378D4—88no—
1379D4—88no—
1380D4—164no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—21no—
1394C2×C4—28no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—24no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—24no—
1437C2×C4—22no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—48no—
1441C2×C4—48no—
1442C2×C4—88no—
1443C2×C4—84no—
1444C2×C4—84no—
1445C2×C4—84no—
1446C2×C4—84no—
1447C2×C4—88no—
1448C2×C4—84no—
1449C2×C4—88no—
1450C2×C4—88no—
1451C2×C4—164no—
1452C2×C4C22×#4112yes—
1453C2×C4C22×#4112yes—
1454C2×C4C22×#4112yes—
1455C2×C4C22×#4112yes—
1456C2×C4C22×#4112yes—
1457C2×C4C22×#4112yes—
1458C2×C4C2×H(5,𝔽2)14yes—
1459C2×C4C2×H(5,𝔽2)14yes—
1460C2×C4C2×H(5,𝔽2)14yes—
1461C2×C4#58514yes—
1462C22—22no—
1463C22—22no—
1464C22—22no—
1465C22—42no—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—44no—
1470C22—42no—
1471C22—44no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—42no—
1476C22—44no—
1477C22—44no—
1478C22—44no—
1479C22—44no—
1480C22—42no—
1481C22—42no—
1482C22—44no—
1483C22—44no—
1484C22—44no—
1485C22—44no—
1486C22—42no—
1487C22—42no—
1488C22—44no—
1489C22—42no—
1490C22—42no—
1491C22C23×#4111yescharacteristic
1492C22C22×H(5,𝔽2)12yes—
1493C22C2×#58512yes—
1494C22H(7,𝔽2)11yescharacteristic
1495C222−1+611yescharacteristic
1496C4—22no—
1497C4—22no—
1498C4—22no—
1499C4—24no—
1500C4—24no—
1501C4—24no—
1502C4—22no—
1503C4—22no—
1504C4—42no—
1505C4—42no—
1506C4—44no—
1507C4—42no—
1508C4—42no—
1509C4—44no—
1510C4—44no—
1511C4—42no—
1512C4—44no—
1513C4—42no—
1514C4—42no—
1515C4—42no—
1516C4—42no—
1517C4—44no—
1518C4—42no—
1519C4#350814yes—
1520C2—42no—
1521C2—82no—
1522C2—84no—
1523C2—82no—
1524C2—82no—
1525C2#6268611yescharacteristic
1526C2C2×#350811yescharacteristic
1527C2#6285611yescharacteristic
1528C2#6292412yes—
1529C2#6292512yes—
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. #42056C2semidirect
2. #42041C2semidirect
3. #41978C2semidirect
4. #41977C2semidirect
5. #41975C2semidirect
6. #40967C2semidirect
7. #40951C2semidirect
8. #39811C2semidirect
9. #39808C2semidirect
10. #37774C2semidirect
11. #37772C2semidirect
12. #37701C2semidirect
13. #37699C2semidirect
14. #37616C2semidirect
15. #37594C2semidirect
16. #37587C2semidirect
17. #37559C2semidirect
18. #36149C2semidirect
19. #36141C2semidirect
20. #35698C2semidirect
21. #35690C2semidirect
22. #35684C2semidirect
23. #35318C2semidirect
24. #35304C2semidirect
25. #34641C2semidirect
26. #34624C2semidirect
27. #34232C2semidirect
28. #34226C2semidirect
29. #34149C2semidirect
967. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#420562
#420412
#419782
#419772
#419752
#409672
#409512
#398112
#398082
#377742
#377722
#377012
#376992
#376162
#375942
#375872
#375592
#361492
#361412
#356982
#356902
#356842
#353182
#353042
#346412
#346242
#342322
#342262
#341492