Finite Group Databasebeta

← #7632367

Subgroups — #7632367

Order 512.

7558 conjugacy classes of subgroups.

The subgroup lattice has 1524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic, complemented
2C2×#3517C211yesmaximal, characteristic, complemented
3#36596C213yesmaximal, complemented
4#36583C211yesmaximal, characteristic, complemented
5#36471C213yesmaximal, complemented
6#36467C211yesmaximal, characteristic, complemented
7#36455C211yesmaximal, characteristic, complemented
8#36430C211yesmaximal, characteristic, complemented
9#36424C213yesmaximal, complemented
10#36412C213yesmaximal, complemented
11#36066C211yesmaximal, characteristic, complemented
12#36062C213yesmaximal, complemented
13#36029C211yesmaximal, characteristic, complemented
14#36015C213yesmaximal, complemented
15#35957C211yesmaximal, characteristic, complemented
16#35930C213yesmaximal, complemented
17#35831C211yesmaximal, characteristic, complemented
18#35768C213yesmaximal, complemented
19#35571C213yesmaximal, complemented
20#35570C213yesmaximal, complemented
21#35569C213yesmaximal, complemented
22#35567C213yesmaximal, complemented
23#35276C213yesmaximal, complemented
24#35171C213yesmaximal, complemented
25#34889C213yesmaximal, complemented
26#34880C213yesmaximal, complemented
27#34312C211yesmaximal, characteristic, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34293C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic, complemented
31C4×#520C211yesmaximal, characteristic, complemented
32#3524—216no—
33#3517—216no—
34C2×#559C2213yes—
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#555C2213yes—
38C2×#553C2213yes—
39C2×#553C2213yes—
40C2×#553C2213yes—
41C2×#552C2213yes—
42C2×#550C2213yes—
43C2×#550C2211yescharacteristic
44C2×#550C2211yescharacteristic
45C2×#550C2211yescharacteristic
46C2×#550C2211yescharacteristic
47C2×#550C2211yescharacteristic
48C2×#550C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2211yescharacteristic
51C2×#548C2211yescharacteristic
52C2×#548C2211yescharacteristic
53C2×#547C2213yes—
54C2×#542C2213yes—
55C2×#540C2213yes—
56C2×#540C2213yes—
57C2×#540C2213yes—
58C2×#532C2213yes—
59C2×#529C2213yes—
60C2×#529C2213yes—
61C2×#529C2213yes—
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×#520C2211yescharacteristic
65C2×#519C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C2×C4×#41C2211yescharacteristic
68C2×C4×#41C2211yescharacteristic
69#2861C2213yes—
70#2858C2213yes—
71#2856C2216yes—
72#2856C2213yes—
73#2854C2216yes—
74#2850C2213yes—
75#2661C2216yes—
76#2661C2216yes—
77#2660C2213yes—
78#2657C2213yes—
79#2620C2213yes—
80#2619C2213yes—
81#2602C2216yes—
82#2602C2216yes—
83#2592C2213yes—
84#2584C2213yes—
85#2567C2213yes—
86#2562C2213yes—
87#2560C2216yes—
88#2559C2216yes—
89#2558C2216yes—
90#2557C2216yes—
91#2556C2213yes—
92#2556C2213yes—
93#2555C2213yes—
94#2555C2216yes—
95#2555C2216yes—
96#2555C2216yes—
97#2555C2213yes—
98#2555C2216yes—
99#2554C2213yes—
100#2554C2213yes—
101#2554C2216yes—
102#2554C2216yes—
103#2553C2213yes—
104#2553C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2548C2213yes—
110#2547C2213yes—
111#2544C2213yes—
112#2544C2213yes—
113#2543C2216yes—
114#2543C2216yes—
115#2541C2213yes—
116#2541C2213yes—
117#2541C2213yes—
118#2541C2213yes—
119#2541C2213yes—
120#2540C2213yes—
121#2540C2213yes—
122#2540C2213yes—
123#2537C2213yes—
124#2537C2213yes—
125#2535C2213yes—
