Finite Group Databasebeta

← #7715662

Subgroups — #7715662

Order 512.

6820 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3554C212yesmaximal, complemented
2#47940C218yesmaximal, complemented
3#47937C218yesmaximal, complemented
4#47797C218yesmaximal, complemented
5#47676C218yesmaximal, complemented
6#39745C212yesmaximal, complemented
7#39739C212yesmaximal, complemented
8#39618C212yesmaximal, complemented
9#39613C212yesmaximal, complemented
10#39171C212yesmaximal, complemented
11#39169C212yesmaximal, complemented
12#39164C212yesmaximal, complemented
13#39161C212yesmaximal, complemented
14#37639C211yesmaximal, characteristic, complemented
15#37542C211yesmaximal, characteristic, complemented
16#37421C211yesmaximal, characteristic, complemented
17#37301C212yesmaximal, complemented
18#37298C211yesmaximal, characteristic, complemented
19#35331C211yesmaximal, characteristic, complemented
20#35303C212yesmaximal, complemented
21#35278C211yesmaximal, characteristic, complemented
22#35276C212yesmaximal, complemented
23#34074C211yesmaximal, characteristic, complemented
24#3554—232no—
25C2×#562C2214yes—
26C2×#562C2214yes—
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#559C2212yes—
30C2×#557C2212yes—
31C2×#554C2212yes—
32C2×#554C2212yes—
33C2×#550C2212yes—
34C2×D4×Q8C2212yes—
35C2×#548C2214yes—
36C2×#547C2214yes—
37C2×#542C2212yes—
38C2×#542C2212yes—
39C2×#542C2214yes—
40C2×#540C2212yes—
41C2×#540C2212yes—
42C2×#539C2214yes—
43C2×#539C2214yes—
44C2×#536C2214yes—
45C2×#533C2211yescharacteristic
46C2×#532C2212yes—
47C2×#529C2212yes—
48#2867C2211yescharacteristic
49#2862C2211yescharacteristic
50#2861C2212yes—
51#2859C2211yescharacteristic
52#2858C2212yes—
53#2858C2211yescharacteristic
54#2856C2212yes—
55#2856C2212yes—
56#2850C2212yes—
57#2850C2212yes—
58#2823C2214yes—
59#2819C2214yes—
60#2733C2218yes—
61#2731C2218yes—
62#2730C2218yes—
63#2729C2218yes—
64#2712C2214yes—
65#2707C2218yes—
66#2705C2218yes—
67#2704C2218yes—
68#2702C2218yes—
69#2696C2218yes—
70#2696C2218yes—
71#2693C2214yes—
72#2692C2218yes—
73#2692C2218yes—
74#2682C2218yes—
75#2682C2218yes—
76#2681C2218yes—
77#2681C2218yes—
78#2676C2218yes—
79#2676C2218yes—
80#2676C2218yes—
81#2675C2214yes—
82#2675C2214yes—
83#2673C2218yes—
84#2673C2218yes—
85#2671C2218yes—
86#2660C2212yes—
87#2660C2212yes—
88#2657C2212yes—
89#2657C2212yes—
90#2641C2212yes—
91#2641C2212yes—
92#2640C2212yes—
93#2640C2212yes—
94#2630C2218yes—
95#2621C2211yescharacteristic
96#2620C2212yes—
97#2619C2211yescharacteristic
98#2619C2211yescharacteristic
99#2619C2212yes—
100#2619C2211yescharacteristic
101#2615C2218yes—
102#2610C2218yes—
103#2609C2214yes—
104#2603C2218yes—
105#2568C2212yes—
106#2566C2212yes—
107#2566C2212yes—
108#2566C2212yes—
109#2566C2212yes—
110#2565C2212yes—
111#2565C2212yes—
112#2563C2212yes—
113#2563C2212yes—
114#2563C2212yes—
115#2563C2212yes—
116#2560C2218yes—
117#2557C2218yes—
118#2555C2218yes—
119#2554C2218yes—
120#2548C2212yes—
121#2545C2212yes—
122#2545C2212yes—
123#2544C2212yes—
124#2544C2212yes—
125#2544C2212yes—
126#2544C2212yes—
127#2543C2218yes—
128#2542C2212yes—
129#2541C2212yes—
130#2541C2212yes—
131#2541C2212yes—
132#2541C2212yes—
133#2541C2212yes—
134#2537C2214yes—
135#2473C2218yes—
136#2465C2218yes—
137#2464C2218yes—
138#2463C2218yes—
139#2461C2218yes—
140#2460C2218yes—
141#2458C2218yes—
142#2456C2218yes—
143#2456C2218yes—
144#2445C2218yes—
145#2443C2218yes—
146#2436C2218yes—
147#2431C2218yes—
148#2430C2218yes—
149#2428C2218yes—
150#2428C2218yes—
151#2427C2218yes—
152#2417C2218yes—
153#2416C2218yes—
154#2409C2218yes—
155#2407C2218yes—
