Finite Group Databasebeta

← #7632343

Subgroups — #7632343

Order 512.

7894 conjugacy classes of subgroups.

The subgroup lattice has 1499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#36579C213yesmaximal, complemented
4#36578C211yesmaximal, characteristic, complemented
5#36482C211yesmaximal, characteristic, complemented
6#36456C211yesmaximal, characteristic, complemented
7#36443C213yesmaximal, complemented
8#36430C211yesmaximal, characteristic, complemented
9#36233C213yesmaximal, complemented
10#36231C213yesmaximal, complemented
11#36019C213yesmaximal, complemented
12#35787C213yesmaximal, complemented
13#35771C211yesmaximal, characteristic, complemented
14#35759C213yesmaximal, complemented
15#35757C211yesmaximal, characteristic, complemented
16#35756C213yesmaximal, complemented
17#35711C211yesmaximal, characteristic, complemented
18#35687C211yesmaximal, characteristic, complemented
19#35675C213yesmaximal, complemented
20#35665C213yesmaximal, complemented
21#35623C213yesmaximal, complemented
22#35521C213yesmaximal, complemented
23#35258C213yesmaximal, complemented
24#35195C213yesmaximal, complemented
25#34741C213yesmaximal, complemented
26#34720C213yesmaximal, complemented
27#34312C211yesmaximal, characteristic, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33#3518—216no—
34C2×Q82C2211yescharacteristic
35C2×#556C2213yes—
36C2×#556C2213yes—
37C2×#556C2213yes—
38C2×#555C2213yes—
39C2×#550C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2211yescharacteristic
42C2×#548C2211yescharacteristic
43C2×#548C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#548C2211yescharacteristic
46C2×#542C2213yes—
47C2×#542C2213yes—
48C2×#533C2213yes—
49C2×#529C2213yes—
50C4×2−1+4—216no—
51C2×#520C2211yescharacteristic
52C2×#520C2213yes—
53C2×#520C2213yes—
54C2×#520C2213yes—
55C2×#519C2211yescharacteristic
56C2×#519C2213yes—
57C2×#519C2211yescharacteristic
58C2×#519C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C2×C4×#41C2213yes—
62C2×C4×#41C2213yes—
63C2×C4×#41C2213yes—
64C22×C4×Q8C2211yescharacteristic
65C22×C4×Q8C2211yescharacteristic
66C22×C4×Q8C2213yes—
67#2857C2213yes—
68#2855C2213yes—
69#2854C2213yes—
70#2852C2216yes—
71#2850C2213yes—
72#2850C2216yes—
73#2636C2216yes—
74#2631C2216yes—
75#2628C2213yes—
76#2620C2213yes—
77#2616C2213yes—
78#2615C2213yes—
79#2610C2216yes—
80#2609C2216yes—
81#2604C2216yes—
82#2601C2216yes—
83#2599C2216yes—
84#2599C2216yes—
85#2592C2216yes—
86#2581C2216yes—
87#2581C2213yes—
88#2568C2213yes—
89#2563C2213yes—
90#2545C2213yes—
91#2544C2213yes—
92#2538C2213yes—
93#2538C2213yes—
94#2535C2213yes—
95#2504C2213yes—
96#2503C2213yes—
97#2487C2213yes—
98#2486C2213yes—
99#2481C2216yes—
100#2481C2216yes—
101#2481C2216yes—
102#2477C2216yes—
103#2477C2216yes—
104#2475C2216yes—
105#2471C2216yes—
106#2469C2216yes—
107#2469C2213yes—
108#2468C2213yes—
109#2467C2213yes—
110#2467C2216yes—
111#2466C2216yes—
112#2466C2213yes—
113#2465C2216yes—
114#2465C2213yes—
115#2464C2213yes—
116#2463C2216yes—
117#2463C2213yes—
118#2462C2213yes—
119#2461C2216yes—
120#2461C2213yes—
121#2460C2213yes—
122#2459C2216yes—
123#2459C2216yes—
124#2459C2216yes—
125#2459C2211yescharacteristic
126#2458C2213yes—
127#2457C2213yes—
128#2457C2216yes—
