Finite Group Databasebeta

← #7985301

Subgroups — #7985301

Order 512.

5357 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59817C212yesmaximal, complemented
3#59465C212yesmaximal, complemented
4#59127C212yesmaximal, complemented
5#47969C218yesmaximal, complemented
6#45497C214yesmaximal, complemented
7#44951C214yesmaximal, complemented
8#44940C214yesmaximal, complemented
9#42931C214yesmaximal, complemented
10#42497C214yesmaximal, complemented
11#39625C212yesmaximal, complemented
12#39618C212yesmaximal, complemented
13#39615C214yesmaximal, complemented
14#39606C212yesmaximal, complemented
15#39497C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17Q8×#127C211yesmaximal, characteristic, complemented
18#36276C212yesmaximal, complemented
19#36274C212yesmaximal, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35279C212yesmaximal, complemented
22#35176C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic, complemented
25#34494C212yesmaximal
26C4×#550C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×#550C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2214yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C22×C4⋊Q8C2212yes—
35C2×C4×#41C2212yes—
36#2868C2211yescharacteristic
37#2868C2212yes—
38#2862C2212yes—
39#2857C2212yes—
40#2857C2214yes—
41#2857C2214yes—
42#2855C2214yes—
43#2841C2218yes—
44#2792C2218yes—
45#2790C2218yes—
46#2784C2218yes—
47#2780C2218yes—
48#2780C2218yes—
49#2768C2218yes—
50#2748C2218yes—
51#2742C2218yes—
52#2734C2218yes—
53#2732C2214yes—
54#2732C2218yes—
55#2729C2218yes—
56#2729C2218yes—
57#2692C2218yes—
58#2692C2218yes—
59#2683C2218yes—
60#2677C2218yes—
61#2667C2218yes—
62#2660C2214yes—
63#2659C2218yes—
64#2629C2214yes—
65#2628C2218yes—
66#2585C2214yes—
67#2582C2211yescharacteristic
68#2582C2212yes—
69#2574C2214yes—
70#2571C2212yes—
71#2570C2214yes—
72#2568C2211yescharacteristic
73#2568C2212yes—
74#2567C2211yescharacteristic
75#2567C2214yes—
76#2566C2214yes—
77#2564C2218yes—
78#2564C2218yes—
79#2563C2214yes—
80#2563C2214yes—
81#2563C2211yescharacteristic
82#2552C2212yes—
83#2552C2211yescharacteristic
84#2552C2211yescharacteristic
85#2551C2212yes—
86#2551C2214yes—
87#2551C2212yes—
88#2551C2214yes—
89#2550C2214yes—
90#2550C2214yes—
91#2549C2218yes—
92#2549C2218yes—
93#2546C2212yes—
94#2546C2211yescharacteristic
95#2542C2214yes—
96#2542C2214yes—
97#2542C2212yes—
98#2542C2214yes—
99#2542C2212yes—
100#2542C2212yes—
101#2542C2212yes—
102#2538C2212yes—
103#2538C2211yescharacteristic
104#2538C2214yes—
105#2538C2214yes—
106#2522C2218yes—
107#2511C2214yes—
108#2511C2212yes—
109#2509C2212yes—
110#2508C2212yes—
111#2507C2214yes—
112#2507C2214yes—
113#2502C2214yes—
114#2497C2212yes—
115#2487C2218yes—
116#2454C2214yes—
117#2454C2214yes—
118#2454C2214yes—
119#2454C2212yes—
120#2453C2212yes—
121#2452C2214yes—
122#2452C2214yes—
123#2452C2214yes—
124#2452C2218yes—
125#2451C2214yes—
126#2450C2218yes—
127#2449C2218yes—
128#2446C2212yes—
129#2446C2214yes—
130#2440C2214yes—
131#2440C2214yes—
132#2440C2214yes—
133#2439C2214yes—
134#2438C2218yes—
135#2434C2214yes—
136#2434C2214yes—
137#2429C2214yes—
138#2423C2214yes—
139#2423C2212yes—
140#2417C2214yes—
141#2417C2214yes—
142#2417C2214yes—
143#2409C2214yes—
144#2409C2214yes—
145#2409C2214yes—
146#2409C2214yes—
147#2402C2214yes—
148#2396C2214yes—
149#2377C2218yes—
150#2366C2211yescharacteristic
151#2366C2212yes—
152#2366C2212yes—
153#2366C2214yes—
154#2365C2212yes—
155#2363C2214yes—
156#2363C2212yes—
157#2361C2214yes—
158#2355C2212yes—
159#2355C2212yes—
160#2354C2212yes—
161#2354C2211yescharacteristic
162Q8×C4⋊C4C2211yescharacteristic
163#2349C2214yes—
164#2349C2214yes—
165#2349C2214yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169#2341C2212yes—
170#2339C2214yes—
171#2330C2214yes—
172#2328C2214yes—
173#2325C2218yes—
174#2324C2214yes—
175#2319C2214yes—
176#2317C2214yes—
177#2311C2214yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×#127C2212yes—
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2214yes—
190#2295C2212yes—
191#2295C2212yes—
192C2×#391C2214yes—
193#2293C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201C23×Q8C2314yes—
202#554—48no—
203#550Q8116yescomplemented
204D4×Q8—48no—
205D4×Q8—48no—
206D4×Q8—48no—
207D4×Q8—48no—
208D4×Q8—416no—
209C2×C4⋊Q8—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2318yes—
224C2×#127C2311yescharacteristic
