Finite Group Databasebeta

← #7714776

Subgroups — #7714776

Order 512.

7822 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C211yesmaximal, characteristic, complemented
2C22×#536C211yesmaximal, characteristic, complemented
3#52083C212yesmaximal, complemented
4#52076C214yesmaximal, complemented
5#52075C214yesmaximal, complemented
6#52072C212yesmaximal, complemented
7#52071C214yesmaximal, complemented
8#47797C218yesmaximal, complemented
9#47795C218yesmaximal, complemented
10#37843C214yesmaximal, complemented
11#37841C214yesmaximal, complemented
12#37655C214yesmaximal, complemented
13#37653C214yesmaximal, complemented
14#37606C212yesmaximal, complemented
15#37258C212yesmaximal, complemented
16#37187C212yesmaximal, complemented
17#35242C212yesmaximal, complemented
18#35149C212yesmaximal, complemented
19#35118C212yesmaximal, complemented
20#34365C211yesmaximal, characteristic, complemented
21C23×#41C2211yescharacteristic
22C24×Q8C2211yescharacteristic
23#3544—216no—
24C2×#563C2212yescomplemented
25C2×#563C2212yescomplemented
26C2×Q82C2211yescharacteristic, complemented
27C2×#555C2211yescharacteristic, complemented
28C2×#554C2212yescomplemented
29C2×#552C2214yes—
30C2×#547C2214yes—
31C2×#544C2214yescomplemented
32C2×#542C2214yescomplemented
33C2×#536—216no—
34C2×#536C2212yes—
35C2×#536C2212yes—
36C2×#536C2212yes—
37C2×#536C2212yes—
38C2×#536C2212yes—
39C2×#536C2212yes—
40C2×#536C2218yes—
41C2×#536C2212yes—
42C2×#535C2212yes—
43C22×C4⋊Q8C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic
45C2×#529C2212yes—
46C22×#124C2211yescharacteristic
47C22×#124C2211yescharacteristic
48C2×#525C2212yes—
49C2×#525C2212yes—
50C22×#123C2214yes—
51C22×C22⋊Q8C2214yes—
52C22×#117C2211yescharacteristic
53#2853C2214yes—
54#2849C2214yes—
55#2849C2214yes—
56#2849C2214yes—
57#2820C2214yescomplemented
58#2819C2214yescomplemented
59#2734C2214yescomplemented
60#2734C2214yescomplemented
61#2733C2214yescomplemented
62#2733C2214yescomplemented
63#2731C2214yescomplemented
64#2731C2214yescomplemented
65#2731C2214yescomplemented
66#2731C2214yescomplemented
67#2730C2218yescomplemented
68#2730C2218yescomplemented
69#2729C2218yescomplemented
70#2729C2218yescomplemented
71#2707C2218yescomplemented
72#2705C2218yescomplemented
73#2704C2218yescomplemented
74#2702C2218yescomplemented
75#2696C2218yescomplemented
76#2694C2218yescomplemented
77#2692C2218yescomplemented
78#2690C2218yescomplemented
79#2683C2218yescomplemented
80#2682C2218yescomplemented
81#2681C2218yescomplemented
82#2681C2218yescomplemented
83#2677C2218yescomplemented
84#2676C2218yescomplemented
85#2674C2218yescomplemented
86#2673C2218yescomplemented
87#2662C2218yescomplemented
88#2632C2214yescomplemented
89#2631C2214yescomplemented
90#2627C2212yes—
91#2626C2212yes—
92#2618C2212yes—
93#2617C2212yes—
94#2614C2214yes—
95#2614C2214yes—
96#2613C2214yes—
97#2613C2214yes—
98#2611C2214yescomplemented
99#2610C2214yescomplemented
100#2610C2218yescomplemented
101#2609C2218yescomplemented
102#2601C2218yescomplemented
103#2599C2214yescomplemented
104#2598C2214yescomplemented
105#2561C2214yes—
106#2560C2218yescomplemented
107#2558C2218yescomplemented
108#2556C2218yescomplemented
109#2554C2218yescomplemented
110#2539C2214yes—
111#2534C2214yes—
112#2534C2214yes—
113#2484C2214yes—
114#2482C2214yes—
115#2477C2218yescomplemented
116#2471C2218yescomplemented
117#2465C2218yescomplemented
118#2463C2218yescomplemented
119#2461C2218yescomplemented
120#2461C2218yescomplemented
121#2458C2218yescomplemented
122#2456C2218yescomplemented