129#2456C2213yes—
130#2456C2216yes—
131#2456C2213yes—
132#2455C2213yes—
133#2452C2213yes—
134#2452C2213yes—
135#2451C2213yes—
136#2451C2213yes—
137#2449C2216yes—
138#2448C2213yes—
139#2448C2213yes—
140#2446C2213yes—
141#2446C2213yes—
142#2439C2213yes—
143#2439C2213yes—
144#2439C2213yes—
145#2439C2213yes—
146#2436C2213yes—
147#2434C2213yes—
148#2432C2213yes—
149#2432C2213yes—
150#2431C2213yes—
151#2431C2213yes—
152#2429C2213yes—
153#2428C2213yes—
154#2427C2213yes—
155#2426C2213yes—
156#2421C2213yes—
157#2421C2213yes—
158#2421C2213yes—
159#2421C2213yes—
160#2415C2213yes—
161#2415C2213yes—
162#2414C2213yes—
163#2414C2213yes—
164#2409C2213yes—
165#2409C2213yes—
166#2407C2213yes—
167#2407C2213yes—
168#2407C2213yes—
169#2407C2213yes—
170#2398C2216yes—
171#2396C2213yes—
172#2392C2216yes—
173#2392C2213yes—
174#2388C2213yes—
175#2388C2213yes—
176#2367C2213yes—
177#2367C2213yes—
178#2366C2213yes—
179#2365C2213yes—
180#2363C2213yes—
181#2363C2213yes—
182#2362C2213yes—
183#2362C2213yes—
184#2361C2213yes—
185#2361C2213yes—
186#2360C2213yes—
187#2360C2213yes—
188#2356C2213yes—
189#2355C2213yes—
190#2352C2213yes—
191#2352C2213yes—
192#2352C2213yes—
193#2352C2213yes—
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2347C2213yes—
201#2346C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2211yescharacteristic
209Q8×C22⋊C4C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212#2328C2213yes—
213#2327C2213yes—
214#2324C2213yes—
215#2324C2213yes—
216#2323C2213yes—
217#2323C2213yes—
218#2320C2213yes—
219#2314C2213yes—
220C4×#124C2213yes—
221C4×#124C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2216yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231#2298C2213yes—
232#2295C2213yes—
233#2293C2213yes—
234#2290C2213yes—
235#2290C2213yes—
236#2290C2216yes—
237#2276C2211yescharacteristic
238C42×Q8C2211yescharacteristic
239C42×D4C2213yes—
240C2×2−1+4—28no—
241C2×2−1+4—28no—
242C2×2−1+4—28no—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C22×#41C2313yes—
246C22×#41C2311yescharacteristic
247C22×#41C2311yescharacteristic
248C23×Q8C2313yes—
249C23×Q8C2311yescharacteristic
250C23×Q8C2311yescharacteristic
251C23×Q8C2311yescharacteristic
252Q82—28no—
253#556—224no—
254#556—224no—
255#556—224no—
256#555—224no—
257#550—28no—
258D4×Q8—28no—
259D4×Q8—28no—
260#548—28no—
261#548—28no—
262#548—28no—
263#548—28no—
264#542—224no—
265#542—224no—
266#533—224no—
267C2×C4⋊Q8C2313yes—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×#127C2313yes—
273#529—224no—
274C2×#126C2316yes—
275C2×#126C2313yes—
276C2×#126C2313yes—
277C2×#126C2316yes—
278C2×#125C2313yes—
279C2×#124C2316yes—
280C2×#124C2313yes—
281C2×#124C2313yes—
282C2×#124C2313yes—
283C2×#124C2311yescharacteristic
284C2×#124C2313yes—
285C2×#124C2316yes—
286C2×#123C2313yes—
287C2×#123C2313yes—
288C2×#123C2313yes—
289C2×#123C2313yes—
290C2×C22⋊Q8C2313yes—
291C2×C22⋊Q8C2313yes—
292C2×C22⋊Q8C2313yes—
293C2×C22⋊Q8C2313yes—
294C2×C22⋊Q8C2313yes—
295C2×C22⋊Q8C2313yes—
296C2×C22⋊Q8C2313yes—
297C2×C22⋊Q8C2313yes—
298C2×C22⋊Q8C2313yes—
299C2×C22⋊Q8C2316yes—
300C2×C22⋊Q8C2316yes—
301C2×C22⋊Q8C2313yes—
302C2×#121C2313yes—
303C2×#121C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310#520—28no—
311#520—224no—