126#2535C2213yes—
127#2521C2213yes—
128#2521C2213yes—
129#2521C2216yes—
130#2519C2211yescharacteristic
131#2519C2213yes—
132#2512C2216yes—
133#2500C2216yes—
134#2498C2216yes—
135#2492C2213yes—
136#2491C2213yes—
137#2490C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2489C2213yes—
143#2464C2213yes—
144#2464C2213yes—
145#2464C2216yes—
146#2464C2216yes—
147#2464C2216yes—
148#2461C2213yes—
149#2461C2213yes—
150#2461C2216yes—
151#2445C2216yes—
152#2431C2216yes—
153#2430C2216yes—
154#2428C2213yes—
155#2428C2213yes—
156#2428C2213yes—
157#2428C2213yes—
158#2428C2213yes—
159#2428C2216yes—
160#2428C2213yes—
161#2427C2213yes—
162#2427C2213yes—
163#2422C2216yes—
164#2417C2213yes—
165#2416C2213yes—
166#2416C2213yes—
167#2416C2213yes—
168#2415C2213yes—
169#2414C2213yes—
170#2414C2213yes—
171#2414C2213yes—
172#2399C2213yes—
173#2397C2213yes—
174#2395C2216yes—
175#2392C2213yes—
176#2392C2213yes—
177#2388C2216yes—
178#2367C2213yes—
179#2367C2213yes—
180#2366C2213yes—
181#2366C2213yes—
182#2363C2213yes—
183#2363C2213yes—
184#2363C2213yes—
185#2363C2213yes—
186#2363C2213yes—
187#2362C2213yes—
188#2361C2213yes—
189#2360C2213yes—
190#2354C2213yes—
191#2354C2213yes—
192#2352C2213yes—
193#2352C2213yes—
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2328C2213yes—
207#2326C2213yes—
208#2324C2213yes—
209#2324C2213yes—
210#2324C2213yes—
211#2323C2213yes—
212C4×#127C2213yes—
213C4×#124C2213yes—
214C4×#124C2213yes—
215C4×#124C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×#121C2213yes—
218C4×#121C2213yes—
219C4×#121C2216yes—
220C4×#121C2213yes—
221C4×#121C2213yes—
222C4×#121C2213yes—
223#2297C2216yes—
224#2293C2213yes—
225#2290C2213yes—
226#2290C2213yes—
227#2276C2211yescharacteristic
228#2276C2211yescharacteristic
229#2275C2213yes—
230#2275C2213yes—
231#2274C2213yes—
232#2274C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×D4C2213yes—
236C42×D4C2213yes—
237C42×D4C2213yes—
238C4×#117C2213yes—
239C2×C4×C4⋊C4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2316yes—
245C23×Q8C2311yescharacteristic
246#559—224no—
247#557—28no—
248#557—28no—
249#555—224no—
250#553—224no—
251#553—224no—
252#553—224no—
253#552—224no—
254#550—28no—
255#550—28no—
256#550—28no—
257#550—28no—
258#550—28no—
259#550—28no—
260#550—224no—
261#548—28no—
262#548—28no—
263#548—28no—
264#548—28no—
265#547—224no—
266#542—224no—
267#540—224no—
268#540—224no—
269#540—224no—
270#532—224no—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×#127C2313yes—
274C2×#127C2313yes—
275C2×#127C2313yes—
276C2×#127C2313yes—
277C2×#127C2313yes—
278C2×#127C2313yes—
279C2×#127C2316yes—
280#529—224no—
281#529—224no—
282#529—224no—
283C2×#126C2316yes—
284C2×#126C2311yescharacteristic
285C2×#126C2313yes—
286C2×#126C2313yes—
287C2×#126C2313yes—
288C2×#125C2313yes—
289C2×#125C2311yescharacteristic
290C2×#125C2313yes—
291C2×#125C2313yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#124C2313yes—
295C2×#124C2313yes—
296C2×#124C2313yes—
297C2×#124C2313yes—
298C2×#124C2313yes—
299C2×#124C2313yes—
300C2×#124C2316yes—
301C2×#124C2313yes—
302C2×#124C2313yes—
303C2×#124C2316yes—
304C2×#123C2316yes—
305C2×#123C2316yes—
306C2×#123C2313yes—
307C2×#123C2316yes—
308C2×#123C2313yes—
309C2×#123C2313yes—
310C2×#123C2313yes—
311C2×#123C2316yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2313yes—
317C2×C22⋊Q8C2313yes—
318C2×#121C2313yes—
