Finite Group Databasebeta

← #7658014

Subgroups — #7658014

Order 512.

4652 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42321C214yesmaximal, complemented
2#41397C214yesmaximal, complemented
3#41025C214yesmaximal, complemented
4#41017C214yesmaximal, complemented
5#41014C214yesmaximal, complemented
6#41002C214yesmaximal, complemented
7#39502C211yesmaximal, characteristic, complemented
8#39373C211yesmaximal, characteristic, complemented
9#39273C212yesmaximal, complemented
10#39271C212yesmaximal, complemented
11#39188C211yesmaximal, characteristic, complemented
12#39186C211yesmaximal, characteristic, complemented
13#37961C212yesmaximal, complemented
14#37774C212yesmaximal, complemented
15#37634C211yesmaximal, characteristic, complemented
16#37550C211yesmaximal, characteristic
17#37519C212yesmaximal, complemented
18#37512C212yesmaximal, complemented
19#36536C211yesmaximal, characteristic, complemented
20#36509C211yesmaximal, characteristic, complemented
21#36209C211yesmaximal, characteristic, complemented
22#36135C211yesmaximal, characteristic, complemented
23#35829C214yesmaximal, complemented
24#35755C214yesmaximal, complemented
25#35345C211yesmaximal, characteristic, complemented
26#35309C212yesmaximal, complemented
27#34631C211yesmaximal, characteristic, complemented
28#34614C212yesmaximal, complemented
29#34235C211yesmaximal, characteristic, complemented
30#34224C211yesmaximal, characteristic, complemented
31#34141C211yesmaximal, characteristic, complemented
32C2×#541C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#529C2212yes—
37C2×C4×#41C2212yes—
38#2864C2211yescharacteristic
39#2864C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2857C2212yes—
43#2855C2212yes—
44#2855C2212yes—
45#2851C2212yes—
46#2831C2214yes—
47#2829C2214yes—
48#2827C2214yes—
49#2827C2214yes—
50#2821C2212yes—
51#2818C2212yes—
52#2816C2212yes—
53#2816C2212yes—
54#2808C2214yes—
55#2807C2214yes—
56#2803C2214yes—
57#2803C2214yes—
58#2802C2214yes—
59#2800C2214yes—
60#2796C2214yes—
61#2794C2214yes—
62#2788C2214yes—
63#2786C2214yes—
64#2783C2214yes—
65#2777C2214yes—
66#2775C2214yes—
67#2773C2214yes—
68#2773C2214yes—
69#2767C2214yes—
70#2752C2214yes—
71#2751C2214yes—
72#2727C2214yes—
73#2727C2214yes—
74#2726C2214yes—
75#2721C2214yes—
76#2705C2214yes—
77#2694C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2664C2214yes—
81#2663C2214yes—
82#2661C2212yes—
83#2661C2212yes—
84#2660C2212yes—
85#2660C2211yescharacteristic
86#2658C2211yescharacteristic
87#2651C2214yes—
88#2651C2214yes—
89#2648C2214yes—
90#2648C2214yes—
91#2642C2211yescharacteristic
92#2641C2212yes—
93#2640C2211yescharacteristic
94#2637C2214yes—
95#2636C2214yes—
96#2636C2214yes—
97#2635C2214yes—
98#2632C2214yes—
99#2630C2214yes—
100#2630C2214yes—
101#2630C2214yes—
102#2629C2212yes—
103#2629C2212yes—
104#2629C2212yes—
105#2625C2212yes—
106#2624C2212yes—
107#2621C2211yescharacteristic
108#2621C2211yescharacteristic
109#2620C2211yescharacteristic
110#2620C2212yes—
111#2620C2211yescharacteristic
112#2616C2212yes—
113#2616C2212yes—
114#2616C2212yes—
115#2615C2212yes—
116#2610C2214yes—
117#2608C2214yes—
118#2608C2214yes—
119#2606C2214yes—
120#2606C2214yes—
121#2602C2214yes—
122#2601C2214yes—
123#2600C2214yes—
124#2599C2214yes—
125#2596C2214yes—
126#2590C2214yes—
127#2580C2214yes—
128#2578C2214yes—
129#2577C2214yes—
130#2575C2214yes—
131#2574C2214yes—
132#2570C2214yes—
133#2563C2212yes—
134#2562C2212yes—
135#2554C2214yes—
136#2553C2214yes—
137#2542C2212yes—
138#2540C2212yes—
139#2536C2211yescharacteristic
140#2536C2211yescharacteristic
141#2536C2211yescharacteristic
142#2536C2211yescharacteristic
143#2536C2211yescharacteristic
144#2536C2211yescharacteristic
145#2535C2211yescharacteristic
146#2535C2211yescharacteristic