312#520—224no—
313#520—224no—
314#519—224no—
315#519—28no—
316#519—28no—
317#519D4116yescomplemented
318C4×#41—224no—
319C4×#41—28no—
320C4×#41—28no—
321C4×#41—224no—
322C4×#41—224no—
323C2×C4×Q8—28no—
324C2×C4×Q8—28no—
325C2×C4×Q8—224no—
326C2×C4×Q8C2313yes—
327C2×C4×Q8C2313yes—
328C2×C4×Q8C2313yes—
329C2×C4×Q8C2316yes—
330C2×C4×Q8C2316yes—
331C2×C4×Q8C2313yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2313yes—
341C2×C4×Q8C2313yes—
342C2×C4×Q8C2313yes—
343C2×C4×Q8C2313yes—
344C2×C4×Q8C2313yes—
345C2×C4×Q8C2313yes—
346C2×C4×Q8C2313yes—
347C2×C4×Q8C2313yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×D4C2313yes—
352C2×C4×D4C2313yes—
353C2×C4×D4C2313yes—
354C2×C4×D4C2313yes—
355C2×C4×D4C2313yes—
356C2×C4×D4C2313yes—
357C2×C4×D4C2313yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2316yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2316yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2316yes—
374C2×C4×D4C2313yes—
375C2×#117C2313yes—
376C2×#117C2313yes—
377C2×#117C2316yes—
378C2×#117C2316yes—
379C2×#117C2313yes—
380C2×#117C2313yes—
381C2×#117C2313yes—
382C2×#117C2313yes—
383C2×#117C2313yes—
384C2×#117C2316yes—
385C2×#117C2313yes—
386C2×#117C2313yes—
387C22×C4⋊C4C2313yes—
388C22×C4⋊C4C2313yes—
389C22×C4⋊C4C2316yes—
390C22×C4⋊C4C2313yes—
391C22×C42C2316yes—
392C22×C42C2313yes—
393C22×C42C2313yes—
394C22×C42C2313yes—
395C22×C42C2313yes—
396#400C2313yes—
397#400C2316yes—
398#400C2316yes—
399#400C2316yes—
400#400C2316yes—
401#399C2316yes—
402#399C2313yes—
403#398C2313yes—
404#398C2316yes—
405#398C2313yes—
406#398C2313yes—
407#397C2316yes—
408#397C2316yes—
409#397C2316yes—
410#397C2316yes—
411#397C2313yes—
412#396C2316yes—
413#396C2316yes—
414#396C2316yes—
415#396C2316yes—
416#396C2313yes—
417#396C2313yes—
418#396C2313yes—
419#396C2313yes—
420#395C2313yes—
421#395C2313yes—
422#395C2316yes—
423#395C2313yes—
424#395C2316yes—
425#394C2316yes—
426#394C2316yes—
427#394C2313yes—
428#394C2313yes—
429#394C2316yes—
430#394C2316yes—
431#394C2313yes—
432#394C2316yes—
433#394C2311yescharacteristic
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2311yescharacteristic
439#393C2316yes—
440#393C2316yes—
441#393C2313yes—
442#393C2316yes—
443#393C2313yes—
444#393C2316yes—
445#393C2311yescharacteristic
446#392C2316yes—
447#392C2313yes—
448#392C2316yes—
449#392C2316yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2311yescharacteristic
454#392C2313yes—
455#392C2313yes—
456#391C2316yes—
457#391C2313yes—
458#391C2316yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2316yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2311yescharacteristic
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2316yes—
478#390C2313yes—
479#390C2313yes—
480#390C2316yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2316yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2316yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#388C2313yes—
504#388C2316yes—
505#388C2313yes—
506#388C2316yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2313yes—
511#388C2316yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2316yes—
516#388C2316yes—
517#388C2316yes—
518#388C2313yes—
519#388C2316yes—
520#388C2316yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2316yes—
