Finite Group Databasebeta

← #7699520

Subgroups — #7699520

Order 512.

7205 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C212yesmaximal, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59831C214yesmaximal, complemented
4#59667C212yesmaximal, complemented
5#59152C214yesmaximal, complemented
6#59149C218yesmaximal, complemented
7#59127C212yesmaximal, complemented
8#59096C214yesmaximal, complemented
9#59081C212yesmaximal, complemented
10#36561C212yesmaximal, complemented
11#36560C211yesmaximal, characteristic, complemented
12#36547C214yesmaximal, complemented
13#36545C212yesmaximal, complemented
14#36274C212yesmaximal, complemented
15#36261C212yesmaximal, complemented
16#36219C214yesmaximal, complemented
17#36134C211yesmaximal, characteristic, complemented
18#36133C214yesmaximal, complemented
19#36133C212yesmaximal, complemented
20#36132C212yesmaximal, complemented
21D4×C4⋊Q8C211yesmaximal, characteristic, complemented
22C4×#554C211yesmaximal, characteristic, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24C4×#547C212yesmaximal
25C4×#547C211yesmaximal, characteristic
26C2×#2365C212yesmaximal, complemented
27Q8×#41—232no—
28C2×Q82C2212yes—
29C2×#557C2214yes—
30C2×#557C2212yes—
31C2×#554C2218yes—
32C2×#554C2214yes—
33C2×#554C2214yes—
34C2×#554C2211yescharacteristic
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2214yes—
38C2×#547C2211yescharacteristic
39C2×#533C2218yes—
40C2×#533C2214yes—
41C2×#533C2214yes—
42C2×#533C2212yes—
43C22×C4⋊Q8C2212yes—
44C2×C4×#41C2214yes—
45C2×C4×#41C2212yes—
46C22×C4×Q8C2214yes—
47C22×C4×Q8C2212yes—
48#2868C2211yescharacteristic
49#2859C2212yes—
50#2857C2212yes—
51#2857C2214yes—
52#2857C2212yes—
53#2855C2218yes—
54#2855C2214yes—
55#2851C2214yes—
56#2734C2214yes—
57#2729C2218yes—
58#2713C2218yes—
59#2704C2218yes—
60#2677C2218yes—
61#2584C2214yes—
62#2583C2218yes—
63#2582C2212yes—
64#2581C2214yes—
65#2579C2218yes—
66#2568C2212yes—
67#2565C2214yes—
68#2564C2218yes—
69#2556C2218yes—
70#2552C2212yes—
71#2551C2212yes—
72#2551C2212yes—
73#2551C2214yes—
74#2551C2212yes—
75#2551C2212yes—
76#2550C2214yes—
77#2549C2218yes—
78#2546C2212yes—
79#2546C2214yes—
80#2546C2212yes—
81#2546C2212yes—
82#2542C2212yes—
83#2538C2212yes—
84#2506C2214yes—
85#2506C2214yes—
86#2506C2214yes—
87#2506C2214yes—
88#2492C2214yes—
89#2473C2218yes—
90#2465C2218yes—
91#2465C2218yes—
92#2465C2218yes—
93#2462C2218yes—
94#2462C2218yes—
95#2462C2218yes—
96#2462C2218yes—
97#2453C2214yes—
98#2452C2214yes—
99#2452C2214yes—
100#2451C2214yes—
101#2451C2218yes—
102#2451C2214yes—
103#2451C2214yes—
104#2451C2214yes—
105#2450C2218yes—
106#2450C2218yes—
107#2449C2218yes—
108#2446C2218yes—
109#2446C2214yes—
110#2441C2214yes—
111#2440C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2439C2214yes—
116#2439C2214yes—
117#2438C2218yes—
118#2438C2218yes—
119#2438C2218yes—
120#2434C2214yes—
121#2434C2214yes—
122#2429C2214yes—
123#2429C2214yes—
124#2423C2214yes—
125#2417C2214yes—
126#2409C2214yes—
127#2370C2212yes—
128#2369C2211yescharacteristic
129#2368C2214yes—
130#2365C2218yes—
131#2365C2211yescharacteristic
132#2365C2214yes—
133#2365C2212yes—
134#2365C2214yes—
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2211yescharacteristic
139#2365C2212yes—
140#2365C2214yes—
141#2365C2214yes—
142#2365C2212yes—
143#2365C2212yes—
144#2362C2212yes—
145#2362C2214yes—
146#2361C2212yes—
147#2361C2214yes—
148#2360C2214yes—
149#2360C2212yes—
150#2360C2212yes—
151#2360C2214yes—
152#2359C2214yes—
153#2359C2218yes—