156#2331C2214yes—
157#2330C2214yes—
158#2329C2214yes—
159#2329C2214yes—
160#2328C2211yescharacteristic
161#2328C2212yes—
162#2328C2211yescharacteristic
163#2328C2212yes—
164#2328C2212yes—
165#2328C2211yescharacteristic
166#2327C2211yescharacteristic
167#2326C2212yes—
168#2326C2212yes—
169#2326C2212yes—
170C4×#127C2212yes—
171C4×#127C2212yes—
172C4×#124C2212yes—
173C4×#124C2212yes—
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2295C2212yes—
177#2295C2212yes—
178#2295C2212yes—
179#2295C2212yes—
180#2285C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C2×#376C2211yescharacteristic
184C22×#41C2314yes—
185C22×#41C2314yes—
186C23×Q8C2314yes—
187#562—232no—
188#562—232no—
189#559—216no—
190#559—216no—
191#559—216no—
192#557—216no—
193#554—216no—
194#554—216no—
195#550—216no—
196D4×Q8—216no—
197#548—232no—
198#547—232no—
199#542—232no—
200#542—216no—
201#542—216no—
202#540—216no—
203#540—216no—
204#539—232no—
205#539—232no—
206#536—232no—
207#533D4116yescomplemented
208#532—216no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2318yes—
225#529—216no—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2312yes—
235C2×#124C2314yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2318yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2318yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2318yes—
288C2×#121C2318yes—
289C2×#121C2318yes—
290C2×#121C2318yes—
291C2×#121C2318yes—
292C2×#121C2318yes—
293C2×#121C2318yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×D4C2312yes—
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×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2318yes—
315C2×C4×D4C2318yes—
316C2×#117C2314yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326#400C2318yes—
327#399C2318yes—
328#398C2314yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#397C2318yes—
334#397C2318yes—
335#397C2314yes—
336#396C2318yes—
337#396C2318yes—
338#396C2318yes—
339#396C2318yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#395C2318yes—
344#395C2318yes—
345#394C2314yes—
346#394C2318yes—
347#394C2314yes—
348#394C2314yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#393C2318yes—
360#393C2318yes—
361#393C2318yes—
362#393C2318yes—
363#393C2318yes—
364#393C2318yes—
365#392C2318yes—
366#392C2318yes—
367#392C2318yes—
368#392C2318yes—
369#392C2318yes—
370#392C2314yes—
371#392C2314yes—
372#392C2314yes—
373#392C2318yes—
374#392C2318yes—
375#392C2318yes—
376#392C2318yes—
377#392C2318yes—
378#391C2318yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2318yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#390C2318yes—
389#390C2312yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#390C2318yes—
394#390C2318yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#390C2312yes—
400#390C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2318yes—
404#390C2318yes—
405#390C2318yes—
406#390C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2314yes—
459#385C2312yes—
460#385C2312yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#382C2312yes—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2312yes—
469#382C2311yescharacteristic
470#382C2312yes—
471#382C2311yescharacteristic
472#382C2312yes—
473#380C2318yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477#380C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2318yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494#376C2311yescharacteristic
495#376C2311yescharacteristic
496#376C2312yes—
497#376C2312yes—
498C2×#95C2314yes—
499C43C2311yescharacteristic
500C43C2312yes—
501C43C2311yescharacteristic