319C2×#121C2313yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2316yes—
325C2×#121C2316yes—
326C2×#121C2313yes—
327C2×#121C2313yes—
328C2×#121C2313yes—
329C2×#121C2313yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332C2×#121C2313yes—
333C2×#121C2316yes—
334C2×#121C2313yes—
335C2×#121C2313yes—
336C2×#121C2313yes—
337C2×#121C2313yes—
338C2×#121C2313yes—
339C2×#121C2316yes—
340C2×#121C2316yes—
341C2×#121C2313yes—
342C2×#121C2313yes—
343C2×#121C2316yes—
344C2×#121C2316yes—
345C2×#121C2316yes—
346C2×#121C2316yes—
347#520—28no—
348#520—28no—
349#520D4116yescomplemented
350#519—28no—
351C4×#41—28no—
352C4×#41—28no—
353C4×#41—28no—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2313yes—
356C2×C4×Q8C2313yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2313yes—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2316yes—
373C2×C4×D4C2316yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2313yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2313yes—
380C2×C4×D4C2313yes—
381C2×C4×D4C2313yes—
382C2×C4×D4C2313yes—
383C2×C4×D4C2313yes—
384C2×C4×D4C2313yes—
385C2×C4×D4C2313yes—
386C2×C4×D4C2313yes—
387C2×C4×D4C2313yes—
388C2×C4×D4C2313yes—
389C2×C4×D4C2313yes—
390C2×C4×D4C2313yes—
391C2×C4×D4C2313yes—
392C2×C4×D4C2316yes—
393C2×C4×D4C2316yes—
394C2×C4×D4C2313yes—
395C2×C4×D4C2313yes—
396C2×#117C2313yes—
397C2×#117C2313yes—
398C2×#117C2313yes—
399C2×#117C2313yes—
400C2×#117C2313yes—
401C2×#117C2313yes—
402C2×#117C2316yes—
403C2×#117C2313yes—
404C2×#117C2313yes—
405C22×C4⋊C4C2313yes—
406C22×C4⋊C4C2313yes—
407C22×C4⋊C4C2313yes—
408C22×C42C2313yes—
409C22×C42C2313yes—
410C22×C42C2313yes—
411C22×C42C2316yes—
412#400C2316yes—
413#399C2313yes—
414#399C2311yescharacteristic
415#399C2313yes—
416#399C2313yes—
417#398C2313yes—
418#398C2313yes—
419#398C2311yescharacteristic
420#398C2316yes—
421#398C2311yescharacteristic
422#398C2313yes—
423#398C2313yes—
424#398C2316yes—
425#397C2316yes—
426#397C2316yes—
427#397C2313yes—
428#397C2316yes—
429#397C2313yes—
430#397C2316yes—
431#396C2313yes—
432#396C2316yes—
433#396C2311yescharacteristic
434#396C2313yes—
435#396C2313yes—
436#395C2313yes—
437#395C2316yes—
438#395C2313yes—
439#395C2313yes—
440#395C2313yes—
441#394C2316yes—
442#394C2316yes—
443#394C2313yes—
444#394C2316yes—
445#394C2316yes—
446#394C2316yes—
447#394C2313yes—
448#394C2316yes—
449#394C2313yes—
450#394C2316yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2316yes—
455#394C2316yes—
456#394C2316yes—
457#393C2316yes—
458#392C2316yes—
459#392C2316yes—
460#392C2316yes—
461#392C2316yes—
462#392C2316yes—
463#392C2313yes—
464#392C2313yes—
465#392C2313yes—
466#392C2313yes—
467#392C2313yes—
468#392C2313yes—
469#392C2316yes—
470#392C2316yes—
471#392C2316yes—
472#391C2316yes—
473#391C2313yes—
474#391C2313yes—
475#391C2313yes—
476#391C2313yes—
477#391C2313yes—
478#391C2313yes—
479#390C2316yes—
480#390C2313yes—
481#390C2313yes—
482#390C2316yes—
483#390C2316yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2316yes—
489#390C2316yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2316yes—
501#390C2316yes—
502#390C2316yes—
503#390C2316yes—
504#390C2313yes—
505#390C2313yes—
506#390C2316yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2316yes—
515#389C2316yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2311yescharacteristic
521#388C2313yes—
522#388C2316yes—
523#388C2316yes—
524#388C2313yes—
