Finite Group Databasebeta

← #7720826

Subgroups — #7720826

Order 512.

5627 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50794C218yesmaximal, complemented
2#50784C218yesmaximal, complemented
3#45386C214yesmaximal, complemented
4#45315C214yesmaximal, complemented
5#45036C214yesmaximal, complemented
6#44889C214yesmaximal, complemented
7#39386C211yesmaximal, characteristic, complemented
8#39386C212yesmaximal, complemented
9#39378C211yesmaximal, characteristic, complemented
10#39372C212yesmaximal, complemented
11#39282C214yesmaximal, complemented
12#39138C212yesmaximal, complemented
13#37332C214yesmaximal, complemented
14#36600C211yesmaximal, characteristic, complemented
15#36592C211yesmaximal, characteristic, complemented
16#36472C212yesmaximal, complemented
17#35287C212yesmaximal, complemented
18#35278C211yesmaximal, characteristic, complemented
19#35278C212yesmaximal, complemented
20#35171C212yesmaximal, complemented
21#34621C211yesmaximal, characteristic, complemented
22#34494C212yesmaximal, complemented
23#34151C211yesmaximal, characteristic, complemented
24C2×#553C2214yes—
25C2×#550C2212yes—
26C2×#550C2214yes—
27C2×#540C2214yes—
28C2×#540C2212yes—
29C2×#540C2212yes—
30C2×#540C2212yes—
31C2×#529C2211yescharacteristic
32#2867C2211yescharacteristic
33#2867C2212yes—
34#2860C2214yes—
35#2859C2212yes—
36#2859C2211yescharacteristic
37#2856C2214yes—
38#2856C2212yes—
39#2854C2214yes—
40#2797C2218yes—
41#2797C2218yes—
42#2752C2218yes—
43#2724C2218yes—
44#2714C2218yes—
45#2714C2218yes—
46#2703C2218yes—
47#2703C2218yes—
48#2701C2218yes—
49#2699C2218yes—
50#2691C2218yes—
51#2688C2218yes—
52#2682C2218yes—
53#2673C2218yes—
54#2673C2218yes—
55#2673C2218yes—
56#2673C2218yes—
57#2673C2218yes—
58#2673C2218yes—
59#2671C2218yes—
60#2661C2218yes—
61#2651C2214yes—
62#2648C2214yes—
63#2647C2211yescharacteristic
64#2644C2212yes—
65#2641C2211yescharacteristic
66#2641C2212yes—
67#2629C2211yescharacteristic
68#2629C2212yes—
69#2624C2212yes—
70#2619C2211yescharacteristic
71#2619C2214yes—
72#2619C2212yes—
73#2619C2212yes—
74#2603C2218yes—
75#2600C2218yes—
76#2593C2218yes—
77#2585C2218yes—
78#2570C2214yes—
79#2554C2218yes—
80#2552C2212yes—
81#2543C2218yes—
82#2541C2214yes—
83#2541C2214yes—
84#2541C2218yes—
85#2541C2212yes—
86#2541C2212yes—
87#2541C2218yes—
88#2541C2214yes—
89#2541C2214yes—
90#2541C2214yes—
91#2537C2212yes—
92#2535C2214yes—
93#2490C2214yes—
94#2490C2214yes—
95#2490C2214yes—
96#2486C2214yes—
97#2468C2218yes—
98#2464C2218yes—
99#2464C2218yes—
100#2457C2218yes—
101#2456C2218yes—
102#2453C2214yes—
103#2445C2214yes—
104#2445C2214yes—
105#2445C2218yes—
106#2445C2218yes—
107#2445C2218yes—
108#2445C2214yes—
109#2444C2218yes—
110#2431C2214yes—
111#2428C2214yes—
112#2428C2214yes—
113#2428C2218yes—
114#2428C2218yes—
115#2428C2214yes—
116#2428C2214yes—
117#2428C2214yes—
118#2428C2214yes—
119#2425C2218yes—
120#2425C2218yes—
121#2422C2214yes—
122#2422C2214yes—
123#2420C2214yes—
124#2416C2214yes—
125#2414C2214yes—
126#2407C2214yes—
127#2395C2214yes—
128#2392C2214yes—
129#2377C2218yes—
130#2374C2214yes—
131#2373C2214yes—
132#2370C2212yes—
133#2370C2214yes—
134#2367C2212yes—
135#2366C2214yes—
136#2366C2212yes—
137#2363C2212yes—
138#2362C2212yes—
139#2361C2214yes—
140#2361C2214yes—
141#2355C2212yes—
142#2349C2214yes—
143D4×C4⋊C4C2212yes—
144#2339C2214yes—
145#2328C2212yes—
146#2328C2214yes—
147#2325C2218yes—
148#2324C2214yes—
149#2324C2214yes—
150#2324C2214yes—