527#388C2316yes—
528#388C2313yes—
529#388C2311yescharacteristic
530#388C2313yes—
531#388C2311yescharacteristic
532#388C2311yescharacteristic
533#388C2313yes—
534#387C2316yes—
535#387C2316yes—
536#387C2313yes—
537#387C2316yes—
538#387C2316yes—
539#387C2313yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2313yes—
545#387C2316yes—
546#387C2313yes—
547#387C2316yes—
548#387C2313yes—
549#387C2313yes—
550#387C2316yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2311yescharacteristic
559#386C2316yes—
560#386C2316yes—
561#386C2313yes—
562#386C2316yes—
563#386C2316yes—
564#386C2316yes—
565#386C2316yes—
566#386C2316yes—
567#386C2316yes—
568#386C2316yes—
569#386C2316yes—
570#386C2313yes—
571#386C2316yes—
572#386C2313yes—
573#386C2316yes—
574#386C2311yescharacteristic
575#386C2313yes—
576#386C2313yes—
577#386C2311yescharacteristic
578#386C2313yes—
579#385C2313yes—
580#385C2316yes—
581#385C2313yes—
582#385C2316yes—
583#385C2313yes—
584#385C2316yes—
585#385C2316yes—
586#385C2313yes—
587#385C2316yes—
588#385C2316yes—
589#385C2313yes—
590#385C2313yes—
591#385C2313yes—
592#385C2313yes—
593#384C2313yes—
594#383C2316yes—
595#382C2313yes—
596#382C2313yes—
597#382C2313yes—
598#382C2313yes—
599#382C2313yes—
600#382C2316yes—
601#381C2316yes—
602#381C2313yes—
603#381C2311yescharacteristic
604#380C2313yes—
605#380C2316yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2316yes—
622C4×C4⋊C4C2313yes—
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2316yes—
632C4×C4⋊C4C2313yes—
633C4×C22⋊C4C2313yes—
634C4×C22⋊C4C2313yes—
635C4×C22⋊C4C2313yes—
636C4×C22⋊C4C2313yes—
637C4×C22⋊C4C2313yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2316yes—
645C4×C22⋊C4C2316yes—
646C4×C22⋊C4C2316yes—
647C4×C22⋊C4C2316yes—
648C4×C22⋊C4C2313yes—
649C4×C22⋊C4C2313yes—
650C4×C22⋊C4C2316yes—
651C4×C22⋊C4C2311yescharacteristic
652#376C2313yes—
653#376C2316yes—
654C43C2313yes—
6552−1+4—2128no—
656C2×#41—212no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—212no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—212no—
664C2×#41—212no—
665C2×#41—212no—
666C2×#41—212no—
667C2×#41—212no—
668C2×#41—212no—
669C2×#41—212no—
670C2×#41#4118yes—
671C22×Q8—212no—
672C22×Q8—24no—
673C22×Q8—212no—
674C22×Q8—24no—
675C22×Q8—24no—
676C22×Q8—24no—
677C22×Q8—24no—
678C22×Q8—24no—
679C22×Q8—24no—
680C22×Q8—212no—
681C22×Q8C2×D418yes—
682C22×Q8#4118yes—
683C22×Q8C2413yes—
684C22×Q8C2413yes—
685C22×Q8C2411yescharacteristic
686C22×Q8C2413yes—
687C22×Q8C2413yes—
688C22×Q8C2416yes—
689C22×Q8C2411yescharacteristic
690C22×D4C2413yes—
691C22×D4C2411yescharacteristic
692C22×D4C2413yes—
693C22×D4C2413yes—
694C22×D4C2411yescharacteristic
695C22×D4C2413yes—
696C22×D4C2413yes—
697C22×D4C2411yescharacteristic
698C22×D4C2413yes—
699C22×D4C2413yes—
700C22×D4C2413yes—
701C22×D4C2416yes—
702C22×D4C2413yes—
703C23×C4C2416yes—
704C23×C4C2413yes—
705C23×C4C2413yes—
706C23×C4C2413yes—
707C23×C4C2411yescharacteristic
708C23×C4C2413yes—
709C23×C4C2411yescharacteristic
710C23×C4C2413yes—
711C23×C4C2413yes—
712C23×C4C2413yes—
713C23×C4C2413yes—
714C23×C4C2416yes—
715C23×C4C2413yes—
716C23×C4C2413yes—
717C23×C4C2413yes—
718C4⋊Q8—212no—
719C4⋊Q8—212no—
720C4⋊Q8—212no—
721C4⋊Q8—212no—
722C4⋊Q8—212no—
