Finite Group Databasebeta

← #7646516

Subgroups — #7646516

Order 512.

5362 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42977C214yesmaximal, complemented
2#42960C214yesmaximal, complemented
3#41980C214yesmaximal, complemented
4#41978C214yesmaximal, complemented
5#39387C212yesmaximal, complemented
6#39386C212yesmaximal, complemented
7#39203C212yesmaximal, complemented
8#39201C212yesmaximal, complemented
9#37670C214yesmaximal, complemented
10#37669C214yesmaximal, complemented
11#37570C214yesmaximal, complemented
12#36818C214yesmaximal, complemented
13#36812C214yesmaximal, complemented
14#35562C214yesmaximal, complemented
15#35293C211yesmaximal, characteristic, complemented
16#35237C211yesmaximal, characteristic, complemented
17#35197C214yesmaximal, complemented
18#35169C214yesmaximal, complemented
19#34936C211yesmaximal, characteristic, complemented
20#34912C211yesmaximal, characteristic, complemented
21#34232C211yesmaximal, characteristic, complemented
22#34155C211yesmaximal, characteristic, complemented
23#34058C211yesmaximal, characteristic, complemented
24C2×#542C2214yescomplemented
25C2×#540C2214yescomplemented
26C2×#532C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#525C2214yes—
29C22×C4×D4C2211yescharacteristic
30#2867C2211yescharacteristic, complemented
31#2862C2211yescharacteristic, complemented
32#2858C2211yescharacteristic, complemented
33#2858C2211yescharacteristic, complemented
34#2854C2218yescomplemented
35#2850C2218yescomplemented
36#2847C2212yes—
37#2847C2212yes—
38#2837C2218yescomplemented
39#2828C2218yes—
40#2798C2218yescomplemented
41#2754C2218yescomplemented
42#2730C2218yescomplemented
43#2712C2218yescomplemented
44#2710C2218yescomplemented
45#2706C2218yes—
46#2705C2218yes—
47#2705C2218yescomplemented
48#2696C2218yes—
49#2693C2218yes—
50#2678C2218yes—
51#2678C2218yes—
52#2673C2218yescomplemented
53#2673C2218yescomplemented
54#2670C2218yes—
55#2668C2218yes—
56#2663C2218yescomplemented
57#2661C2218yes—
58#2661C2218yes—
59#2649C2218yescomplemented
60#2648C2218yescomplemented
61#2648C2218yescomplemented
62#2631C2214yes—
63#2625C2214yescomplemented
64#2624C2214yescomplemented
65#2620C2214yescomplemented
66#2619C2214yes—
67#2619C2214yescomplemented
68#2608C2212yes—
69#2607C2212yes—
70#2606C2212yescomplemented
71#2605C2212yescomplemented
72#2580C2214yescomplemented
73#2571C2214yescomplemented
74#2570C2214yescomplemented
75#2570C2212yescomplemented
76#2563C2212yes—
77#2559C2218yescomplemented
78#2557C2218yescomplemented
79#2555C2218yes—
80#2553C2218yescomplemented
81#2550C2212yescomplemented
82#2548C2214yes—
83#2548C2214yes—
84#2544C2214yescomplemented
85#2544C2212yescomplemented
86#2544C2212yescomplemented
87#2542C2212yes—
88#2541C2212yes—
89#2541C2214yes—
90#2541C2212yes—
91#2541C2214yes—
92#2540C2212yes—
93#2540C2212yes—
94#2539C2214yes—
95#2538C2214yescomplemented
96#2535C2214yes—
97#2513C2214yes—
98#2513C2214yes—
99#2513C2214yescomplemented
100#2512C2214yescomplemented
101#2504C2212yes—
102#2501C2212yes—
103#2491C2214yescomplemented
104#2489C2214yescomplemented
105#2476C2218yescomplemented
106#2471C2218yescomplemented
107#2467C2218yescomplemented
108#2459C2218yescomplemented
109#2457C2218yescomplemented
110#2457C2218yescomplemented
111#2445C2214yes—
112#2445C2214yes—
113#2445C2214yescomplemented
114#2445C2214yescomplemented
115#2444C2218yescomplemented
116#2441C2212yes—
117#2439C2212yes—
118#2433C2212yes—
119#2433C2212yes—
120#2431C2214yes—
121#2431C2212yes—
122#2431C2212yes—
123#2428C2214yescomplemented
124#2428C2214yescomplemented
125#2427C2218yescomplemented
126#2427C2214yescomplemented
127#2426C2214yescomplemented
128#2425C2218yescomplemented
129#2422C2214yescomplemented
130#2421C2214yescomplemented
131#2420C2218yescomplemented
132#2404C2214yes—
133#2397C2214yes—
134#2396C2214yes—
135#2372C2214yescomplemented
