Finite Group Databasebeta

← #7699867

Subgroups — #7699867

Order 512.

4961 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59904C214yesmaximal, complemented
2#59869C211yesmaximal, characteristic, complemented
3#59784C218yesmaximal, complemented
4#59582C214yesmaximal, complemented
5#59450C212yesmaximal, complemented
6#59299C214yesmaximal, complemented
7#59242C212yesmaximal, complemented
8#59079C212yesmaximal, complemented
9#36599C212yesmaximal, complemented
10#36598C211yesmaximal, characteristic, complemented
11#36451C214yesmaximal, complemented
12#36449C212yesmaximal, complemented
13#36408C214yesmaximal, complemented
14#36406C212yesmaximal
15#36405C212yesmaximal, complemented
16#36314C214yesmaximal, complemented
17#36313C212yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19#36177C212yesmaximal, complemented
20#36134C211yesmaximal, characteristic, complemented
21C4×#554C211yesmaximal, characteristic, complemented
22C4×#556C211yesmaximal, characteristic, complemented
23C4×#556C212yesmaximal, complemented
24C4×#547C211yesmaximal, characteristic
25#34145C212yesmaximal, complemented
26#34121C212yesmaximal, complemented
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#554C2211yescharacteristic
30C2×#547C2211yescharacteristic
31C2×#533C2212yes—
32C2×C4×#41C2212yes—
33#2868C2211yescharacteristic
34#2864C2218yes—
35#2863C2214yes—
36#2862C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2855C2214yes—
41#2809C2214yes—
42#2787C2218yes—
43#2771C2218yes—
44#2750C2218yes—
45#2728C2218yes—
46#2585C2218yes—
47#2582C2212yes—
48#2578C2218yes—
49#2576C2218yes—
50#2575C2218yes—
51#2573C2218yes—
52#2571C2214yes—
53#2571C2212yes—
54#2571C2212yes—
55#2570C2214yes—
56#2569C2218yes—
57#2568C2214yes—
58#2568C2212yes—
59#2568C2212yes—
60#2553C2218yes—
61#2553C2218yes—
62#2552C2212yes—
63#2547C2212yes—
64#2547C2212yes—
65#2546C2212yes—
66#2546C2212yes—
67#2542C2212yes—
68#2538C2212yes—
69#2533C2218yes—
70#2533C2218yes—
71#2530C2218yes—
72#2530C2218yes—
73#2528C2218yes—
74#2524C2218yes—
75#2524C2218yes—
76#2515C2218yes—
77#2514C2214yes—
78#2514C2214yes—
79#2514C2214yes—
80#2511C2214yes—
81#2511C2214yes—
82#2509C2214yes—
83#2508C2214yes—
84#2508C2214yes—
85#2503C2214yes—
86#2499C2214yes—
87#2499C2214yes—
88#2496C2214yes—
89#2496C2214yes—
90#2495C2214yes—
91#2495C2218yes—
92#2493C2218yes—
93#2489C2214yes—
94#2489C2214yes—
95#2485C2214yes—
96#2478C2218yes—
97#2468C2218yes—
98#2453C2214yes—
99#2447C2214yes—
100#2446C2214yes—
101#2446C2214yes—
102#2442C2214yes—
103#2441C2214yes—
104#2432C2214yes—
105#2429C2214yes—
106#2427C2214yes—
107#2427C2214yes—
108#2423C2214yes—
109#2421C2214yes—
110#2421C2218yes—
111#2415C2214yes—
112#2373C2214yes—
113#2373C2218yes—
114#2370C2212yes—
115#2370C2214yes—
116#2370C2214yes—
117#2369C2211yescharacteristic
118#2369C2212yes—
119#2368C2218yes—
120#2368C2214yes—
121#2367C2212yes—
122#2367C2214yes—
123#2365C2212yes—
124#2365C2214yes—
125#2365C2212yes—
126#2365C2212yes—
127#2365C2212yes—
128#2365C2211yescharacteristic
129#2365C2211yescharacteristic
130#2362C2214yes—
131#2362C2212yes—
132#2362C2212yes—
133#2361C2212yes—
134#2360C2214yes—
135#2360C2214yes—
136#2360C2214yes—
137#2360C2212yes—
138#2359C2214yes—
139#2357C2214yes—
140#2356C2214yes—
141#2356C2214yes—
142#2356C2212yes—
143#2355C2212yes—
144#2355C2212yes—
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2354C2212yes—
150#2354C2211yescharacteristic
151#2354C2211yescharacteristic
152#2353C2218yes—
153#2352C2214yes—
154#2352C2214yes—
155Q8×C4⋊C4C2212yes—
156#2349C2212yes—
157D4×C4⋊C4C2211yescharacteristic
158D4×C4⋊C4C2211yescharacteristic
159#2347C2214yes—
160#2347C2212yes—
161#2345C2214yes—
162#2345C2212yes—
163#2344C2212yes—
164#2339C2212yes—
165C4×C4⋊Q8C2211yescharacteristic
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×#125C2212yes—
170C4×#126C2214yes—
171C4×#126C2218yes—
172C4×#124C2212yes—
173C4×#124C2214yes—
174C4×C22⋊Q8C2214yes—
175C4×C22⋊Q8C2214yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×#123C2214yes—
180C4×#121C2212yes—
181#2298C2218yes—
182#2297C2214yes—
