Finite Group Databasebeta

← #7654821

Subgroups — #7654821

Order 512.

8014 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3481C212yesmaximal, complemented
2#41995C218yesmaximal, complemented
3#41981C214yesmaximal, complemented
4#39130C214yesmaximal, complemented
5#39118C214yesmaximal, complemented
6#37846C214yesmaximal, complemented
7#37838C214yesmaximal, complemented
8#37658C214yesmaximal, complemented
9#37650C214yesmaximal, complemented
10#37621C212yesmaximal, complemented
11#37620C211yesmaximal, characteristic, complemented
12#36157C214yesmaximal, complemented
13#36096C214yesmaximal, complemented
14#35732C214yesmaximal, complemented
15#35236C212yesmaximal, complemented
16#35189C212yesmaximal, complemented
17#35165C212yesmaximal, complemented
18#34935C212yesmaximal, complemented
19C2×#2537C211yesmaximal, characteristic, complemented
20#34188C211yesmaximal, characteristic, complemented
21#3481—232no—
22C2×#559C2212yescomplemented
23C2×#554C2212yescomplemented
24C2×#554C2212yescomplemented
25C2×#553C2212yes—
26C2×#553C2214yescomplemented
27C2×#553C2212yescomplemented
28C2×#551C2214yescomplemented
29C2×#551C2214yescomplemented
30C2×#546C2212yes—
31C2×#546C2214yes—
32C2×#546C2212yescomplemented
33C2×D42C2212yescomplemented
34C2×#535C2214yescomplemented
35C2×#532C2212yescomplemented
36C2×#529C2212yescomplemented
37C2×#529C2212yescomplemented
38C2×#529C2214yescomplemented
39C2×#525C2214yes—
40C2×#525C2214yescomplemented
41C2×#525C2214yescomplemented
42C22×#121C2214yescomplemented
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2212yescomplemented
45C22×C4×D4C2214yescomplemented
46C22×C4×D4C2212yescomplemented
47C22×C4×D4C2212yescomplemented
48#2851C2214yescomplemented
49#2850C2214yescomplemented
50#2848C2214yescomplemented
51#2847C2214yescomplemented
52#2847C2214yescomplemented
53#2847C2214yescomplemented
54#2823C2214yescomplemented
55#2813C2218yescomplemented
56#2733C2214yescomplemented
57#2730C2218yescomplemented
58#2728C2214yescomplemented
59#2699C2214yescomplemented
60#2694C2218yescomplemented
61#2690C2218yescomplemented
62#2687C2218yescomplemented
63#2679C2214yescomplemented
64#2678C2218yescomplemented
65#2678C2218yescomplemented
66#2676C2218yescomplemented
67#2673C2218yescomplemented
68#2672C2218yescomplemented
69#2669C2218yescomplemented
70#2662C2218yescomplemented
71#2636C2218yescomplemented
72#2630C2218yescomplemented
73#2629C2214yescomplemented
74#2628C2214yescomplemented
75#2620C2214yescomplemented
76#2619C2214yescomplemented
77#2618C2214yescomplemented
78#2617C2218yescomplemented
79#2616C2214yescomplemented
80#2615C2214yescomplemented
81#2601C2218yescomplemented
82#2582C2211yescharacteristic, complemented
83#2562C2214yescomplemented
84#2562C2214yescomplemented
85#2560C2218yescomplemented
86#2554C2218yescomplemented
87#2549C2214yescomplemented
88#2547C2214yescomplemented
89#2544C2218yescomplemented
90#2541C2214yescomplemented
91#2540C2214yescomplemented
92#2540C2214yescomplemented
93#2538C2212yescomplemented
94#2538C2212yescomplemented
95#2538C2212yescomplemented
96#2537C2211yescharacteristic
97#2537C2214yescomplemented
98#2537C2214yescomplemented
99#2537C2211yescharacteristic, complemented
100#2537C2212yescomplemented
101#2537C2212yescomplemented
102#2537C2212yescomplemented
103#2537C2214yescomplemented
104#2537C2211yescharacteristic, complemented
105#2536C2214yescomplemented
106#2535C2214yescomplemented
107#2535C2214yescomplemented
108#2535C2214yescomplemented
109#2534C2218yescomplemented
110#2487C2214yescomplemented
111#2486C2214yescomplemented
112#2485C2214yescomplemented
113#2481C2218yescomplemented
114#2472C2218yescomplemented
115#2467C2218yescomplemented
116#2464C2218yescomplemented
117#2461C2218yescomplemented
118#2457C2218yescomplemented
119#2456C2218yescomplemented
120#2445C2218yescomplemented
121#2444C2218yescomplemented
122#2443C2218yescomplemented