136#2369C2212yescomplemented
137#2366C2212yescomplemented
138#2366C2212yescomplemented
139#2365C2212yescomplemented
140#2363C2214yes—
141#2363C2214yes—
142#2363C2214yes—
143#2353C2214yescomplemented
144#2341C2212yes—
145#2339C2212yes—
146#2333C2214yes—
147#2328C2214yes—
148#2328C2214yescomplemented
149#2324C2214yescomplemented
150#2323C2214yescomplemented
151#2319C2212yes—
152#2319C2212yes—
153#2319C2212yes—
154#2319C2212yes—
155#2319C2212yescomplemented
156#2316C2212yes—
157#2312C2212yes—
158#2312C2212yes—
159#2309C2212yes—
160C4×C4⋊Q8C2212yescomplemented
161C4×#127C2214yes—
162C4×#125C2212yescomplemented
163C4×#124C2214yescomplemented
164#2297C2214yes—
165#2295C2214yescomplemented
166#2293C2212yes—
167#2293C2212yes—
168#2293C2214yes—
169#2293C2212yescomplemented
170#2293C2212yescomplemented
171#2283C2211yescharacteristic
172#2280C2214yes—
173#2275C2212yescomplemented
174C42×D4C2212yescomplemented
175C42×D4C2212yescomplemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C22×#41C2312yes—
180C22×#41C2312yes—
181C23×D4C2311yescharacteristic
182C24×C4C2312yes—
183#542—416no—
184#540—416no—
185#532—28no—
186#532—28no—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2311yescharacteristic
190C2×#127C2311yescharacteristic
191C2×#127C2311yescharacteristic
192C2×#127C2314yes—
193C2×#127C2314yes—
194C2×#127C2314yes—
195C2×#127C2314yes—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#126C2318yes—
199C2×#125C2312yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#124C2318yes—
204C2×#124C2318yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207#525—416no—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×#121C2314yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2318yes—
224C2×#121C2314yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2318yes—
228C2×#120C2318yes—
229C2×#120C2314yes—
230C2×#120C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×D4—28no—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4C2312yes—
256C22×C42C2314yes—
257C22×C42C2311yescharacteristic
258#400C2314yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#399C2318yes—
263#399C2314yes—
264#399C2314yes—
265#399C2314yes—
266#399C2318yes—
267#398C2314yes—
268#398C2318yes—
269#398C2314yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2314yes—
281#396C2314yes—
282#396C2318yes—
283#395C2314yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2314yes—
301#392C2314yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2314yes—
310#392C2318yes—
311#392C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2318yes—
320#390C2314yes—
321#390C2318yes—
322#390C2318yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2318yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#390C2318yes—
342#390C2314yes—
343#390C2314yes—
344#390C2318yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2314yes—
352#389C2312yes—
353#389C2314yes—
354#389C2318yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2314yes—
389#387C2314yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2314yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#385C2318yes—
409#385C2318yes—
410#384C2314yes—
411#384C2312yes—
412#383C2312yes—
413#382C2312yes—
414#382C2314yes—
415#382C2314yes—
416#382C2312yes—
417#382C2318yes—
418#381C2314yes—
419#381C2314yes—
420#381C2314yes—
421#381C2312yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2318yes—
432#379C2314yes—
433#379C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2312yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2314yes—
467#376C2312yes—
468#376C2312yes—
469#376C2312yes—
470#376C2312yes—
471C2×#95C2314yes—
472C43C2311yescharacteristic
473C43C2312yes—
474C43C2311yescharacteristic
475C43C2312yes—
476C25C2412yes—
477C2×#41—28no—
478C2×#41—28no—
479C2×#41—48no—
480C2×#41—82no—
481C2×#41—82no—
482C22×Q8C2412yes—
483C22×Q8C2414yes—
484C22×Q8C2412yes—
485C22×D4—24no—
