Finite Group Databasebeta

← #7688575

Subgroups — #7688575

Order 512.

4975 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59504C214yesmaximal, complemented
3#59434C212yesmaximal, complemented
4#59430C214yesmaximal, complemented
5#59235C212yesmaximal, complemented
6#59134C212yesmaximal, complemented
7#45390C214yesmaximal, complemented
8#44825C218yesmaximal, complemented
9#40166C214yesmaximal, complemented
10#40155C214yesmaximal, complemented
11#39737C212yesmaximal, complemented
12#38958C212yesmaximal
13#36598C211yesmaximal, characteristic, complemented
14#36556C212yesmaximal, complemented
15#36480C212yesmaximal, complemented
16#36450C212yesmaximal, complemented
17#36301C212yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35817C214yesmaximal, complemented
21#34978C212yesmaximal, complemented
22#34941C211yesmaximal, characteristic, complemented
23#34311C212yesmaximal, complemented
24#34209C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×#555C211yesmaximal, characteristic
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#555C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×#519C2214yes—
33#2868C2211yescharacteristic
34#2864C2214yes—
35#2863C2214yes—
36#2862C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2806C2214yes—
40#2777C2218yes—
41#2772C2218yes—
42#2762C2218yes—
43#2755C2218yes—
44#2744C2218yes—
45#2741C2218yes—
46#2738C2218yes—
47#2716C2218yes—
48#2700C2218yes—
49#2700C2218yes—
50#2637C2218yes—
51#2620C2214yes—
52#2612C2218yes—
53#2609C2218yes—
54#2605C2218yes—
55#2601C2218yes—
56#2594C2218yes—
57#2588C2218yes—
58#2584C2214yes—
59#2582C2214yes—
60#2582C2212yes—
61#2577C2218yes—
62#2574C2214yes—
63#2573C2218yes—
64#2571C2212yes—
65#2570C2214yes—
66#2568C2212yes—
67#2568C2212yes—
68#2567C2212yes—
69#2567C2211yescharacteristic
70#2563C2211yescharacteristic
71#2562C2214yes—
72#2552C2212yes—
73#2552C2212yes—
74#2552C2211yescharacteristic
75#2551C2212yes—
76#2551C2212yes—
77#2547C2212yes—
78#2547C2212yes—
79#2546C2212yes—
80#2545C2214yes—
81#2538C2211yescharacteristic
82#2528C2218yes—
83#2527C2218yes—
84#2520C2218yes—
85#2514C2214yes—
86#2511C2214yes—
87#2511C2214yes—
88#2509C2214yes—
89#2508C2214yes—
90#2508C2212yes—
91#2507C2214yes—
92#2499C2214yes—
93#2499C2214yes—
94#2497C2212yes—
95#2497C2214yes—
96#2497C2214yes—
97#2496C2214yes—
98#2496C2214yes—
99#2494C2214yes—
100#2494C2214yes—
101#2492C2214yes—
102#2489C2214yes—
103#2485C2214yes—
104#2481C2218yes—
105#2479C2218yes—
106#2477C2218yes—
107#2469C2218yes—
108#2465C2218yes—
109#2454C2212yes—
110#2448C2214yes—
111#2446C2214yes—
112#2446C2214yes—
113#2441C2214yes—
114#2441C2214yes—
115#2440C2214yes—
116#2440C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2436C2214yes—
121#2434C2214yes—
122#2423C2212yes—
123#2420C2214yes—
124#2420C2214yes—
125#2417C2214yes—
126#2396C2218yes—
127#2396C2214yes—
128#2373C2214yes—
129#2372C2214yes—
130#2369C2211yescharacteristic
131#2369C2212yes—
132#2367C2212yes—
133#2365C2212yes—
134#2365C2214yes—
135#2365C2214yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2211yescharacteristic
139#2365C2214yes—
140#2365C2212yes—
141#2363C2212yes—
142#2363C2212yes—
143#2362C2218yes—
144#2362C2214yes—
145#2362C2212yes—
146#2356C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2214yes—
150#2355C2212yes—
151#2354C2211yescharacteristic
152#2354C2214yes—
153#2354C2211yescharacteristic
154#2354C2211yescharacteristic
155#2352C2214yes—
156Q8×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159#2347C2212yes—
160#2347C2214yes—
161#2346C2212yes—
162#2346C2212yes—
163#2344C2218yes—
164#2344C2214yes—
165#2344C2214yes—
166Q8×C22⋊C4C2214yes—
167#2327C2218yes—
168#2323C2218yes—
169#2323C2214yes—
170#2310C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2214yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2214yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2214yes—
178C4×#125C2214yes—
179C4×#125C2212yes—
180C4×#125C2214yes—
181C4×#126C2214yes—
182C4×#124C2214yes—
183C4×#124C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2293C2212yes—
189#2293C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C4×#117C2212yes—
197C4×#117C2212yes—
198C4×#117C2212yes—
199C23×Q8C2314yes—
200#556—28no—
201#556—48no—
202#555—28no—
203D4×Q8—216no—
204C2×C4⋊Q8—216no—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229#519—416no—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2318yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2318yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2314yes—
250C2×C4×D4C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2318yes—
258C2×#117C2318yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265#401C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#399C2314yes—
275#399C2318yes—
276#398C2318yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#396C2314yes—
290#396C2314yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#395C2314yes—
296#395C2318yes—
297#395C2318yes—
298#395C2318yes—
299#394C2318yes—
300#394C2318yes—
301#393C2314yes—
302#393C2318yes—
303#393C2318yes—
304#391C2318yes—
305#391C2318yes—
306#391C2314yes—
307#391C2312yes—
308#391C2312yes—
309#391C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#390C2312yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2318yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2318yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2318yes—
386#388C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2318yes—
418#386C2314yes—
419#385C2318yes—
420#385C2314yes—
421#385C2318yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2314yes—
428#384C2311yescharacteristic
429#384C2314yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#383C2314yes—