723#127—212no—
724#126—212no—
725#126—224no—
726#126—212no—
727#126—224no—
728#125—212no—
729#124—212no—
730#124—212no—
731#124—212no—
732#124—24no—
733#124—224no—
734#124—212no—
735#124—224no—
736#123—212no—
737#123—212no—
738#123—46no—
739#123—46no—
740C22⋊Q8—212no—
741C22⋊Q8—212no—
742C22⋊Q8—212no—
743C22⋊Q8—212no—
744C22⋊Q8—212no—
745C22⋊Q8—212no—
746C22⋊Q8—212no—
747C22⋊Q8—212no—
748C22⋊Q8—224no—
749C22⋊Q8—212no—
750C22⋊Q8—46no—
751C22⋊Q8—412no—
752#121—212no—
753#121—212no—
754#121—212no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—46no—
760C4×Q8—212no—
761C4×Q8—24no—
762C4×Q8—212no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—24no—
766C4×Q8—24no—
767C4×Q8—24no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—212no—
771C4×Q8—212no—
772C4×Q8—212no—
773C4×Q8—212no—
774C4×Q8—212no—
775C4×Q8—212no—
776C4×Q8—224no—
777C4×Q8—212no—
778C4×Q8—212no—
779C4×Q8—212no—
780C4×Q8—224no—
781C4×Q8C2×D418yes—
782C4×Q8C2×D4124yes—
783C4×Q8C2×D4124yes—
784C4×Q8C2×D418yes—
785C4×D4—212no—
786C4×D4—212no—
787C4×D4—212no—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—212no—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—212no—
797C4×D4—24no—
798C4×D4—224no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—224no—
803C4×D4—212no—
804C4×D4—212no—
805C4×D4—212no—
806C4×D4—46no—
807C4×D4—412no—
808C4×D4—46no—
809#117—212no—
810#117—212no—
811#117—224no—
812#117—212no—
813#117—212no—
814#117—212no—
815#117—224no—
816#117—212no—
817#117—212no—
818#117—224no—
819#117C2×D4124yes—
820#117C2×D4124yes—
821C2×C4⋊C4—212no—
822C2×C4⋊C4—212no—
823C2×C4⋊C4—212no—
824C2×C4⋊C4—224no—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2416yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2416yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2416yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2416yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2416yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2416yes—
878C2×C22⋊C4C2416yes—
879C2×C22⋊C4C2416yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2416yes—
899C2×C22⋊C4C2416yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2416yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2411yescharacteristic
915C2×C22⋊C4C2411yescharacteristic
916C2×C22⋊C4C2411yescharacteristic
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2416yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2411yescharacteristic
922C2×C42—212no—
923C2×C42—212no—
924C2×C42—224no—
925C2×C42—212no—
926C2×C42—212no—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2416yes—
932C2×C42C2416yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2411yescharacteristic
940C2×C42C2413yes—
941C2×C42C2413yes—
942C2×C42C2413yes—
943C2×C42C2413yes—
944C2×C42C2411yescharacteristic
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2416yes—
948C2×C42C2411yescharacteristic
949C2×C42C2413yes—
950C2×C42C2413yes—
951C2×C42C2416yes—
952C2×C42C2413yes—
953#95C2411yescharacteristic
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2416yes—
960#95C2416yes—
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2413yes—
964#95C2411yescharacteristic
965#95C2413yes—
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2416yes—