147#2529C2214yes—
148#2526C2214yes—
149#2525C2214yes—
150#2524C2214yes—
151#2519C2214yes—
152#2519C2214yes—
153#2518C2214yes—
154#2518C2214yes—
155#2518C2214yes—
156#2518C2214yes—
157#2517C2214yes—
158#2516C2214yes—
159#2516C2214yes—
160#2515C2214yes—
161#2508C2214yes—
162#2500C2214yes—
163#2497C2212yes—
164#2496C2212yes—
165#2495C2212yes—
166#2495C2212yes—
167#2495C2214yes—
168#2490C2212yes—
169#2489C2212yes—
170#2489C2212yes—
171#2489C2212yes—
172#2485C2214yes—
173#2479C2214yes—
174#2478C2214yes—
175#2469C2214yes—
176#2468C2214yes—
177#2468C2214yes—
178#2467C2214yes—
179#2466C2214yes—
180#2466C2214yes—
181#2466C2214yes—
182#2462C2214yes—
183#2462C2214yes—
184#2460C2214yes—
185#2460C2214yes—
186#2458C2214yes—
187#2455C2214yes—
188#2454C2214yes—
189#2441C2214yes—
190#2429C2212yes—
191#2429C2212yes—
192#2427C2212yes—
193#2426C2212yes—
194#2423C2212yes—
195#2423C2212yes—
196#2423C2212yes—
197#2422C2212yes—
198#2396C2214yes—
199#2396C2214yes—
200#2395C2214yes—
201#2392C2214yes—
202#2392C2214yes—
203#2392C2214yes—
204#2373C2214yes—
205#2373C2214yes—
206#2370C2212yes—
207#2367C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2366C2212yes—
211#2365C2212yes—
212#2365C2212yes—
213#2365C2212yes—
214#2364C2212yes—
215#2364C2212yes—
216#2361C2212yes—
217#2361C2212yes—
218#2360C2214yes—
219#2359C2214yes—
220#2357C2211yescharacteristic
221#2356C2211yescharacteristic
222#2356C2211yescharacteristic
223#2356C2211yescharacteristic
224#2353C2214yes—
225#2351C2211yescharacteristic
226#2351C2211yescharacteristic
227#2351C2211yescharacteristic
228#2349C2211yescharacteristic
229#2347C2212yes—
230#2346C2214yes—
231#2343C2212yes—
232#2343C2212yes—
233#2343C2212yes—
234#2336C2214yes—
235#2330C2212yes—
236#2330C2212yes—
237#2323C2212yes—
238#2323C2212yes—
239#2322C2214yes—
240#2320C2212yes—
241#2318C2212yes—
242#2314C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#124C2211yescharacteristic
246C4×#124C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253#2297C2212yes—
254#2293C2211yescharacteristic
255#2293C2211yescharacteristic
256#2290C2212yes—
257#2290C2212yes—
258#2285C2212yes—
259#2283C2211yescharacteristic
260#2283C2211yescharacteristic
261#2276C2212yes—
262#2275C2212yes—
263C42×D4C2211yescharacteristic
264C42×D4C2211yescharacteristic
265C4×#117C2211yescharacteristic
266C2×C4×C4⋊C4C2211yescharacteristic
267C22×#41C2312yes—
268#541—48no—
269#533—28no—
270#532—28no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×#127C2311yescharacteristic
277#529—28no—
278#529—48no—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#125C2311yescharacteristic
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#123C2312yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2311yescharacteristic
300C2×C22⋊Q8C2311yescharacteristic
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×#121C2311yescharacteristic
308C2×#121C2311yescharacteristic
309C2×#121C2311yescharacteristic
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2312yes—
313C4×#41—48no—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2311yescharacteristic
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2311yescharacteristic
349C22×C4⋊C4C2312yes—
350C22×C42C2312yes—
351C22×C42C2312yes—
352C22×C42C2312yes—
353C22×C42C2311yescharacteristic
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2312yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#392C2314yes—
461#392C2312yes—
462#392C2314yes—
463#392C2312yes—
464#392C2314yes—
465#392C2314yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2311yescharacteristic
469#391C2311yescharacteristic
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2311yescharacteristic
478#390C2314yes—
479#390C2312yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2311yescharacteristic