123#2452C2218yescomplemented
124#2449C2218yescomplemented
125#2445C2218yescomplemented
126#2443C2218yescomplemented
127#2436C2214yescomplemented
128#2436C2214yescomplemented
129#2434C2214yescomplemented
130#2434C2214yescomplemented
131#2432C2214yes—
132#2432C2214yes—
133#2431C2214yes—
134#2431C2214yes—
135#2413C2214yes—
136#2413C2214yes—
137#2411C2214yes—
138#2411C2214yes—
139#2409C2218yescomplemented
140#2409C2218yescomplemented
141#2407C2218yes—
142#2407C2218yes—
143#2406C2214yes—
144#2404C2214yes—
145#2381C2212yescomplemented
146#2381C2212yescomplemented
147#2369C2212yescomplemented
148#2369C2212yescomplemented
149#2344C2214yes—
150#2344C2214yes—
151#2331C2218yescomplemented
152#2322C2214yes—
153#2321C2214yes—
154#2310C2212yes—
155#2310C2212yes—
156#2310C2212yes—
157#2309C2212yes—
158#2283C2212yes—
159#2280C2212yes—
160#2280C2212yes—
161C22×#41—28no—
162C22×#41—44no—
163C22×#41—44no—
164C22×#41C2312yes—
165C22×#41C2314yes—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C23×Q8—28no—
170C23×Q8—44no—
171C23×Q8—44no—
172C23×Q8C2312yes—
173C23×Q8C2311yescharacteristic
174C23×Q8C2312yes—
175C23×Q8C2314yes—
176C23×Q8C2312yes—
177C23×Q8C2311yescharacteristic
178C23×Q8C2311yescharacteristic
179C23×D4C2312yes—
180C23×D4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2312yes—
183C24×C4C2312yes—
184#563—216no—
185#563—216no—
186Q82—28no—
187#555—28no—
188#554—216no—
189#552—232no—
190#547—232no—
191#544—232no—
192#542—232no—
193#536—216no—
194#536—216no—
195#536—264no—
196#536—216no—
197#536—216no—
198#536—216no—
199#536—216no—
200#536—48no—
201#535—48no—
202C2×C4⋊Q8—28no—
203C2×C4⋊Q8D4116yescomplemented
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2314yes—
219#529—216no—
220C2×#126C2314yes—
221C2×#126C2314yes—
222C2×#126C2314yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#125C2314yes—
226C2×#125C2314yes—
227C2×#124—28no—
228C2×#124—28no—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242#525—48no—
243#525—48no—
244C2×#123—232no—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2318yes—
250C2×#123C2318yes—
251C2×#123C2318yes—
252C2×#123C2318yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8—232no—
258C2×C22⋊Q8C2318yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2318yes—
265C2×C22⋊Q8C2318yes—
266C2×C22⋊Q8C2318yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2318yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2318yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2318yes—
287C2×C4×D4C2318yes—
288C2×#117—28no—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2314yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2314yes—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309#400C2314yes—
310#400C2318yes—
311#399C2318yes—
312#399C2314yes—
313#399C2318yes—
314#398C2318yes—
315#398C2314yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#395C2318yes—
331#395C2314yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#395C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2314yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#393C2318yes—
348#393C2318yes—
349#393C2318yes—
350#393C2314yes—
351#393C2318yes—
352#393C2318yes—
353#393C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2314yes—
357#392C2318yes—
358#392C2318yes—
359#392C2318yes—
360#392C2318yes—
361#391C2318yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#390C2318yes—
373#390C2318yes—
374#390C2314yes—
375#390C2314yes—
376#390C2318yes—
377#390C2318yes—
378#390C2318yes—
379#390C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C2314yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#385C2314yes—