435#383C2318yes—
436#382C2312yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2318yes—
444#382C2312yes—
445#381C2318yes—
446#381C2318yes—
447#380C2312yes—
448#380C2312yes—
449#380C2314yes—
450#380C2314yes—
451#380C2312yes—
452#380C2312yes—
453#380C2314yes—
454#380C2314yes—
455#380C2312yes—
456#380C2318yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518#376C2314yes—
519#376C2314yes—
520#376C2314yes—
521C43C2314yes—
522C43C2314yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8—216no—
526C22×Q8—216no—
527C22×Q8—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2414yes—
530C22×Q8C2418yes—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2418yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C4⋊Q8—216no—
545C4⋊Q8—216no—
546C4⋊Q8—216no—
547C4⋊Q8—216no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—44no—
553C4⋊Q8#4118yes—
554#126—216no—
555#126—416no—
556#125—28no—
557#125—48no—
558#124—28no—
559#124—216no—
560#124—48no—
561C22⋊Q8—216no—
562C22⋊Q8—28no—
563C22⋊Q8—232no—
564C22⋊Q8—48no—
565C22⋊Q8—44no—
566#121—28no—
567#121—28no—
568C4×Q8—28no—
569C4×Q8—28no—
570C4×Q8—216no—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—44no—
575C4×Q8—416no—
576C4×Q8—44no—
577C4×Q8—416no—
578C4×Q8—42no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×D4—216no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—48no—
588C4×D4#4118yes—
589#117—28no—
590#117—28no—
591#117—28no—
592#117—28no—
593#117—28no—
594#117—48no—
595#117—48no—
596#117—416no—
597#117—416no—
598#117—44no—
599C2×C4⋊C4—216no—
600C2×C4⋊C4—216no—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C42—28no—
679C2×C42—28no—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2418yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759C24C2512yes—
760C24C2512yes—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—216no—
764C2×Q8—28no—
765C2×Q8—216no—
766C2×Q8—28no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—48no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—464no—
779C2×Q8C2×#4118yes—
780C2×D4—28no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4C2×#4114yes—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—216no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—216no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—48no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4C2×#4118yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2518yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—216no—
835C4⋊C4—216no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—216no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—216no—
853C4⋊C4—24no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—42no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4C2×#4118yes—
884C4⋊C4C2×#4118yes—
885C4⋊C4C2×#4114yes—
886C4⋊C4H(5,𝔽2)14yes—
887C4⋊C42−1+414yes—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—48no—
910C22⋊C4C2×#4118yes—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—28no—
915C42—28no—
916C42—28no—
917C42—24no—
918C42—28no—
919C42—28no—
920C42—24no—
921C42—216no—
922C42—28no—
923C42—22no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—28no—
928C42—22no—
929C42—24no—
930C42—24no—
931C42—28no—
932C42—22no—
933C42—44no—
934C42—44no—
935C42—41no—
936C42—42no—
937C42—44no—
938C42—48no—
939C42—48no—
940C42—42no—
941C42C2×#4114yes—
942C42C2×#4114yes—
943C422−1+414yes—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23C22×#4114yes—
958C23C2611yescharacteristic
959Q8—216no—
960Q8—432no—
961Q8—416no—
962Q8—44no—
963Q8—84no—
964Q8—84no—
965D4—28no—
966D4—44no—
967D4—88no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—216no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—432no—
1028C2×C4—48no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4114yes—
1033C2×C4C22×#4118yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×H(5,𝔽2)14yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4C2×2−1+412yes—
1042C2×C4C2×2−1+414yes—
1043C2×C4C2×2−1+412yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4#58512yes—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22C23×#4111yescharacteristic
1062C22C23×#4111yescharacteristic
1063C22C22×H(5,𝔽2)11yescharacteristic
1064C22C22×2−1+411yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C2×#58511yescharacteristic
1067C222−1+611yescharacteristic
1068C4—22no—
1069C4—22no—
1070C4—24no—
1071C4—22no—
1072C4—24no—
1073C4—24no—
1074C4—28no—
1075C4—44no—
1076C4—44no—
1077C4—42no—
1078C4—44no—
1079C4—42no—
1080C4—44no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—44no—
1088C4—48no—
1089C4#348114yes—
1090C4#350914yes—
1091C4#351814yes—
1092C2—44no—
1093C2—82no—
1094C2C2×#348111yescharacteristic
1095C2C2×#351811yescharacteristic
1096C2C2×#350911yescharacteristic
1097C2#6291511yescharacteristic
1098C2#6299511yescharacteristic
1099C2#6299811yescharacteristic
1100C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59504C2semidirect
3. #59434C2semidirect
4. #59430C2semidirect
5. #59235C2semidirect
6. #59134C2semidirect
7. #45390C2semidirect
8. #44825C2semidirect
9. #40166C2semidirect
10. #40155C2semidirect
11. #39737C2semidirect
13. #36598C2semidirect
14. #36556C2semidirect
15. #36480C2semidirect
16. #36450C2semidirect
17. #36301C2semidirect
18. #36188C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35817C2semidirect
21. #34978C2semidirect
22. #34941C2semidirect
23. #34311C2semidirect
24. #34209C2semidirect
25. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#595042
#594342
#594302
#592352
#591342
#453902
#448252
#401662
#401552
#397372
#389582
#365982
#365562
#364802
#364502
#363012
#361882
D4×C4⋊Q82
#358172
#349782
#349412
#343112
#342092
C4×#5562
C4×#5552