525#388C2316yes—
526#388C2316yes—
527#388C2316yes—
528#388C2316yes—
529#388C2316yes—
530#388C2316yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2316yes—
535#388C2316yes—
536#388C2313yes—
537#388C2313yes—
538#388C2316yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2316yes—
543#388C2313yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2311yescharacteristic
548#388C2313yes—
549#388C2311yescharacteristic
550#388C2311yescharacteristic
551#388C2311yescharacteristic
552#388C2313yes—
553#387C2316yes—
554#387C2313yes—
555#387C2313yes—
556#387C2311yescharacteristic
557#387C2313yes—
558#386C2316yes—
559#386C2313yes—
560#386C2316yes—
561#386C2316yes—
562#386C2313yes—
563#386C2316yes—
564#386C2316yes—
565#386C2316yes—
566#386C2316yes—
567#386C2313yes—
568#386C2316yes—
569#386C2313yes—
570#386C2313yes—
571#386C2316yes—
572#386C2316yes—
573#386C2316yes—
574#386C2316yes—
575#386C2313yes—
576#386C2313yes—
577#386C2313yes—
578#385C2313yes—
579#385C2316yes—
580#385C2316yes—
581#385C2313yes—
582#385C2313yes—
583#385C2313yes—
584#384C2313yes—
585#384C2316yes—
586#384C2313yes—
587#382C2313yes—
588#382C2313yes—
589#382C2313yes—
590#382C2311yescharacteristic
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2316yes—
600#380C2313yes—
601#380C2313yes—
602C4×C4⋊C4C2316yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2316yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2311yescharacteristic
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C22⋊C4C2316yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631C4×C22⋊C4C2313yes—
632C4×C22⋊C4C2313yes—
633C4×C22⋊C4C2313yes—
634C4×C22⋊C4C2313yes—
635C4×C22⋊C4C2316yes—
636C4×C22⋊C4C2316yes—
637C4×C22⋊C4C2316yes—
638C4×C22⋊C4C2316yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2316yes—
642C4×C22⋊C4C2316yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2316yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2313yes—
649C4×C22⋊C4C2313yes—
650#376C2313yes—
651#376C2313yes—
652C2×#95C2316yes—
653C43C2313yes—
654C43C2313yes—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—24no—
665C2×#41—24no—
666C2×#41—224no—
667C2×#41—412no—
668C2×#41—86no—
669C2×#41C2×D418yes—
670C22×Q8—24no—
671C22×Q8—24no—
672C22×Q8—24no—
673C22×Q8C2413yes—
674C22×Q8C2413yes—
675C22×Q8C2413yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2416yes—
685C22×D4C2416yes—
686C22×D4C2413yes—
687C22×D4C2413yes—
688C22×D4C2413yes—
689C22×D4C2413yes—
690C22×D4C2416yes—
691C22×D4C2413yes—
692C22×D4C2413yes—
693C22×D4C2413yes—
694C22×D4C2416yes—
695C22×D4C2416yes—
696C22×D4C2416yes—
697C23×C4C2413yes—
698C23×C4C2413yes—
699C23×C4C2413yes—
700C23×C4C2413yes—
701C23×C4C2413yes—
702C23×C4C2413yes—
703C23×C4C2413yes—
704C23×C4C2416yes—
705C23×C4C2416yes—
706C23×C4C2413yes—
707C23×C4C2413yes—
708C23×C4C2413yes—
709C23×C4C2413yes—
710C23×C4C2416yes—
711C4⋊Q8—212no—
712C4⋊Q8—212no—
713#127—212no—
714#127—212no—
715#127—212no—
716#127—212no—
717#127—212no—
718#127—212no—
719#127—86no—
720#126—24no—
721#126—212no—
722#126—224no—
723#126—212no—
724#126—212no—
725#125—24no—
726#125—212no—
727#125—212no—
728#125—212no—
729#125—212no—
730#125—212no—
731#124—212no—
732#124—212no—
733#124—212no—
734#124—224no—
735#124—212no—
736#124—212no—
737#124—212no—
738#124—46no—
739#124—46no—
740#124—86no—
741#123—224no—
742#123—224no—
743#123—212no—
744#123—212no—
745#123—224no—
746#123—212no—