486C22×D4—44no—
487C22×D4C2412yes—
488C22×D4C2412yes—
489C22×D4C2412yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2412yes—
493C22×D4C2418yes—
494C22×D4C2412yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C22×D4C2412yes—
498C22×D4C2418yes—
499C22×D4C2418yes—
500C22×D4C2418yes—
501C22×D4C2418yes—
502C22×D4C2418yes—
503C23×C4—28no—
504C23×C4—48no—
505C23×C4C2414yes—
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2414yes—
511C23×C4C2414yes—
512C23×C4C2418yes—
513C23×C4C2418yes—
514C23×C4C2411yescharacteristic
515C4⋊Q8—28no—
516C4⋊Q8—24no—
517C4⋊Q8—24no—
518#127—24no—
519#127—24no—
520#127—48no—
521#127—48no—
522#127—48no—
523#127—48no—
524#127—82no—
525#127—82no—
526#126—416no—
527#125—28no—
528#124—28no—
529#124—28no—
530#124—48no—
531#124—416no—
532#124—88no—
533#124—82no—
534#124—82no—
535#123—416no—
536#123—416no—
537#123—416no—
538#123—416no—
539#123—88no—
540C22⋊Q8—216no—
541C22⋊Q8—48no—
542C22⋊Q8—416no—
543#121—28no—
544#121—28no—
545#121—28no—
546#121—28no—
547#121—216no—
548#121—416no—
549#121—48no—
550#121—416no—
551#121—48no—
552#121—48no—
553#121—88no—
554#121—88no—
555#120—416no—
556#120—84no—
557#120—84no—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×D4—216no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—28no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—416no—
570C4×D4—48no—
571C4×D4—48no—
572C4×D4—416no—
573C4×D4—48no—
574#117—28no—
575#117—44no—
576#117—48no—
577#117—48no—
578#117—44no—
579#117—84no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C22⋊C4—28no—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C42—84no—
652C2×C42#4118yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2418yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#95C2412yes—
677#95C2412yes—
678#95C2418yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2414yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2414yes—
688#95C2414yes—
689#95C2412yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709C24—24no—
710C24—44no—
711C24—44no—
712C24—42no—
713C24—42no—
714C24C2514yes—
715C24C2514yes—
716C24C2514yes—
717C24C2511yescharacteristic
718#41—816no—
719#41—816no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—28no—
723C2×Q8—28no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—44no—
746C2×D4—416no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—216no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—48no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—48no—
789C22×C4—48no—
790C22×C4—44no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—816no—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C22×C4C2×#4114yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—216no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4H(5,𝔽2)18yes—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—216no—
856C22⋊C4—216no—
857C22⋊C4—216no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C42—28no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—28no—
893C42—28no—
894C42—42no—
895C42—42no—
896C42—48no—
897C42—44no—
898C42—42no—
899C42—42no—
900C42—48no—
901C42—41no—
902C42—41no—
903C42—41no—
904C42—41no—
905C42C2×#4114yes—
906C42C2×#4114yes—
907C42C2×#4114yes—
908C42C2×#4114yes—
909C23—22no—
910C23—22no—
911C23—21no—
912C23—21no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—28no—
918C23—28no—
919C23—24no—
920C23—28no—
921C23—28no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—48no—
931C23—84no—
932C23—84no—
933C23—88no—
934C23—88no—
935C23C22×#4112yes—
936C23C2611yescharacteristic
937Q8—48no—
938Q8—88no—
939Q8—84no—
940D4—48no—
941D4—48no—
942D4—48no—
943D4—48no—
944D4—48no—
945D4—48no—
946D4—84no—
947D4—816no—
948D4—84no—
949D4—88no—
950D4—88no—
951D4—816no—
952D4—168no—
953D4—168no—
954D4—168no—
955D4—168no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—24no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—44no—
