Finite Group Databasebeta

← #7645742

Subgroups — #7645742

Order 512.

7034 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3491C211yesmaximal, characteristic, complemented
2C22×#552C211yesmaximal, characteristic, complemented
3#42167C218yesmaximal, complemented
4#41984C218yesmaximal, complemented
5#38429C218yesmaximal, complemented
6#38427C218yesmaximal, complemented
7#37549C212yesmaximal, complemented
8#37538C212yesmaximal, complemented
9#36971C212yesmaximal, complemented
10#36968C212yesmaximal, complemented
11#36968C212yesmaximal, complemented
12#36719C212yesmaximal, complemented
13#35447C212yesmaximal, complemented
14#35349C212yesmaximal, complemented
15#35302C212yesmaximal, complemented
16#35247C212yesmaximal, complemented
17#35090C211yesmaximal, characteristic, complemented
18#35089C211yesmaximal, characteristic, complemented
19#35089C212yesmaximal, complemented
20#34985C211yesmaximal, characteristic, complemented
21#34984C211yesmaximal, characteristic
22C2×#2413C212yesmaximal, complemented
23#34052C211yesmaximal, characteristic, complemented
24#3491—216no—
25C2×#552—216no—
26C2×#552C2218yescomplemented
27C2×#552C2214yescomplemented
28C2×#552C2218yescomplemented
29C2×#552C2214yescomplemented
30C2×#551C2214yescomplemented
31C2×#551C2214yescomplemented
32C2×#543C2211yescharacteristic
33C2×#539C2212yes—
34C2×#539C2212yes—
35C2×#534C2211yescharacteristic
36C2×#534C2212yes—
37C2×#529C2212yes—
38C2×#529C2212yes—
39C22×#126C2211yescharacteristic, complemented
40C22×#126C2211yescharacteristic, complemented
41C22×#125C2211yescharacteristic, complemented
42C22×#125C2211yescharacteristic, complemented
43C22×#125C2211yescharacteristic, complemented
44C22×#123C2211yescharacteristic
45C22×#123C2212yes—
46C22×#123C2211yescharacteristic
47C22×#123C2212yes—
48C22×C22⋊Q8C2211yescharacteristic
49C22×C22⋊Q8C2211yescharacteristic, complemented
50C2×#518C2212yes—
51C22×C4×Q8C2211yescharacteristic, complemented
52C22×C4×D4C2211yescharacteristic
53C22×#117C2211yescharacteristic
54C22×#117C2212yes—
55C22×#117C2211yescharacteristic
56C22×#117C2211yescharacteristic, complemented
57C23×C4⋊C4C2211yescharacteristic
58#2855C2212yescomplemented
59#2855C2212yescomplemented
60#2855C2212yescomplemented
61#2854C2218yes—
62#2854C2212yes—
63#2854C2212yes—
64#2854C2212yes—
65#2848C2212yescomplemented
66#2847C2212yes—
67#2823C2218yescomplemented
68#2822C2214yescomplemented
69#2820C2214yescomplemented
70#2727C2218yescomplemented
71#2726C2218yescomplemented
72#2726C2218yescomplemented
73#2725C2218yescomplemented
74#2725C2218yescomplemented
75#2725C2218yescomplemented
76#2707C2218yescomplemented
77#2707C2218yescomplemented
78#2705C2218yescomplemented
79#2704C2218yescomplemented
80#2704C2218yescomplemented
81#2704C2218yescomplemented
82#2702C2218yescomplemented
83#2702C2218yescomplemented
84#2683C2218yescomplemented
85#2681C2218yescomplemented
86#2664C2214yescomplemented
87#2664C2218yescomplemented
88#2662C2214yescomplemented
89#2637C2218yescomplemented
90#2637C2214yescomplemented
91#2636C2214yescomplemented
92#2629C2218yescomplemented
93#2629C2214yescomplemented
94#2627C2212yescomplemented
95#2627C2212yescomplemented
96#2627C2212yescomplemented
97#2626C2212yescomplemented
98#2620C2214yescomplemented
99#2618C2218yes—
100#2618C2212yes—
101#2618C2212yes—
102#2618C2212yes—
103#2617C2212yes—
104#2609C2218yescomplemented
105#2601C2218yescomplemented
106#2601C2218yescomplemented
107#2592C2214yescomplemented
108#2584C2214yescomplemented
109#2584C2214yescomplemented
110#2582C2214yescomplemented
111#2579C2214yescomplemented
112#2579C2214yescomplemented
113#2562C2214yescomplemented
114#2538C2214yescomplemented
115#2534C2214yescomplemented
116#2534C2214yescomplemented
117#2487C2214yescomplemented
118#2486C2214yescomplemented
119#2486C2214yescomplemented