747#123—224no—
748#123—212no—
749C22⋊Q8—212no—
750C22⋊Q8—212no—
751C22⋊Q8—212no—
752C22⋊Q8—212no—
753C22⋊Q8—212no—
754C22⋊Q8—212no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—212no—
760#121—224no—
761#121—212no—
762#121—224no—
763#121—212no—
764#121—212no—
765#121—212no—
766#121—212no—
767#121—212no—
768#121—212no—
769#121—212no—
770#121—212no—
771#121—212no—
772#121—212no—
773#121—212no—
774#121—212no—
775#121—224no—
776#121—224no—
777#121—412no—
778#121—46no—
779#121—46no—
780#121—86no—
781#121—86no—
782#121—86no—
783#121—86no—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—24no—
788C4×Q8—24no—
789C4×Q8—24no—
790C4×Q8—212no—
791C4×Q8—212no—
792C4×Q8—212no—
793C4×Q8—212no—
794C4×Q8C2×D418yes—
795C4×Q8C2×D418yes—
796C4×Q8#4118yescomplemented
797C4×Q8#4118yescomplemented
798C4×D4—212no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—224no—
803C4×D4—224no—
804C4×D4—212no—
805C4×D4—212no—
806C4×D4—212no—
807C4×D4—212no—
808C4×D4—212no—
809C4×D4—212no—
810C4×D4—212no—
811C4×D4—212no—
812C4×D4—212no—
813C4×D4—212no—
814C4×D4—212no—
815C4×D4—212no—
816C4×D4—212no—
817C4×D4—212no—
818C4×D4—212no—
819C4×D4—212no—
820C4×D4—46no—
821C4×D4—46no—
822C4×D4—86no—
823C4×D4—86no—
824C4×D4C2×D4124yes—
825C4×D4C2×D4124yes—
826#117—224no—
827#117—212no—
828#117—212no—
829#117—212no—
830#117—212no—
831#117—212no—
832#117—212no—
833#117—212no—
834#117C2×D4124yes—
835C2×C4⋊C4—212no—
836C2×C4⋊C4—212no—
837C2×C4⋊C4C2×D4124yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2416yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2416yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2416yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2413yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2413yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2413yes—
883C2×C4⋊C4C2413yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2416yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2416yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2416yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2416yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2416yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2411yescharacteristic
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2416yes—
921C2×C22⋊C4C2416yes—
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2416yes—
925C2×C22⋊C4C2416yes—
926C2×C22⋊C4C2416yes—
927C2×C22⋊C4C2413yes—
928C2×C22⋊C4C2413yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2416yes—
932C2×C22⋊C4C2416yes—
933C2×C22⋊C4C2416yes—
934C2×C22⋊C4C2413yes—
935C2×C22⋊C4C2413yes—
936C2×C22⋊C4C2413yes—
937C2×C22⋊C4C2413yes—
938C2×C22⋊C4C2413yes—
939C2×C22⋊C4C2413yes—
940C2×C22⋊C4C2413yes—
941C2×C42—212no—
942C2×C42—212no—
943C2×C42—212no—
944C2×C42—86no—
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2416yes—
948C2×C42C2413yes—
949C2×C42C2413yes—
950C2×C42C2413yes—
951C2×C42C2413yes—
952C2×C42C2411yescharacteristic
953C2×C42C2413yes—
954C2×C42C2413yes—
955C2×C42C2413yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2413yes—
961C2×C42C2413yes—
962C2×C42C2416yes—
963C2×C42C2413yes—
964C2×C42C2413yes—
965C2×C42C2416yes—
966C2×C42C2413yes—
967C2×C42C2413yes—
968C2×C42C2413yes—
969C2×C42C2413yes—
970C2×C42C2413yes—
971C2×C42C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2416yes—
975#95C2416yes—
976#95C2411yescharacteristic
977#95C2411yescharacteristic
