Finite Group Databasebeta

← #7658727

Subgroups — #7658727

Order 512.

7178 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C212yesmaximal, complemented
2#42393C214yesmaximal, complemented
3#41961C214yesmaximal, complemented
4#41949C214yesmaximal, complemented
5#41945C214yesmaximal, complemented
6#41938C214yesmaximal, complemented
7#41934C214yesmaximal, complemented
8#40598C218yesmaximal, complemented
9#40586C214yesmaximal, complemented
10#37618C212yesmaximal, complemented
11#37559C212yesmaximal, complemented
12#37552C212yesmaximal, complemented
13#37454C211yesmaximal, characteristic, complemented
14#37446C212yesmaximal, complemented
15#36687C212yesmaximal, complemented
16C2×#2815C211yesmaximal, characteristic, complemented
17#35979C214yesmaximal, complemented
18#35694C214yesmaximal, complemented
19#35683C214yesmaximal, complemented
20#34177C211yesmaximal, characteristic, complemented
21#3494—232no—
22C2×#555C2214yescomplemented
23C2×#553C2214yescomplemented
24C2×#553C2214yescomplemented
25C2×#551C2214yes—
26C2×#551C2214yes—
27C2×#547C2214yescomplemented
28C2×#546C2214yes—
29C2×#546C2214yes—
30C2×#544C2212yes—
31C2×#542C2212yescomplemented
32C2×#542C2212yescomplemented
33C2×#540C2212yescomplemented
34C2×#540C2212yescomplemented
35C2×#535C2212yes—
36C2×#532C2212yescomplemented
37C2×#532C2212yescomplemented
38C2×#529C2212yescomplemented
39C2×#529C2212yescomplemented
40C2×#525C2212yes—
41C22×#121C2212yes—
42C2×#520C2212yes—
43C2×#518C2212yes—
44C22×#117C2211yescharacteristic
45#2821C2214yescomplemented
46#2820C2214yescomplemented
47#2819C2214yescomplemented
48#2818C2214yescomplemented
49#2817C2211yescharacteristic, complemented
50#2816C2212yescomplemented
51#2816C2212yescomplemented
52#2816C2212yescomplemented
53#2815C2211yescharacteristic
54#2815C2214yes—
55#2815C2214yes—
56#2815C2212yes—
57#2815C2211yescharacteristic
58#2815C2214yes—
59#2815C2212yescomplemented
60#2815C2212yescomplemented
61#2815C2211yescharacteristic, complemented
62#2813C2218yescomplemented
63#2716C2218yescomplemented
64#2714C2218yescomplemented
65#2712C2214yescomplemented
66#2694C2218yescomplemented
67#2693C2214yescomplemented
68#2690C2218yescomplemented
69#2676C2218yescomplemented
70#2676C2218yescomplemented
71#2675C2214yescomplemented
72#2675C2214yescomplemented
73#2674C2218yescomplemented
74#2673C2218yescomplemented
75#2673C2218yescomplemented
76#2671C2218yescomplemented
77#2664C2214yescomplemented
78#2662C2214yescomplemented
79#2661C2218yescomplemented
80#2657C2214yescomplemented
81#2656C2214yescomplemented
82#2640C2214yescomplemented
83#2639C2214yescomplemented
84#2638C2214yescomplemented
85#2637C2214yescomplemented
86#2636C2214yescomplemented
87#2635C2218yescomplemented
88#2635C2214yescomplemented
89#2633C2214yescomplemented
90#2631C2214yescomplemented
91#2631C2214yescomplemented
92#2631C2214yescomplemented
93#2630C2218yescomplemented
94#2623C2214yes—
95#2621C2214yescomplemented
96#2619C2214yescomplemented
97#2617C2214yes—
98#2615C2218yescomplemented
99#2613C2214yes—
100#2611C2214yescomplemented
101#2610C2214yescomplemented
102#2603C2214yescomplemented
103#2603C2214yescomplemented
104#2602C2218yescomplemented
105#2600C2214yescomplemented
106#2599C2214yescomplemented
107#2598C2214yescomplemented
108#2592C2214yescomplemented
109#2557C2218yescomplemented
110#2555C2218yescomplemented
111#2549C2214yes—
112#2547C2214yescomplemented