123#2433C2214yes—
124#2424C2218yescomplemented
125#2418C2218yescomplemented
126#2418C2218yescomplemented
127#2417C2214yescomplemented
128#2416C2214yescomplemented
129#2415C2214yescomplemented
130#2414C2214yescomplemented
131#2414C2214yescomplemented
132#2414C2214yescomplemented
133#2411C2218yescomplemented
134#2410C2218yescomplemented
135#2408C2214yescomplemented
136#2408C2214yescomplemented
137#2407C2214yescomplemented
138#2403C2218yescomplemented
139#2392C2218yescomplemented
140C2×#394C2214yescomplemented
141#2364C2214yescomplemented
142#2358C2218yescomplemented
143#2355C2214yescomplemented
144#2354C2214yescomplemented
145#2352C2214yescomplemented
146#2352C2214yescomplemented
147D4×C22⋊C4C2214yescomplemented
148#2324C2214yescomplemented
149#2324C2214yescomplemented
150#2324C2214yescomplemented
151#2323C2214yescomplemented
152#2314C2214yescomplemented
153#2311C2212yes—
154#2311C2214yescomplemented
155C4×#121C2214yescomplemented
156C4×#121C2214yescomplemented
157#2285C2212yescomplemented
158#2285C2212yescomplemented
159#2285C2211yescharacteristic, complemented
160C2×#384C2211yescharacteristic, complemented
161#2280C2214yescomplemented
162C2×#380C2214yescomplemented
163#2274C2212yescomplemented
164C22×#41C2312yes—
165C22×#41C2314yes—
166C22×#41C2311yescharacteristic
167C23×D4C2312yes—
168C23×D4C2312yes—
169C23×D4C2314yes—
170C23×D4C2314yes—
171C24×C4C2314yes—
172C24×C4C2314yes—
173#559—216no—
174#554—216no—
175#554—216no—
176#553—216no—
177#553—216no—
178#553—232no—
179#551—232no—
180#551—232no—
181#546—232no—
182#546—216no—
183#546—216no—
184D42—216no—
185#535—416no—
186#532—216no—
187C2×C4⋊Q8C2312yes—
188C2×#127C2312yes—
189C2×#127C2318yes—
190#529—232no—
191#529—216no—
192#529—216no—
193C2×#126C2314yes—
194C2×#126C2314yes—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#125C2312yes—
198C2×#125C2312yes—
199C2×#125C2314yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#124C2314yes—
204C2×#124C2318yes—
205#525—232no—
206#525—232no—
207#525—416no—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×#123C2314yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121—416no—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2318yes—
249C2×#121C2318yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×#120C2314yes—
253C2×#120C2314yes—
254C2×#120C2318yes—
255C2×#120C2318yes—
256C2×#120C2318yes—
257C2×#120C2318yes—
258C4×#41—216no—
259C4×#41D4116yescomplemented
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×D4—232no—
264C2×C4×D4—216no—
265C2×C4×D4—216no—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2318yes—
288C2×C4×D4C2318yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×#117C2314yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C22⋊C4C2314yes—
307C22×C22⋊C4C2314yes—
308C22×C22⋊C4C2314yes—
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2318yes—
311C22×C42C2314yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314#400C2318yes—
315#400C2318yes—
316#399C2318yes—
317#399C2318yes—
318#398C2314yes—
319#398C2314yes—
320#398C2318yes—
321#398C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#395C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2314yes—
345#394C2318yes—
346#394C2318yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2318yes—
352#393C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#392C2318yes—
362#391C2318yes—
363#391C2314yes—
364#391C2314yes—
365#390C2318yes—
366#390C2314yes—
367#390C2318yes—
368#390C2314yes—
369#390C2314yes—
370#390C2318yes—
371#390C2318yes—
372#390C2318yes—
373#390C2318yes—
374#390C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#384C2312yes—
417#384C2311yescharacteristic
418#384C2314yes—
419#384C2311yescharacteristic
420#384C2312yes—
421#382C2312yes—
422#382C2314yes—
423#382C2314yes—
424#381C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2314yes—
445#379C2318yes—