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2411yescharacteristic
983#95C2411yescharacteristic
984#95C2413yes—
985#95C2413yes—
986#95C2411yescharacteristic
987#95C2411yescharacteristic
988#95C2411yescharacteristic
989#95C2411yescharacteristic
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2416yes—
1001#95C2413yes—
1002#95C2416yes—
1003#95C2416yes—
1004#95C2413yes—
1005#95C2411yescharacteristic
1006#95C2411yescharacteristic
1007#95C2416yes—
1008#95C2413yes—
1009#95C2413yes—
1010C24C2511yescharacteristic
1011C24C2513yes—
1012C24C2513yes—
1013C24C2513yes—
1014C24C2513yes—
1015#41—232no—
1016#41—416no—
1017#41—416no—
1018#41—416no—
1019#41—848no—
1020C2×Q8—26no—
1021C2×Q8—26no—
1022C2×Q8—26no—
1023C2×Q8—26no—
1024C2×Q8—26no—
1025C2×Q8—26no—
1026C2×Q8—43no—
1027C2×Q8—43no—
1028C2×Q8—43no—
1029C2×Q8—416no—
1030C2×Q8C22×D414yes—
1031C2×Q8C2×#4114yes—
1032C2×Q8C2×#4114yes—
1033C2×D4—26no—
1034C2×D4—26no—
1035C2×D4—212no—
1036C2×D4—212no—
1037C2×D4—26no—
1038C2×D4—26no—
1039C2×D4—212no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—26no—
1043C2×D4—26no—
1044C2×D4—26no—
1045C2×D4—212no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—26no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—26no—
1055C2×D4—26no—
1056C2×D4—26no—
1057C2×D4—26no—
1058C2×D4—212no—
1059C2×D4—212no—
1060C2×D4—26no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—46no—
1065C2×D4—46no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—46no—
1069C2×D4—43no—
1070C2×D4—46no—
1071C2×D4—46no—
1072C2×D4—43no—
1073C2×D4—43no—
1074C2×D4—43no—
1075C2×D4—43no—
1076C2×D4—43no—
1077C2×D4—46no—
1078C2×D4—46no—
1079C2×D4—43no—
1080C2×D4—43no—
1081C2×D4—46no—
1082C2×D4—46no—
1083C2×D4—43no—
1084C2×D4—43no—
1085C2×D4—43no—
1086C2×D4—43no—
1087C2×D4—43no—
1088C2×D4—43no—
1089C2×D4—46no—
1090C2×D4—46no—
1091C2×D4—46no—
1092C2×D4C22×D4112yes—
1093C22×C4—26no—
1094C22×C4—26no—
1095C22×C4—26no—
1096C22×C4—26no—
1097C22×C4—26no—
1098C22×C4—26no—
1099C22×C4—26no—
1100C22×C4—26no—
1101C22×C4—26no—
1102C22×C4—26no—
1103C22×C4—26no—
1104C22×C4—26no—
1105C22×C4—26no—
1106C22×C4—26no—
1107C22×C4—26no—
1108C22×C4—26no—
1109C22×C4—26no—
1110C22×C4—26no—
1111C22×C4—26no—
1112C22×C4—26no—
1113C22×C4—26no—
1114C22×C4—212no—
1115C22×C4—26no—
1116C22×C4—212no—
1117C22×C4—43no—
1118C22×C4—46no—
1119C22×C4—46no—
1120C22×C4—43no—
1121C22×C4—46no—
1122C22×C4—43no—
1123C22×C4—43no—
1124C22×C4—43no—
1125C22×C4—43no—
1126C22×C4—43no—
1127C22×C4—43no—
1128C22×C4—46no—
1129C22×C4—43no—
1130C22×C4—46no—
1131C22×C4—43no—
1132C22×C4—46no—
1133C22×C4C22×D4112yes—
1134C22×C4C22×D4124yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2513yes—
1137C22×C4C2513yes—
1138C22×C4C2513yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2513yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2513yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2513yes—
1148C22×C4C2513yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2513yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2513yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2513yes—
1157C22×C4C2513yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2513yes—
1161C4⋊C4—26no—
1162C4⋊C4—26no—
1163C4⋊C4—22no—
1164C4⋊C4—26no—
1165C4⋊C4—26no—
1166C4⋊C4—26no—
1167C4⋊C4—26no—
1168C4⋊C4—26no—
1169C4⋊C4—26no—
1170C4⋊C4—212no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—26no—
