Finite Group Databasebeta

← #7732616

Subgroups — #7732616

Order 512.

6214 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
1#51086C214yesmaximal, complemented
2#50715C214yesmaximal, complemented
3#47031C214yesmaximal, complemented
4#46454C214yesmaximal, complemented
5#44957C214yesmaximal, complemented
6#44876C214yesmaximal, complemented
7#39810C214yesmaximal, complemented
8#39745C214yesmaximal, complemented
9#39434C214yesmaximal, complemented
10#39386C212yesmaximal, complemented
11#39202C212yesmaximal, complemented
12#37782C214yesmaximal, complemented
13#37618C211yesmaximal, characteristic, complemented
14#37332C214yesmaximal, complemented
15#36469C212yesmaximal, complemented
16#36128C212yesmaximal, complemented
17#35571C214yesmaximal, complemented
18#35274C211yesmaximal, characteristic, complemented
19#35274C211yesmaximal, characteristic, complemented
20#34912C211yesmaximal, characteristic, complemented
21#34364C211yesmaximal, characteristic, complemented
22#34232C211yesmaximal, characteristic, complemented
23#34086C211yesmaximal, characteristic, complemented
24C2×#559C2214yescomplemented
25C2×#550C2214yescomplemented
26C2×#540C2214yescomplemented
27C2×#535C2214yes—
28C2×#535C2214yes—
29C2×#532C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#532C2214yescomplemented
32C22×#127C2211yescharacteristic
33#2867C2211yescharacteristic
34#2867C2212yes—
35#2867C2211yescharacteristic
36#2858C2211yescharacteristic
37#2858C2211yescharacteristic
38#2858C2212yes—
39#2856C2214yescomplemented
40#2854C2214yescomplemented
41#2815C2214yes—
42#2797C2218yescomplemented
43#2797C2218yescomplemented
44#2752C2218yescomplemented
45#2752C2218yescomplemented
46#2712C2218yescomplemented
47#2710C2218yescomplemented
48#2703C2218yescomplemented
49#2699C2218yescomplemented
50#2688C2218yescomplemented
51#2678C2218yes—
52#2678C2218yes—
53#2673C2218yescomplemented
54#2673C2218yescomplemented
55#2673C2218yescomplemented
56#2673C2218yescomplemented
57#2673C2218yescomplemented
58#2673C2218yescomplemented
59#2671C2218yescomplemented
60#2670C2218yes—
61#2668C2218yes—
62#2657C2214yes—
63#2657C2214yes—
64#2657C2212yescomplemented
65#2640C2212yescomplemented
66#2631C2214yescomplemented
67#2624C2214yescomplemented
68#2619C2214yescomplemented
69#2615C2212yes—
70#2615C2212yes—
71#2608C2212yes—
72#2607C2212yes—
73#2606C2212yescomplemented
74#2605C2212yescomplemented
75#2602C2218yescomplemented
76#2602C2218yescomplemented
77#2592C2214yescomplemented
78#2570C2212yescomplemented
79#2557C2218yescomplemented
80#2557C2218yescomplemented
81#2557C2218yescomplemented
82#2555C2218yescomplemented
83#2550C2212yescomplemented
84#2548C2214yescomplemented
85#2548C2214yescomplemented
86#2547C2212yescomplemented
87#2544C2214yescomplemented
88#2544C2214yescomplemented
89#2543C2218yescomplemented
90#2541C2212yes—
91#2541C2212yes—
92#2541C2212yes—
93#2541C2212yes—
94#2541C2212yes—
95#2541C2214yes—
96#2541C2212yes—
97#2541C2214yescomplemented
98#2541C2212yescomplemented
99#2541C2214yescomplemented
100#2541C2214yescomplemented
101#2539C2218yes—
102#2535C2214yescomplemented
103#2491C2214yescomplemented
104#2490C2214yescomplemented
105#2464C2218yescomplemented
106#2459C2218yescomplemented
107#2448C2214yescomplemented
108#2447C2214yescomplemented
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2441C2212yes—
112#2439C2212yes—
113#2433C2214yes—
114#2433C2214yes—
115#2433C2212yes—
116#2433C2214yes—
117#2433C2212yes—
118#2431C2214yes—
119#2431C2218yescomplemented
120#2431C2218yescomplemented
121#2431C2218yescomplemented
122#2430C2218yescomplemented
123#2428C2218yescomplemented
124#2428C2214yescomplemented
125#2428C2214yescomplemented
126#2428C2218yescomplemented
127#2428C2214yescomplemented
128#2428C2218yescomplemented
129#2428C2214yescomplemented
130#2424C2218yes—
131#2424C2218yes—
132#2422C2214yescomplemented
133#2420C2214yescomplemented
134#2404C2218yes—
135#2396C2214yes—
136#2380C2214yes—
137#2367C2214yescomplemented
138#2366C2212yes—
139#2366C2212yes—
140#2366C2214yescomplemented
141#2366C2212yescomplemented
142#2365C2212yescomplemented
143#2363C2214yes—
144#2353C2214yescomplemented
145#2341C2212yes—
146#2339C2212yes—
147D4×C22⋊C4C2212yes—