154#2355C2211yescharacteristic
155#2354C2211yescharacteristic
156#2354C2212yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2211yescharacteristic
159#2349C2212yes—
160#2349C2214yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2211yescharacteristic
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2211yescharacteristic
166D4×C4⋊C4C2211yescharacteristic
167#2345C2212yes—
168#2344C2212yes—
169#2344C2214yes—
170Q8×C22⋊C4C2212yes—
171#2339C2212yes—
172#2339C2214yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2211yescharacteristic
178C4×#125C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#123C2218yes—
186C4×#123C2214yes—
187C4×#121C2214yes—
188C4×#121C2212yes—
189C2×#391C2214yes—
190C2×#389C2214yes—
191C2×#387C2218yes—
192C42×Q8C2211yescharacteristic
193C42×D4C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C2×C4×C4⋊C4C2214yes—
198C2×C4×C4⋊C4C2212yes—
199C2×C4×C4⋊C4C2212yes—
200C22×#41C2312yes—
201C23×Q8C2312yes—
202C23×Q8C2314yes—
203Q82—216no—
204#557—232no—
205#557—216no—
206#554—264no—
207#554—232no—
208#554—232no—
209#554D4116yescomplemented
210D4×Q8—28no—
211D4×Q8—232no—
212D4×Q8—216no—
213#547Q8116yescomplemented
214#533—216no—
215#533—232no—
216#533—232no—
217#533—264no—
218C2×C4⋊Q8—216no—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2318yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2318yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#125C2318yes—
239C2×#125C2318yes—
240C2×#125C2318yes—
241C2×#125C2312yes—
242C2×#123C2314yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2318yes—
251C2×C22⋊Q8C2318yes—
252C2×C22⋊Q8C2318yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×#121C2312yes—
259C4×#41—232no—
260C4×#41—216no—
261C2×C4×Q8—216no—
262C2×C4×Q8—232no—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2314yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2318yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2318yes—
279C2×C4×Q8C2318yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4C2318yes—
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2318yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×#117C2314yes—
300C2×#117C2318yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C22×C4⋊C4C2318yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C42C2314yes—
313C22×C42C2318yes—
314C22×C42C2314yes—
315C22×C42C2312yes—
316C22×C42C2312yes—
317C22×C42C2314yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#399C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#395C2318yes—
336#395C2318yes—
337#395C2318yes—
338#395C2318yes—
339#395C2318yes—
340#395C2318yes—
341#395C2318yes—
342#395C2318yes—
343#393C2318yes—
344#393C2318yes—
345#391C2312yes—
346#391C2314yes—
347#391C2312yes—
348#391C2314yes—
349#391C2312yes—
350#391C2314yes—
351#391C2314yes—
352#391C2312yes—
353#391C2314yes—
354#391C2314yes—
355#391C2312yes—
356#391C2314yes—
357#391C2314yes—
358#391C2318yes—
359#391C2318yes—
360#391C2314yes—
361#391C2318yes—
362#391C2312yes—
363#391C2318yes—
364#391C2318yes—
365#391C2314yes—
366#390C2312yes—
367#390C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2318yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#389C2318yes—
392#389C2318yes—
393#389C2314yes—
394#389C2312yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2314yes—
439#386C2314yes—
440#386C2318yes—
441#386C2314yes—
442#386C2318yes—
443#385C2314yes—
444#385C2318yes—
445#385C2314yes—
446#385C2318yes—
447#385C2318yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2314yes—