488#390C2312yes—
489#390C2314yes—
490#390C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
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#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#386C2312yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2312yes—
615#386C2312yes—
616#386C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2312yes—
629#385C2312yes—
630#385C2312yes—
631#385C2314yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2314yes—
636#384C2312yes—
637#383C2312yes—
638#383C2312yes—
639#383C2312yes—
640#383C2312yes—
641#383C2314yes—
642#383C2312yes—
643#383C2314yes—
644#382C2314yes—
645#382C2311yescharacteristic
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2311yescharacteristic
653#382C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2311yescharacteristic
656#382C2311yescharacteristic
657#382C2314yes—
658#381C2312yes—
659#381C2312yes—
660#381C2314yes—
661#381C2312yes—
662#381C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728#376C2312yes—
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731#376C2312yes—
732#376C2312yes—
733#376C2312yes—
734#376C2312yes—
735C2×#95C2311yescharacteristic
736C2×#95C2311yescharacteristic
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—28no—
741C2×#41—44no—
742C2×#41—44no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2411yescharacteristic
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×D4C2411yescharacteristic
749C22×D4C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C4⋊Q8—24no—
772C4⋊Q8—24no—
773C4⋊Q8—24no—
774C4⋊Q8—24no—
775C4⋊Q8—42no—
776#127—24no—
777#126—28no—
778#126—48no—
779#126—48no—
780#126—48no—
781#126—48no—
782#125—24no—
783#125—28no—
784#125—28no—
785#125—44no—
786#125—48no—
787#125—48no—
788#124—24no—
789#124—28no—
790#124—24no—
791#124—42no—
792#123—28no—
793#123—48no—
794#123—48no—
795C22⋊Q8—24no—
796C22⋊Q8—24no—
797C22⋊Q8—24no—
798C22⋊Q8—28no—
799C22⋊Q8—44no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803C22⋊Q8—44no—
804C22⋊Q8—44no—
805#121—24no—
806#121—28no—
807#121—24no—
808#121—24no—
809#121—44no—
810#121—44no—
811C4×Q8—24no—
812C4×Q8—28no—
813C4×Q8—24no—
814C4×Q8—24no—
815C4×Q8—48no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—24no—
823C4×D4—24no—
824C4×D4—24no—
825C4×D4—28no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—48no—
830C4×D4—48no—
831C4×D4—44no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—44no—
837C4×D4—48no—
838#117—28no—
839#117—28no—
840#117—24no—
841#117—28no—
842#117—48no—
843#117—42no—
844#117—44no—
845#117—48no—
846C2×C4⋊C4—44no—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C42—28no—
959C2×C42—44no—
960C2×C42—44no—
961C2×C42#4118yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2414yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2411yescharacteristic
996#95C2411yescharacteristic
997#95C2411yescharacteristic
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
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—
1056#95C2414yes—
1057#95C2414yes—
1058C24C2512yes—
1059C24C2512yes—
1060C24C2512yes—
1061C24C2511yescharacteristic
1062#41—432no—
1063C2×Q8—22no—
1064C2×Q8—24no—
1065C2×Q8—22no—
1066C2×Q8—22no—
1067C2×Q8—24no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—22no—
1074C2×Q8—42no—
1075C2×Q8—44no—
1076C2×Q8—42no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—22no—
1081C2×D4—22no—
1082C2×D4—22no—
1083C2×D4—24no—
1084C2×D4—24no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—42no—
1088C2×D4—42no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—28no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—42no—
1137C22×C4C2×#4114yes—
1138C22×C4C2×#4114yes—
1139C22×C4C2×#4114yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2511yescharacteristic