120#2450C2218yescomplemented
121#2450C2218yescomplemented
122#2449C2218yescomplemented
123#2449C2218yescomplemented
124#2438C2218yescomplemented
125#2438C2218yescomplemented
126#2438C2218yescomplemented
127#2437C2218yescomplemented
128#2425C2218yes—
129#2425C2218yes—
130#2425C2218yes—
131#2424C2218yes—
132#2413C2218yescomplemented
133#2413C2214yescomplemented
134#2413C2218yescomplemented
135#2413C2214yescomplemented
136#2413C2214yescomplemented
137#2413C2214yescomplemented
138#2413C2218yescomplemented
139#2413C2218yescomplemented
140#2413C2214yescomplemented
141#2413C2214yescomplemented
142#2413C2214yescomplemented
143#2413C2214yescomplemented
144#2412C2218yescomplemented
145#2411C2214yescomplemented
146#2411C2218yescomplemented
147#2411C2214yescomplemented
148#2411C2214yescomplemented
149#2411C2214yescomplemented
150#2409C2214yescomplemented
151C2×#398C2214yescomplemented
152C2×#396C2214yescomplemented
153#2324C2214yescomplemented
154#2323C2214yescomplemented
155#2323C2218yescomplemented
156#2317C2218yescomplemented
157#2316C2212yescomplemented
158#2316C2212yescomplemented
159#2315C2211yescharacteristic
160#2315C2211yescharacteristic
161#2315C2212yes—
162#2315C2212yes—
163#2308C2212yes—
164#2308C2212yes—
165#2296C2218yescomplemented
166C2×#389C2214yescomplemented
167C2×#388C2214yescomplemented
168C2×#386C2212yes—
169C2×#385C2212yes—
170#2285C2212yescomplemented
171#2285C2212yescomplemented
172C2×#381C2212yes—
173C23×Q8C2311yescharacteristic
174C23×D4C2311yescharacteristic
175C23×D4C2312yes—
176C24×C4C2311yescharacteristic
177C24×C4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180#552—264no—
181#552—264no—
182#552—232no—
183#552—232no—
184#551—232no—
185#551—232no—
186#543—28no—
187#539—216no—
188#539—216no—
189#534—28no—
190#534—48no—
191#529—216no—
192#529—216no—
193C2×#126—28no—
194C2×#126—28no—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#126C2314yes—
198C2×#126C2314yes—
199C2×#126C2318yes—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#125—28no—
203C2×#125—28no—
204C2×#125—28no—
205C2×#125C2314yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2318yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#123—28no—
216C2×#123—216no—
217C2×#123—28no—
218C2×#123—48no—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2318yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×#123C2314yes—
234C2×C22⋊Q8—28no—
235C2×C22⋊Q8—28no—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2318yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×#121C2314yes—
249C2×#121C2318yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×#120C2314yes—
253#518—216no—
254C2×C4×Q8—28no—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4—28no—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2318yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×#117—28no—
268C2×#117—28no—
269C2×#117—48no—
270C2×#117D4116yescomplemented
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C2×#117C2314yes—
275C2×#117C2318yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C22×C4⋊C4—28no—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2314yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2312yes—
319C22×C22⋊C4C2314yes—
320C22×C22⋊C4C2314yes—
321C22×C22⋊C4C2311yescharacteristic
322C22×C22⋊C4C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2314yes—
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329#400C2314yes—
330#400C2314yes—
331#400C2318yes—
332#400C2314yes—
333#399C2318yes—
334#399C2314yes—
335#398C2318yes—
336#398C2318yes—
337#398C2314yes—
338#398C2314yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2314yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#397C2318yes—
352#397C2318yes—
353#397C2314yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2318yes—
