Finite Group Databasebeta

← #7657170

Subgroups — #7657170

Order 512.

5510 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42940C213yesmaximal, complemented
2#42937C213yesmaximal, complemented
3#42923C213yesmaximal, complemented
4#42920C213yesmaximal, complemented
5#42712C213yesmaximal, complemented
6#42709C213yesmaximal, complemented
7#42560C213yesmaximal, complemented
8#42547C213yesmaximal, complemented
9#40076C213yesmaximal, complemented
10#40068C213yesmaximal, complemented
11#39532C213yesmaximal, complemented
12#39525C213yesmaximal, complemented
13#37516C213yesmaximal, complemented
14#37494C213yesmaximal, complemented
15Q8×#126C211yesmaximal, characteristic, complemented
16Q8×#124C211yesmaximal, characteristic, complemented
17#36444C211yesmaximal, characteristic, complemented
18#36432C211yesmaximal, characteristic, complemented
19#35948C211yesmaximal, characteristic, complemented
20#35920C211yesmaximal, characteristic, complemented
21#35831C211yesmaximal, characteristic, complemented
22#35771C211yesmaximal, characteristic, complemented
23#35757C211yesmaximal, characteristic, complemented
24#35748C211yesmaximal, characteristic, complemented
25#35723C211yesmaximal, characteristic, complemented
26#35687C211yesmaximal, characteristic, complemented
27#35016C213yesmaximal, complemented
28#34589C213yesmaximal, complemented
29#34293C211yesmaximal, characteristic, complemented
30#34259C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45#2863C2213yes—
46#2862C2213yes—
47#2857C2213yes—
48#2855C2213yes—
49#2832C2216yes—
50#2831C2216yes—
51#2826C2216yes—
52#2824C2216yes—
53#2797C2216yes—
54#2779C2216yes—
55#2771C2216yes—
56#2761C2216yes—
57#2753C2216yes—
58#2752C2216yes—
59#2751C2216yes—
60#2751C2216yes—
61#2751C2216yes—
62#2750C2216yes—
63#2743C2216yes—
64#2730C2216yes—
65#2714C2216yes—
66#2702C2216yes—
67#2696C2216yes—
68#2676C2216yes—
69#2666C2213yes—
70#2665C2213yes—
71#2665C2216yes—
72#2662C2211yescharacteristic
73#2662C2216yes—
74#2661C2213yes—
75#2653C2213yes—
76#2653C2213yes—
77#2651C2213yes—
78#2650C2213yes—
79#2650C2216yes—
80#2649C2213yes—
81#2648C2213yes—
82#2648C2213yes—
83#2648C2213yes—
84#2645C2213yes—
85#2643C2216yes—
86#2640C2213yes—
87#2639C2216yes—
88#2636C2213yes—
89#2635C2213yes—
90#2631C2213yes—
91#2630C2213yes—
92#2628C2213yes—
93#2625C2213yes—
94#2620C2213yes—
95#2620C2213yes—
96#2616C2213yes—
97#2615C2213yes—
98#2592C2213yes—
99#2586C2216yes—
100#2580C2213yes—
101#2574C2216yes—
102#2568C2213yes—
103#2563C2213yes—
104#2547C2213yes—
105#2547C2213yes—
106#2545C2213yes—
107#2544C2213yes—
108#2542C2213yes—
109#2538C2213yes—
110#2537C2213yes—
111#2537C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2511C2213yes—
115#2511C2213yes—
116#2511C2213yes—
117#2511C2213yes—
118#2505C2216yes—
119#2499C2213yes—
120#2499C2213yes—
121#2497C2213yes—
122#2497C2213yes—
123#2497C2213yes—
124#2496C2213yes—
125#2496C2213yes—
126#2496C2213yes—
127#2492C2213yes—
128#2492C2213yes—
129#2492C2213yes—
130#2492C2213yes—
131#2492C2213yes—
132#2492C2213yes—
133#2491C2213yes—
134#2491C2213yes—
135#2485C2213yes—
136#2485C2213yes—
137#2467C2216yes—
138#2459C2216yes—
139#2452C2213yes—
140#2452C2213yes—
141#2450C2216yes—
142#2450C2216yes—
143#2447C2213yes—
144#2447C2213yes—
145#2446C2213yes—
146#2446C2213yes—
147#2444C2216yes—
148#2440C2213yes—
149#2440C2213yes—
150#2436C2213yes—
151#2434C2213yes—
152#2432C2213yes—
153#2432C2213yes—
154#2431C2213yes—
155#2431C2213yes—
156#2429C2213yes—
157#2428C2213yes—
158#2427C2213yes—
159#2427C2213yes—
160#2427C2213yes—
161#2426C2213yes—
162#2423C2213yes—
163#2422C2213yes—