151#2319C2214yes—
152#2311C2214yes—
153C4×#127C2211yescharacteristic
154C4×#127C2212yes—
155C4×#127C2214yes—
156C4×#127C2212yes—
157C4×#125C2211yescharacteristic
158C4×#125C2212yes—
159C4×#121C2212yes—
160#2298C2212yes—
161#2295C2211yescharacteristic
162#2293C2212yes—
163#2293C2212yes—
164#2293C2211yescharacteristic
165#2290C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2211yescharacteristic
170C4×#117C2212yes—
171C22×#41C2314yes—
172#553—416no—
173#550—216no—
174#550—416no—
175#540—48no—
176#540—48no—
177#540—48no—
178#540—416no—
179C2×#127C2312yes—
180C2×#127C2311yescharacteristic
181C2×#127C2312yes—
182C2×#127C2314yes—
183C2×#127C2314yes—
184C2×#127C2312yes—
185C2×#127C2318yes—
186C2×#127C2314yes—
187C2×#127C2314yes—
188C2×#127C2314yes—
189C2×#127C2318yes—
190C2×#127C2318yes—
191#529—28no—
192C2×#126C2312yes—
193C2×#126C2318yes—
194C2×#125C2311yescharacteristic
195C2×#125C2312yes—
196C2×#125C2311yescharacteristic
197C2×#125C2314yes—
198C2×#124C2311yescharacteristic
199C2×#123C2312yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×C22⋊Q8C2311yescharacteristic
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2314yes—
211C2×#121C2311yescharacteristic
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2318yes—
217C2×#121C2314yes—
218C2×#121C2312yes—
219C2×#121C2318yes—
220C2×#121C2314yes—
221C2×#121C2318yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#121C2318yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2318yes—
228C2×#121C2314yes—
229C2×#121C2318yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2318yes—
248C2×C4×D4C2318yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2314yes—
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#400C2318yes—
259#400C2314yes—
260#399C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2314yes—
266#397C2314yes—
267#397C2318yes—
268#397C2314yes—
269#397C2314yes—
270#397C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#396C2314yes—
275#396C2318yes—
276#396C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#394C2314yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#392C2318yes—
296#392C2318yes—
297#392C2314yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#391C2312yes—
311#391C2314yes—
312#390C2312yes—
313#390C2314yes—
314#390C2314yes—
315#390C2314yes—
316#390C2318yes—
317#390C2314yes—
318#390C2318yes—
319#390C2312yes—
320#390C2314yes—
321#390C2314yes—
322#390C2318yes—
323#390C2314yes—
324#390C2314yes—
325#390C2318yes—
326#390C2318yes—
327#390C2314yes—
328#390C2318yes—
329#390C2312yes—
330#390C2314yes—
331#390C2314yes—
332#390C2318yes—
333#390C2312yes—
334#390C2314yes—
335#390C2312yes—
336#390C2318yes—
337#389C2312yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2314yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#387C2314yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2314yes—
373#387C2318yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2314yes—
392#386C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2314yes—
403#384C2311yescharacteristic
404#384C2314yes—
405#384C2312yes—
406#382C2311yescharacteristic
407#382C2312yes—
408#382C2314yes—
409#381C2318yes—
410#381C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2312yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2312yes—
445#376C2312yes—
446#376C2311yescharacteristic
447#376C2312yes—
448#376C2311yescharacteristic
449C2×#95C2318yes—
450C43C2311yescharacteristic