148D4×C22⋊C4C2212yes—
149D4×C22⋊C4C2212yes—
150D4×C22⋊C4C2212yes—
151#2337C2212yescomplemented
152#2337C2212yescomplemented
153#2333C2212yes—
154#2333C2212yes—
155#2333C2214yes—
156#2331C2212yescomplemented
157#2328C2214yes—
158#2328C2214yes—
159#2328C2212yescomplemented
160#2324C2212yes—
161#2324C2212yes—
162#2324C2214yescomplemented
163#2319C2212yescomplemented
164#2308C2214yes—
165C4×C4⋊Q8C2212yescomplemented
166C4×#125C2212yescomplemented
167C4×#124C2214yescomplemented
168C4×#121C2214yescomplemented
169#2297C2214yes—
170#2295C2214yescomplemented
171#2293C2212yescomplemented
172#2290C2214yescomplemented
173#2283C2211yescharacteristic
174#2283C2211yescharacteristic
175#2275C2212yescomplemented
176C42×D4C2212yescomplemented
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C22×#41C2312yes—
180C22×#41C2312yes—
181C22×#41C2318yes—
182C23×D4C2312yes—
183C23×D4C2312yes—
184C23×D4C2312yes—
185#559—416no—
186#550—416no—
187#540—416no—
188#535—416no—
189#535—416no—
190#532—28no—
191#532—28no—
192#532—416no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2311yescharacteristic
196C2×#127—28no—
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2311yescharacteristic
200C2×#127C2311yescharacteristic
201C2×#127C2311yescharacteristic
202C2×#127C2311yescharacteristic
203C2×#127C2314yes—
204C2×#127C2312yes—
205C2×#127C2314yes—
206C2×#127C2314yes—
207C2×#127C2318yes—
208C2×#127C2314yes—
209C2×#127C2314yes—
210C2×#127C2314yes—
211C2×#127C2314yes—
212C2×#127C2314yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#127C2314yes—
217C2×#127C2312yes—
218C2×#125C2312yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2318yes—
224C2×#124C2314yes—
225C2×#124C2318yes—
226C2×#124C2318yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2318yes—
241C2×#121C2314yes—
242C2×#121C2318yes—
243C2×#121C2318yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2318yes—
252C2×#120C2318yes—
253C2×#120C2318yes—
254C2×#120C2318yes—
255C2×#120C2318yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2318yes—
271C2×C4×D4C2318yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2314yes—
277C22×C42C2314yes—
278C22×C42C2311yescharacteristic
279#400C2314yes—
280#399C2314yes—
281#399C2318yes—
282#398C2314yes—
283#398C2314yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C2314yes—
291#396C2314yes—
292#395C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#393C2318yes—
306#393C2314yes—
307#393C2314yes—
308#393C2314yes—
309#392C2318yes—
310#392C2318yes—
311#392C2314yes—
312#392C2314yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#392C2318yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2318yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2318yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2318yes—
352#390C2318yes—
353#390C2312yes—
354#390C2314yes—
355#390C2314yes—
356#390C2312yes—
357#390C2314yes—
358#390C2312yes—
359#390C2312yes—
360#390C2314yes—
361#390C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2318yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#385C2314yes—
420#385C2314yes—
421#385C2318yes—
422#385C2318yes—
423#384C2312yes—
424#383C2312yes—
425#383C2312yes—
426#382C2312yes—
427#382C2312yes—
428#382C2312yes—
429#381C2312yes—
430#381C2312yes—
431#381C2314yes—
432#381C2318yes—
433#380C2314yes—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2314yes—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2314yes—
440#379C2314yes—
441#379C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471#376C2312yes—
472#376C2312yes—
473#376C2312yes—
474#376C2312yes—
475C2×#95C2314yes—
476C43C2311yescharacteristic
477C43C2311yescharacteristic
478C43C2312yes—
479C25C2414yes—
480C2×#41—28no—
481C2×#41—28no—
482C2×#41—48no—
483C2×#41—416no—
484C2×#41—48no—
485C2×#41—416no—
486C2×#41—88no—
487C22×Q8C2412yes—
488C22×Q8C2414yes—
489C22×Q8C2412yes—
490C22×D4—28no—
491C22×D4—28no—
492C22×D4—28no—
493C22×D4—48no—
494C22×D4—48no—
495C22×D4—82no—
496C22×D4—82no—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2418yes—
505C22×D4C2418yes—
506C22×D4C2412yes—
507C22×D4C2412yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2418yes—
511C22×D4C2418yes—
512C22×D4C2414yes—
513C22×D4C2414yes—