164#2421C2213yes—
165#2420C2213yes—
166#2417C2213yes—
167#2416C2213yes—
168#2415C2213yes—
169#2415C2213yes—
170#2415C2213yes—
171#2414C2213yes—
172#2409C2213yes—
173#2409C2213yes—
174#2407C2213yes—
175#2407C2213yes—
176#2407C2213yes—
177#2407C2213yes—
178#2401C2213yes—
179#2398C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2392C2213yes—
183#2392C2213yes—
184#2388C2213yes—
185#2388C2213yes—
186#2367C2213yes—
187#2366C2213yes—
188#2363C2213yes—
189#2363C2213yes—
190#2363C2213yes—
191#2362C2213yes—
192#2354C2213yes—
193#2354C2213yes—
194#2351C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2339C2213yes—
215#2339C2213yes—
216#2339C2213yes—
217#2339C2213yes—
218#2329C2216yes—
219#2326C2213yes—
220#2324C2213yes—
221#2318C2216yes—
222#2311C2213yes—
223#2310C2213yes—
224C4×#127C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2297C2213yes—
233C2×#391C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2313yes—
250Q82—44no—
251#550—28no—
252D4×Q8—44no—
253D4×Q8—44no—
254#548—28no—
255#548—44no—
256#548—44no—
257#548—44no—
258C2×C4⋊Q8C2313yes—
259C2×C4⋊Q8C2313yes—
260C2×C4⋊Q8C2313yes—
261C2×C4⋊Q8C2313yes—
262C2×C4⋊Q8C2313yes—
263C2×#127C2313yes—
264C2×#126C2311yescharacteristic
265C2×#126C2316yes—
266C2×#124C2313yes—
267C2×#124C2311yescharacteristic
268C2×#124C2313yes—
269C2×#124C2313yes—
270C2×#124C2313yes—
271C2×#124C2316yes—
272C2×#123C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2316yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2316yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2316yes—
291#520—44no—
292#519—44no—
293C4×#41—44no—
294C4×#41—44no—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2316yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C2×#117C2313yes—
328C2×#117C2313yes—
329C22×C4⋊C4C2313yes—
330C22×C42C2313yes—
331C22×C42C2313yes—
332#401C2313yes—
333#400C2316yes—
334#400C2316yes—
335#400C2316yes—
336#400C2316yes—
337#400C2316yes—
338#400C2316yes—
339#400C2316yes—
340#400C2316yes—
341#400C2316yes—
342#400C2313yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#399C2316yes—
350#399C2313yes—
351#399C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2316yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#397C2313yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2316yes—
363#397C2316yes—
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2316yes—
379#396C2313yes—
380#396C2311yescharacteristic
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2311yescharacteristic
385#396C2313yes—
386#395C2313yes—
387#395C2316yes—
388#395C2316yes—
389#395C2313yes—
390#395C2311yescharacteristic
391#394C2313yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2313yes—
396#394C2316yes—
397#394C2316yes—
398#394C2316yes—
399#394C2313yes—
400#394C2316yes—
401#394C2316yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2311yescharacteristic
407#394C2313yes—
408#394C2313yes—
409#394C2311yescharacteristic
410#394C2313yes—
411#394C2313yes—
412#394C2311yescharacteristic
413#394C2313yes—
414#394C2313yes—
415#393C2316yes—
416#393C2316yes—
417#393C2316yes—
418#393C2316yes—
419#393C2316yes—
420#393C2313yes—
421#393C2313yes—
422#393C2316yes—
423#393C2313yes—
424#393C2313yes—
425#393C2311yescharacteristic
426#392C2316yes—
427#392C2316yes—
428#392C2313yes—
429#392C2313yes—
430#392C2313yes—
431#392C2313yes—
432#392C2313yes—
433#392C2313yes—
434#392C2313yes—
435#392C2311yescharacteristic
436#391C2313yes—
437#391C2316yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2316yes—
447#391C2316yes—
448#391C2316yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2316yes—
