Finite Group Databasebeta

← #7686917

Subgroups — #7686917

Order 512.

7677 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#59315C213yesmaximal, complemented
4#59117C213yesmaximal, complemented
5#59115C213yesmaximal, complemented
6#59112C213yesmaximal, complemented
7#59066C213yesmaximal, complemented
8#44931C213yesmaximal, complemented
9#44928C213yesmaximal, complemented
10#44888C213yesmaximal, complemented
11#44880C213yesmaximal, complemented
12#38050C213yesmaximal, complemented
13#37869C213yesmaximal, complemented
14#37792C213yesmaximal, complemented
15#37764C213yesmaximal, complemented
16#36455C211yesmaximal, characteristic, complemented
17#36433C211yesmaximal, characteristic, complemented
18#36433C211yesmaximal, characteristic, complemented
19#36433C211yesmaximal, characteristic, complemented
20#36431C211yesmaximal, characteristic, complemented
21#36361C213yesmaximal, complemented
22#36126C213yesmaximal, complemented
23#36029C211yesmaximal, characteristic, complemented
24#36005C211yesmaximal, characteristic, complemented
25#35937C211yesmaximal, characteristic, complemented
26#35748C211yesmaximal, characteristic, complemented
27#34735C213yesmaximal, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32#3517—216no—
33#3483—216no—
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#555C2213yes—
37C2×#555C2213yes—
38C2×#555C2213yes—
39C2×#553C2213yes—
40C2×#553C2213yes—
41C2×#550C2211yescharacteristic
42C2×#550C2211yescharacteristic
43C2×#550C2213yes—
44C2×#550C2213yes—
45C2×#550C2211yescharacteristic
46C2×#550C2211yescharacteristic
47C2×#550C2211yescharacteristic
48C2×#550C2211yescharacteristic
49C2×#547C2213yes—
50C2×#547C2216yes—
51C2×#540C2213yes—
52C2×#540C2213yes—
53C2×#532C2213yes—
54C2×#532C2213yes—
55C2×#532C2213yes—
56C2×#532C2213yes—
57C2×#529C2213yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×C4×#41C2213yes—
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67#2856C2213yes—
68#2854C2213yes—
69#2854C2213yes—
70#2854C2213yes—
71#2851C2213yes—
72#2717C2216yes—
73#2710C2216yes—
74#2708C2216yes—
75#2701C2216yes—
76#2686C2216yes—
77#2682C2216yes—
78#2674C2216yes—
79#2672C2216yes—
80#2672C2216yes—
81#2671C2216yes—
82#2671C2216yes—
83#2671C2216yes—
84#2671C2216yes—
85#2671C2216yes—
86#2660C2213yes—
87#2628C2213yes—
88#2624C2213yes—
89#2619C2213yes—
90#2584C2213yes—
91#2580C2213yes—
92#2580C2213yes—
93#2566C2213yes—
94#2551C2213yes—
95#2551C2213yes—
96#2550C2213yes—
97#2550C2213yes—
98#2546C2213yes—
99#2542C2213yes—
100#2541C2213yes—
101#2541C2213yes—
102#2537C2213yes—
103#2535C2213yes—
104#2521C2216yes—
105#2501C2213yes—
106#2500C2213yes—
107#2500C2213yes—
108#2500C2213yes—
109#2491C2216yes—
110#2487C2213yes—
111#2485C2213yes—
112#2485C2213yes—
113#2485C2213yes—
114#2479C2216yes—
115#2479C2213yes—
116#2478C2213yes—
117#2475C2213yes—
118#2474C2213yes—
119#2470C2216yes—
120#2469C2213yes—
121#2468C2213yes—
122#2462C2211yescharacteristic
123#2461C2213yes—
124#2461C2216yes—
125#2461C2216yes—
126#2455C2216yes—
127#2454C2213yes—
