Finite Group Databasebeta

← #7715257

Subgroups — #7715257

Order 512.

6816 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3548C211yesmaximal, characteristic, complemented
2C2×#3557C211yesmaximal, characteristic, complemented
3#52033C218yesmaximal, complemented
4#51784C218yesmaximal, complemented
5#46417C218yesmaximal, complemented
6#46368C218yesmaximal, complemented
7#39747C212yesmaximal, complemented
8#39745C212yesmaximal, complemented
9#39613C212yesmaximal, complemented
10#39611C212yesmaximal, complemented
11#39174C212yesmaximal, complemented
12#39169C212yesmaximal, complemented
13#39163C212yesmaximal, complemented
14#39161C212yesmaximal, complemented
15#37616C212yesmaximal, complemented
16#37420C211yesmaximal, characteristic, complemented
17#37301C212yesmaximal, complemented
18#37298C211yesmaximal, characteristic, complemented
19#35332C211yesmaximal, characteristic, complemented
20#35303C212yesmaximal, complemented
21#35278C211yesmaximal, characteristic, complemented
22#35276C212yesmaximal, complemented
23#34074C211yesmaximal, characteristic, complemented
24#3557—216no—
25#3548—216no—
26C2×#563C2214yes—
27C2×#562C2214yes—
28C2×#559C2212yes—
29C2×#557C2212yes—
30C2×#556C2212yes—
31C2×#554C2212yes—
32C2×#554C2212yes—
33C2×#554C2212yes—
34C2×#552C2214yes—
35C2×#550C2212yes—
36C2×#550C2212yes—
37C2×#547C2214yes—
38C2×#542C2214yes—
39C2×#542C2212yes—
40C2×#541C2211yescharacteristic
41C2×#540C2211yescharacteristic
42C2×#540C2211yescharacteristic
43C2×#540C2211yescharacteristic
44C2×#540C2212yes—
45C2×#539C2214yes—
46C2×#537C2214yes—
47C2×#537C2214yes—
48C2×#533C2211yescharacteristic
49C2×#532C2212yes—
50C2×#529C2212yes—
51#2867C2211yescharacteristic
52#2861C2212yes—
53#2859C2211yescharacteristic
54#2859C2211yescharacteristic
55#2858C2212yes—
56#2858C2211yescharacteristic
57#2856C2212yes—
58#2856C2212yes—
59#2850C2212yes—
60#2850C2212yes—
61#2813C2218yes—
62#2732C2218yes—
63#2730C2218yes—
64#2729C2218yes—
65#2728C2218yes—
66#2714C2218yes—
67#2714C2218yes—
68#2711C2218yes—
69#2711C2218yes—
70#2707C2218yes—
71#2705C2218yes—
72#2704C2218yes—
73#2702C2218yes—
74#2691C2218yes—
75#2683C2218yes—
76#2682C2218yes—
77#2681C2218yes—
78#2681C2218yes—
79#2676C2218yes—
80#2676C2218yes—
81#2676C2218yes—
82#2675C2218yes—
83#2673C2218yes—
84#2673C2218yes—
85#2671C2218yes—
86#2660C2212yes—
87#2660C2212yes—
88#2657C2212yes—
89#2657C2212yes—
90#2642C2211yescharacteristic
91#2641C2211yescharacteristic
92#2641C2212yes—
93#2641C2211yescharacteristic
94#2641C2211yescharacteristic
95#2640C2212yes—
96#2636C2218yes—
97#2620C2212yes—
98#2620C2212yes—
99#2620C2218yes—
100#2619C2212yes—
101#2619C2212yes—
102#2610C2218yes—
103#2603C2218yes—
104#2568C2212yes—
105#2566C2212yes—
106#2566C2212yes—
107#2566C2212yes—
108#2566C2212yes—
109#2566C2212yes—
110#2566C2212yes—
111#2565C2212yes—
112#2565C2212yes—
113#2563C2212yes—
114#2559C2218yes—
115#2558C2218yes—
116#2555C2218yes—
117#2554C2218yes—
118#2548C2212yes—
119#2548C2212yes—
120#2548C2212yes—
121#2547C2212yes—
122#2544C2212yes—
123#2544C2212yes—
124#2544C2212yes—
125#2544C2212yes—
126#2543C2218yes—
127#2542C2212yes—
128#2542C2212yes—
129#2541C2212yes—
130#2541C2212yes—
131#2541C2212yes—
132#2541C2212yes—
133#2481C2218yes—
134#2477C2218yes—
135#2473C2218yes—
136#2465C2218yes—
137#2464C2218yes—
138#2463C2218yes—
139#2461C2218yes—
140#2449C2218yes—
141#2449C2218yes—
142#2445C2218yes—
143#2443C2218yes—
144#2432C2218yes—
145#2431C2218yes—