466#390C2316yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2316yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2311yescharacteristic
477#390C2311yescharacteristic
478#390C2316yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2316yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2313yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2316yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2311yescharacteristic
513#388C2316yes—
514#388C2313yes—
515#388C2311yescharacteristic
516#388C2316yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2313yes—
526#387C2313yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2313yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2313yes—
537#386C2316yes—
538#386C2313yes—
539#386C2316yes—
540#386C2316yes—
541#386C2313yes—
542#386C2313yes—
543#386C2313yes—
544#386C2313yes—
545#386C2316yes—
546#386C2313yes—
547#386C2313yes—
548#386C2313yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2316yes—
553#385C2316yes—
554#385C2316yes—
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2313yes—
559#385C2316yes—
560#385C2316yes—
561#385C2313yes—
562#385C2313yes—
563#385C2316yes—
564#384C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#383C2313yes—
570#382C2316yes—
571#382C2313yes—
572#382C2313yes—
573#381C2316yes—
574#381C2316yes—
575#381C2316yes—
576#381C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586#380C2316yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2311yescharacteristic
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629#376C2313yes—
630C2×#95C2316yes—
631C2×#95C2316yes—
632C43C2313yes—
6332−1+4—464no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—212no—
640C2×#41—212no—
641C2×#41—212no—
642C2×#41—46no—
643C2×#41—46no—
644C2×#41—46no—
645C2×#41—46no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41#4118yes—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—212no—
659C22×Q8—46no—
660C22×Q8—46no—
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2413yes—
664C22×Q8C2411yescharacteristic
665C22×Q8C2413yes—
666C22×Q8C2416yes—
667C22×Q8C2411yescharacteristic
668C22×D4C2413yes—
669C22×D4C2413yes—
670C22×D4C2413yes—
671C22×D4C2411yescharacteristic
672C22×D4C2411yescharacteristic
673C22×D4C2413yes—
674C22×D4C2416yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2411yescharacteristic
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C23×C4C2413yes—
682C23×C4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2413yes—
688C23×C4C2413yes—
689C23×C4C2416yes—
690C23×C4C2416yes—
691C23×C4C2413yes—
692C4⋊Q8—46no—
693C4⋊Q8—46no—
694C4⋊Q8—46no—
695C4⋊Q8—46no—
696C4⋊Q8—46no—
697#127—212no—
698#126—24no—
699#126—86no—
700#124—212no—
701#124—24no—
702#124—46no—
703#124—46no—
704#124—46no—
705#124—86no—
706#123—46no—
707C22⋊Q8—212no—
708C22⋊Q8—412no—
709C22⋊Q8—46no—
710C22⋊Q8—46no—
711C22⋊Q8—46no—
712C22⋊Q8—46no—
713C22⋊Q8—46no—
714C22⋊Q8—46no—
715C22⋊Q8—46no—
716C22⋊Q8—86no—
717#121—212no—
718#121—212no—
719#121—212no—
720#121—46no—
721#121—46no—
722#121—46no—
723#121—46no—
724#121—86no—
725C4×Q8—24no—
726C4×Q8—24no—
727C4×Q8—24no—
728C4×Q8—24no—
729C4×Q8—24no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—24no—
735C4×Q8—46no—
736C4×Q8—46no—
737C4×Q8—46no—
738C4×D4—212no—
739C4×D4—212no—
740C4×D4—212no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—46no—
748C4×D4—46no—
749C4×D4—46no—
750C4×D4—46no—
751C4×D4—46no—
752C4×D4—46no—
753C4×D4—86no—
754#117—46no—
755#117—46no—
756#117—46no—
757#117—46no—
758#117—46no—
759C2×C4⋊C4—46no—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2416yes—