451C43C2312yes—
452C43C2312yes—
453C43C2311yescharacteristic
454C2×#41—216no—
455C2×#41—48no—
456C2×#41—48no—
457C22×Q8C2411yescharacteristic
458C22×D4C2411yescharacteristic
459C22×D4C2414yes—
460C22×D4C2412yes—
461C22×D4C2414yes—
462C22×D4C2418yes—
463C22×D4C2418yes—
464C22×D4C2414yes—
465C22×D4C2414yes—
466C22×D4C2418yes—
467C22×D4C2418yes—
468C22×D4C2412yes—
469C22×D4C2418yes—
470C22×D4C2414yes—
471C22×D4C2418yes—
472C22×D4C2418yes—
473C22×D4C2418yes—
474C22×D4C2418yes—
475C22×D4C2418yes—
476C23×C4C2414yes—
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2412yes—
480C23×C4C2418yes—
481C23×C4C2414yes—
482C23×C4C2411yescharacteristic
483C23×C4C2418yes—
484C23×C4C2418yes—
485C23×C4C2418yes—
486#127—28no—
487#127—216no—
488#127—24no—
489#127—28no—
490#127—48no—
491#127—44no—
492#127—48no—
493#127—48no—
494#127—416no—
495#127—88no—
496#127—88no—
497#127—84no—
498#126—28no—
499#126—416no—
500#125—24no—
501#125—216no—
502#125—24no—
503#125—28no—
504#124—24no—
505#123—28no—
506#123—416no—
507#123—416no—
508#123—416no—
509#123—416no—
510#123—416no—
511#123—416no—
512C22⋊Q8—24no—
513#121—24no—
514#121—216no—
515#121—232no—
516#121—216no—
517#121—216no—
518#121—416no—
519#121—416no—
520#121—416no—
521#121—416no—
522#121—416no—
523#121—416no—
524#121—416no—
525#121—48no—
526#121—44no—
527#121—416no—
528#121—48no—
529#121—48no—
530#121—48no—
531#121—48no—
532#121—48no—
533#121—84no—
534#121—88no—
535#121—88no—
536C4×Q8—28no—
537C4×Q8#4118yes—
538C4×D4—28no—
539C4×D4—24no—
540C4×D4—28no—
541C4×D4—28no—
542C4×D4—216no—
543C4×D4—416no—
544C4×D4—48no—
545C4×D4—48no—
546C4×D4—48no—
547C4×D4—48no—
548C4×D4—416no—
549C4×D4—48no—
550C4×D4—48no—
551C4×D4—48no—
552C4×D4—88no—
553C4×D4—84no—
554C4×D4—88no—
555#117—28no—
556#117—28no—
557#117—24no—
558#117—28no—
559#117—42no—
560#117—48no—
561C2×C4⋊C4—48no—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C42—24no—
632C2×C42—44no—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2412yes—
636C2×C42C2411yescharacteristic
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2418yes—
649C2×C42C2414yes—
650C2×C42C2412yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2412yes—
660#95C2412yes—
661#95C2412yes—
662#95C2414yes—
663#95C2412yes—
664#95C2414yes—
665#95C2414yes—
666#95C2412yes—
667#95C2412yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2418yes—
676#95C2418yes—
677#95C2414yes—
678#95C2418yes—
679#95C2414yes—
680#95C2418yes—
681#95C2418yes—
682C24C2512yes—
683C24C2511yescharacteristic
684C24C2518yes—
685C24C2514yes—
686#41—832no—
687C2×Q8—24no—
688C2×Q8C2×#4114yes—
689C2×D4—22no—
690C2×D4—24no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—28no—
695C2×D4—216no—
696C2×D4—216no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—28no—
705C2×D4—216no—
706C2×D4—24no—
707C2×D4—28no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—24no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—216no—
754C22×C4—28no—
755C22×C4—44no—
756C22×C4—48no—
757C22×C4—48no—
758C22×C4—42no—
759C22×C4—44no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—48no—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2511yescharacteristic
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—22no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—216no—
802C4⋊C4—28no—
803C4⋊C4—216no—
804C4⋊C4—24no—
805C4⋊C4—48no—
806C4⋊C4—42no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—48no—
814C4⋊C4—44no—