128#2452C2213yes—
129#2452C2213yes—
130#2452C2213yes—
131#2449C2213yes—
132#2445C2213yes—
133#2445C2213yes—
134#2445C2213yes—
135#2445C2213yes—
136#2445C2213yes—
137#2445C2213yes—
138#2445C2213yes—
139#2445C2213yes—
140#2443C2216yes—
141#2443C2213yes—
142#2441C2213yes—
143#2440C2213yes—
144#2440C2213yes—
145#2439C2213yes—
146#2438C2213yes—
147#2432C2216yes—
148#2430C2216yes—
149#2430C2216yes—
150#2430C2216yes—
151#2430C2213yes—
152#2430C2216yes—
153#2428C2213yes—
154#2428C2213yes—
155#2428C2213yes—
156#2428C2213yes—
157#2427C2216yes—
158#2425C2216yes—
159#2425C2213yes—
160#2422C2213yes—
161#2422C2213yes—
162#2422C2213yes—
163#2422C2213yes—
164#2422C2213yes—
165#2420C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2419C2213yes—
169#2416C2213yes—
170#2416C2216yes—
171#2416C2213yes—
172#2414C2213yes—
173#2414C2213yes—
174#2413C2213yes—
175#2407C2216yes—
176#2406C2213yes—
177#2406C2216yes—
178#2399C2213yes—
179#2396C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2366C2213yes—
183#2366C2213yes—
184#2363C2213yes—
185#2363C2213yes—
186#2361C2216yes—
187#2361C2213yes—
188#2361C2213yes—
189#2359C2216yes—
190#2352C2213yes—
191#2352C2213yes—
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202#2349C2213yes—
203#2349C2213yes—
204#2349C2213yes—
205#2349C2213yes—
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208D4×C4⋊C4C2213yes—
209D4×C4⋊C4C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2328C2213yes—
219#2328C2213yes—
220#2324C2213yes—
221#2324C2213yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231#2296C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234C2×#389C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2285C2213yes—
238#2276C2211yescharacteristic
239C2×C4×C4⋊C4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2313yes—
245C22×#41C2316yes—
246C22×#41C2316yes—
247Q82—28no—
248#557—28no—
249#555—224no—
250#555—224no—
251#555—224no—
252#553—224no—
253#553—224no—
254#550—28no—
255#550—28no—
256#550—28no—
257#550—28no—
258#550—224no—
259#550—224no—
260#550—28no—
261#550D4116yescomplemented
262#547—224no—
263#547—424no—
264#540—224no—
265#540—224no—
266#532—224no—
267#532—224no—
268#532—224no—
269#532—224no—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2316yes—
275C2×#127C2313yes—
276C2×#127C2313yes—
277C2×#127C2313yes—
278C2×#127C2313yes—
279C2×#127C2313yes—
280C2×#127C2313yes—
281#529—224no—
282C2×#126C2313yes—
283C2×#126C2313yes—
284C2×#125C2313yes—
285C2×#125C2311yescharacteristic
286C2×#125C2313yes—
287C2×#124C2313yes—
288C2×#124C2316yes—
289C2×#124C2316yes—
290C2×#124C2316yes—
291C2×#123C2313yes—
292C2×#123C2316yes—
293C2×#123C2313yes—
294C2×#123C2316yes—
295C2×#123C2313yes—
296C2×#123C2316yes—
297C2×#123C2316yes—
298C2×#123C2316yes—
299C2×#123C2313yes—
300C2×#123C2313yes—
301C2×#123C2316yes—
302C2×#123C2316yes—
303C2×C22⋊Q8C2313yes—
304C2×C22⋊Q8C2313yes—
305C2×C22⋊Q8C2316yes—
306C2×C22⋊Q8C2316yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311C2×#121C2313yes—
312C2×#121C2313yes—
313C2×#121C2316yes—
314C2×#121C2316yes—