793C2×C4⋊C4C2416yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2416yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2416yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C42—46no—
860C2×C42—46no—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2416yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2416yes—
877C2×C42C2413yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2411yescharacteristic
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2413yes—
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2411yescharacteristic
921#95C2416yes—
922#95C2416yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2416yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935#95C2416yes—
936#95C2416yes—
937C24C2511yescharacteristic
938C24C2513yes—
939C24C2511yescharacteristic
940C24C2511yescharacteristic
941C24C2513yes—
942#41—232no—
943#41—448no—
944#41—448no—
945#41—448no—
946#41—416no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—26no—
953C2×Q8—26no—
954C2×Q8—26no—
955C2×Q8—26no—
956C2×Q8—26no—
957C2×Q8—22no—
958C2×Q8—41no—
959C2×Q8—43no—
960C2×Q8—43no—
961C2×Q8—41no—
962C2×Q8—46no—
963C2×Q8—46no—
964C2×Q8—46no—
965C2×Q8—448no—
966C2×Q8—416no—
967C2×Q8—416no—
968C2×Q8—416no—
969C2×Q8C2×#4114yes—
970C2×Q8H(5,𝔽2)14yes—
971C2×Q8H(5,𝔽2)14yes—
972C2×D4—26no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—26no—
976C2×D4—212no—
977C2×D4—26no—
978C2×D4—22no—
979C2×D4—26no—
980C2×D4—26no—
981C2×D4—26no—
982C2×D4—26no—
983C2×D4—26no—
984C2×D4—22no—
985C2×D4—22no—
986C2×D4—41no—
987C2×D4—41no—
988C2×D4—43no—
989C2×D4—41no—
990C2×D4—41no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—43no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—46no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—46no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4C2×#41112yes—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—212no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—26no—
1027C22×C4—26no—
1028C22×C4—26no—
1029C22×C4—46no—
1030C22×C4—46no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—46no—
1041C22×C4—46no—
1042C22×C4—46no—
1043C22×C4C2×#41112yes—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2513yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2513yes—
1070C4⋊C4—22no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—26no—
1080C4⋊C4—26no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—26no—
1088C4⋊C4—26no—
1089C4⋊C4—43no—
1090C4⋊C4—41no—
1091C4⋊C4—43no—
1092C4⋊C4—46no—
1093C4⋊C4—41no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—46no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—46no—
1106C4⋊C4—46no—
1107C4⋊C4—46no—
1108C4⋊C4—46no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—46no—
1112C4⋊C4—43no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—212no—
1116C22⋊C4—22no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—26no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—26no—
1128C22⋊C4—22no—
1129C22⋊C4—43no—
1130C22⋊C4—41no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—46no—
1139C22⋊C4—46no—
1140C22⋊C4—43no—
1141C22⋊C4—41no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—46no—
1152C22⋊C4—46no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—46no—
1158C22⋊C4—43no—
1159C22⋊C4—46no—
1160C22⋊C4—46no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—41no—
1180C42—41no—
1181C42—43no—
1182C42—43no—
1183C42—43no—
1184C42—46no—
1185C42—43no—
1186C42—43no—
1187C42—46no—
1188C422−1+414yescomplemented
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—21no—
1196C23—23no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—23no—