815C4⋊C4C2×#4114yes—
816C4⋊C4C2×#4118yes—
817C4⋊C4H(5,𝔽2)18yes—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—28no—
821C22⋊C4—216no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—28no—
826C22⋊C4—24no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—216no—
830C22⋊C4—216no—
831C22⋊C4—42no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C42—22no—
858C42—22no—
859C42—22no—
860C42—24no—
861C42—22no—
862C42—28no—
863C42—24no—
864C42—28no—
865C42—28no—
866C42—24no—
867C42—22no—
868C42—24no—
869C42—22no—
870C42—44no—
871C42—44no—
872C42—42no—
873C42—48no—
874C42—44no—
875C42—42no—
876C42C2×#4114yes—
877C42C2×#4118yes—
878C42H(5,𝔽2)14yes—
879C23—22no—
880C23—21no—
881C23—24no—
882C23—28no—
883C23—22no—
884C23—22no—
885C23—21no—
886C23—24no—
887C23—28no—
888C23—28no—
889C23—24no—
890C23—28no—
891C23—24no—
892C23—24no—
893C23—21no—
894C23—24no—
895C23—28no—
896C23—22no—
897C23—24no—
898C23—28no—
899C23—28no—
900C23—24no—
901C23—24no—
902C23—22no—
903C23C2611yescharacteristic
904Q8—28no—
905D4—44no—
906D4—416no—
907D4—48no—
908D4—416no—
909D4—88no—
910D4—84no—
911D4—816no—
912D4—88no—
913D4—816no—
914D4—816no—
915D4—816no—
916D4—816no—
917D4—88no—
918D4—168no—
919D4—168no—
920D4—168no—
921D4—168no—
922D4—168no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—28no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—44no—
965C2×C4—416no—
966C2×C4—44no—
967C2×C4—48no—
968C2×C4—82no—
969C2×C4—88no—
970C2×C4—816no—
971C2×C4—168no—
972C2×C4—168no—
973C2×C4—168no—
974C2×C4C22×#4112yes—
975C2×C4C22×#4114yes—
976C2×C4C22×#4114yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C2×H(5,𝔽2)18yes—
980C2×C4C2×H(5,𝔽2)14yes—
981C2×C4C2×H(5,𝔽2)14yes—
982C2×C4C2×H(5,𝔽2)12yes—
983C2×C4#58512yes—
984C22—42no—
985C22—41no—
986C22—44no—
987C22—48no—
988C22—44no—
989C22—41no—
990C22—48no—
991C22—42no—
992C22—41no—
993C22—44no—
994C22—48no—
995C22—42no—
996C22—44no—
997C22—48no—
998C22—48no—
999C22—44no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—42no—
1006C22—48no—
1007C22—48no—
1008C22C23×#4111yescharacteristic
1009C22C22×H(5,𝔽2)11yescharacteristic
1010C22C22×H(5,𝔽2)12yes—
1011C22C2×#58511yescharacteristic
1012C22H(7,𝔽2)12yes—
1013C4—24no—
1014C4—22no—
1015C4—24no—
1016C4—24no—
1017C4—28no—
1018C4—41no—
1019C4—42no—
1020C4—41no—
1021C4—44no—
1022C4—41no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4—48no—
1027C4—42no—
1028C4—44no—
1029C4—42no—
1030C4#350814yes—
1031C4#351714yes—
1032C2—81no—
1033C2—82no—
1034C2—84no—
1035C2—88no—
1036C2C2×#351711yescharacteristic
1037C2C2×#350811yescharacteristic
1038C2#6285811yescharacteristic
1039C2#6291612yes—
1040C2#6292012yes—
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. #50794C2semidirect
2. #50784C2semidirect
3. #45386C2semidirect
4. #45315C2semidirect
5. #45036C2semidirect
6. #44889C2semidirect
7. #39386C2semidirect
8. #39386C2semidirect
9. #39378C2semidirect
10. #39372C2semidirect
11. #39282C2semidirect
12. #39138C2semidirect
13. #37332C2semidirect
14. #36600C2semidirect
15. #36592C2semidirect
16. #36472C2semidirect
17. #35287C2semidirect
18. #35278C2semidirect
19. #35278C2semidirect
20. #35171C2semidirect
21. #34621C2semidirect
22. #34494C2semidirect
23. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#507942
#507842
#453862
#453152
#450362
#448892
#393862
#393782
#393722
#392822
#391382
#373322
#366002
#365922
#364722
#352872
#352782
#351712
#346212
#344942
#341512