315C2×#121C2313yes—
316C2×#121C2316yes—
317C2×#121C2316yes—
318C2×#121C2316yes—
319C2×#121C2316yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2316yes—
325C2×#121C2316yes—
326C2×#121C2313yes—
327C2×#121C2316yes—
328C2×#121C2316yes—
329C2×#121C2313yes—
330C2×#121C2313yes—
331#520—28no—
332#520—28no—
333#520—28no—
334C4×#41—28no—
335C4×#41—28no—
336C4×#41—28no—
337C4×#41—28no—
338C4×#41—28no—
339C4×#41—224no—
340C2×C4×Q8C2313yes—
341C2×C4×Q8C2313yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×D4C2313yes—
355C2×C4×D4C2313yes—
356C2×C4×D4C2313yes—
357C2×C4×D4C2313yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2316yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2313yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2316yes—
380C2×C4×D4C2316yes—
381C2×C4×D4C2313yes—
382C2×#117C2313yes—
383C2×#117C2313yes—
384C2×#117C2313yes—
385C2×#117C2313yes—
386C2×#117C2313yes—
387C2×#117C2313yes—
388C2×#117C2313yes—
389C2×#117C2313yes—
390C2×#117C2313yes—
391C2×#117C2313yes—
392C2×#117C2313yes—
393C22×C4⋊C4C2313yes—
394C22×C4⋊C4C2313yes—
395C22×C4⋊C4C2313yes—
396C22×C4⋊C4C2313yes—
397C22×C4⋊C4C2316yes—
398C22×C4⋊C4C2313yes—
399C22×C42C2313yes—
400C22×C42C2313yes—
401C22×C42C2313yes—
402C22×C42C2313yes—
403C22×C42C2313yes—
404#400C2313yes—
405#400C2313yes—
406#399C2316yes—
407#399C2316yes—
408#399C2316yes—
409#399C2313yes—
410#399C2313yes—
411#398C2316yes—
412#398C2311yescharacteristic
413#398C2311yescharacteristic
414#398C2313yes—
415#398C2313yes—
416#398C2313yes—
417#398C2313yes—
418#398C2313yes—
419#398C2313yes—
420#397C2313yes—
421#397C2313yes—
422#397C2313yes—
423#397C2313yes—
424#397C2316yes—
425#397C2316yes—
426#397C2316yes—
427#396C2316yes—
428#396C2316yes—
429#396C2313yes—
430#396C2313yes—
431#396C2313yes—
432#396C2313yes—
433#395C2313yes—
434#395C2316yes—
435#395C2311yescharacteristic
436#395C2311yescharacteristic
437#395C2313yes—
438#395C2313yes—
439#395C2316yes—
440#395C2316yes—
441#394C2313yes—
442#394C2316yes—
443#394C2316yes—
444#394C2316yes—
445#394C2313yes—
446#394C2313yes—
447#394C2313yes—
448#394C2313yes—
449#394C2316yes—
450#394C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2316yes—
454#394C2316yes—
455#394C2316yes—
456#394C2316yes—
457#394C2316yes—
458#394C2316yes—
459#394C2316yes—
460#393C2313yes—
461#393C2316yes—
462#393C2316yes—
463#392C2316yes—
464#392C2316yes—
465#392C2313yes—
466#392C2316yes—
467#392C2316yes—
468#391C2316yes—
469#391C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2316yes—
475#390C2316yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2316yes—
490#389C2313yes—
491#389C2316yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2316yes—
506#389C2316yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2311yescharacteristic
517#389C2313yes—
518#389C2311yescharacteristic
519#388C2316yes—
520#388C2316yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2316yes—
525#388C2316yes—
526#388C2316yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#387C2313yes—