502C2×#41—216no—
503C2×#41—216no—
504C2×#41—88no—
505C2×#41—88no—
506C22×Q8—216no—
507C22×Q8—88no—
508C22×Q8C2412yes—
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×Q8C2414yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2418yes—
523C22×D4C2414yes—
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C22×D4C2418yes—
528C22×D4C2418yes—
529C22×D4C2414yes—
530C22×D4C2414yes—
531C22×D4C2414yes—
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C23×C4C2414yes—
535C23×C4C2414yes—
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C4⋊Q8—216no—
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—42no—
550C4⋊Q8C2×D4116yes—
551#127—28no—
552#127—28no—
553#127—28no—
554#127—28no—
555#127—44no—
556#127—44no—
557#127—42no—
558#127—42no—
559#127—42no—
560#127—88no—
561#126—216no—
562#126—216no—
563#126—216no—
564#125—216no—
565#125—216no—
566#125—28no—
567#125—28no—
568#125—28no—
569#125C2×D4116yes—
570#124—216no—
571#124—216no—
572#124—216no—
573#124—216no—
574#124—216no—
575#124—28no—
576#124—216no—
577#124—28no—
578#124—28no—
579#124—28no—
580#124—44no—
581#124—44no—
582#124—88no—
583#123—216no—
584#123—216no—
585#123—216no—
586#123—216no—
587#123—216no—
588#123—216no—
589#123—216no—
590#123—216no—
591#123—216no—
592#123—216no—
593#123—216no—
594#123—216no—
595#123—216no—
596C22⋊Q8—216no—
597C22⋊Q8—216no—
598C22⋊Q8—28no—
599C22⋊Q8—216no—
600C22⋊Q8—216no—
601C22⋊Q8—216no—
602C22⋊Q8—216no—
603C22⋊Q8—216no—
604C22⋊Q8—216no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—216no—
608C22⋊Q8—88no—
609C22⋊Q8C2×D4116yes—
610C22⋊Q8C2×D4116yes—
611#121—28no—
612#121—28no—
613#121—28no—
614#121—216no—
615#121—216no—
616#121—216no—
617#121—216no—
618#121—216no—
619#121—216no—
620#121—216no—
621#121—216no—
622#121—88no—
623#121—88no—
624#121—88no—
625#121—88no—
626#121—88no—
627#121—88no—
628#121—88no—
629C4×Q8—216no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×Q8—28no—
633C4×Q8C2×D4116yes—
634C4×Q8C2×D4116yes—
635C4×D4—216no—
636C4×D4—216no—
637C4×D4—216no—
638C4×D4—216no—
639C4×D4—28no—
640C4×D4—216no—
641C4×D4—28no—
642C4×D4—28no—
643C4×D4—28no—
644C4×D4—28no—
645C4×D4—28no—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—28no—
649C4×D4—88no—
650C4×D4—88no—
651#117—216no—
652#117—42no—
653#117—42no—
654#117C2×D418yes—
655#117C2×D418yes—
656C2×C4⋊C4—216no—
657C2×C4⋊C4—216no—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
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⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2411yescharacteristic
732C2×C22⋊C4C2412yes—
733C2×C22⋊C4C2411yescharacteristic
734C2×C42—24no—
735C2×C42—42no—
736C2×C42C2×D418yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2412yes—
744C2×C42C2411yescharacteristic
745C2×C42C2412yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2412yes—
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757C2×C42C2411yescharacteristic
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779#95C2414yes—
780#95C2414yes—
781#95C2418yes—
782#95C2418yes—
783C24C2514yes—
784C24C2514yes—
785C24C2514yes—
786C24C2511yescharacteristic
787#41—832no—
788#41—832no—
789C2×Q8—24no—
790C2×Q8—28no—
791C2×Q8—28no—
792C2×Q8—28no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—44no—
796C2×Q8—48no—
797C2×Q8—44no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—832no—
801C2×Q8C22×D418yes—
802C2×Q8C22×D418yes—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—216no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