113#2543C2214yescomplemented
114#2543C2214yescomplemented
115#2541C2214yescomplemented
116#2540C2214yescomplemented
117#2535C2214yescomplemented
118#2535C2214yescomplemented
119#2498C2214yes—
120#2482C2214yes—
121#2481C2218yescomplemented
122#2477C2218yescomplemented
123#2472C2218yes—
124#2471C2218yescomplemented
125#2467C2218yescomplemented
126#2464C2218yescomplemented
127#2463C2218yescomplemented
128#2456C2218yescomplemented
129#2456C2218yescomplemented
130#2450C2218yes—
131#2443C2218yescomplemented
132#2437C2218yes—
133#2433C2214yes—
134#2431C2218yescomplemented
135#2430C2214yes—
136#2428C2218yescomplemented
137#2424C2218yes—
138#2410C2218yes—
139#2410C2218yes—
140#2407C2218yescomplemented
141#2404C2214yes—
142#2398C2214yescomplemented
143#2397C2214yescomplemented
144#2392C2214yescomplemented
145#2392C2214yescomplemented
146C2×#397C2214yes—
147#2388C2218yescomplemented
148C2×#392C2214yes—
149C2×#392C2214yes—
150#2364C2214yes—
151#2358C2218yes—
152#2343C2214yes—
153#2343C2214yes—
154#2343C2214yescomplemented
155#2343C2214yescomplemented
156D4×C22⋊C4C2214yes—
157#2315C2212yes—
158#2313C2214yescomplemented
159#2283C2212yescomplemented
160#2283C2212yescomplemented
161C2×#381C2211yescharacteristic
162C2×#381C2211yescharacteristic
163#2273C2212yes—
164C22×#41C2312yes—
165C22×#41C2314yes—
166C22×#41C2314yes—
167C23×D4C2312yes—
168C23×D4C2314yes—
169C23×D4C2314yes—
170C24×C4C2311yescharacteristic
171#555—232no—
172#553—232no—
173#553—232no—
174#551—232no—
175#551—232no—
176#547—232no—
177#546—232no—
178#546—232no—
179#544—216no—
180#542—216no—
181#542—216no—
182#540—216no—
183#540—216no—
184#535—216no—
185#532—216no—
186#532—216no—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2314yes—
190C2×#127C2312yes—
191C2×#127C2312yes—
192C2×#127C2318yes—
193#529—216no—
194#529—216no—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#126C2314yes—
198C2×#126C2314yes—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2314yes—
202C2×#124C2312yes—
203C2×#124C2314yes—
204C2×#124C2314yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2318yes—
209#525—216no—
210C2×#123C2314yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×#121—216no—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#121C2318yes—
249C2×#120C2314yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×#120C2318yes—
253#520—216no—
254#518—216no—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2318yes—
275C2×#117D4116yescomplemented
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C2×#117C2314yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2318yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C42C2312yes—
296#400C2314yes—
297#400C2318yes—
298#400C2318yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2318yes—
303#399C2318yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2318yes—
308#398C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2318yes—
320#397C2314yes—
321#397C2318yes—
322#397C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#395C2314yes—
328#395C2318yes—
329#394C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#393C2314yes—
344#393C2314yes—
345#393C2314yes—
346#393C2318yes—
347#393C2318yes—
348#393C2318yes—
349#392C2314yes—
350#392C2318yes—
351#392C2314yes—
352#392C2318yes—
353#392C2314yes—
354#392C2314yes—
355#392C2314yes—
356#392C2318yes—
357#392C2314yes—
358#392C2314yes—
359#392C2314yes—
360#392C2314yes—
361#392C2318yes—