423#385C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#383C2314yes—
434#382C2314yes—
435#381C2314yes—
436#381C2314yes—
437#381C2314yes—
438#381C2314yes—
439#381C2314yes—
440#381C2314yes—
441#380C2312yes—
442#380C2312yes—
443#380C2318yes—
444#380C2318yes—
445#379C2314yes—
446#379C2314yes—
447#379C2314yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456#376C2314yes—
457C25C2412yes—
458C25C2411yescharacteristic
459C2×#41—28no—
460C2×#41—216no—
461C2×#41—28no—
462C2×#41—28no—
463C2×#41—28no—
464C2×#41—44no—
465C2×#41—48no—
466C2×#41—44no—
467C2×#41—44no—
468C2×#41—48no—
469C2×#41—44no—
470C2×#41—44no—
471C2×#41—44no—
472C2×#41—44no—
473C2×#41—44no—
474C2×#41—464no—
475C22×Q8—28no—
476C22×Q8—216no—
477C22×Q8—28no—
478C22×Q8—28no—
479C22×Q8—24no—
480C22×Q8—28no—
481C22×Q8—42no—
482C22×Q8—44no—
483C22×Q8—42no—
484C22×Q8—42no—
485C22×Q8—42no—
486C22×Q8—44no—
487C22×Q8—48no—
488C22×Q8—44no—
489C22×Q8—42no—
490C22×Q8—42no—
491C22×Q8—44no—
492C22×Q8—48no—
493C22×Q8—44no—
494C22×Q8—464no—
495C22×Q8C2×D418yes—
496C22×Q8C2×D418yes—
497C22×Q8C2414yes—
498C22×Q8C2414yes—
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2412yes—
502C22×Q8C2412yes—
503C22×Q8C2412yes—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2412yes—
507C22×Q8C2412yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—28no—
511C22×D4—28no—
512C22×D4—24no—
513C22×D4—44no—
514C22×D4—42no—
515C22×D4—42no—
516C22×D4C2414yes—
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2412yes—
520C22×D4C2418yes—
521C22×D4C2412yes—
522C22×D4C2412yes—
523C22×D4C2412yes—
524C22×D4C2412yes—
525C22×D4C2418yes—
526C22×D4C2418yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—28no—
531C23×C4—28no—
532C23×C4—28no—
533C23×C4—28no—
534C23×C4—44no—
535C23×C4—44no—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C4⋊Q8—28no—
553C4⋊Q8—216no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—216no—
560C4⋊Q8—48no—
561C4⋊Q8C2×D4132yes—
562C4⋊Q8C2×D418yes—
563C4⋊Q8C2×D418yes—
564C4⋊Q8C2×D418yes—
565C4⋊Q8C2×D418yes—
566#127—48no—
567#126—216no—
568#126—216no—
569#126—216no—
570#125—216no—
571#125—216no—
572#125—216no—
573#125—28no—
574#124—28no—
575#124—216no—
576#124—28no—
577#124—28no—
578#124—28no—
579#124—28no—
580#124—28no—
581#124—216no—
582#124—28no—
583#124—28no—
584#124—28no—
585#124—48no—
586#124—48no—
587#123—216no—
588#123—216no—
589#123—216no—
590#123—216no—
591#123—232no—
592#123—232no—
593#123—232no—
594#123—232no—
595#123—216no—
596#123—216no—
597#123—48no—
598#123—48no—
599C22⋊Q8—216no—
600C22⋊Q8—216no—
601C22⋊Q8—216no—
602C22⋊Q8—216no—
603C22⋊Q8—28no—
604C22⋊Q8—232no—
605C22⋊Q8—232no—
606C22⋊Q8—232no—
607C22⋊Q8—232no—
608C22⋊Q8—216no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—48no—
612C22⋊Q8—416no—
613C22⋊Q8—48no—
614#121—28no—
615#121—216no—
616#121—48no—
617#121—416no—
618#121—48no—
619#120—216no—
620#120—48no—
621#120—48no—
622C4×Q8—216no—
623C4×Q8—28no—
624C4×D4—216no—
625C4×D4—216no—
626C4×D4—28no—
627C4×D4—416no—
628C4×D4—416no—
629#117—28no—
630#117—28no—
631#117—216no—
632#117—216no—
633#117—28no—
634#117—28no—
635#117—216no—
636#117—44no—
637#117—44no—
638#117—44no—
639#117—44no—
640C2×C4⋊C4—28no—
641C2×C4⋊C4—216no—
642C2×C4⋊C4—216no—
643C2×C4⋊C4C2×D4132yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C22⋊C4—28no—
676C2×C22⋊C4—216no—
677C2×C22⋊C4—216no—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C42—24no—
710C2×C42C2×D418yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2418yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24—22no—