537#387C2316yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2311yescharacteristic
543#387C2311yescharacteristic
544#387C2311yescharacteristic
545#387C2311yescharacteristic
546#387C2311yescharacteristic
547#387C2311yescharacteristic
548#387C2313yes—
549#386C2316yes—
550#386C2316yes—
551#386C2313yes—
552#386C2313yes—
553#386C2316yes—
554#386C2316yes—
555#386C2316yes—
556#386C2316yes—
557#386C2316yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#386C2313yes—
563#386C2313yes—
564#386C2316yes—
565#386C2313yes—
566#386C2313yes—
567#386C2313yes—
568#386C2313yes—
569#386C2313yes—
570#385C2313yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2313yes—
575#385C2313yes—
576#385C2313yes—
577#385C2316yes—
578#385C2316yes—
579#385C2316yes—
580#385C2313yes—
581#385C2313yes—
582#385C2316yes—
583#385C2316yes—
584#385C2316yes—
585#385C2316yes—
586#385C2313yes—
587#385C2313yes—
588#385C2316yes—
589#385C2313yes—
590#385C2313yes—
591#385C2313yes—
592#385C2313yes—
593#385C2313yes—
594#384C2313yes—
595#384C2313yes—
596#384C2313yes—
597#384C2313yes—
598#384C2313yes—
599#382C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#382C2313yes—
604#381C2313yes—
605#381C2313yes—
606#381C2313yes—
607#380C2316yes—
608#380C2316yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2316yes—
618#380C2316yes—
619#380C2313yes—
620#380C2313yes—
621C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2316yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2311yescharacteristic
637C4×C4⋊C4C2313yes—
638C4×C4⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2316yes—
648C4×C22⋊C4C2316yes—
649#376C2313yes—
650C2×#95C2316yes—
651C2×#95C2313yes—
652C2×#95C2313yes—
653C2×#41—24no—
654C2×#41—24no—
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—212no—
664C2×#41—224no—
665C2×#41—224no—
666C2×#41—412no—
667C2×#41—46no—
668C2×#41—46no—
669C2×#41—412no—
670C2×#41—86no—
671C2×#41—86no—
672C2×#41C2×D418yes—
673C2×#41C2×D418yes—
674C22×Q8C2411yescharacteristic
675C22×Q8C2413yes—
676C22×Q8C2416yes—
677C22×Q8C2411yescharacteristic
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2416yes—
686C22×D4C2416yes—
687C22×D4C2413yes—
688C22×D4C2413yes—
689C22×D4C2416yes—
690C22×D4C2416yes—
691C22×D4C2416yes—
692C22×D4C2413yes—
693C22×D4C2416yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2413yes—
698C23×C4C2413yes—
699C23×C4C2413yes—
700C23×C4C2413yes—
701C23×C4C2413yes—
702C23×C4C2413yes—
703C23×C4C2413yes—
704C23×C4C2413yes—
705C23×C4C2416yes—
706C23×C4C2416yes—
707C23×C4C2416yes—
708C23×C4C2413yes—
709C23×C4C2413yes—
710C23×C4C2413yes—
711C4⋊Q8—212no—
712C4⋊Q8—212no—
713C4⋊Q8—212no—
714C4⋊Q8—212no—
715C4⋊Q8—412no—
716#127—212no—
717#127—212no—
718#127—212no—
719#127—212no—
720#127—212no—
721#127C2×D4124yes—
722#126—212no—
723#126—212no—
724#125—24no—
725#125—212no—
726#125—212no—
727#124—224no—
728#124—212no—
729#124—224no—
730#124—224no—
731#123—212no—
732#123—224no—
733#123—212no—
734#123—212no—
735#123—224no—
736#123—412no—
737#123—46no—
738#123—412no—
739#123—412no—
740#123—412no—
741#123—46no—
742#123—86no—