225C2×#127C2312yes—
226C2×#125C2312yes—
227C2×#125C2312yes—
228C2×#125C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2318yes—
243C2×#121C2312yes—
244C2×#121C2314yes—
245C4×#41—48no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2314yes—
281C22×C42C2312yes—
282C22×C42C2314yes—
283#400C2314yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#399C2314yes—
291#399C2318yes—
292#399C2318yes—
293#399C2318yes—
294#399C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2314yes—
306#398C2314yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2314yes—
318#396C2318yes—
319#396C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2314yes—
323#395C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#393C2318yes—
330#393C2314yes—
331#393C2318yes—
332#393C2318yes—
333#393C2318yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#391C2318yes—
351#391C2318yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2314yes—
360#390C2312yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C2314yes—
365#390C2318yes—
366#390C2312yes—
367#390C2314yes—
368#390C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2312yes—
381#389C2318yes—
382#389C2318yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2312yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2314yes—
392#389C2318yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2314yes—
455#384C2314yes—
456#384C2314yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2314yes—
463#382C2312yes—
464#382C2312yes—
465#382C2314yes—
466#382C2314yes—
467#382C2314yes—
468#382C2314yes—
469#381C2318yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2318yes—
477#380C2318yes—
478#380C2318yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2312yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2311yescharacteristic
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523C2×#95C2318yes—
524C2×#95C2318yes—
525C43C2312yes—
526C43C2312yes—
527C43C2311yescharacteristic
528C2×#41—44no—
529C2×#41—44no—
530C2×#41C2×Q8116yescomplemented
531C22×Q8—216no—
532C22×Q8—48no—
533C22×Q8—48no—
534C22×Q8—48no—
535C22×Q8—48no—
536C22×Q8—48no—
537C22×Q8C2412yes—
538C22×Q8C2414yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
541C22×Q8C2412yes—
542C22×Q8C2418yes—
543C22×Q8C2418yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2414yes—
549C22×D4C2414yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2418yes—
555C23×C4C2414yes—
556C23×C4C2418yes—
557C23×C4C2418yes—
558C23×C4C2414yes—
559C4⋊Q8—28no—
560C4⋊Q8—24no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—24no—
564C4⋊Q8—48no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567C4⋊Q8—48no—
568C4⋊Q8—48no—
569C4⋊Q8—48no—
570C4⋊Q8—44no—
571C4⋊Q8—48no—
572C4⋊Q8—416no—
573#127C2×Q818yescomplemented
574#127C2×Q8116yescomplemented
575#125—28no—
576#125—44no—
577#125—48no—
578C22⋊Q8—28no—
579C22⋊Q8—416no—
580C22⋊Q8—416no—
581C22⋊Q8—416no—
582C22⋊Q8—416no—
583C22⋊Q8—416no—
584C22⋊Q8—416no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588C22⋊Q8—48no—
589C22⋊Q8—416no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592#121C2×Q8116yescomplemented
593#121C2×Q8132yescomplemented
594C4×Q8—24no—
595C4×Q8—24no—
596C4×Q8—24no—
597C4×Q8—24no—
598C4×Q8—28no—
599C4×Q8—44no—
600C4×Q8—42no—
601C4×Q8—44no—
602C4×Q8—48no—
603C4×Q8C2×Q818yescomplemented
604C4×D4—24no—
605C4×D4—28no—
606C4×D4—28no—
607C4×D4—24no—
608C4×D4—28no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—416no—
621C4×D4C2×Q818yescomplemented
622C4×D4C2×Q8116yescomplemented
623#117—48no—
624#117—48no—
625#117—44no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4—48no—
628C2×C4⋊C4—48no—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2411yescharacteristic
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2412yes—
712C2×C42—28no—
713C2×C42—48no—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2418yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2411yescharacteristic
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2414yes—
759#95C2412yes—
760#95C2412yes—
761#95C2412yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781C24C2512yes—
782C24C2514yes—
783#41—432no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—24no—
790C2×Q8—28no—
791C2×Q8—28no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—216no—
795C2×Q8—22no—
796C2×Q8—42no—