358#396C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#396C2318yes—
368#396C2318yes—
369#396C2318yes—
370#395C2314yes—
371#395C2314yes—
372#395C2318yes—
373#395C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2314yes—
381#394C2318yes—
382#393C2318yes—
383#393C2314yes—
384#392C2314yes—
385#391C2318yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#390C2318yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2318yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2318yes—
408#389C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#386C2314yes—
432#386C2314yes—
433#386C2318yes—
434#386C2318yes—
435#386C2314yes—
436#386C2314yes—
437#386C2314yes—
438#386C2314yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#385C2314yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2314yes—
453#385C2318yes—
454#385C2314yes—
455#385C2318yes—
456#385C2318yes—
457#384C2314yes—
458#384C2314yes—
459#382C2314yes—
460#382C2314yes—
461#381C2314yes—
462#381C2314yes—
463#381C2314yes—
464#381C2314yes—
465#381C2318yes—
466#380C2318yes—
467#380C2318yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2318yes—
475#380C2314yes—
476#380C2318yes—
477#380C2314yes—
478#379C2314yes—
479#379C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C2×#95C2314yes—
485C2×#95C2314yes—
486C2×#95C2314yes—
487C2×#95C2314yes—
488C25C2412yes—
489C25C2411yescharacteristic
490C25C2411yescharacteristic
491C22×Q8—24no—
492C22×Q8—44no—
493C22×Q8C2414yes—
494C22×Q8C2412yes—
495C22×Q8C2412yes—
496C22×D4—24no—
497C22×D4—28no—
498C22×D4—28no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—28no—
502C22×D4C2414yes—
503C22×D4C2414yes—
504C22×D4C2414yes—
505C22×D4C2412yes—
506C22×D4C2412yes—
507C22×D4C2418yes—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—24no—
515C23×C4—44no—
516C23×C4—44no—
517C23×C4C2×D418yes—
518C23×C4C2411yescharacteristic
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C23×C4C2412yes—
535C23×C4C2414yes—
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543#126—232no—
544#126—216no—
545#126—216no—
546#126—216no—
547#126—216no—
548#126—216no—
549#126—216no—
550#125—232no—
551#125—232no—
552#125—216no—
553#125—216no—
554#125—216no—
555#125—216no—
556#125—28no—
557#125—28no—
558#124—28no—
559#124—28no—
560#123—216no—
561#123—216no—
562#123—216no—
563#123—216no—
564#123—216no—
565#123—216no—
566#123—216no—
567#123—216no—
568#123—232no—
569#123—216no—
570#123—416no—
571#123—48no—
572#123—48no—
573#123—48no—
574#123—48no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—232no—
578C22⋊Q8—216no—
579C22⋊Q8—216no—
580C22⋊Q8—232no—
581C22⋊Q8—216no—
582C22⋊Q8—216no—
583C22⋊Q8—416no—
584C22⋊Q8—48no—
585#121—28no—
586#121—28no—
587#121—48no—
588#121—416no—
589#120—216no—
590#120—48no—
591#120—48no—
592C4×Q8—216no—
593C4×Q8—216no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×D4—216no—
597C4×D4—216no—
598C4×D4—232no—
599C4×D4—216no—
600C4×D4—216no—
601C4×D4—28no—
602C4×D4—28no—
603#117—232no—
604#117—216no—
605#117—216no—
606#117—216no—
607#117—216no—
608#117—216no—
609#117—48no—
610#117—48no—
611#117—48no—
612#117—48no—
613#117C2×D4132yes—
614#117C2×D4132yes—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—216no—
620C2×C4⋊C4—216no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—28no—
632C2×C4⋊C4—28no—
633C2×C4⋊C4—48no—
634C2×C4⋊C4—48no—
635C2×C4⋊C4—48no—
636C2×C4⋊C4C2×D418yes—
637C2×C4⋊C4C2×D418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C22⋊C4—24no—
685C2×C22⋊C4—28no—
686C2×C22⋊C4—28no—
687C2×C22⋊C4—28no—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—28no—
694C2×C22⋊C4—28no—
695C2×C22⋊C4—216no—
696C2×C22⋊C4—48no—
697C2×C22⋊C4—48no—
698C2×C22⋊C4C2×D418yes—
699C2×C22⋊C4C2×D418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C42—24no—
734C2×C42—24no—
735C2×C42—24no—
736C2×C42—48no—
737C2×C42C2×D418yes—