978#95C2416yes—
979#95C2416yes—
980#95C2416yes—
981#95C2416yes—
982#95C2416yes—
983#95C2413yes—
984#95C2413yes—
985#95C2416yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2411yescharacteristic
991#95C2411yescharacteristic
992#95C2416yes—
993#95C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2413yes—
996#95C2416yes—
997#95C2416yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001C24C2511yescharacteristic
1002C24C2513yes—
1003C24C2511yescharacteristic
1004C24C2513yes—
1005C24C2511yescharacteristic
1006#41—296no—
1007#41—296no—
1008#41—296no—
1009#41—232no—
1010#41—416no—
1011C2×Q8—296no—
1012C2×Q8—232no—
1013C2×Q8—232no—
1014C2×Q8—26no—
1015C2×Q8—26no—
1016C2×Q8—22no—
1017C2×Q8—26no—
1018C2×Q8—212no—
1019C2×Q8—26no—
1020C2×Q8—26no—
1021C2×Q8—26no—
1022C2×Q8—26no—
1023C2×Q8—26no—
1024C2×Q8—26no—
1025C2×Q8—26no—
1026C2×Q8—22no—
1027C2×Q8—41no—
1028C2×Q8—46no—
1029C2×Q8—46no—
1030C2×Q8—416no—
1031C2×Q8C22×D4112yes—
1032C2×Q8C22×D414yes—
1033C2×Q8C2×#41112yes—
1034C2×Q8C2×#4114yes—
1035C2×Q8C2×#4114yes—
1036C2×D4—26no—
1037C2×D4—22no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—22no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—26no—
1045C2×D4—26no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—212no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—22no—
1055C2×D4—26no—
1056C2×D4—26no—
1057C2×D4—26no—
1058C2×D4—22no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—46no—
1065C2×D4—43no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—43no—
1069C2×D4—43no—
1070C2×D4—43no—
1071C2×D4—43no—
1072C2×D4—43no—
1073C2×D4—46no—
1074C2×D4C2×#41112yes—
1075C22×C4—212no—
1076C22×C4—212no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—212no—
1080C22×C4—26no—
1081C22×C4—26no—
1082C22×C4—26no—
1083C22×C4—26no—
1084C22×C4—22no—
1085C22×C4—26no—
1086C22×C4—22no—
1087C22×C4—26no—
1088C22×C4—26no—
1089C22×C4—26no—
1090C22×C4—26no—
1091C22×C4—26no—
1092C22×C4—26no—
1093C22×C4—26no—
1094C22×C4—26no—
1095C22×C4—22no—
1096C22×C4—26no—
1097C22×C4—26no—
1098C22×C4—22no—
1099C22×C4—26no—
1100C22×C4—212no—
1101C22×C4—26no—
1102C22×C4—26no—
1103C22×C4—41no—
1104C22×C4—43no—
1105C22×C4—43no—
1106C22×C4—41no—
1107C22×C4—46no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—46no—
1114C22×C4—43no—
1115C22×C4—43no—
1116C22×C4—43no—
1117C22×C4C22×D4112yes—
1118C22×C4C2×#41112yes—
1119C22×C4C2×#41112yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2513yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2513yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2513yes—
1127C22×C4C2513yes—
1128C22×C4C2513yes—
1129C22×C4C2513yes—
1130C22×C4C2513yes—
1131C22×C4C2513yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2513yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C22×C4C2513yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2513yes—
1139C22×C4C2513yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2513yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2513yes—
1146C4⋊C4—26no—
1147C4⋊C4—212no—
1148C4⋊C4—26no—
1149C4⋊C4—212no—
1150C4⋊C4—26no—
1151C4⋊C4—26no—
1152C4⋊C4—22no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—26no—
1162C4⋊C4—212no—
1163C4⋊C4—26no—
1164C4⋊C4—26no—
1165C4⋊C4—22no—