743C22⋊Q8—212no—
744C22⋊Q8—212no—
745C22⋊Q8—412no—
746C22⋊Q8—86no—
747#121—212no—
748#121—224no—
749#121—212no—
750#121—212no—
751#121—224no—
752#121—224no—
753#121—224no—
754#121—212no—
755#121—224no—
756#121—224no—
757#121—212no—
758#121—212no—
759#121—212no—
760#121—212no—
761#121—212no—
762#121—212no—
763#121—212no—
764#121—412no—
765#121—412no—
766#121—46no—
767#121—412no—
768#121—86no—
769#121C2×D4124yes—
770#121C2×D4124yes—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—212no—
782C4×Q8—212no—
783C4×Q8C2×D418yes—
784C4×Q8#4118yescomplemented
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—212no—
798C4×D4—212no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—212no—
803C4×D4—212no—
804C4×D4—224no—
805C4×D4—212no—
806C4×D4—212no—
807C4×D4—212no—
808C4×D4—212no—
809C4×D4—212no—
810C4×D4—412no—
811C4×D4—412no—
812C4×D4C2×D4124yes—
813#117—212no—
814#117—212no—
815#117—212no—
816#117—212no—
817#117—212no—
818#117—212no—
819#117—212no—
820#117—212no—
821#117—212no—
822#117—212no—
823#117—212no—
824C2×C4⋊C4—212no—
825C2×C4⋊C4—212no—
826C2×C4⋊C4—212no—
827C2×C4⋊C4—212no—
828C2×C4⋊C4—46no—
829C2×C4⋊C4—412no—
830C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2416yes—
870C2×C4⋊C4C2416yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2416yes—
877C2×C4⋊C4C2416yes—
878C2×C4⋊C4C2413yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2416yes—
881C2×C4⋊C4C2413yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2413yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2416yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2416yes—
891C2×C22⋊C4C2416yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2416yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2416yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
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⋊C4C2413yes—
913C2×C22⋊C4C2416yes—
914C2×C22⋊C4C2416yes—
915C2×C22⋊C4C2416yes—
916C2×C22⋊C4C2416yes—
917C2×C22⋊C4C2416yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2416yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2416yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2416yes—
926C2×C22⋊C4C2413yes—
927C2×C22⋊C4C2413yes—
928C2×C22⋊C4C2413yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2413yes—
932C2×C42—212no—
933C2×C42—212no—
934C2×C42—212no—
935C2×C42—212no—
936C2×C42—212no—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2413yes—
940C2×C42C2413yes—
941C2×C42C2413yes—
942C2×C42C2413yes—
943C2×C42C2413yes—
944C2×C42C2413yes—
945C2×C42C2413yes—
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2413yes—
950C2×C42C2413yes—
951C2×C42C2413yes—
952C2×C42C2413yes—
953C2×C42C2413yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2416yes—
957C2×C42C2413yes—
958C2×C42C2413yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2413yes—
962#95C2413yes—
963#95C2416yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2416yes—
971#95C2411yescharacteristic
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2411yescharacteristic
981#95C2411yescharacteristic