514C22×D4C2412yes—
515C22×D4C2414yes—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C22×D4C2418yes—
519C22×D4C2418yes—
520C22×D4C2418yes—
521C22×D4C2418yes—
522C22×D4C2418yes—
523C22×D4C2418yes—
524C23×C4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2414yes—
528C23×C4C2418yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2418yes—
532C23×C4C2418yes—
533C23×C4C2411yescharacteristic
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—24no—
537#127—28no—
538#127—28no—
539#127—24no—
540#127—24no—
541#127—28no—
542#127—24no—
543#127—24no—
544#127—216no—
545#127—48no—
546#127—48no—
547#127—416no—
548#127—48no—
549#127—48no—
550#127—48no—
551#127—48no—
552#127—82no—
553#127—84no—
554#127—82no—
555#127—82no—
556#127—84no—
557#127—82no—
558#125—28no—
559#124—28no—
560#124—28no—
561#124—216no—
562#124—416no—
563#124—48no—
564#124—48no—
565#124—416no—
566#124—416no—
567#123—416no—
568#123—416no—
569#123—416no—
570#123—416no—
571#121—28no—
572#121—28no—
573#121—28no—
574#121—28no—
575#121—216no—
576#121—216no—
577#121—416no—
578#121—416no—
579#121—416no—
580#121—416no—
581#121—416no—
582#121—416no—
583#121—48no—
584#121—48no—
585#121—48no—
586#121—416no—
587#121—48no—
588#121—416no—
589#121—88no—
590#121—88no—
591#121—88no—
592#120—416no—
593#120—416no—
594#120—416no—
595#120—416no—
596C4×Q8—216no—
597C4×Q8—48no—
598C4×D4—216no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—28no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—48no—
610C4×D4—416no—
611C4×D4—416no—
612#117—28no—
613#117—28no—
614#117—48no—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C22⋊C4—84no—
640C2×C22⋊C4—84no—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C42—48no—
680C2×C42#4118yescomplemented
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2411yescharacteristic
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2418yes—
705#95C2412yes—
706#95C2414yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733C24—28no—
734C24—44no—
735C24—44no—
736C24—48no—
737C24—48no—
738C24C2514yes—
739C24C2514yes—
740C24C2514yes—
741C24C2514yes—
742C24C2511yescharacteristic
743#41—816no—
744#41—816no—
745#41—864no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—28no—
750C2×Q8—28no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—28no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—216no—
779C2×D4—216no—
780C2×D4—216no—
781C2×D4—216no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—48no—
808C2×D4—48no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—48no—
813C2×D4—48no—
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—816no—
825C2×D4—816no—
826C2×D4—816no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—216no—
836C22×C4—44no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4C2×#4114yes—
852C22×C4C2×#4114yes—
853C22×C4C2×#4114yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4H(5,𝔽2)18yes—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—24no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—28no—
906C22⋊C4—216no—
907C22⋊C4—216no—
908C22⋊C4—216no—
909C22⋊C4—216no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C42—24no—
935C42—28no—
936C42—28no—
937C42—24no—
938C42—24no—
939C42—28no—
940C42—28no—
941C42—44no—
942C42—44no—
943C42—48no—
944C42—41no—
945C42—42no—
946C42—41no—
947C42—41no—
948C42—41no—
949C42—42no—
950C42C2×#4114yes—
951C42C2×#4114yes—
952C42C2×#4114yes—
953C42C2×#4114yes—
954C42H(5,𝔽2)18yes—
955C23—22no—
956C23—22no—
957C23—21no—
958C23—21no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—28no—
964C23—24no—
965C23—28no—
966C23—28no—
967C23—28no—
968C23—24no—
969C23—28no—
970C23—24no—
971C23—28no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—416no—
982C23—88no—
983C23—88no—
984C23—168no—
985C23—168no—
986C23C22×#4112yes—
987C23C2611yescharacteristic
988Q8—416no—
989Q8—48no—
990Q8—84no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—48no—
995D4—48no—
996D4—48no—
997D4—48no—
998D4—84no—
999D4—84no—
1000D4—816no—
1001D4—816no—
1002D4—88no—
1003D4—88no—
1004D4—84no—
1005D4—84no—
1006D4—88no—
1007D4—84no—
1008D4—816no—
1009D4—816no—
1010D4—88no—
1011D4—88no—
1012D4—816no—
1013D4—168no—
1014D4—168no—
1015D4—168no—
1016D4—168no—