746C24—22no—
747C24—24no—
748C24—24no—
749C24—24no—
750C24—44no—
751C24—48no—
752C24H(5,𝔽2)14yes—
753C24C2514yes—
754C24C2514yes—
755C24C2512yes—
756C24C2511yescharacteristic
757#41—432no—
758#41—464no—
759#41—432no—
760#41—816no—
761#41—816no—
762C2×Q8—24no—
763C2×Q8—28no—
764C2×Q8—28no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—416no—
772C2×Q8—41no—
773C2×Q8—42no—
774C2×Q8—44no—
775C2×Q8—41no—
776C2×Q8—42no—
777C2×Q8—41no—
778C2×Q8—44no—
779C2×Q8—41no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—416no—
785C2×Q8—41no—
786C2×Q8—42no—
787C2×Q8—41no—
788C2×Q8—42no—
789C2×Q8—41no—
790C2×Q8—41no—
791C2×Q8—44no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—432no—
797C2×Q8—432no—
798C2×Q8—464no—
799C2×Q8—432no—
800C2×Q8—416no—
801C2×Q8C22×D414yes—
802C2×Q8C22×D414yes—
803C2×Q8C22×D418yes—
804C2×Q8C22×D418yes—
805C2×Q8C22×D414yes—
806C2×Q8C22×D414yes—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—216no—
813C2×D4—24no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—44no—
827C2×D4—432no—
828C2×D4—416no—
829C2×D4—48no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C22×C4—232no—
842C22×C4—22no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—28no—
863C22×C4—28no—
864C22×C4—28no—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—28no—
868C22×C4—28no—
869C22×C4—28no—
870C22×C4—28no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—432no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—432no—
884C22×C4C22×D414yes—
885C22×C4C22×D418yes—
886C22×C4C22×D418yes—
887C22×C4C22×D418yes—
888C22×C4H(5,𝔽2)14yes—
889C22×C4C2518yes—
890C22×C4C2518yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—216no—
909C4⋊C4—216no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—24no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—216no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4C22×D4116yes—
933C4⋊C4C22×D4116yes—
934C4⋊C4C22×D4116yes—
935C4⋊C4C22×D4116yes—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—216no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—216no—
943C22⋊C4—216no—
944C22⋊C4—216no—
945C22⋊C4—216no—
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—216no—
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—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—28no—
972C42—24no—
973C42—24no—
974C42—48no—
975C42—44no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42C22×D418yes—
980C42C22×D414yes—
981C42C22×D414yes—
982C23—24no—
983C23—22no—
984C23—22no—
985C23—28no—
986C23—28no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—28no—
994C23—28no—
995C23—28no—
996C23—28no—
997C23—48no—
998C23—48no—
999C23—48no—
1000C23—416no—
1001C23—48no—
1002C23—88no—
1003C23—88no—
1004C23C23×D412yes—
1005C23C2×H(5,𝔽2)14yes—
1006C23C2×H(5,𝔽2)12yes—
1007C23C2×H(5,𝔽2)12yes—
1008C23C2611yescharacteristic
1009Q8—44no—
1010Q8—48no—
1011Q8—44no—
1012Q8—44no—
1013Q8—48no—
1014Q8—44no—
1015Q8—416no—
1016Q8—416no—
1017Q8—48no—
1018Q8—48no—
1019Q8—48no—
1020Q8—84no—
1021Q8—84no—
1022D4—416no—
1023D4—416no—
1024D4—48no—
1025D4—48no—
1026D4—48no—
1027D4—416no—
1028D4—84no—
1029D4—84no—
1030D4—816no—
1031D4—816no—
1032D4—168no—
1033C2×C4—216no—
1034C2×C4—216no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—216no—
1054C2×C4—216no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—28no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—28no—
1072C2×C4—28no—
1073C2×C4—48no—
1074C2×C4—416no—
1075C2×C4—416no—
1076C2×C4—416no—
1077C2×C4—416no—