1166C4⋊C4—26no—
1167C4⋊C4—26no—
1168C4⋊C4—26no—
1169C4⋊C4—26no—
1170C4⋊C4—26no—
1171C4⋊C4—26no—
1172C4⋊C4—26no—
1173C4⋊C4—212no—
1174C4⋊C4—26no—
1175C4⋊C4—26no—
1176C4⋊C4—26no—
1177C4⋊C4—26no—
1178C4⋊C4—41no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—43no—
1182C4⋊C4—43no—
1183C4⋊C4—46no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—43no—
1187C4⋊C4C22×D4112yes—
1188C4⋊C4C22×D4112yes—
1189C4⋊C4C22×D4112yes—
1190C4⋊C4C22×D4112yes—
1191C22⋊C4—22no—
1192C22⋊C4—26no—
1193C22⋊C4—22no—
1194C22⋊C4—26no—
1195C22⋊C4—26no—
1196C22⋊C4—26no—
1197C22⋊C4—212no—
1198C22⋊C4—26no—
1199C22⋊C4—22no—
1200C22⋊C4—26no—
1201C22⋊C4—212no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—22no—
1205C22⋊C4—212no—
1206C22⋊C4—212no—
1207C22⋊C4—212no—
1208C22⋊C4—22no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—22no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—26no—
1216C22⋊C4—212no—
1217C22⋊C4—22no—
1218C22⋊C4—26no—
1219C22⋊C4—26no—
1220C22⋊C4—22no—
1221C22⋊C4—41no—
1222C22⋊C4—43no—
1223C22⋊C4—41no—
1224C22⋊C4—46no—
1225C22⋊C4—41no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4—41no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—46no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—46no—
1235C22⋊C4—46no—
1236C22⋊C4—43no—
1237C22⋊C4—43no—
1238C22⋊C4—43no—
1239C22⋊C4—43no—
1240C22⋊C4—43no—
1241C22⋊C4C22×D4112yes—
1242C22⋊C4C22×D414yes—
1243C42—26no—
1244C42—22no—
1245C42—26no—
1246C42—26no—
1247C42—22no—
1248C42—26no—
1249C42—212no—
1250C42—26no—
1251C42—26no—
1252C42—26no—
1253C42—26no—
1254C42—26no—
1255C42—212no—
1256C42—26no—
1257C42—26no—
1258C42—26no—
1259C42—26no—
1260C42—26no—
1261C42—43no—
1262C42—41no—
1263C42—43no—
1264C42—46no—
1265C42—43no—
1266C42C22×D4112yes—
1267C42C22×D4124yes—
1268C42C22×D4112yes—
1269C23—23no—
1270C23—21no—
1271C23—21no—
1272C23—21no—
1273C23—21no—
1274C23—23no—
1275C23—23no—
1276C23—21no—
1277C23—23no—
1278C23—21no—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—23no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—23no—
1287C23—23no—
1288C23—21no—
1289C23—21no—
1290C23—23no—
1291C23—21no—
1292C23—23no—
1293C23—23no—
1294C23—21no—
1295C23—21no—
1296C23—23no—
1297C23—23no—
1298C23—21no—
1299C23—23no—
1300C23—21no—
1301C23C23×D412yes—
1302C23C22×#4116yes—
1303C23C22×#4112yes—
1304C23C2611yescharacteristic
1305Q8—224no—
1306Q8—224no—
1307Q8—224no—
1308Q8—44no—
1309Q8—412no—
1310Q8—812no—
1311Q8#525116yes—
1312D4—224no—
1313D4—224no—
1314D4—28no—
1315D4—224no—
1316D4—44no—
1317D4—412no—
1318D4—44no—
1319D4—412no—
1320D4—86no—
1321D4—812no—
1322D4—86no—
1323D4—86no—
1324D4—86no—
1325C2×C4—248no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—23no—
1329C2×C4—21no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—21no—
1334C2×C4—23no—
1335C2×C4—21no—
1336C2×C4—23no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—23no—
1340C2×C4—21no—
1341C2×C4—23no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—224no—
1345C2×C4—224no—
1346C2×C4—224no—
1347C2×C4—21no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—21no—
1364C2×C4—23no—
1365C2×C4—21no—
1366C2×C4—23no—
1367C2×C4—21no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—23no—
1372C2×C4—23no—