1201C23—23no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23—21no—
1210C23—23no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—23no—
1215C23—21no—
1216C23—21no—
1217C23—23no—
1218C23—21no—
1219C23—21no—
1220C23—23no—
1221C23—21no—
1222C23—21no—
1223C23C22×#4116yes—
1224C23C2611yescharacteristic
1225Q8—44no—
1226Q8—412no—
1227Q8—412no—
1228Q8—412no—
1229Q8—412no—
1230Q8—166no—
1231Q8#538116yes—
1232D4—224no—
1233D4—412no—
1234D4—44no—
1235D4—44no—
1236D4—44no—
1237D4—412no—
1238D4—412no—
1239D4—412no—
1240D4—86no—
1241D4—812no—
1242D4—86no—
1243D4—86no—
1244D4—86no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—224no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—21no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—21no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—23no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—23no—
1316C2×C4—424no—
1317C2×C4—412no—
1318C2×C4—412no—
1319C2×C4—412no—
1320C2×C4—412no—
1321C2×C4—86no—
1322C2×C4—86no—
1323C2×C4—86no—
1324C2×C4—86no—
1325C2×C4—166no—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4116yes—
1328C2×C4C2×H(5,𝔽2)16yes—
1329C2×C4C2×H(5,𝔽2)16yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4C2×2−1+412yes—
1332C2×C4C2×2−1+412yes—
1333C2×C4#58512yes—
1334C22—26no—
1335C22—26no—
1336C22—26no—
1337C22—43no—
1338C22—43no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—43no—
1347C22—41no—
1348C22—41no—
1349C22—43no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—43no—
1356C22—41no—
1357C22—43no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—43no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—43no—
1369C22C23×#4111yescharacteristic
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C22×H(5,𝔽2)11yescharacteristic
1372C22C22×2−1+411yescharacteristic
1373C22C2×#58511yescharacteristic
1374C22H(7,𝔽2)11yescharacteristic
1375C222−1+611yescharacteristic
1376C4—22no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—41no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—41no—
1386C4—43no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—43no—
1392C4—43no—
1393C4—43no—
1394C4—43no—
1395C4—43no—
1396C4—43no—
1397C4—41no—
1398C4—43no—
1399C4—43no—
1400C4—43no—
1401C4C2×#538112yes—
1402C2—46no—
1403C2—83no—
1404C2—81no—
1405C2—81no—
1406C2—81no—
1407C2C22×#53811yescharacteristic
1408C2#6280511yescharacteristic
1409C2#6285711yescharacteristic
1410C2#6289711yescharacteristic
1411C2#6291311yescharacteristic
1412C2#6291711yescharacteristic
1413C2#6292311yescharacteristic
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. #42940C2semidirect
2. #42937C2semidirect
3. #42923C2semidirect
4. #42920C2semidirect
5. #42712C2semidirect
6. #42709C2semidirect
7. #42560C2semidirect
8. #42547C2semidirect
9. #40076C2semidirect
10. #40068C2semidirect
11. #39532C2semidirect
12. #39525C2semidirect
13. #37516C2semidirect
14. #37494C2semidirect
15. Q8×#126C2semidirect
16. Q8×#124C2semidirect
17. #36444C2semidirect
18. #36432C2semidirect
19. #35948C2semidirect
20. #35920C2semidirect
21. #35831C2semidirect
22. #35771C2semidirect
23. #35757C2semidirect
24. #35748C2semidirect
25. #35723C2semidirect
26. #35687C2semidirect
27. #35016C2semidirect
28. #34589C2semidirect
29. #34293C2semidirect
30. #34259C2semidirect
31. C4×#550C2semidirect
1188. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#429402
#429372
#429232
#429202
#427122
#427092
#425602
#425472
#400762
#400682
#395322
#395252
#375162
#374942
Q8×#1262
Q8×#1242
#364442
#364322
#359482
#359202
#358312
#357712
#357572
#357482
#357232
#356872
#350162
#345892
#342932
#342592
C4×#5502