362#392C2318yes—
363#392C2318yes—
364#392C2318yes—
365#392C2318yes—
366#392C2314yes—
367#392C2318yes—
368#392C2314yes—
369#392C2314yes—
370#392C2314yes—
371#392C2318yes—
372#392C2318yes—
373#392C2318yes—
374#392C2314yes—
375#392C2314yes—
376#391C2318yes—
377#391C2318yes—
378#390C2318yes—
379#390C2318yes—
380#390C2318yes—
381#390C2318yes—
382#390C2318yes—
383#389C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#385C2318yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#383C2314yes—
425#383C2314yes—
426#382C2314yes—
427#382C2314yes—
428#381C2311yescharacteristic
429#381C2312yes—
430#381C2311yescharacteristic
431#381C2312yes—
432#381C2312yes—
433#381C2314yes—
434#381C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2318yes—
439#380C2318yes—
440#379C2318yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450#376C2314yes—
451#376C2314yes—
452C2×#95C2314yes—
453C2×#95C2314yes—
454C2×#95C2314yes—
455C25C2414yes—
456C25C2411yescharacteristic
457C2×#41—28no—
458C2×#41—216no—
459C2×#41—216no—
460C2×#41—48no—
461C2×#41—88no—
462C2×#41—88no—
463C22×Q8C2412yes—
464C22×Q8C2414yes—
465C22×Q8C2414yes—
466C22×D4—216no—
467C22×D4—28no—
468C22×D4—48no—
469C22×D4—48no—
470C22×D4—88no—
471C22×D4—88no—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2412yes—
476C22×D4C2412yes—
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2414yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2414yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C23×C4—44no—
494C23×C4C2×D418yes—
495C23×C4C2412yes—
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2411yescharacteristic
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C4⋊Q8—216no—
512C4⋊Q8—28no—
513C4⋊Q8—28no—
514#127—28no—
515#127—28no—
516#127—88no—
517#126—216no—
518#126—216no—
519#126—216no—
520#126—216no—
521#125—216no—
522#125—28no—
523#125—28no—
524#124—216no—
525#124—216no—
526#124—28no—
527#124—28no—
528#124—216no—
529#124—216no—
530#124—88no—
531#123—216no—
532#123—216no—
533#123—216no—
534#123—216no—
535#123—216no—
536#123—216no—
537#123—216no—
538#123—216no—
539#123—216no—
540C22⋊Q8—28no—
541C22⋊Q8—28no—
542C22⋊Q8—216no—
543C22⋊Q8—216no—
544C22⋊Q8—216no—
545C22⋊Q8—216no—
546C22⋊Q8—88no—
547#121—28no—
548#121—28no—
549#121—28no—
550#121—28no—
551#121—216no—
552#121—216no—
553#121—28no—
554#121—28no—
555#121—216no—
556#121—216no—
557#121—216no—
558#121—216no—
559#121—216no—
560#121—216no—
561#121—216no—
562#121—216no—
563#121—48no—
564#121—88no—
565#121—88no—
566#121—88no—
567#121—88no—
568#121—88no—
569#120—216no—
570#120—216no—
571#120—216no—
572#120—416no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—216no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—216no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—216no—
590C4×D4—216no—
591C4×D4—88no—
592C4×D4—88no—
593#117—28no—
594#117—216no—
595#117—216no—
596#117—216no—
597#117C2×D4116yes—
598#117C2×D4116yes—
599#117C2×D4116yescomplemented
600#117C2×D4116yescomplemented
601C2×C4⋊C4—28no—
602C2×C4⋊C4—216no—
603C2×C4⋊C4C2×D4116yescomplemented
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C22⋊C4—216no—
630C2×C22⋊C4—216no—
631C2×C22⋊C4—216no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4—44no—
634C2×C22⋊C4—88no—
635C2×C22⋊C4C2×D418yes—
636C2×C22⋊C4C2×D418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2411yescharacteristic
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2411yescharacteristic