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—24no—
1174C4⋊C4—22no—
1175C4⋊C4—24no—
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—22no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—28no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—24no—
1282C42—24no—
1283C42—24no—
1284C42—22no—
1285C42—24no—
1286C42—28no—
1287C42—28no—
1288C42—22no—
1289C42—22no—
1290C42—42no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—42no—
1295C42—42no—
1296C42—44no—
1297C42—44no—
1298C42—44no—
1299C42—42no—
1300C42—42no—
1301C42—44no—
1302C42—44no—
1303C42—44no—
1304C42—44no—
1305C42C2×#4114yes—
1306C42C2×#4114yes—
1307C42C2×#4114yes—
1308C42C2×#4114yes—
1309C42H(5,𝔽2)14yes—
1310C23—21no—
1311C23—22no—
1312C23—21no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—24no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—24no—
1331C23—22no—
1332C23—22no—
1333C23C22×#4112yes—
1334C23C2611yescharacteristic
1335Q8—48no—
1336Q8—48no—
1337Q8—44no—
1338Q8—44no—
1339Q8—44no—
1340D4—44no—
1341D4—44no—
1342D4—48no—
1343D4—48no—
1344D4—48no—
1345D4—48no—
1346D4—44no—
1347D4—84no—
1348D4—88no—
1349D4—88no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—28no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—24no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—24no—
1412C2×C4—24no—
1413C2×C4—22no—
1414C2×C4—44no—
1415C2×C4—44no—
1416C2×C4—48no—
1417C2×C4—48no—
1418C2×C4—48no—
1419C2×C4—84no—
1420C2×C4—84no—
1421C2×C4—88no—
1422C2×C4—84no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—84no—
1426C2×C4C22×#4112yes—
1427C2×C4C22×#4112yes—
1428C2×C4C22×#4112yes—
1429C2×C4C22×#4112yes—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4112yes—
1432C2×C4C2×H(5,𝔽2)14yes—
1433C2×C4C2×H(5,𝔽2)12yes—
1434C2×C4#58514yes—
1435C2×C4#58512yes—
1436C22—22no—
1437C22—22no—
1438C22—22no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—44no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22C23×#4111yescharacteristic
1461C22C22×H(5,𝔽2)11yescharacteristic
1462C22C2×#58511yescharacteristic
1463C22C2×#58512yes—
1464C222−1+612yes—
1465C4—22no—
1466C4—22no—
1467C4—22no—
1468C4—24no—
1469C4—24no—
1470C4—22no—
1471C4—22no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—44no—
1481C4—42no—
1482C4—42no—
1483C4—44no—
1484C4—44no—
1485C4—42no—
1486C4—42no—
1487C4—44no—
1488C4—42no—
1489C4—42no—
1490C4—42no—
1491C4#350614yes—
1492C2—42no—
1493C2—82no—
1494C2—82no—
1495C2—82no—
1496C2#6268611yescharacteristic
1497C2C2×#350611yescharacteristic
1498C2#6286011yescharacteristic
1499C2#6292712yes—
1500C2#6293912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37550C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42321C2semidirect
2. #41397C2semidirect
3. #41025C2semidirect
4. #41017C2semidirect
5. #41014C2semidirect
6. #41002C2semidirect
7. #39502C2semidirect
8. #39373C2semidirect
9. #39273C2semidirect
10. #39271C2semidirect
11. #39188C2semidirect
12. #39186C2semidirect
13. #37961C2semidirect
14. #37774C2semidirect
15. #37634C2semidirect
17. #37519C2semidirect
18. #37512C2semidirect
19. #36536C2semidirect
20. #36509C2semidirect
21. #36209C2semidirect
22. #36135C2semidirect
23. #35829C2semidirect
24. #35755C2semidirect
25. #35345C2semidirect
26. #35309C2semidirect
27. #34631C2semidirect
28. #34614C2semidirect
29. #34235C2semidirect
30. #34224C2semidirect
31. #34141C2semidirect

Maximal subgroups

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

subgroupindex
#423212
#413972
#410252
#410172
#410142
#410022
#395022
#393732
#392732
#392712
#391882
#391862
#379612
#377742
#376342
#375502
#375192
#375122
#365362
#365092
#362092
#361352
#358292
#357552
#353452
#353092
#346312
#346142
#342352
#342242
#341412