183#2296C2214yes—
184#2295C2218yes—
185#2295C2214yes—
186#2285C2212yes—
187#2283C2214yes—
188C42×Q8C2214yes—
189C42×Q8C2212yes—
190C42×Q8C2211yescharacteristic
191C42×D4C2211yescharacteristic
192C42×D4C2212yes—
193C42×D4C2211yescharacteristic
194C4×#117C2214yes—
195C4×#117C2214yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200#556—28no—
201#556—216no—
202#554—28no—
203#547—28no—
204#533—216no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126C2314yes—
213C2×#126C2318yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2314yes—
217C2×#124C2312yes—
218C2×#123C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×#121C2312yes—
228C4×#41—216no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C42C2314yes—
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267#401C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#396C2318yes—
292#394C2318yes—
293#394C2318yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2312yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2318yes—
306#391C2314yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#390C2312yes—
316#390C2314yes—
317#390C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2318yes—
336#389C2318yes—
337#389C2314yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2318yes—
351#388C2314yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#388C2314yes—
362#388C2318yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2314yes—
368#387C2318yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2318yes—
396#386C2314yes—
397#386C2318yes—
398#386C2314yes—
399#386C2318yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2314yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2312yes—
414#384C2314yes—
415#384C2312yes—
416#384C2312yes—
417#384C2312yes—
418#383C2318yes—
419#383C2314yes—
420#383C2318yes—
421#383C2318yes—
422#382C2312yes—
423#382C2314yes—
424#382C2314yes—
425#382C2318yes—
426#382C2314yes—
427#382C2314yes—
428#382C2312yes—
429#382C2318yes—
430#382C2314yes—
431#382C2314yes—
432#381C2314yes—
433#381C2318yes—
434#381C2318yes—
435#380C2314yes—
436#380C2318yes—
437#380C2318yes—
438#380C2314yes—
439#380C2312yes—
440#380C2314yes—
441#380C2312yes—
442#380C2314yes—
443#380C2312yes—
444#380C2314yes—
445#380C2312yes—
446#380C2314yes—
447#380C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2318yes—
500C4×C22⋊C4C2318yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2318yes—
516#376C2318yes—
517#376C2314yes—
518#376C2318yes—
519C2×#95C2314yes—
520C2×#95C2314yes—
521C43C2314yes—
522C43C2318yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—28no—
526C2×#41—28no—
527C2×#41—44no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×D4C2414yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C4⋊Q8—28no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—28no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8#4118yescomplemented
553#126—216no—
554#126—232no—
555#125—216no—
556#125—28no—
557#124—28no—
558#124—216no—
559#123—216no—
560C22⋊Q8—216no—
561C22⋊Q8—216no—
562C22⋊Q8—28no—
563C22⋊Q8—28no—
564C22⋊Q8—216no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—48no—
568#121—28no—
569C4×Q8—216no—
570C4×Q8—28no—
571C4×Q8—216no—
572C4×Q8—216no—
573C4×Q8—28no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—28no—
579C4×Q8—44no—
580C4×Q8—44no—
581C4×Q8—48no—
582C4×D4—28no—
583C4×D4—216no—
584C4×D4—28no—
585C4×D4—216no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—42no—
589C4×D4—44no—
590C4×D4—42no—
591C4×D4#4118yes—
592C4×D4#4118yes—
593#117—28no—
594#117—216no—
595#117—28no—
596#117—216no—
597#117—28no—
598#117—216no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—28no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C42—216no—
676C2×C42—28no—
677C2×C42—28no—
678C2×C42—48no—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2412yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#95C2412yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2414yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2412yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C24C2512yes—