679C2×C22⋊C4C2411yescharacteristic
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2411yescharacteristic
682C2×C42C2×D4116yescomplemented
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24—24no—
714C24—28no—
715C24—216no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—48no—
720C24C22×D414yes—
721C24C2514yes—
722C24C2514yes—
723C24C2514yes—
724C24C2511yescharacteristic
725C24C2511yescharacteristic
726C24C2511yescharacteristic
727#41—432no—
728#41—832no—
729#41—832no—
730C2×Q8—24no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—44no—
734C2×Q8—48no—
735C2×Q8—48no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—44no—
760C2×D4—48no—
761C2×D4—432no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—44no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—832no—
786C2×D4—832no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—416no—
798C22×C4—42no—
799C22×C4—44no—
800C22×C4—42no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4C22×D418yes—
817C22×C4C22×D414yes—
818C22×C4C22×D418yes—
819C22×C4C22×D418yes—
820C22×C4C22×D414yes—
821C22×C4C22×D418yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C4⋊C4—28no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4C22×D418yes—
858C4⋊C4C22×D418yes—
859C4⋊C4C22×D418yes—
860C4⋊C4C22×D418yes—
861C22⋊C4—28no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—42no—
883C22⋊C4—44no—
884C22⋊C4—42no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4C22×D414yes—
901C22⋊C4C22×D418yes—
902C22⋊C4C22×D414yes—
903C22⋊C4C22×D414yes—
904C22⋊C4C22×D418yes—
905C22⋊C4C22×D414yes—
906C42—28no—
907C42—28no—
908C42—28no—
909C42—48no—
910C42—48no—
911C42C22×D418yes—
912C42C22×D418yes—
913C42C22×D418yes—
914C42C22×D418yes—
915C23—24no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—28no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—28no—
925C23—28no—
926C23—28no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—24no—
936C23—48no—
937C23—416no—
938C23—88no—
939C23—816no—
940C23—88no—
941C23—816no—
942C23—88no—
943C23C23×D412yes—
944C23C23×D412yes—
945C23C23×D412yes—
946C23#58514yes—
947C23C2611yescharacteristic
948Q8—48no—
949Q8—88no—
950Q8—88no—
951D4—416no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—416no—
956D4—416no—
957D4—416no—
958D4—416no—
959D4—416no—
960D4—88no—
961D4—88no—
962D4—88no—
963D4—88no—
964D4—88no—
965D4—88no—
966D4—88no—
967D4—816no—
968D4—88no—
969D4—816no—
970D4—164no—
971D4—168no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—216no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—24no—
997C2×C4—44no—
998C2×C4—48no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—416no—
1003C2×C4—88no—
1004C2×C4—88no—
1005C2×C4—88no—
1006C2×C4—88no—
1007C2×C4—88no—
1008C2×C4—88no—
1009C2×C4—88no—
1010C2×C4—88no—
1011C2×C4—164no—
1012C2×C4C23×D414yes—
1013C2×C4C23×D414yes—
1014C2×C4C23×D414yes—
1015C2×C4C23×D414yes—
1016C2×C4C23×D414yes—
1017C2×C4C23×D414yes—
1018C22—28no—
1019C22—24no—
1020C22—24no—
1021C22—24no—
1022C22—22no—
1023C22—22no—
1024C22—44no—
1025C22—44no—
1026C22—48no—
1027C22—48no—
1028C22—48no—
1029C22—48no—
1030C22—48no—
1031C22—48no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—88no—
1042C22—1616no—
1043C22#344914yes—
1044C22C24×D411yescharacteristic
1045C22C2×#58512yes—
1046C22H(7,𝔽2)14yes—
1047C4—24no—
1048C4—24no—
1049C4—24no—
1050C4—24no—
1051C4—24no—
1052C4—24no—
1053C4—44no—