1078C2×C4—416no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—88no—
1082C2×C4—88no—
1083C2×C4C23×D414yes—
1084C2×C4C23×D412yes—
1085C2×C4C23×D412yes—
1086C2×C4C23×D414yes—
1087C2×C4C23×D414yes—
1088C2×C4C23×D414yes—
1089C2×C4C23×D414yes—
1090C2×C4C23×D414yes—
1091C2×C4C2×H(5,𝔽2)14yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—28no—
1097C22—416no—
1098C22—44no—
1099C22—44no—
1100C22—44no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—48no—
1105C22—48no—
1106C22—48no—
1107C22—44no—
1108C22—48no—
1109C22—44no—
1110C22—816no—
1111C22#348414yes—
1112C22C24×D411yescharacteristic
1113C22C22×H(5,𝔽2)11yescharacteristic
1114C22C22×H(5,𝔽2)11yescharacteristic
1115C222−1+614yes—
1116C4—24no—
1117C4—22no—
1118C4—22no—
1119C4—24no—
1120C4—24no—
1121C4—24no—
1122C4—24no—
1123C4—24no—
1124C4—24no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—44no—
1130C4—48no—
1131C4—48no—
1132C2—24no—
1133C2—44no—
1134C2—84no—
1135C2—84no—
1136C2C2×#348411yescharacteristic
1137C2#6284812yes—
1138C2#6287112yes—
1139C2#6288612yes—
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×#3544C2semidirect
2. C22×#536C2semidirect
3. #52083C2semidirect
4. #52076C2semidirect
5. #52075C2semidirect
6. #52072C2semidirect
7. #52071C2semidirect
8. #47797C2semidirect
9. #47795C2semidirect
10. #37843C2semidirect
11. #37841C2semidirect
12. #37655C2semidirect
13. #37653C2semidirect
14. #37606C2semidirect
15. #37258C2semidirect
16. #37187C2semidirect
17. #35242C2semidirect
18. #35149C2semidirect
19. #35118C2semidirect
20. #34365C2semidirect
24. C2×#563C22semidirect
25. C2×#563C22semidirect
26. C2×Q82C22semidirect
27. C2×#555C22semidirect
28. C2×#554C22semidirect
31. C2×#544C22semidirect
32. C2×#542C22semidirect
57. #2820C22semidirect
58. #2819C22semidirect
59. #2734C22semidirect
60. #2734C22semidirect
61. #2733C22semidirect
62. #2733C22semidirect
63. #2731C22semidirect
64. #2731C22semidirect
65. #2731C22semidirect
66. #2731C22semidirect
67. #2730C22semidirect
68. #2730C22semidirect
69. #2729C22semidirect
70. #2729C22semidirect
71. #2707C22semidirect
72. #2705C22semidirect
73. #2704C22semidirect
74. #2702C22semidirect
75. #2696C22semidirect
76. #2694C22semidirect
77. #2692C22semidirect
78. #2690C22semidirect
79. #2683C22semidirect
80. #2682C22semidirect
81. #2681C22semidirect
82. #2681C22semidirect
83. #2677C22semidirect
84. #2676C22semidirect
85. #2674C22semidirect
86. #2673C22semidirect
87. #2662C22semidirect
88. #2632C22semidirect
89. #2631C22semidirect
98. #2611C22semidirect
99. #2610C22semidirect
100. #2610C22semidirect
101. #2609C22semidirect
102. #2601C22semidirect
103. #2599C22semidirect
104. #2598C22semidirect
106. #2560C22semidirect
107. #2558C22semidirect
108. #2556C22semidirect
109. #2554C22semidirect
115. #2477C22semidirect
116. #2471C22semidirect
117. #2465C22semidirect
118. #2463C22semidirect
119. #2461C22semidirect
120. #2461C22semidirect
121. #2458C22semidirect
122. #2456C22semidirect
123. #2452C22semidirect
124. #2449C22semidirect
125. #2445C22semidirect
126. #2443C22semidirect
127. #2436C22semidirect
128. #2436C22semidirect
129. #2434C22semidirect
130. #2434C22semidirect
139. #2409C22semidirect
140. #2409C22semidirect
145. #2381C22semidirect
146. #2381C22semidirect
147. #2369C22semidirect
148. #2369C22semidirect
151. #2331C22semidirect
203. C2×C4⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
C22×#5362
#520832
#520762
#520752
#520722
#520712
#477972
#477952
#378432
#378412
#376552
#376532
#376062
#372582
#371872
#352422
#351492
#351182
#343652