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—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—24no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—42no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4C22×D414yes—
871C22×C4C22×D418yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2514yes—
882C22×C4C2512yes—
883C22×C4C2512yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2511yescharacteristic
889C22×C4C2512yes—
890C22×C4C2511yescharacteristic
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4C22×D418yes—
921C4⋊C4C22×D418yes—
922C4⋊C4C22×D418yes—
923C4⋊C4C22×D418yes—
924C4⋊C4C22×D418yes—
925C4⋊C4C22×D418yes—
926C4⋊C4C22×D418yes—
927C4⋊C4C22×D418yes—
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—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4C22×D414yes—
965C22⋊C4C22×D418yes—
966C22⋊C4C22×D414yes—
967C42—28no—
968C42—28no—
969C42—28no—
970C42—24no—
971C42—22no—
972C42—24no—
973C42—24no—
974C42—22no—
975C42—22no—
976C42—42no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42C22×D414yes—
982C42C22×D414yes—
983C42C22×D418yes—
984C42C22×D414yes—
985C42C22×D418yes—
986C42C22×D414yes—
987C422−1+414yes—
988C23—21no—
989C23—21no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—28no—
1001C23—28no—
1002C23—28no—
1003C23—28no—
1004C23—28no—
1005C23—28no—
1006C23C23×D412yes—
1007C23C2611yescharacteristic
1008Q8—48no—
1009Q8—48no—
1010Q8—416no—
1011Q8—48no—
1012Q8—88no—
1013Q8—88no—
1014D4—416no—
1015D4—48no—
1016D4—48no—
1017D4—48no—
1018D4—88no—
1019D4—88no—
1020D4—88no—
1021D4—816no—
1022D4—88no—
1023D4—88no—
1024D4—88no—
1025D4—88no—
1026D4—88no—
1027D4—816no—
1028D4—168no—
1029D4—164no—
1030D4—164no—
1031D4—164no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—28no—
1064C2×C4—24no—
1065C2×C4—48no—
1066C2×C4—416no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4—84no—
1070C2×C4—88no—
1071C2×C4—88no—
1072C2×C4—88no—
1073C2×C4—88no—
1074C2×C4—88no—
1075C2×C4—88no—
1076C2×C4—84no—
1077C2×C4C23×D414yes—
1078C2×C4C23×D414yes—
1079C2×C4C23×D414yes—
1080C2×C4C23×D412yes—
1081C2×C4C23×D414yes—
1082C2×C4C23×D414yes—
1083C2×C4C23×D414yes—
1084C2×C4C23×D412yes—
1085C2×C4C2×2−1+414yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4#58512yes—
1088C22—22no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—48no—
1102C22—48no—
1103C22—48no—
1104C22—48no—
1105C22—48no—
1106C22—48no—
1107C22C24×D411yescharacteristic
1108C22C22×2−1+411yescharacteristic
1109C22C2×#58511yescharacteristic
1110C22H(7,𝔽2)14yes—
1111C4—22no—
1112C4—24no—
1113C4—24no—
1114C4—24no—
1115C4—24no—
1116C4—24no—
1117C4—24no—
1118C4—24no—
1119C4—44no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4#349714yes—
1130C2—42no—
1131C2—84no—
1132C2—84no—
1133C2—84no—
1134C2C2×#349711yescharacteristic
1135C2#6285212yes—
1136C2#6288112yes—
1137C2#6288512yes—
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×#3554C2semidirect
2. #47940C2semidirect
3. #47937C2semidirect
4. #47797C2semidirect
5. #47676C2semidirect
6. #39745C2semidirect
7. #39739C2semidirect
8. #39618C2semidirect
9. #39613C2semidirect
10. #39171C2semidirect
11. #39169C2semidirect
12. #39164C2semidirect
13. #39161C2semidirect
14. #37639C2semidirect
15. #37542C2semidirect
16. #37421C2semidirect
17. #37301C2semidirect
18. #37298C2semidirect
19. #35331C2semidirect
20. #35303C2semidirect
21. #35278C2semidirect
22. #35276C2semidirect
23. #34074C2semidirect
207. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35542
#479402
#479372
#477972
#476762
#397452
#397392
#396182
#396132
#391712
#391692
#391642
#391612
#376392
#375422
#374212
#373012
#372982
#353312
#353032
#352782
#352762
#340742