453#385C2314yes—
454#385C2314yes—
455#385C2314yes—
456#385C2318yes—
457#385C2314yes—
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2314yes—
465#384C2312yes—
466#384C2312yes—
467#382C2312yes—
468#382C2314yes—
469#381C2314yes—
470#381C2318yes—
471#380C2314yes—
472#380C2318yes—
473#380C2314yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2314yes—
478#380C2312yes—
479#380C2314yes—
480#380C2312yes—
481#380C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2318yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2314yes—
533C4×C22⋊C4C2318yes—
534C2×#95C2314yes—
535C2×#95C2314yes—
536C2×#95C2318yes—
537C2×#95C2318yes—
538C43C2312yes—
539C43C2311yescharacteristic
540C2×#41—28no—
541C2×#41—28no—
542C2×#41C2×Q8116yescomplemented
543C22×Q8—28no—
544C22×Q8—216no—
545C22×Q8—28no—
546C22×Q8—216no—
547C22×Q8—48no—
548C22×Q8—44no—
549C22×Q8C2414yes—
550C22×Q8C2414yes—
551C22×Q8C2418yes—
552C22×Q8C2411yescharacteristic
553C22×Q8C2412yes—
554C22×Q8C2412yes—
555C22×Q8C2418yes—
556C22×Q8C2412yes—
557C22×D4C2411yescharacteristic
558C22×D4C2414yes—
559C22×D4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2418yes—
562C23×C4C2412yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2414yes—
567C23×C4C2412yes—
568C23×C4C2414yes—
569C23×C4C2414yes—
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C4⋊Q8—216no—
574C4⋊Q8—232no—
575C4⋊Q8—216no—
576C4⋊Q8—232no—
577C4⋊Q8—216no—
578C4⋊Q8—216no—
579C4⋊Q8—216no—
580C4⋊Q8—216no—
581C4⋊Q8—216no—
582C4⋊Q8—28no—
583C4⋊Q8—28no—
584C4⋊Q8—28no—
585C4⋊Q8—48no—
586C4⋊Q8—44no—
587C4⋊Q8C2×D418yes—
588C4⋊Q8C2×Q818yescomplemented
589C4⋊Q8#4118yescomplemented
590#125—232no—
591#125—216no—
592#125—232no—
593#125—232no—
594#125—216no—
595#125C2×D4116yes—
596#123C2×Q8132yescomplemented
597C22⋊Q8—216no—
598C22⋊Q8—28no—
599C22⋊Q8—216no—
600C22⋊Q8—232no—
601C22⋊Q8—232no—
602C22⋊Q8—216no—
603C22⋊Q8—232no—
604C22⋊Q8—216no—
605C22⋊Q8—232no—
606C22⋊Q8—232no—
607C22⋊Q8—232no—
608C22⋊Q8—48no—
609C22⋊Q8C2×D4116yes—
610C22⋊Q8C2×D4132yes—
611C22⋊Q8C2×Q8116yescomplemented
612#121C2×Q8116yescomplemented
613C4×Q8—28no—
614C4×Q8—216no—
615C4×Q8—28no—
616C4×Q8—216no—
617C4×Q8—216no—
618C4×Q8—232no—
619C4×Q8—216no—
620C4×Q8—232no—
621C4×Q8—216no—
622C4×Q8—28no—
623C4×Q8—216no—
624C4×Q8—232no—
625C4×Q8—28no—
626C4×Q8—216no—
627C4×Q8—216no—
628C4×Q8—28no—
629C4×Q8—24no—
630C4×Q8—44no—
631C4×Q8—42no—
632C4×Q8C2×D418yes—
633C4×D4—216no—
634C4×D4—28no—
635C4×D4—24no—
636C4×D4—28no—
637C4×D4—216no—
638C4×D4—232no—
639C4×D4—28no—
640C4×D4—232no—
641C4×D4—216no—
642C4×D4—24no—
643C4×D4—44no—
644C4×D4—42no—
645C4×D4C2×D418yes—
646C4×D4C2×D4116yes—
647C4×D4C2×Q818yescomplemented
648C4×D4C2×Q818yescomplemented
649#117—216no—
650#117—28no—
651#117—232no—
652#117—216no—
653C2×C4⋊C4—232no—
654C2×C4⋊C4—216no—
655C2×C4⋊C4—28no—
656C2×C4⋊C4—216no—
657C2×C4⋊C4—216no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4C2×D4116yes—
661C2×C4⋊C4C2×Q8116yescomplemented
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2414yes—
739C2×C42—232no—
740C2×C42—216no—
741C2×C42—28no—
742C2×C42—216no—
743C2×C42—28no—
744C2×C42—48no—
745C2×C42C2412yes—
746C2×C42C2414yes—
747C2×C42C2418yes—
748C2×C42C2414yes—
749C2×C42C2418yes—
750C2×C42C2412yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2418yes—
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2411yescharacteristic
759C2×C42C2412yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2414yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2412yes—