982#95C2411yescharacteristic
983#95C2411yescharacteristic
984#95C2411yescharacteristic
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2416yes—
992#95C2411yescharacteristic
993#95C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2413yes—
996#95C2413yes—
997#95C2416yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2413yes—
1003#95C2416yes—
1004C24C2513yes—
1005C24C2513yes—
1006C24C2513yes—
1007C24C2513yes—
1008#41—232no—
1009#41—232no—
1010#41—448no—
1011#41—416no—
1012#41—416no—
1013#41—848no—
1014#41—848no—
1015C2×Q8—22no—
1016C2×Q8—26no—
1017C2×Q8—212no—
1018C2×Q8—26no—
1019C2×Q8—22no—
1020C2×Q8—22no—
1021C2×Q8—43no—
1022C2×Q8—46no—
1023C2×Q8—46no—
1024C2×Q8C22×D414yes—
1025C2×Q8C2×#4114yes—
1026C2×Q82−1+414yes—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—26no—
1030C2×D4—212no—
1031C2×D4—26no—
1032C2×D4—212no—
1033C2×D4—212no—
1034C2×D4—212no—
1035C2×D4—26no—
1036C2×D4—26no—
1037C2×D4—26no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—212no—
1043C2×D4—26no—
1044C2×D4—26no—
1045C2×D4—26no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—26no—
1049C2×D4—26no—
1050C2×D4—46no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—46no—
1056C2×D4—43no—
1057C2×D4—46no—
1058C2×D4—46no—
1059C2×D4—46no—
1060C2×D4—46no—
1061C2×D4—46no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—46no—
1065C2×D4—43no—
1066C2×D4—46no—
1067C2×D4—46no—
1068C2×D4—46no—
1069C2×D4—43no—
1070C2×D4—46no—
1071C2×D4C22×D4112yes—
1072C2×D4C22×D4112yes—
1073C2×D4C22×D4112yes—
1074C2×D4C22×D4124yes—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—26no—
1080C22×C4—26no—
1081C22×C4—26no—
1082C22×C4—26no—
1083C22×C4—26no—
1084C22×C4—26no—
1085C22×C4—212no—
1086C22×C4—26no—
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—26no—
1096C22×C4—26no—
1097C22×C4—26no—
1098C22×C4—26no—
1099C22×C4—26no—
1100C22×C4—26no—
1101C22×C4—26no—
1102C22×C4—212no—
1103C22×C4—26no—
1104C22×C4—212no—
1105C22×C4—43no—
1106C22×C4—43no—
1107C22×C4—43no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—43no—
1114C22×C4—46no—
1115C22×C4—46no—
1116C22×C4—43no—
1117C22×C4—46no—
1118C22×C4—46no—
1119C22×C4—43no—
1120C22×C4—43no—
1121C22×C4—46no—
1122C22×C4—43no—
1123C22×C4—46no—
1124C22×C4C22×D4112yes—
1125C22×C4C22×D4112yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2513yes—
1130C22×C4C2513yes—
1131C22×C4C2513yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2513yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C22×C4C2513yes—
1137C22×C4C2513yes—
1138C22×C4C2513yes—
1139C22×C4C2513yes—
1140C22×C4C2513yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2513yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2513yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2513yes—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—26no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—26no—
1163C4⋊C4—26no—
1164C4⋊C4—26no—
1165C4⋊C4—26no—
1166C4⋊C4—26no—
1167C4⋊C4—26no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—212no—
1171C4⋊C4—22no—
1172C4⋊C4—26no—