738C2×C42C2×D418yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2418yes—
745C2×C42C2418yes—
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24—22no—
771C24—24no—
772C24—24no—
773C24—22no—
774C24—22no—
775C24—24no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—42no—
780C24—44no—
781C24—44no—
782C24C22×D414yes—
783C24H(5,𝔽2)14yes—
784C242−1+414yes—
785C24C2512yes—
786C24C2514yes—
787C24C2512yes—
788C24C2511yescharacteristic
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—28no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—416no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—48no—
813C2×D4—416no—
814C2×D4—432no—
815C22×C4—232no—
816C22×C4—22no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—28no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—28no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—44no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—44no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—416no—
872C22×C4—416no—
873C22×C4—416no—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C22×D418yes—
877C22×C4C22×D418yes—
878C22×C4C22×D414yes—
879C22×C4C22×D414yes—
880C22×C4C22×D414yes—
881C22×C4C22×D414yes—
882C22×C4C2518yes—
883C22×C4C2514yes—
884C22×C4C2518yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2514yes—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2511yescharacteristic
898C22×C4C2512yes—
899C22×C4C2511yescharacteristic
900C22×C4C2512yes—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—216no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—48no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C4⋊C4C22×D4116yes—
946C4⋊C4C22×D4116yes—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—216no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4C22×D4116yes—
979C22⋊C4C22×D4116yes—
980C42—28no—
981C42—28no—
982C42—28no—
983C42—28no—
984C42—28no—
985C42—48no—
986C42—48no—
987C42C22×D418yes—
988C42C22×D418yes—
989C42C22×D418yes—
990C42C22×D418yes—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—28no—
1002C23—24no—
1003C23—24no—
1004C23—28no—
1005C23—44no—
1006C23—44no—
1007C23—48no—
1008C23—48no—
1009C23—44no—
1010C23—44no—
1011C23—44no—
1012C23—48no—
1013C23—84no—
1014C23—84no—
1015C23—84no—
1016C23—84no—
1017C23—88no—
1018C23—88no—
1019C23#537116yes—
1020C23C23×D414yes—
1021C23C23×D412yes—
1022C23C2×H(5,𝔽2)12yes—
1023C23C2×H(5,𝔽2)14yes—
1024C23C2×2−1+412yes—
1025C23C2×2−1+414yes—
1026C23C2611yescharacteristic
1027Q8—416no—
1028Q8—84no—
1029Q8—84no—
1030D4—416no—
1031D4—416no—
1032D4—416no—
1033D4—84no—
1034D4—84no—
1035D4—168no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—216no—
1050C2×C4—216no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—28no—
1063C2×C4—28no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—28no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—28no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—44no—
1088C2×C4—416no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—416no—
1094C2×C4—44no—
1095C2×C4—48no—
1096C2×C4—88no—
1097C2×C4—88no—
1098C2×C4—84no—
1099C2×C4—84no—
1100C2×C4—88no—
1101C2×C4C23×D414yes—
1102C2×C4C23×D414yes—
1103C2×C4C23×D414yes—
1104C2×C4C23×D414yes—
1105C2×C4C23×D412yes—
1106C2×C4C23×D412yes—
1107C2×C4C23×D414yes—
1108C2×C4#58514yes—
1109C22—22no—
1110C22—24no—
1111C22—22no—
1112C22—24no—
1113C22—28no—
1114C22—24no—
1115C22—24no—
1116C22—28no—
1117C22—416no—
1118C22—42no—
1119C22—44no—
1120C22—44no—
1121C22—42no—
1122C22—44no—
1123C22—48no—
1124C22—44no—
1125C22—48no—
1126C22—42no—
1127C22—44no—
1128C22—88no—
1129C22—168no—
1130C22C2×#53714yes—
1131C22C2×#53718yes—
1132C22C24×D411yescharacteristic
1133C22C22×H(5,𝔽2)11yescharacteristic
1134C22C22×2−1+411yescharacteristic
1135C22C2×#58512yes—
1136C222−1+612yes—
1137C4—24no—
1138C4—24no—
1139C4—24no—