769C2×C42C2411yescharacteristic
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776#95C2412yes—
777#95C2414yes—
778#95C2412yes—
779#95C2414yes—
780#95C2414yes—
781#95C2418yes—
782#95C2414yes—
783#95C2414yes—
784#95C2418yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792#95C2414yes—
793#95C2412yes—
794#95C2414yes—
795#95C2412yes—
796#95C2414yes—
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2418yes—
804#95C2414yes—
805#95C2418yes—
806#95C2412yes—
807#95C2412yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2418yes—
812#95C2414yes—
813#95C2414yes—
814#95C2418yes—
815#95C2418yes—
816C24C2512yes—
817C24C2512yes—
818#41—264no—
819C2×Q8—24no—
820C2×Q8—24no—
821C2×Q8—216no—
822C2×Q8—28no—
823C2×Q8—28no—
824C2×Q8—216no—
825C2×Q8—22no—
826C2×Q8—28no—
827C2×Q8—216no—
828C2×Q8—28no—
829C2×Q8—24no—
830C2×Q8—22no—
831C2×Q8—24no—
832C2×Q8—28no—
833C2×Q8—42no—
834C2×Q8—44no—
835C2×Q8—48no—
836C2×Q8—42no—
837C2×Q8—48no—
838C2×Q8—48no—
839C2×Q8—464no—
840C2×Q8—432no—
841C2×Q8C22×D414yes—
842C2×Q8C22×D418yes—
843C2×Q8C22×Q818yes—
844C2×Q8C2×#4118yes—
845C2×D4—28no—
846C2×D4—28no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4C22×D414yes—
850C2×D4C22×Q814yes—
851C2×D4C22×Q8116yes—
852C2×D4C22×Q814yes—
853C2×D42−1+414yes—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—216no—
863C22×C4—24no—
864C22×C4—28no—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—216no—
870C22×C4—28no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—42no—
887C22×C4—44no—
888C22×C4C22×D418yes—
889C22×C4C22×D4116yes—
890C22×C4C22×Q818yes—
891C22×C4C22×Q8116yes—
892C22×C4C22×Q818yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2514yes—
897C22×C4C2511yescharacteristic
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2512yes—
902C22×C4C2518yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2511yescharacteristic
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2511yescharacteristic
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2514yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C4⋊C4—28no—
918C4⋊C4—216no—
919C4⋊C4—28no—
920C4⋊C4—216no—
921C4⋊C4—28no—
922C4⋊C4—216no—
923C4⋊C4—28no—
924C4⋊C4—24no—
925C4⋊C4—216no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—216no—
929C4⋊C4—24no—
930C4⋊C4—28no—
931C4⋊C4—216no—
932C4⋊C4—216no—
933C4⋊C4—28no—
934C4⋊C4—216no—
935C4⋊C4—216no—
936C4⋊C4—216no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—28no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—48no—
960C4⋊C4—44no—
961C4⋊C4—48no—
962C4⋊C4—44no—
963C4⋊C4C22×D414yes—
964C4⋊C4C22×D418yes—
965C4⋊C4C22×D4116yes—
966C4⋊C4C22×D418yes—
967C4⋊C4C22×D418yes—
968C4⋊C4C22×D414yes—
969C4⋊C4C22×D4116yes—
970C4⋊C4C22×Q814yes—
971C4⋊C4C22×Q818yes—
972C4⋊C4C22×Q8116yes—
973C4⋊C4C22×Q814yes—
974C4⋊C4C22×Q818yes—
975C4⋊C4C2×#4118yes—
976C4⋊C4C2×#4118yes—
977C22⋊C4—216no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—24no—
981C22⋊C4—216no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—24no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—42no—
988C22⋊C4—48no—
989C22⋊C4C22×D4116yes—
990C22⋊C4C22×D418yes—
991C22⋊C4C22×Q818yes—
992C22⋊C4C22×Q818yes—
993C22⋊C4C22×Q8116yes—
994C42—28no—
995C42—24no—
996C42—216no—
997C42—28no—
998C42—24no—
999C42—28no—
1000C42—28no—
1001C42—216no—
1002C42—24no—
1003C42—216no—
1004C42—28no—
1005C42—28no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—22no—
1011C42—24no—
1012C42—24no—
1013C42—28no—
1014C42—22no—
1015C42—22no—