1176C4⋊C4—212no—
1177C4⋊C4—26no—
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—26no—
1181C4⋊C4—26no—
1182C4⋊C4—26no—
1183C4⋊C4—26no—
1184C4⋊C4—26no—
1185C4⋊C4—22no—
1186C4⋊C4—26no—
1187C4⋊C4—22no—
1188C4⋊C4—22no—
1189C4⋊C4—26no—
1190C4⋊C4—26no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—43no—
1194C4⋊C4—43no—
1195C4⋊C4—46no—
1196C4⋊C4—43no—
1197C4⋊C4—46no—
1198C4⋊C4—43no—
1199C4⋊C4—43no—
1200C4⋊C4—43no—
1201C4⋊C4C22×D4112yes—
1202C4⋊C4C22×D4112yes—
1203C4⋊C4C22×D4112yes—
1204C4⋊C4C22×D414yes—
1205C4⋊C4C2×#41112yes—
1206C4⋊C4C2×#41112yes—
1207C22⋊C4—26no—
1208C22⋊C4—212no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—22no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—212no—
1216C22⋊C4—26no—
1217C22⋊C4—212no—
1218C22⋊C4—26no—
1219C22⋊C4—22no—
1220C22⋊C4—22no—
1221C22⋊C4—26no—
1222C22⋊C4—26no—
1223C22⋊C4—26no—
1224C22⋊C4—26no—
1225C22⋊C4—212no—
1226C22⋊C4—26no—
1227C22⋊C4—26no—
1228C22⋊C4—212no—
1229C22⋊C4—26no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—26no—
1233C22⋊C4—26no—
1234C22⋊C4—26no—
1235C22⋊C4—26no—
1236C22⋊C4—26no—
1237C22⋊C4—26no—
1238C22⋊C4—212no—
1239C22⋊C4—212no—
1240C22⋊C4—26no—
1241C22⋊C4—26no—
1242C22⋊C4—26no—
1243C22⋊C4—22no—
1244C22⋊C4—26no—
1245C22⋊C4—22no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—46no—
1249C22⋊C4—46no—
1250C22⋊C4—46no—
1251C22⋊C4—43no—
1252C22⋊C4—43no—
1253C22⋊C4—43no—
1254C22⋊C4—43no—
1255C22⋊C4—46no—
1256C22⋊C4—46no—
1257C22⋊C4—46no—
1258C22⋊C4—43no—
1259C22⋊C4—43no—
1260C22⋊C4—43no—
1261C22⋊C4—43no—
1262C22⋊C4C22×D4112yes—
1263C22⋊C4C22×D4112yes—
1264C42—22no—
1265C42—22no—
1266C42—26no—
1267C42—26no—
1268C42—26no—
1269C42—26no—
1270C42—212no—
1271C42—26no—
1272C42—26no—
1273C42—22no—
1274C42—26no—
1275C42—26no—
1276C42—26no—
1277C42—22no—
1278C42—22no—
1279C42—43no—
1280C42—43no—
1281C42—46no—
1282C42—46no—
1283C42—43no—
1284C42—43no—
1285C42—43no—
1286C42—43no—
1287C42C22×D4112yes—
1288C42C22×D4112yes—
1289C42C2×#41112yes—
1290C42C2×#41112yes—
1291C23—23no—
1292C23—23no—
1293C23—23no—
1294C23—23no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—21no—
1299C23—23no—
1300C23—23no—
1301C23—23no—
1302C23—23no—
1303C23—21no—
1304C23—21no—
1305C23—23no—
1306C23—23no—
1307C23—23no—
1308C23—23no—
1309C23—21no—
1310C23—23no—
1311C23—23no—
1312C23—23no—
1313C23—23no—
1314C23—21no—
1315C23—23no—
1316C23—23no—
1317C23—23no—
1318C23—23no—
1319C23—23no—
1320C23—21no—
1321C23—23no—
1322C23—23no—
1323C23—23no—
1324C23—21no—
1325C23C23×D416yes—
1326C23C2611yescharacteristic
1327Q8—412no—
1328Q8—412no—
1329Q8—86no—
1330Q8#532116yes—
1331D4—224no—
1332D4—412no—
1333D4—412no—
1334D4—412no—
1335D4—412no—
1336D4—412no—
1337D4—86no—
1338D4—86no—
1339D4—86no—
1340D4—86no—
1341D4—812no—
1342D4—86no—
1343D4—812no—
1344D4—812no—
1345D4—86no—
1346D4—812no—
1347D4—86no—
1348D4—86no—
1349D4—812no—
1350D4—812no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—21no—
1362C2×C4—23no—
1363C2×C4—21no—
1364C2×C4—23no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—21no—
1368C2×C4—23no—
1369C2×C4—21no—
1370C2×C4—23no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—224no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—23no—
1379C2×C4—21no—
1380C2×C4—23no—
1381C2×C4—23no—
1382C2×C4—23no—
1383C2×C4—23no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—23no—
1387C2×C4—23no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—23no—