146#2430C2218yes—
147#2428C2218yes—
148#2428C2218yes—
149#2426C2218yes—
150#2416C2218yes—
151#2414C2218yes—
152#2407C2218yes—
153#2407C2218yes—
154#2407C2218yes—
155#2331C2214yes—
156#2330C2214yes—
157#2329C2214yes—
158#2329C2214yes—
159#2328C2212yes—
160#2328C2212yes—
161#2328C2212yes—
162#2328C2212yes—
163#2326C2212yes—
164#2326C2212yes—
165#2326C2212yes—
166#2326C2212yes—
167C4×#127C2212yes—
168C4×#127C2212yes—
169C4×#124C2212yes—
170C4×#124C2212yes—
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2295C2212yes—
174#2295C2212yes—
175#2295C2212yes—
176#2295C2212yes—
177#2285C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C4×#117C2211yescharacteristic
180C2×#376C2211yescharacteristic
181C22×#41C2314yes—
182C22×#41C2314yes—
183C22×#41C2314yes—
184#563—232no—
185#562—232no—
186#559—216no—
187#557—216no—
188#556—216no—
189#554—216no—
190#554—216no—
191#554—216no—
192#552—232no—
193#550—216no—
194#550—216no—
195#547—232no—
196#542—232no—
197#542—216no—
198#541—28no—
199#540—28no—
200#540—28no—
201#540—216no—
202#540—28no—
203#539—232no—
204#537—232no—
205#537—232no—
206#533D4116yescomplemented
207#532—216no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2312yes—
214C2×#127C2311yescharacteristic
215C2×#127C2312yes—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2312yes—
222C2×#127C2318yes—
223#529—216no—
224C2×#126C2314yes—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2311yescharacteristic
230C2×#125C2312yes—
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#125C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2318yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2318yes—
271C2×C22⋊Q8C2318yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2318yes—
290C2×#121C2318yes—
291C2×#121C2318yes—
292C2×#121C2318yes—
293C2×#121C2318yes—
294C2×#121C2318yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2318yes—
314C2×C4×D4C2318yes—
315C2×#117C2314yes—
316C2×#117C2314yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2314yes—
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327#400C2318yes—
328#400C2318yes—
329#399C2318yes—
330#399C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#397C2318yes—
336#397C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#395C2318yes—
346#395C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#393C2318yes—
364#393C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2318yes—
371#392C2318yes—
372#392C2318yes—
373#392C2318yes—
374#392C2318yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2318yes—
379#391C2312yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2312yes—
387#390C2312yes—
388#390C2318yes—
389#390C2318yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2318yes—
399#390C2318yes—
400#390C2318yes—
401#390C2318yes—
402#390C2318yes—
403#390C2318yes—
404#390C2318yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2312yes—
458#385C2314yes—
459#385C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#382C2312yes—
466#382C2312yes—
467#382C2312yes—
468#382C2312yes—
469#382C2312yes—
470#380C2318yes—
471#380C2314yes—
472#380C2318yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486#376C2311yescharacteristic
487#376C2312yes—
488#376C2312yes—
489#376C2312yes—
490#376C2311yescharacteristic
491#376C2312yes—
492#376C2312yes—
493C2×#95C2314yes—
494C43C2311yescharacteristic
495C43C2312yes—
496C43C2311yescharacteristic
497C2×#41—216no—
498C2×#41—216no—
499C2×#41—216no—