446#379C2318yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2318yes—
457C2×#95C2314yes—
458C25C2414yes—
459C25C2414yes—
460C2×#41—28no—
461C2×#41—28no—
462C2×#41—216no—
463C2×#41—48no—
464C2×#41—48no—
465C2×#41—42no—
466C2×#41—42no—
467C2×#41—44no—
468C2×#41C2×D418yes—
469C22×Q8C2412yes—
470C22×Q8C2414yes—
471C22×Q8C2411yescharacteristic
472C22×D4—216no—
473C22×D4—28no—
474C22×D4—28no—
475C22×D4—28no—
476C22×D4—28no—
477C22×D4—44no—
478C22×D4—44no—
479C22×D4—48no—
480C22×D4—48no—
481C22×D4—48no—
482C22×D4—416no—
483C22×D4C2414yes—
484C22×D4C2412yes—
485C22×D4C2412yes—
486C22×D4C2414yes—
487C22×D4C2414yes—
488C22×D4C2414yes—
489C22×D4C2414yes—
490C22×D4C2412yes—
491C22×D4C2412yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2418yes—
495C22×D4C2414yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2418yes—
499C22×D4C2414yes—
500C22×D4C2418yes—
501C22×D4C2414yes—
502C22×D4C2411yescharacteristic
503C23×C4—216no—
504C23×C4—216no—
505C23×C4—48no—
506C23×C4—48no—
507C23×C4—48no—
508C23×C4—48no—
509C23×C4C2414yes—
510C23×C4C2414yes—
511C23×C4C2414yes—
512C23×C4C2414yes—
513C23×C4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2414yes—
519C23×C4C2414yes—
520C23×C4C2414yes—
521C23×C4C2414yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2414yes—
525C23×C4C2412yes—
526C4⋊Q8—28no—
527#127—28no—
528#127—416no—
529#126—216no—
530#126—216no—
531#126—216no—
532#126—216no—
533#125—216no—
534#125—28no—
535#125—28no—
536#124—216no—
537#124—28no—
538#124—28no—
539#124—216no—
540#124—416no—
541#123—216no—
542#123—216no—
543#123—216no—
544#123—216no—
545#123—216no—
546#123—216no—
547#123—216no—
548#123—216no—
549#123—416no—
550C22⋊Q8—216no—
551C22⋊Q8—28no—
552C22⋊Q8—28no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—216no—
556C22⋊Q8—216no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559C22⋊Q8—48no—
560#121—216no—
561#121—216no—
562#121—216no—
563#121—216no—
564#121—216no—
565#121—28no—
566#121—28no—
567#121—28no—
568#121—28no—
569#121—216no—
570#121—216no—
571#121—216no—
572#121—216no—
573#121—416no—
574#121—416no—
575#121—48no—
576#121—48no—
577#121—48no—
578#121—48no—
579#121—48no—
580#121—48no—
581#121—48no—
582#120—216no—
583#120—216no—
584#120—216no—
585#120—216no—
586#120—416no—
587#120—416no—
588#120—416no—
589#120—416no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8C2×D4116yescomplemented
593C4×D4—216no—
594C4×D4—216no—
595C4×D4—216no—
596C4×D4—216no—
597C4×D4—216no—
598C4×D4—216no—
599C4×D4—216no—
600C4×D4—216no—
601C4×D4—28no—
602C4×D4—216no—
603C4×D4—216no—
604C4×D4—216no—
605C4×D4—28no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—28no—
612C4×D4—28no—
613C4×D4—28no—
614C4×D4—416no—
615C4×D4—416no—
616C4×D4C2×D4116yes—
617C4×D4C2×D4116yes—
618C4×D4C2×D4116yescomplemented
619#117—28no—
620#117—216no—
621#117—216no—
622#117—216no—
623#117—44no—
624#117—48no—
625#117—48no—
626#117C2×D418yes—
627#117C2×D4116yescomplemented
628C2×C4⋊C4—28no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—216no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C22⋊C4—216no—
665C2×C22⋊C4—216no—
666C2×C22⋊C4—216no—
667C2×C22⋊C4—216no—
668C2×C22⋊C4—416no—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2411yescharacteristic
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2411yescharacteristic
709C2×C22⋊C4C2412yes—
710C2×C42—216no—
711C2×C42C2×D418yes—
712C2×C42C2×D4116yescomplemented
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741C24—28no—
742C24—28no—
743C24—28no—
744C24—28no—
745C24—28no—
746C24—28no—
747C24—44no—
748C24—44no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—44no—
753C24—44no—
754C24—44no—
755C24C2514yes—
756C24C2514yes—
757C24C2512yes—
758C24C2514yes—
759C24C2511yescharacteristic
760#41—416no—
761#41—432no—
762#41—832no—
763C2×Q8—24no—
764C2×Q8—28no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—41no—