1393C2×C4—23no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—23no—
1399C2×C4—23no—
1400C2×C4—23no—
1401C2×C4—23no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—23no—
1406C2×C4—23no—
1407C2×C4—23no—
1408C2×C4—23no—
1409C2×C4—23no—
1410C2×C4—23no—
1411C2×C4—21no—
1412C2×C4—23no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—23no—
1416C2×C4—424no—
1417C2×C4—412no—
1418C2×C4—412no—
1419C2×C4—412no—
1420C2×C4—412no—
1421C2×C4—412no—
1422C2×C4—412no—
1423C2×C4—86no—
1424C2×C4—86no—
1425C2×C4—86no—
1426C2×C4—86no—
1427C2×C4—812no—
1428C2×C4—812no—
1429C2×C4C23×D416yes—
1430C2×C4C23×D412yes—
1431C2×C4C23×D412yes—
1432C2×C4C23×D416yes—
1433C2×C4C23×D412yes—
1434C2×C4C23×D416yes—
1435C2×C4C22×#4112yes—
1436C2×C4C22×#4116yes—
1437C2×C4C22×#4112yes—
1438C2×C4C22×#4116yes—
1439C2×C4C22×#4116yes—
1440C2×C4C22×#4116yes—
1441C2×C4#58512yes—
1442C2×C4#58512yes—
1443C22—26no—
1444C22—26no—
1445C22—26no—
1446C22—43no—
1447C22—43no—
1448C22—43no—
1449C22—43no—
1450C22—43no—
1451C22—43no—
1452C22—43no—
1453C22—41no—
1454C22—43no—
1455C22—43no—
1456C22—43no—
1457C22—41no—
1458C22—43no—
1459C22—43no—
1460C22—43no—
1461C22—41no—
1462C22—41no—
1463C22—43no—
1464C22—43no—
1465C22—43no—
1466C22—43no—
1467C22—43no—
1468C22—43no—
1469C22—41no—
1470C22—41no—
1471C22—43no—
1472C22—43no—
1473C22—43no—
1474C22—41no—
1475C22—43no—
1476C22—43no—
1477C22—43no—
1478C22C24×D411yescharacteristic
1479C22C23×#4111yescharacteristic
1480C22C23×#4111yescharacteristic
1481C22C2×#58511yescharacteristic
1482C22C2×#58511yescharacteristic
1483C22H(7,𝔽2)11yescharacteristic
1484C22H(7,𝔽2)11yescharacteristic
1485C4—26no—
1486C4—22no—
1487C4—26no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—26no—
1493C4—22no—
1494C4—26no—
1495C4—22no—
1496C4—41no—
1497C4—43no—
1498C4—41no—
1499C4—43no—
1500C4—43no—
1501C4—41no—
1502C4—43no—
1503C4—43no—
1504C4—41no—
1505C4—43no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—43no—
1510C4C2×#532112yes—
1511C2—46no—
1512C2—83no—
1513C2—83no—
1514C2—83no—
1515C2—81no—
1516C2C22×#53211yescharacteristic
1517C2#6279311yescharacteristic
1518C2#6285811yescharacteristic
1519C2#6298711yescharacteristic
1520C2#6300311yescharacteristic
1521C2#6300611yescharacteristic
1522C2#6300811yescharacteristic
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×#3524C2semidirect
2. C2×#3517C2semidirect
3. #36596C2semidirect
4. #36583C2semidirect
5. #36471C2semidirect
6. #36467C2semidirect
7. #36455C2semidirect
8. #36430C2semidirect
9. #36424C2semidirect
10. #36412C2semidirect
11. #36066C2semidirect
12. #36062C2semidirect
13. #36029C2semidirect
14. #36015C2semidirect
15. #35957C2semidirect
16. #35930C2semidirect
17. #35831C2semidirect
18. #35768C2semidirect
19. #35571C2semidirect
20. #35570C2semidirect
21. #35569C2semidirect
22. #35567C2semidirect
23. #35276C2semidirect
24. #35171C2semidirect
25. #34889C2semidirect
26. #34880C2semidirect
27. #34312C2semidirect
28. #34295C2semidirect
29. #34293C2semidirect
30. C4×#550C2semidirect
31. C4×#520C2semidirect
349. #520D4semidirect
796. C4×Q8#41semidirect
797. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×#35172
#365962
#365832
#364712
#364672
#364552
#364302
#364242
#364122
#360662
#360622
#360292
#360152
#359572
#359302
#358312
#357682
#355712
#355702
#355692
#355672
#352762
#351712
#348892
#348802
#343122
#342952
#342932
C4×#5502
C4×#5202