797C2×Q8—48no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—48no—
801C2×Q8—48no—
802C2×Q8—42no—
803C2×Q8—832no—
804C2×Q8—832no—
805C2×Q8C22×Q814yes—
806C2×Q8H(5,𝔽2)14yes—
807C2×D4—22no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4C22×Q814yes—
820C2×D4C22×Q818yes—
821C2×D4C22×Q818yes—
822C2×D4C22×Q8116yes—
823C2×D4C22×Q818yes—
824C2×D4C22×Q8116yes—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—216no—
836C22×C4—28no—
837C22×C4—44no—
838C22×C4—42no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4C22×Q818yes—
851C22×C4C22×Q8116yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2511yescharacteristic
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2518yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—22no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—42no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4C22×Q814yes—
933C4⋊C4C22×Q818yes—
934C4⋊C4C22×Q814yes—
935C4⋊C42−1+414yes—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—24no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4C22×Q818yes—
958C22⋊C4C22×Q8116yes—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—22no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—22no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—22no—
975C42—44no—
976C42—44no—
977C42—41no—
978C42—42no—
979C42—42no—
980C42—48no—
981C42—42no—
982C42C22×Q818yes—
983C42C22×Q814yes—
984C42H(5,𝔽2)14yes—
985C42H(5,𝔽2)14yes—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23—24no—
996C23—22no—
997C23—24no—
998C23C23×Q814yes—
999C23C23×Q818yes—
1000C23C2611yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—416no—
1005Q8—84no—
1006Q8—816no—
1007Q8—816no—
1008D4—216no—
1009D4—28no—
1010D4—216no—
1011D4—48no—
1012D4—416no—
1013D4—416no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—216no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—416no—
1071C2×C4—48no—
1072C2×C4—416no—
1073C2×C4—48no—
1074C2×C4—88no—
1075C2×C4—816no—
1076C2×C4—816no—
1077C2×C4—168no—
1078C2×C4C23×Q812yes—
1079C2×C4C23×Q814yes—
1080C2×C4C23×Q814yes—
1081C2×C4C23×Q814yes—
1082C2×C4C23×Q812yes—
1083C2×C4C23×Q812yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)14yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×2−1+414yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4#58512yes—
1095C22—24no—
1096C22—28no—
1097C22—24no—
1098C22—28no—
1099C22—24no—
1100C22—28no—
1101C22—42no—
1102C22—44no—
1103C22—42no—
1104C22—44no—
1105C22—44no—
1106C22—42no—
1107C22—42no—
1108C22—44no—
1109C22C24×Q811yescharacteristic
1110C22C22×H(5,𝔽2)11yescharacteristic
1111C22C22×H(5,𝔽2)11yescharacteristic
1112C22C22×H(5,𝔽2)11yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C2×#58511yescharacteristic
1115C222−1+611yescharacteristic
1116C4—22no—
1117C4—24no—
1118C4—24no—
1119C4—24no—
1120C4—24no—
1121C4—22no—
1122C4—22no—
1123C4—24no—
1124C4—44no—
1125C4—42no—
1126C4—44no—
1127C4—48no—
1128C4—41no—
1129C4—42no—
1130C4—42no—
1131C4—44no—
1132C4—42no—
1133C4—44no—
1134C4—44no—
1135C4—42no—
1136C4—42no—
1137C4#350114yes—
1138C4#350314yes—
1139C4#354314yes—
1140C2—44no—
1141C2—48no—
1142C2C2×#354311yescharacteristic
1143C2C2×#350111yescharacteristic
1144C2C2×#350311yescharacteristic
1145C2#6293111yescharacteristic
1146C2#6294211yescharacteristic
1147C2Q8×H(5,𝔽2)11yescharacteristic
1148C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59817C2semidirect
3. #59465C2semidirect
4. #59127C2semidirect
5. #47969C2semidirect
6. #45497C2semidirect
7. #44951C2semidirect
8. #44940C2semidirect
9. #42931C2semidirect
10. #42497C2semidirect
11. #39625C2semidirect
12. #39618C2semidirect
13. #39615C2semidirect
14. #39606C2semidirect
15. #39497C2semidirect
16. #36598C2semidirect
17. Q8×#127C2semidirect
18. #36276C2semidirect
19. #36274C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35279C2semidirect
22. #35176C2semidirect
23. #34951C2semidirect
24. #34941C2semidirect
203. #550Q8semidirect
530. C2×#41C2×Q8semidirect
573. #127C2×Q8semidirect
574. #127C2×Q8semidirect
592. #121C2×Q8semidirect
593. #121C2×Q8semidirect
603. C4×Q8C2×Q8semidirect
621. C4×D4C2×Q8semidirect
622. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598232
#598172
#594652
#591272
#479692
#454972
#449512
#449402
#429312
#424972
#396252
#396182
#396152
#396062
#394972
#365982
Q8×#1272
#362762
#362742
D4×C4⋊Q82
#352792
#351762
#349512
#349412
#344942
C4×#5502