768C2×Q8—41no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8C22×D414yes—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—216no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—216no—
786C2×D4—216no—
787C2×D4—24no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—28no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—432no—
800C2×D4—432no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—41no—
809C2×D4—41no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—48no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—48no—
824C2×D4—48no—
825C2×D4—48no—
826C2×D4—48no—
827C2×D4—44no—
828C2×D4—464no—
829C2×D4—832no—
830C2×D4C22×D418yes—
831C2×D4C22×D414yes—
832C2×D4H(5,𝔽2)18yes—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—832no—
879C22×C4—832no—
880C22×C4C22×D414yes—
881C22×C4C22×D418yes—
882C22×C4C22×D418yes—
883C22×C4C22×D418yes—
884C22×C4C22×D418yes—
885C22×C4C2518yes—
886C22×C4C2514yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2512yes—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4C22×D418yes—
929C4⋊C4C22×D418yes—
930C4⋊C4C22×D418yes—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—216no—
935C22⋊C4—216no—
936C22⋊C4—216no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4C22×D414yes—
969C22⋊C4C22×D418yes—
970C22⋊C4C22×D414yes—
971C22⋊C4C22×D418yes—
972C42—28no—
973C42—28no—
974C42—28no—
975C42—44no—
976C42—48no—
977C42—48no—
978C42C22×D418yes—
979C42C22×D414yes—
980C42C22×D418yes—
981C42C22×D414yes—
982C42C22×D418yes—
983C42C22×D418yes—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—416no—
1018C23—88no—
1019C23—88no—
1020C23—88no—
1021C23—88no—
1022C23—88no—
1023C23—88no—
1024C23—88no—
1025C23—88no—
1026C23C23×D414yes—
1027C23C23×D412yes—
1028C23C2×H(5,𝔽2)18yes—
1029C23#58512yes—
1030C23#58512yes—
1031C23C2611yescharacteristic
1032Q8—44no—
1033Q8—48no—
1034Q8—88no—
1035D4—216no—
1036D4—216no—
1037D4—44no—
1038D4—416no—
1039D4—416no—
1040D4—416no—
1041D4—416no—
1042D4—416no—
1043D4—416no—
1044D4—416no—
1045D4—48no—
1046D4—48no—
1047D4—88no—
1048D4—816no—
1049D4—816no—
1050D4—88no—
1051D4—88no—
1052D4—88no—
1053D4—164no—
1054D4—168no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—28no—
1068C2×C4—216no—
1069C2×C4—216no—
1070C2×C4—216no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—28no—
1077C2×C4—28no—
1078C2×C4—28no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—28no—
1084C2×C4—24no—
1085C2×C4—28no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—48no—
1094C2×C4—416no—
1095C2×C4—416no—
1096C2×C4—416no—
1097C2×C4—416no—
1098C2×C4—416no—
1099C2×C4—88no—
1100C2×C4—88no—
1101C2×C4—88no—
1102C2×C4—88no—
1103C2×C4—88no—
1104C2×C4—88no—
1105C2×C4—88no—
1106C2×C4C23×D414yes—
1107C2×C4C23×D414yes—
1108C2×C4C23×D412yes—
1109C2×C4C23×D412yes—
1110C2×C4C23×D414yes—
1111C2×C4C23×D414yes—
1112C2×C4C23×D414yes—
1113C2×C4C2×H(5,𝔽2)14yes—
1114C2×C4#58514yes—
1115C22—22no—
1116C22—24no—
1117C22—22no—
1118C22—24no—
1119C22—28no—
1120C22—28no—
1121C22—24no—
1122C22—24no—
1123C22—28no—
1124C22—24no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—44no—
1129C22—42no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—832no—
1148C22—832no—
1149C22#344914yes—
1150C22C24×D411yescharacteristic
1151C22C22×H(5,𝔽2)12yes—
1152C22C2×#58511yescharacteristic
1153C22C2×#58511yescharacteristic
1154C22C2×#58512yes—
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—22no—
1159C4—22no—
1160C4—24no—
1161C4—44no—
1162C4—44no—
1163C4—48no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4—44no—
1168C4—44no—
1169C4#348818yes—
1170C2—24no—
1171C2—48no—
1172C2—44no—
1173C2—84no—
1174C2—84no—
1175C2C2×#344911yescharacteristic
1176C2C2×#348812yes—
1177C2#6301211yescharacteristic
1178C2#6301812yes—
1179C2#6302811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3481C2semidirect
2. #41995C2semidirect
3. #41981C2semidirect
4. #39130C2semidirect
5. #39118C2semidirect