1002C2×C4—416no—
1003C2×C4—416no—
1004C2×C4—816no—
1005C2×C4—88no—
1006C2×C4—88no—
1007C2×C4—84no—
1008C2×C4—168no—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4112yes—
1014C2×C4C22×#4112yes—
1015C2×C4C2×H(5,𝔽2)18yes—
1016C2×C4C2×H(5,𝔽2)14yes—
1017C2×C4#58514yes—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—42no—
1022C22—42no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—48no—
1030C22—44no—
1031C22—48no—
1032C22—44no—
1033C22—48no—
1034C22—44no—
1035C22—48no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—816no—
1041C22C23×#4111yescharacteristic
1042C22C22×H(5,𝔽2)12yes—
1043C22C2×#58512yes—
1044C22H(7,𝔽2)11yescharacteristic
1045C22H(7,𝔽2)11yescharacteristic
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—28no—
1050C4—22no—
1051C4—44no—
1052C4—44no—
1053C4—44no—
1054C4—44no—
1055C4—42no—
1056C4—44no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4#345514yes—
1064C4#350814yes—
1065C2—42no—
1066C2—84no—
1067C2—84no—
1068C2—84no—
1069C2C2×#345511yescharacteristic
1070C2C2×#350811yescharacteristic
1071C2#6285511yescharacteristic
1072C2#6292012yes—
1073C2#6292312yes—
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. #42977C2semidirect
2. #42960C2semidirect
3. #41980C2semidirect
4. #41978C2semidirect
5. #39387C2semidirect
6. #39386C2semidirect
7. #39203C2semidirect
8. #39201C2semidirect
9. #37670C2semidirect
10. #37669C2semidirect
11. #37570C2semidirect
12. #36818C2semidirect
13. #36812C2semidirect
14. #35562C2semidirect
15. #35293C2semidirect
16. #35237C2semidirect
17. #35197C2semidirect
18. #35169C2semidirect
19. #34936C2semidirect
20. #34912C2semidirect
21. #34232C2semidirect
22. #34155C2semidirect
23. #34058C2semidirect
24. C2×#542C22semidirect
25. C2×#540C22semidirect
30. #2867C22semidirect
31. #2862C22semidirect
32. #2858C22semidirect
33. #2858C22semidirect
34. #2854C22semidirect
35. #2850C22semidirect
38. #2837C22semidirect
40. #2798C22semidirect
41. #2754C22semidirect
42. #2730C22semidirect
43. #2712C22semidirect
44. #2710C22semidirect
47. #2705C22semidirect
52. #2673C22semidirect
53. #2673C22semidirect
56. #2663C22semidirect
59. #2649C22semidirect
60. #2648C22semidirect
61. #2648C22semidirect
63. #2625C22semidirect
64. #2624C22semidirect
65. #2620C22semidirect
67. #2619C22semidirect
70. #2606C22semidirect
71. #2605C22semidirect
72. #2580C22semidirect
73. #2571C22semidirect
74. #2570C22semidirect
75. #2570C22semidirect
77. #2559C22semidirect
78. #2557C22semidirect
80. #2553C22semidirect
81. #2550C22semidirect
84. #2544C22semidirect
85. #2544C22semidirect
86. #2544C22semidirect
95. #2538C22semidirect
99. #2513C22semidirect
100. #2512C22semidirect
103. #2491C22semidirect
104. #2489C22semidirect
105. #2476C22semidirect
106. #2471C22semidirect
107. #2467C22semidirect
108. #2459C22semidirect
109. #2457C22semidirect
110. #2457C22semidirect
113. #2445C22semidirect
114. #2445C22semidirect
115. #2444C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2427C22semidirect
126. #2427C22semidirect
127. #2426C22semidirect
128. #2425C22semidirect
129. #2422C22semidirect
130. #2421C22semidirect
131. #2420C22semidirect
135. #2372C22semidirect
136. #2369C22semidirect
137. #2366C22semidirect
138. #2366C22semidirect
139. #2365C22semidirect
143. #2353C22semidirect
148. #2328C22semidirect
149. #2324C22semidirect
150. #2323C22semidirect
155. #2319C22semidirect
160. C4×C4⋊Q8C22semidirect
162. C4×#125C22semidirect
163. C4×#124C22semidirect
165. #2295C22semidirect
169. #2293C22semidirect
170. #2293C22semidirect
173. #2275C22semidirect
174. C42×D4C22semidirect
175. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#429772
#429602
#419802
#419782
#393872
#393862
#392032
#392012
#376702
#376692
#375702
#368182
#368122
#355622
#352932
#352372
#351972
#351692
#349362
#349122
#342322
#341552
#340582