1016C42—44no—
1017C42—44no—
1018C42—41no—
1019C42—42no—
1020C42—42no—
1021C42C22×D418yes—
1022C42C22×D414yes—
1023C42C22×Q814yes—
1024C42C2×#4114yes—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23C23×D414yes—
1036C23C23×Q814yes—
1037C23C23×Q814yes—
1038C23C2×2−1+414yes—
1039C23C2611yescharacteristic
1040Q8—216no—
1041Q8—216no—
1042Q8—28no—
1043Q8—48no—
1044Q8—432no—
1045Q8—416no—
1046Q8—416no—
1047Q8—816no—
1048D4—232no—
1049D4—28no—
1050D4D4×Q8116yescomplemented
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—24no—
1073C2×C4—232no—
1074C2×C4—216no—
1075C2×C4—216no—
1076C2×C4—216no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—28no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—28no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—28no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—416no—
1108C2×C4—416no—
1109C2×C4—48no—
1110C2×C4—432no—
1111C2×C4—48no—
1112C2×C4—88no—
1113C2×C4—84no—
1114C2×C4—88no—
1115C2×C4—88no—
1116C2×C4C23×D414yes—
1117C2×C4C23×D418yes—
1118C2×C4C23×D414yes—
1119C2×C4C23×D412yes—
1120C2×C4C23×D414yes—
1121C2×C4C23×D412yes—
1122C2×C4C23×D412yes—
1123C2×C4C23×Q812yes—
1124C2×C4C23×Q814yes—
1125C2×C4C23×Q814yes—
1126C2×C4C23×Q818yes—
1127C2×C4C23×Q812yes—
1128C2×C4C23×Q812yes—
1129C2×C4C22×#4112yes—
1130C2×C4C22×#4118yes—
1131C2×C4C22×#4112yes—
1132C2×C4C22×#4112yes—
1133C2×C4C2×2−1+412yes—
1134C2×C4#58512yes—
1135C2×C4#58512yes—
1136C22—24no—
1137C22—24no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22C2×D4×Q818yes—
1150C22C24×D411yescharacteristic
1151C22C24×Q811yescharacteristic
1152C22C23×#4111yescharacteristic
1153C22C22×2−1+411yescharacteristic
1154C22C2×#58511yescharacteristic
1155C22C2×#58511yescharacteristic
1156C222−1+611yescharacteristic
1157C4—24no—
1158C4—28no—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—24no—
1163C4—28no—
1164C4—24no—
1165C4—28no—
1166C4—24no—
1167C4—24no—
1168C4—42no—
1169C4—44no—
1170C4—44no—
1171C4—42no—
1172C4—42no—
1173C4—41no—
1174C4—44no—
1175C4—42no—
1176C4—42no—
1177C4—48no—
1178C4C2×D4×Q814yes—
1179C4D4×#4114yes—
1180C4Q8×#4114yescomplemented
1181C2—28no—
1182C2—44no—
1183C2C22×D4×Q811yescharacteristic
1184C2C2×D4×#4111yescharacteristic
1185C2C2×Q8×#4111yescharacteristic
1186C2#6298811yescharacteristic
1187C2#6299811yescharacteristic
1188C2#6300411yescharacteristic
1189C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
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×Q8×#41C2semidirect
2. #59832C2semidirect
3. #59831C2semidirect
4. #59667C2semidirect
5. #59152C2semidirect
6. #59149C2semidirect
7. #59127C2semidirect
8. #59096C2semidirect
9. #59081C2semidirect
10. #36561C2semidirect
11. #36560C2semidirect
12. #36547C2semidirect
13. #36545C2semidirect
14. #36274C2semidirect
15. #36261C2semidirect
16. #36219C2semidirect
17. #36134C2semidirect
18. #36133C2semidirect
19. #36133C2semidirect
20. #36132C2semidirect
21. D4×C4⋊Q8C2semidirect
22. C4×#554C2semidirect
23. C4×D4×Q8C2semidirect
26. C2×#2365C2semidirect
209. #554D4semidirect
213. #547Q8semidirect
542. C2×#41C2×Q8semidirect
588. C4⋊Q8C2×Q8semidirect
589. C4⋊Q8#41semidirect
596. #123C2×Q8semidirect
611. C22⋊Q8C2×Q8semidirect
612. #121C2×Q8semidirect
647. C4×D4C2×Q8semidirect
648. C4×D4C2×Q8semidirect
661. C2×C4⋊C4C2×Q8semidirect
1050. D4D4×Q8semidirect
1180. C4Q8×#41semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
#598322
#598312
#596672
#591522
#591492
#591272
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