1173C4⋊C4—26no—
1174C4⋊C4—26no—
1175C4⋊C4—26no—
1176C4⋊C4—22no—
1177C4⋊C4—26no—
1178C4⋊C4—22no—
1179C4⋊C4—26no—
1180C4⋊C4—26no—
1181C4⋊C4—26no—
1182C4⋊C4—26no—
1183C4⋊C4—26no—
1184C4⋊C4—26no—
1185C4⋊C4—26no—
1186C4⋊C4—22no—
1187C4⋊C4—26no—
1188C4⋊C4—22no—
1189C4⋊C4—22no—
1190C4⋊C4—26no—
1191C4⋊C4—22no—
1192C4⋊C4—43no—
1193C4⋊C4—43no—
1194C4⋊C4—46no—
1195C4⋊C4—46no—
1196C4⋊C4—43no—
1197C4⋊C4—43no—
1198C4⋊C4—43no—
1199C4⋊C4—46no—
1200C4⋊C4—46no—
1201C4⋊C4—43no—
1202C4⋊C4—46no—
1203C4⋊C4—43no—
1204C4⋊C4C22×D4112yes—
1205C4⋊C4C22×D414yes—
1206C4⋊C4C2×#41112yes—
1207C4⋊C4H(5,𝔽2)14yes—
1208C22⋊C4—26no—
1209C22⋊C4—212no—
1210C22⋊C4—26no—
1211C22⋊C4—212no—
1212C22⋊C4—212no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—26no—
1216C22⋊C4—26no—
1217C22⋊C4—26no—
1218C22⋊C4—26no—
1219C22⋊C4—212no—
1220C22⋊C4—26no—
1221C22⋊C4—26no—
1222C22⋊C4—26no—
1223C22⋊C4—26no—
1224C22⋊C4—26no—
1225C22⋊C4—212no—
1226C22⋊C4—26no—
1227C22⋊C4—26no—
1228C22⋊C4—26no—
1229C22⋊C4—26no—
1230C22⋊C4—26no—
1231C22⋊C4—26no—
1232C22⋊C4—26no—
1233C22⋊C4—26no—
1234C22⋊C4—26no—
1235C22⋊C4—26no—
1236C22⋊C4—46no—
1237C22⋊C4—46no—
1238C22⋊C4—43no—
1239C22⋊C4—46no—
1240C22⋊C4—46no—
1241C22⋊C4—46no—
1242C22⋊C4—46no—
1243C22⋊C4—43no—
1244C22⋊C4—46no—
1245C22⋊C4—43no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—46no—
1249C22⋊C4—43no—
1250C22⋊C4—43no—
1251C22⋊C4—43no—
1252C22⋊C4—43no—
1253C22⋊C4C22×D4112yes—
1254C22⋊C4C22×D4112yes—
1255C42—22no—
1256C42—22no—
1257C42—22no—
1258C42—26no—
1259C42—22no—
1260C42—26no—
1261C42—26no—
1262C42—26no—
1263C42—26no—
1264C42—26no—
1265C42—26no—
1266C42—26no—
1267C42—26no—
1268C42—26no—
1269C42—22no—
1270C42—26no—
1271C42—26no—
1272C42—26no—
1273C42—26no—
1274C42—46no—
1275C42C22×D4112yes—
1276C42C2×#41112yes—
1277C23—23no—
1278C23—23no—
1279C23—23no—
1280C23—23no—
1281C23—23no—
1282C23—23no—
1283C23—23no—
1284C23—23no—
1285C23—23no—
1286C23—23no—
1287C23—23no—
1288C23—23no—
1289C23—23no—
1290C23—23no—
1291C23—23no—
1292C23—23no—
1293C23—23no—
1294C23—23no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—23no—
1299C23—23no—
1300C23—23no—
1301C23—23no—
1302C23—23no—
1303C23C23×D416yes—
1304C23C23×D416yes—
1305C23C2611yescharacteristic
1306Q8—28no—
1307Q8—412no—
1308Q8—812no—
1309Q8#547116yescomplemented
1310D4—224no—
1311D4—224no—
1312D4—412no—
1313D4—424no—
1314D4—412no—
1315D4—412no—
1316D4—412no—
1317D4—412no—
1318D4—412no—
1319D4—86no—
1320D4—812no—
1321D4—812no—
1322D4—86no—
1323D4—812no—
1324D4—812no—
1325D4—812no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—23no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—23no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—224no—
1349C2×C4—224no—
1350C2×C4—23no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—21no—
1372C2×C4—23no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—21no—
1378C2×C4—23no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—23no—
1383C2×C4—23no—
1384C2×C4—23no—
1385C2×C4—23no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—23no—
1390C2×C4—21no—