1054C4—44no—
1055C4—48no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4—44no—
1061C2—24no—
1062C2—42no—
1063C2—42no—
1064C2—84no—
1065C2—84no—
1066C2—84no—
1067C2C2×#344911yescharacteristic
1068C2#6285212yes—
1069C2#6304214yes—
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×#3494C2semidirect
2. #42393C2semidirect
3. #41961C2semidirect
4. #41949C2semidirect
5. #41945C2semidirect
6. #41938C2semidirect
7. #41934C2semidirect
8. #40598C2semidirect
9. #40586C2semidirect
10. #37618C2semidirect
11. #37559C2semidirect
12. #37552C2semidirect
13. #37454C2semidirect
14. #37446C2semidirect
15. #36687C2semidirect
16. C2×#2815C2semidirect
17. #35979C2semidirect
18. #35694C2semidirect
19. #35683C2semidirect
20. #34177C2semidirect
22. C2×#555C22semidirect
23. C2×#553C22semidirect
24. C2×#553C22semidirect
27. C2×#547C22semidirect
31. C2×#542C22semidirect
32. C2×#542C22semidirect
33. C2×#540C22semidirect
34. C2×#540C22semidirect
36. C2×#532C22semidirect
37. C2×#532C22semidirect
38. C2×#529C22semidirect
39. C2×#529C22semidirect
45. #2821C22semidirect
46. #2820C22semidirect
47. #2819C22semidirect
48. #2818C22semidirect
49. #2817C22semidirect
50. #2816C22semidirect
51. #2816C22semidirect
52. #2816C22semidirect
59. #2815C22semidirect
60. #2815C22semidirect
61. #2815C22semidirect
62. #2813C22semidirect
63. #2716C22semidirect
64. #2714C22semidirect
65. #2712C22semidirect
66. #2694C22semidirect
67. #2693C22semidirect
68. #2690C22semidirect
69. #2676C22semidirect
70. #2676C22semidirect
71. #2675C22semidirect
72. #2675C22semidirect
73. #2674C22semidirect
74. #2673C22semidirect
75. #2673C22semidirect
76. #2671C22semidirect
77. #2664C22semidirect
78. #2662C22semidirect
79. #2661C22semidirect
80. #2657C22semidirect
81. #2656C22semidirect
82. #2640C22semidirect
83. #2639C22semidirect
84. #2638C22semidirect
85. #2637C22semidirect
86. #2636C22semidirect
87. #2635C22semidirect
88. #2635C22semidirect
89. #2633C22semidirect
90. #2631C22semidirect
91. #2631C22semidirect
92. #2631C22semidirect
93. #2630C22semidirect
95. #2621C22semidirect
96. #2619C22semidirect
98. #2615C22semidirect
100. #2611C22semidirect
101. #2610C22semidirect
102. #2603C22semidirect
103. #2603C22semidirect
104. #2602C22semidirect
105. #2600C22semidirect
106. #2599C22semidirect
107. #2598C22semidirect
108. #2592C22semidirect
109. #2557C22semidirect
110. #2555C22semidirect
112. #2547C22semidirect
113. #2543C22semidirect
114. #2543C22semidirect
115. #2541C22semidirect
116. #2540C22semidirect
117. #2535C22semidirect
118. #2535C22semidirect
121. #2481C22semidirect
122. #2477C22semidirect
124. #2471C22semidirect
125. #2467C22semidirect
126. #2464C22semidirect
127. #2463C22semidirect
128. #2456C22semidirect
129. #2456C22semidirect
131. #2443C22semidirect
134. #2431C22semidirect
136. #2428C22semidirect
140. #2407C22semidirect
142. #2398C22semidirect
143. #2397C22semidirect
144. #2392C22semidirect
145. #2392C22semidirect
147. #2388C22semidirect
154. #2343C22semidirect
155. #2343C22semidirect
158. #2313C22semidirect
159. #2283C22semidirect
160. #2283C22semidirect
275. C2×#117D4semidirect
599. #117C2×D4semidirect
600. #117C2×D4semidirect
603. C2×C4⋊C4C2×D4semidirect
682. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34942
#423932
#419612
#419492
#419452
#419382
#419342
#405982
#405862
#376182
#375592
#375522
#374542
#374462
#366872
C2×#28152
#359792
#356942
#356832
#341772