1017D4—168no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—28no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—44no—
1059C2×C4—416no—
1060C2×C4—416no—
1061C2×C4—88no—
1062C2×C4—88no—
1063C2×C4—816no—
1064C2×C4—816no—
1065C2×C4—168no—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C2×H(5,𝔽2)18yes—
1073C2×C4C2×H(5,𝔽2)14yes—
1074C2×C4C2×H(5,𝔽2)14yes—
1075C2×C4C2×H(5,𝔽2)14yes—
1076C2×C4C2×H(5,𝔽2)14yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—42no—
1081C22—42no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—44no—
1093C22—44no—
1094C22—44no—
1095C22—48no—
1096C22—48no—
1097C22—44no—
1098C22—48no—
1099C22—44no—
1100C22—48no—
1101C22—48no—
1102C22—48no—
1103C22—44no—
1104C22—1616no—
1105C22C23×#4111yescharacteristic
1106C22C22×H(5,𝔽2)12yes—
1107C22C22×H(5,𝔽2)12yes—
1108C22H(7,𝔽2)11yescharacteristic
1109C22H(7,𝔽2)11yescharacteristic
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—24no—
1115C4—28no—
1116C4—24no—
1117C4—44no—
1118C4—44no—
1119C4—44no—
1120C4—44no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4#350814yes—
1127C4#350814yes—
1128C2—42no—
1129C2—84no—
1130C2—84no—
1131C2—84no—
1132C2—84no—
1133C2C2×#350811yescharacteristic
1134C2C2×#350811yescharacteristic
1135C2#6285511yescharacteristic
1136C2#6291212yes—
1137C2#6291612yes—
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. #51086C2semidirect
2. #50715C2semidirect
3. #47031C2semidirect
4. #46454C2semidirect
5. #44957C2semidirect
6. #44876C2semidirect
7. #39810C2semidirect
8. #39745C2semidirect
9. #39434C2semidirect
10. #39386C2semidirect
11. #39202C2semidirect
12. #37782C2semidirect
13. #37618C2semidirect
14. #37332C2semidirect
15. #36469C2semidirect
16. #36128C2semidirect
17. #35571C2semidirect
18. #35274C2semidirect
19. #35274C2semidirect
20. #34912C2semidirect
21. #34364C2semidirect
22. #34232C2semidirect
23. #34086C2semidirect
24. C2×#559C22semidirect
25. C2×#550C22semidirect
26. C2×#540C22semidirect
31. C2×#532C22semidirect
39. #2856C22semidirect
40. #2854C22semidirect
42. #2797C22semidirect
43. #2797C22semidirect
44. #2752C22semidirect
45. #2752C22semidirect
46. #2712C22semidirect
47. #2710C22semidirect
48. #2703C22semidirect
49. #2699C22semidirect
50. #2688C22semidirect
53. #2673C22semidirect
54. #2673C22semidirect
55. #2673C22semidirect
56. #2673C22semidirect
57. #2673C22semidirect
58. #2673C22semidirect
59. #2671C22semidirect
64. #2657C22semidirect
65. #2640C22semidirect
66. #2631C22semidirect
67. #2624C22semidirect
68. #2619C22semidirect
73. #2606C22semidirect
74. #2605C22semidirect
75. #2602C22semidirect
76. #2602C22semidirect
77. #2592C22semidirect
78. #2570C22semidirect
79. #2557C22semidirect
80. #2557C22semidirect
81. #2557C22semidirect
82. #2555C22semidirect
83. #2550C22semidirect
84. #2548C22semidirect
85. #2548C22semidirect
86. #2547C22semidirect
87. #2544C22semidirect
88. #2544C22semidirect
89. #2543C22semidirect
97. #2541C22semidirect
98. #2541C22semidirect
99. #2541C22semidirect
100. #2541C22semidirect
102. #2535C22semidirect
103. #2491C22semidirect
104. #2490C22semidirect
105. #2464C22semidirect
106. #2459C22semidirect
107. #2448C22semidirect
108. #2447C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
119. #2431C22semidirect
120. #2431C22semidirect
121. #2431C22semidirect
122. #2430C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2428C22semidirect
128. #2428C22semidirect
129. #2428C22semidirect
132. #2422C22semidirect
133. #2420C22semidirect
137. #2367C22semidirect
140. #2366C22semidirect
141. #2366C22semidirect
142. #2365C22semidirect
144. #2353C22semidirect
151. #2337C22semidirect
152. #2337C22semidirect
156. #2331C22semidirect
159. #2328C22semidirect
162. #2324C22semidirect
163. #2319C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#125C22semidirect
167. C4×#124C22semidirect
168. C4×#121C22semidirect
170. #2295C22semidirect
171. #2293C22semidirect
172. #2290C22semidirect
175. #2275C22semidirect
176. C42×D4C22semidirect
680. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#510862
#507152
#470312
#464542
#449572
#448762
#398102
#397452
#394342
#393862
#392022
#377822
#376182
#373322
#364692
#361282
#355712
#352742
#349122
#343642
#342322
#340862