1373C2×C4—21no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—23no—
1380C2×C4—23no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—23no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—23no—
1388C2×C4—21no—
1389C2×C4—23no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—23no—
1393C2×C4—23no—
1394C2×C4—23no—
1395C2×C4—44no—
1396C2×C4—412no—
1397C2×C4—412no—
1398C2×C4—44no—
1399C2×C4—412no—
1400C2×C4—412no—
1401C2×C4—812no—
1402C2×C4—86no—
1403C2×C4—86no—
1404C2×C4—86no—
1405C2×C4—86no—
1406C2×C4C23×D416yes—
1407C2×C4C23×D412yes—
1408C2×C4C23×D416yes—
1409C2×C4C23×D416yes—
1410C2×C4C23×D412yes—
1411C2×C4C23×D416yes—
1412C2×C4C22×#4116yes—
1413C2×C4C22×#4112yes—
1414C2×C4C22×#4116yes—
1415C2×C4C22×#4116yes—
1416C2×C4#58512yes—
1417C2×C4#58512yes—
1418C22—26no—
1419C22—22no—
1420C22—22no—
1421C22—26no—
1422C22—22no—
1423C22—22no—
1424C22—22no—
1425C22—26no—
1426C22—22no—
1427C22—41no—
1428C22—41no—
1429C22—43no—
1430C22—41no—
1431C22—43no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—43no—
1436C22—41no—
1437C22—43no—
1438C22—41no—
1439C22—43no—
1440C22—41no—
1441C22—43no—
1442C22—43no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—43no—
1447C22—43no—
1448C22—41no—
1449C22—41no—
1450C22—43no—
1451C22—41no—
1452C22—43no—
1453C22C24×D411yescharacteristic
1454C22C23×#4111yescharacteristic
1455C22C23×#4111yescharacteristic
1456C22C2×#58511yescharacteristic
1457C22C2×#58511yescharacteristic
1458C222−1+611yescharacteristic
1459C222−1+611yescharacteristic
1460C4—22no—
1461C4—22no—
1462C4—22no—
1463C4—26no—
1464C4—26no—
1465C4—22no—
1466C4—26no—
1467C4—26no—
1468C4—22no—
1469C4—41no—
1470C4—43no—
1471C4—41no—
1472C4—43no—
1473C4—43no—
1474C4—43no—
1475C4—43no—
1476C4—41no—
1477C4—43no—
1478C4—41no—
1479C4—43no—
1480C4—43no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—43no—
1485C4C2×#525112yes—
1486C2—46no—
1487C2—42no—
1488C2—42no—
1489C2—83no—
1490C2—81no—
1491C2C22×#52511yescharacteristic
1492C2#6279311yescharacteristic
1493C2#6285011yescharacteristic
1494C2#6299511yescharacteristic
1495C2#6300211yescharacteristic
1496C2#6300211yescharacteristic
1497C2#6300911yescharacteristic
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. C2×#3518C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #36579C2semidirect
4. #36578C2semidirect
5. #36482C2semidirect
6. #36456C2semidirect
7. #36443C2semidirect
8. #36430C2semidirect
9. #36233C2semidirect
10. #36231C2semidirect
11. #36019C2semidirect
12. #35787C2semidirect
13. #35771C2semidirect
14. #35759C2semidirect
15. #35757C2semidirect
16. #35756C2semidirect
17. #35711C2semidirect
18. #35687C2semidirect
19. #35675C2semidirect
20. #35665C2semidirect
21. #35623C2semidirect
22. #35521C2semidirect
23. #35258C2semidirect
24. #35195C2semidirect
25. #34741C2semidirect
26. #34720C2semidirect
27. #34312C2semidirect
28. #34295C2semidirect
29. #34291C2semidirect
30. #34262C2semidirect
31. C4×#548C2semidirect
317. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×C4×2−1+42
#365792
#365782
#364822
#364562
#364432
#364302
#362332
#362312
#360192
#357872
#357712
#357592
#357572
#357562
#357112
#356872
#356752
#356652
#356232
#355212
#352582
#351952
#347412
#347202
#343122
#342952
#342912
#342622
C4×#5482