500C2×#41—88no—
501C2×#41—88no—
502C2×#41—88no—
503C22×Q8C2412yes—
504C22×Q8C2414yes—
505C22×Q8C2414yes—
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×D4C2412yes—
509C22×D4C2412yes—
510C22×D4C2412yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C22×D4C2414yes—
514C22×D4C2418yes—
515C22×D4C2414yes—
516C22×D4C2414yes—
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2418yes—
523C22×D4C2418yes—
524C22×D4C2418yes—
525C23×C4C2411yescharacteristic
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2414yes—
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C4⋊Q8—216no—
539C4⋊Q8—28no—
540C4⋊Q8—24no—
541C4⋊Q8—28no—
542C4⋊Q8C2×D4116yes—
543#127—28no—
544#127—24no—
545#127—28no—
546#127—24no—
547#127—24no—
548#127—28no—
549#127—44no—
550#127—44no—
551#127—44no—
552#127—88no—
553#126—216no—
554#126—216no—
555#126—216no—
556#126—216no—
557#126—216no—
558#125—216no—
559#125—216no—
560#125—216no—
561#125—28no—
562#125—24no—
563#125—28no—
564#125—24no—
565#125—24no—
566#125—24no—
567#125C2×D4116yes—
568#124—216no—
569#124—216no—
570#124—28no—
571#124—216no—
572#124—28no—
573#124—28no—
574#124—44no—
575#124—44no—
576#124—44no—
577#124—88no—
578#123—216no—
579#123—216no—
580#123—216no—
581#123—216no—
582#123—216no—
583#123—216no—
584#123—216no—
585#123—216no—
586#123—216no—
587C22⋊Q8—216no—
588C22⋊Q8—216no—
589C22⋊Q8—216no—
590C22⋊Q8—216no—
591C22⋊Q8—28no—
592C22⋊Q8—216no—
593C22⋊Q8—216no—
594C22⋊Q8—216no—
595C22⋊Q8—216no—
596C22⋊Q8—216no—
597C22⋊Q8—216no—
598C22⋊Q8—216no—
599C22⋊Q8—88no—
600C22⋊Q8—88no—
601C22⋊Q8C2×D4116yes—
602C22⋊Q8C2×D4116yes—
603#121—28no—
604#121—216no—
605#121—28no—
606#121—28no—
607#121—216no—
608#121—216no—
609#121—216no—
610#121—216no—
611#121—216no—
612#121—216no—
613#121—216no—
614#121—216no—
615#121—216no—
616#121—216no—
617#121—216no—
618#121—88no—
619#121—88no—
620#121—88no—
621#121—88no—
622#121—88no—
623#121—88no—
624C4×Q8—216no—
625C4×Q8—28no—
626C4×Q8—28no—
627C4×Q8—28no—
628C4×Q8C2×D4116yes—
629C4×Q8C2×D4116yes—
630C4×D4—216no—
631C4×D4—216no—
632C4×D4—28no—
633C4×D4—216no—
634C4×D4—28no—
635C4×D4—28no—
636C4×D4—28no—
637C4×D4—28no—
638C4×D4—28no—
639C4×D4—28no—
640C4×D4—28no—
641C4×D4—28no—
642C4×D4—88no—
643C4×D4—88no—
644#117—216no—
645#117—216no—
646#117—42no—
647#117—42no—
648#117C2×D418yes—
649#117C2×D418yes—
650C2×C4⋊C4—216no—
651C2×C4⋊C4—216no—
652C2×C4⋊C4—216no—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2418yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2411yescharacteristic
729C2×C22⋊C4C2411yescharacteristic
730C2×C42—24no—
731C2×C42—42no—
732C2×C42C2×D418yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2411yescharacteristic
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2412yes—
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2412yes—
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2412yes—
753C2×C42C2411yescharacteristic
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776C24C2514yes—
777C24C2514yes—
778C24C2514yes—
779C24C2511yescharacteristic
780#41—832no—
781#41—832no—
782#41—832no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8C22×D418yes—
793C2×Q8C22×D418yes—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—216no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—48no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—48no—
824C2×D4—48no—
825C2×D4—48no—
826C2×D4—48no—
827C2×D4—48no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—48no—