6. #37846C2semidirect
7. #37838C2semidirect
8. #37658C2semidirect
9. #37650C2semidirect
10. #37621C2semidirect
11. #37620C2semidirect
12. #36157C2semidirect
13. #36096C2semidirect
14. #35732C2semidirect
15. #35236C2semidirect
16. #35189C2semidirect
17. #35165C2semidirect
18. #34935C2semidirect
19. C2×#2537C2semidirect
20. #34188C2semidirect
22. C2×#559C22semidirect
23. C2×#554C22semidirect
24. C2×#554C22semidirect
26. C2×#553C22semidirect
27. C2×#553C22semidirect
28. C2×#551C22semidirect
29. C2×#551C22semidirect
32. C2×#546C22semidirect
33. C2×D42C22semidirect
34. C2×#535C22semidirect
35. C2×#532C22semidirect
36. C2×#529C22semidirect
37. C2×#529C22semidirect
38. C2×#529C22semidirect
40. C2×#525C22semidirect
41. C2×#525C22semidirect
42. C22×#121C22semidirect
44. C2×C4×#41C22semidirect
45. C22×C4×D4C22semidirect
46. C22×C4×D4C22semidirect
47. C22×C4×D4C22semidirect
48. #2851C22semidirect
49. #2850C22semidirect
50. #2848C22semidirect
51. #2847C22semidirect
52. #2847C22semidirect
53. #2847C22semidirect
54. #2823C22semidirect
55. #2813C22semidirect
56. #2733C22semidirect
57. #2730C22semidirect
58. #2728C22semidirect
59. #2699C22semidirect
60. #2694C22semidirect
61. #2690C22semidirect
62. #2687C22semidirect
63. #2679C22semidirect
64. #2678C22semidirect
65. #2678C22semidirect
66. #2676C22semidirect
67. #2673C22semidirect
68. #2672C22semidirect
69. #2669C22semidirect
70. #2662C22semidirect
71. #2636C22semidirect
72. #2630C22semidirect
73. #2629C22semidirect
74. #2628C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2618C22semidirect
78. #2617C22semidirect
79. #2616C22semidirect
80. #2615C22semidirect
81. #2601C22semidirect
82. #2582C22semidirect
83. #2562C22semidirect
84. #2562C22semidirect
85. #2560C22semidirect
86. #2554C22semidirect
87. #2549C22semidirect
88. #2547C22semidirect
89. #2544C22semidirect
90. #2541C22semidirect
91. #2540C22semidirect
92. #2540C22semidirect
93. #2538C22semidirect
94. #2538C22semidirect
95. #2538C22semidirect
97. #2537C22semidirect
98. #2537C22semidirect
99. #2537C22semidirect
100. #2537C22semidirect
101. #2537C22semidirect
102. #2537C22semidirect
103. #2537C22semidirect
104. #2537C22semidirect
105. #2536C22semidirect
106. #2535C22semidirect
107. #2535C22semidirect
108. #2535C22semidirect
109. #2534C22semidirect
110. #2487C22semidirect
111. #2486C22semidirect
112. #2485C22semidirect
113. #2481C22semidirect
114. #2472C22semidirect
115. #2467C22semidirect
116. #2464C22semidirect
117. #2461C22semidirect
118. #2457C22semidirect
119. #2456C22semidirect
120. #2445C22semidirect
121. #2444C22semidirect
122. #2443C22semidirect
124. #2424C22semidirect
125. #2418C22semidirect
126. #2418C22semidirect
127. #2417C22semidirect
128. #2416C22semidirect
129. #2415C22semidirect
130. #2414C22semidirect
131. #2414C22semidirect
132. #2414C22semidirect
133. #2411C22semidirect
134. #2410C22semidirect
135. #2408C22semidirect
136. #2408C22semidirect
137. #2407C22semidirect
138. #2403C22semidirect
139. #2392C22semidirect
140. C2×#394C22semidirect
141. #2364C22semidirect
142. #2358C22semidirect
143. #2355C22semidirect
144. #2354C22semidirect
145. #2352C22semidirect
146. #2352C22semidirect
147. D4×C22⋊C4C22semidirect
148. #2324C22semidirect
149. #2324C22semidirect
150. #2324C22semidirect
151. #2323C22semidirect
152. #2314C22semidirect
154. #2311C22semidirect
155. C4×#121C22semidirect
156. C4×#121C22semidirect
157. #2285C22semidirect
158. #2285C22semidirect
159. #2285C22semidirect
160. C2×#384C22semidirect
161. #2280C22semidirect
162. C2×#380C22semidirect
163. #2274C22semidirect
259. C4×#41D4semidirect
592. C4×Q8C2×D4semidirect
618. C4×D4C2×D4semidirect
627. #117C2×D4semidirect
712. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34812
#419952
#419812
#391302
#391182
#378462
#378382
#376582
#376502
#376212
#376202
#361572
#360962
#357322
#352362
#351892
#351652
#349352
C2×#25372
#341882