1140C4—24no—
1141C4—24no—
1142C4—22no—
1143C4—24no—
1144C4—22no—
1145C4—42no—
1146C4—42no—
1147C4—44no—
1148C4—42no—
1149C4—44no—
1150C4—48no—
1151C4—48no—
1152C4—42no—
1153C4—42no—
1154C4—44no—
1155C4—42no—
1156C2—24no—
1157C2—28no—
1158C2—82no—
1159C2—84no—
1160C2C22×#53711yescharacteristic
1161C2#6281111yescharacteristic
1162C2#6285911yescharacteristic
1163C2#6290112yes—
1164C2#6290412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34984C2
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×#3491C2semidirect
2. C22×#552C2semidirect
3. #42167C2semidirect
4. #41984C2semidirect
5. #38429C2semidirect
6. #38427C2semidirect
7. #37549C2semidirect
8. #37538C2semidirect
9. #36971C2semidirect
10. #36968C2semidirect
11. #36968C2semidirect
12. #36719C2semidirect
13. #35447C2semidirect
14. #35349C2semidirect
15. #35302C2semidirect
16. #35247C2semidirect
17. #35090C2semidirect
18. #35089C2semidirect
19. #35089C2semidirect
20. #34985C2semidirect
22. C2×#2413C2semidirect
23. #34052C2semidirect
26. C2×#552C22semidirect
27. C2×#552C22semidirect
28. C2×#552C22semidirect
29. C2×#552C22semidirect
30. C2×#551C22semidirect
31. C2×#551C22semidirect
39. C22×#126C22semidirect
40. C22×#126C22semidirect
41. C22×#125C22semidirect
42. C22×#125C22semidirect
43. C22×#125C22semidirect
49. C22×C22⋊Q8C22semidirect
51. C22×C4×Q8C22semidirect
56. C22×#117C22semidirect
58. #2855C22semidirect
59. #2855C22semidirect
60. #2855C22semidirect
65. #2848C22semidirect
67. #2823C22semidirect
68. #2822C22semidirect
69. #2820C22semidirect
70. #2727C22semidirect
71. #2726C22semidirect
72. #2726C22semidirect
73. #2725C22semidirect
74. #2725C22semidirect
75. #2725C22semidirect
76. #2707C22semidirect
77. #2707C22semidirect
78. #2705C22semidirect
79. #2704C22semidirect
80. #2704C22semidirect
81. #2704C22semidirect
82. #2702C22semidirect
83. #2702C22semidirect
84. #2683C22semidirect
85. #2681C22semidirect
86. #2664C22semidirect
87. #2664C22semidirect
88. #2662C22semidirect
89. #2637C22semidirect
90. #2637C22semidirect
91. #2636C22semidirect
92. #2629C22semidirect
93. #2629C22semidirect
94. #2627C22semidirect
95. #2627C22semidirect
96. #2627C22semidirect
97. #2626C22semidirect
98. #2620C22semidirect
104. #2609C22semidirect
105. #2601C22semidirect
106. #2601C22semidirect
107. #2592C22semidirect
108. #2584C22semidirect
109. #2584C22semidirect
110. #2582C22semidirect
111. #2579C22semidirect
112. #2579C22semidirect
113. #2562C22semidirect
114. #2538C22semidirect
115. #2534C22semidirect
116. #2534C22semidirect
117. #2487C22semidirect
118. #2486C22semidirect
119. #2486C22semidirect
120. #2450C22semidirect
121. #2450C22semidirect
122. #2449C22semidirect
123. #2449C22semidirect
124. #2438C22semidirect
125. #2438C22semidirect
126. #2438C22semidirect
127. #2437C22semidirect
132. #2413C22semidirect
133. #2413C22semidirect
134. #2413C22semidirect
135. #2413C22semidirect
136. #2413C22semidirect
137. #2413C22semidirect
138. #2413C22semidirect
139. #2413C22semidirect
140. #2413C22semidirect
141. #2413C22semidirect
142. #2413C22semidirect
143. #2413C22semidirect
144. #2412C22semidirect
145. #2411C22semidirect
146. #2411C22semidirect
147. #2411C22semidirect
148. #2411C22semidirect
149. #2411C22semidirect
150. #2409C22semidirect
151. C2×#398C22semidirect
152. C2×#396C22semidirect
153. #2324C22semidirect
154. #2323C22semidirect
155. #2323C22semidirect
156. #2317C22semidirect
157. #2316C22semidirect
158. #2316C22semidirect
165. #2296C22semidirect
166. C2×#389C22semidirect
167. C2×#388C22semidirect
170. #2285C22semidirect
171. #2285C22semidirect
270. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34912
C22×#5522
#421672
#419842
#384292
#384272
#375492
#375382
#369712
#369682
#367192
#354472
#353492
#353022
#352472
#350902
#350892
#349852
#349842
C2×#24132
#340522