763#41—432no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8C2×#4118yes—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—44no—
786C2×D4C2×#4114yes—
787C2×D4C2×#4114yes—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—44no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4C2×#4118yes—
817C22×C4C2×#4118yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2518yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2511yescharacteristic
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—24no—
857C4⋊C4—216no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—44no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4C2×#4114yes—
890C4⋊C4C2×#4118yes—
891C4⋊C4C2×#4114yes—
892C4⋊C4C2×#4118yes—
893C4⋊C42−1+414yes—
894C22⋊C4—28no—
895C22⋊C4—216no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—216no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—28no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—42no—
909C22⋊C4—44no—
910C22⋊C4—42no—
911C22⋊C4—48no—
912C22⋊C4C2×#4118yes—
913C22⋊C4C2×#4118yes—
914C42—24no—
915C42—28no—
916C42—24no—
917C42—24no—
918C42—28no—
919C42—28no—
920C42—24no—
921C42—24no—
922C42—24no—
923C42—216no—
924C42—28no—
925C42—216no—
926C42—24no—
927C42—24no—
928C42—28no—
929C42—28no—
930C42—22no—
931C42—24no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—22no—
936C42—22no—
937C42—44no—
938C42—44no—
939C42—41no—
940C42—42no—
941C42—48no—
942C42—44no—
943C42—44no—
944C42—48no—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C42C2×#4114yes—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23C22×#4114yes—
961C23C22×#4114yes—
962C23C2611yescharacteristic
963Q8—48no—
964Q8—48no—
965Q8—48no—
966Q8—416no—
967Q8—44no—
968D4—28no—
969D4—28no—
970D4—416no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—216no—
986C2×C4—216no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—28no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—84no—
1033C2×C4—88no—
1034C2×C4—84no—
1035C2×C4—88no—
1036C2×C4—88no—
1037C2×C4C22×#4114yes—
1038C2×C4C22×#4114yes—
1039C2×C4C22×#4112yes—
1040C2×C4C22×#4112yes—
1041C2×C4C22×#4118yes—
1042C2×C4C22×#4112yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C2×2−1+414yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4#58512yes—
1052C2×C4#58512yes—
1053C22—24no—
1054C22—24no—
1055C22—24no—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22C23×#4111yescharacteristic
1068C22C23×#4111yescharacteristic
1069C22C23×#4111yescharacteristic
1070C22C22×2−1+411yescharacteristic
1071C22C2×#58511yescharacteristic
1072C22C2×#58511yescharacteristic
1073C222−1+611yescharacteristic
1074C4—22no—
1075C4—28no—
1076C4—22no—
1077C4—22no—
1078C4—24no—
1079C4—24no—
1080C4—24no—
1081C4—42no—
1082C4—42no—
1083C4—44no—
1084C4—42no—
1085C4—44no—
1086C4—42no—
1087C4—41no—
1088C4—44no—
1089C4—44no—
1090C4—44no—
1091C4—42no—
1092C4—48no—
1093C4—42no—
1094C4—42no—
1095C4#347514yes—
1096C4#348014yes—
1097C4#348214yes—
1098C2—44no—
1099C2—44no—
1100C2C2×#347511yescharacteristic
1101C2C2×#348011yescharacteristic
1102C2C2×#348211yescharacteristic
1103C2#6299111yescharacteristic
1104C2#6300111yescharacteristic
1105C2#6300911yescharacteristic
1106C2#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. #59904C2semidirect
2. #59869C2semidirect
3. #59784C2semidirect
4. #59582C2semidirect
5. #59450C2semidirect
6. #59299C2semidirect
7. #59242C2semidirect
8. #59079C2semidirect
9. #36599C2semidirect
10. #36598C2semidirect
11. #36451C2semidirect
12. #36449C2semidirect
13. #36408C2semidirect
15. #36405C2semidirect
16. #36314C2semidirect
17. #36313C2semidirect
18. #36188C2semidirect
19. #36177C2semidirect
20. #36134C2semidirect
21. C4×#554C2semidirect
22. C4×#556C2semidirect
23. C4×#556C2semidirect
25. #34145C2semidirect
26. #34121C2semidirect
552. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599042
#598692
#597842
#595822
#594502
#592992
#592422
#590792
#365992
#365982
#364512
#364492
#364082
#364062
#364052
#363142
#363132
#361882
#361772
#361342
C4×#5542
C4×#5562
C4×#5472
#341452
#341212