833C2×D4—48no—
834C2×D4—48no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—42no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4C22×D414yes—
861C22×C4C22×D418yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4C22×D418yes—
913C4⋊C4C22×D418yes—
914C4⋊C4C22×D418yes—
915C4⋊C4C22×D418yes—
916C4⋊C4C22×D418yes—
917C4⋊C4C22×D418yes—
918C4⋊C4C22×D418yes—
919C4⋊C4C22×D418yes—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—216no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4C22×D418yes—
956C22⋊C4C22×D414yes—
957C22⋊C4C22×D414yes—
958C42—28no—
959C42—28no—
960C42—28no—
961C42—24no—
962C42—22no—
963C42—24no—
964C42—22no—
965C42—24no—
966C42—22no—
967C42—42no—
968C42—44no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42C22×D414yes—
973C42C22×D414yes—
974C42C22×D418yes—
975C42C22×D414yes—
976C42C22×D418yes—
977C42C22×D414yes—
978C422−1+414yes—
979C23—21no—
980C23—21no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—28no—
992C23—28no—
993C23—28no—
994C23—28no—
995C23—28no—
996C23—28no—
997C23C23×D412yes—
998C23C2611yescharacteristic
999Q8—48no—
1000Q8—48no—
1001Q8—48no—
1002Q8—88no—
1003Q8—88no—
1004D4—416no—
1005D4—48no—
1006D4—48no—
1007D4—48no—
1008D4—88no—
1009D4—816no—
1010D4—88no—
1011D4—88no—
1012D4—88no—
1013D4—88no—
1014D4—88no—
1015D4—88no—
1016D4—88no—
1017D4—88no—
1018D4—816no—
1019D4—168no—
1020D4—168no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—28no—
1054C2×C4—48no—
1055C2×C4—416no—
1056C2×C4—416no—
1057C2×C4—88no—
1058C2×C4—88no—
1059C2×C4—88no—
1060C2×C4—84no—
1061C2×C4—88no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4—88no—
1065C2×C4—84no—
1066C2×C4C23×D414yes—
1067C2×C4C23×D414yes—
1068C2×C4C23×D414yes—
1069C2×C4C23×D412yes—
1070C2×C4C23×D414yes—
1071C2×C4C23×D414yes—
1072C2×C4C23×D414yes—
1073C2×C4C23×D412yes—
1074C2×C4C2×2−1+414yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4#58512yes—
1077C22—22no—
1078C22—24no—
1079C22—42no—
1080C22—42no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—48no—
1091C22—48no—
1092C22—48no—
1093C22—48no—
1094C22—48no—
1095C22—48no—
1096C22C24×D411yescharacteristic
1097C22C22×2−1+411yescharacteristic
1098C22C2×#58511yescharacteristic
1099C22H(7,𝔽2)14yes—
1100C4—22no—
1101C4—24no—
1102C4—24no—
1103C4—24no—
1104C4—24no—
1105C4—24no—
1106C4—24no—
1107C4—24no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—44no—
1112C4—44no—
1113C4—42no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4#349714yes—
1119C2—42no—
1120C2—84no—
1121C2—84no—
1122C2—84no—
1123C2C2×#349711yescharacteristic
1124C2#6285212yes—
1125C2#6288112yes—
1126C2#6288312yes—
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×#3548C2semidirect
2. C2×#3557C2semidirect
3. #52033C2semidirect
4. #51784C2semidirect
5. #46417C2semidirect
6. #46368C2semidirect
7. #39747C2semidirect
8. #39745C2semidirect
9. #39613C2semidirect
10. #39611C2semidirect
11. #39174C2semidirect
12. #39169C2semidirect
13. #39163C2semidirect
14. #39161C2semidirect
15. #37616C2semidirect
16. #37420C2semidirect
17. #37301C2semidirect
18. #37298C2semidirect
19. #35332C2semidirect
20. #35303C2semidirect
21. #35278C2semidirect
22. #35276C2semidirect
23. #34074C2semidirect
206. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35482
C2×#35572
#520332
#517842
#464172
#463682
#397472
#397452
#396132
#396112
#391742
#391692
#391632
#391612
#376162
#374202
#373012
#372982
#353322
#353032
#352782
#352762
#340742