1391C2×C4—23no—
1392C2×C4—23no—
1393C2×C4—23no—
1394C2×C4—23no—
1395C2×C4—412no—
1396C2×C4—412no—
1397C2×C4—412no—
1398C2×C4—412no—
1399C2×C4—412no—
1400C2×C4—412no—
1401C2×C4—412no—
1402C2×C4—412no—
1403C2×C4—412no—
1404C2×C4—412no—
1405C2×C4—86no—
1406C2×C4—812no—
1407C2×C4—812no—
1408C2×C4—86no—
1409C2×C4—812no—
1410C2×C4C23×D412yes—
1411C2×C4C23×D412yes—
1412C2×C4C23×D412yes—
1413C2×C4C23×D416yes—
1414C2×C4C23×D416yes—
1415C2×C4C22×#4112yes—
1416C2×C4C22×#4116yes—
1417C2×C4C22×#4116yes—
1418C2×C4C2×H(5,𝔽2)12yes—
1419C2×C4C2×H(5,𝔽2)12yes—
1420C2×C4C2×H(5,𝔽2)12yes—
1421C2×C4C2×2−1+416yes—
1422C2×C4#58512yes—
1423C2×C4#58512yes—
1424C22—26no—
1425C22—26no—
1426C22—26no—
1427C22—26no—
1428C22—26no—
1429C22—26no—
1430C22—43no—
1431C22—43no—
1432C22—43no—
1433C22—43no—
1434C22—43no—
1435C22—43no—
1436C22—43no—
1437C22—43no—
1438C22—43no—
1439C22—43no—
1440C22—43no—
1441C22—43no—
1442C22—43no—
1443C22—43no—
1444C22—43no—
1445C22—43no—
1446C22—43no—
1447C22—43no—
1448C22—43no—
1449C22—43no—
1450C22—43no—
1451C22—43no—
1452C22C24×D411yescharacteristic
1453C22C23×#4111yescharacteristic
1454C22C22×H(5,𝔽2)11yescharacteristic
1455C22C22×2−1+411yescharacteristic
1456C22C2×#58511yescharacteristic
1457C22C2×#58511yescharacteristic
1458C22H(7,𝔽2)11yescharacteristic
1459C4—22no—
1460C4—22no—
1461C4—26no—
1462C4—22no—
1463C4—22no—
1464C4—26no—
1465C4—22no—
1466C4—22no—
1467C4—22no—
1468C4—22no—
1469C4—22no—
1470C4—43no—
1471C4—43no—
1472C4—43no—
1473C4—43no—
1474C4—41no—
1475C4—43no—
1476C4—43no—
1477C4—43no—
1478C4—43no—
1479C4—41no—
1480C4—43no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—41no—
1485C4C2×#547112yes—
1486C2—46no—
1487C2—46no—
1488C2—83no—
1489C2—83no—
1490C2C22×#54711yescharacteristic
1491C2#6280011yescharacteristic
1492C2#6281111yescharacteristic
1493C2#6295211yescharacteristic
1494C2D4×H(5,𝔽2)11yescharacteristic
1495C2#6300611yescharacteristic
1496C2#6303911yescharacteristic
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×#3517C2semidirect
2. C2×#3483C2semidirect
3. #59315C2semidirect
4. #59117C2semidirect
5. #59115C2semidirect
6. #59112C2semidirect
7. #59066C2semidirect
8. #44931C2semidirect
9. #44928C2semidirect
10. #44888C2semidirect
11. #44880C2semidirect
12. #38050C2semidirect
13. #37869C2semidirect
14. #37792C2semidirect
15. #37764C2semidirect
16. #36455C2semidirect
17. #36433C2semidirect
18. #36433C2semidirect
19. #36433C2semidirect
20. #36431C2semidirect
21. #36361C2semidirect
22. #36126C2semidirect
23. #36029C2semidirect
24. #36005C2semidirect
25. #35937C2semidirect
26. #35748C2semidirect
27. #34735C2semidirect
28. #34295C2semidirect
29. #34295C2semidirect
30. #34250C2semidirect
31. C4⋊C4×#41C2semidirect
261. #550D4semidirect
784. C4×Q8#41semidirect
1309. Q8#547semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34832
#593152
#591172
#591152
#591122
#590662
#449312
#449282
#448882
#448802
#380502
#378692
#377922
#377642
#364552
#364332
#364312
#363612
#361262
#360292
#360052
#359372
#357482
#347352
#342952
#342502
C4⋊C4×#412