Finite Group Databasebeta

← #7746768

Subgroups — #7746768

Order 512.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C212yesmaximal, complemented
2#45429C212yesmaximal, complemented
3#45307C214yesmaximal, complemented
4#45267C212yesmaximal, complemented
5#45107C214yesmaximal, complemented
6#45104C214yesmaximal, complemented
7#44890C214yesmaximal, complemented
8#44885C214yesmaximal, complemented
9#42926C214yesmaximal, complemented
10#42442C214yesmaximal, complemented
11#42440C214yesmaximal, complemented
12#36151C211yesmaximal, characteristic, complemented
13#36149C211yesmaximal, characteristic, complemented
14#36149C212yesmaximal, complemented
15#36129C212yesmaximal, complemented
16#36127C211yesmaximal, characteristic, complemented
17D4×C4⋊Q8C211yesmaximal, characteristic, complemented
18#36020C212yesmaximal, complemented
19#35806C214yesmaximal, complemented
20#35763C214yesmaximal, complemented
21#35737C212yesmaximal, complemented
22#35322C211yesmaximal, characteristic, complemented
23#35280C212yesmaximal, complemented
24#34547C211yesmaximal, characteristic, complemented
25#34207C211yesmaximal, characteristic, complemented
26#3511—232no—
27C2×#556C2214yes—
28C2×#555C2214yes—
29C2×#554C2214yes—
30C2×#553C2214yes—
31C2×#553C2214yes—
32C2×D4×Q8C2212yes—
33C2×#548C2214yes—
34C2×#548C2214yes—
35C2×#547C2214yes—
36C2×#547C2212yes—
37C2×#542C2214yes—
38C2×#542C2214yes—
39C2×#537C2214yes—
40C2×#533C2212yes—
41C2×#533C2212yes—
42C2×#532C2212yes—
43C2×#532C2212yes—
44C2×#532C2211yescharacteristic
45C22×C4⋊Q8C2212yes—
46C2×#520C2214yes—
47C2×#520C2212yes—
48C2×C4×#41C2212yes—
49#2868C2211yescharacteristic
50#2862C2212yes—
51#2862C2211yescharacteristic
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2814C2218yes—
57#2722C2218yes—
58#2717C2218yes—
59#2715C2218yes—
60#2708C2218yes—
61#2700C2218yes—
62#2698C2218yes—
63#2691C2218yes—
64#2689C2218yes—
65#2688C2218yes—
66#2686C2218yes—
67#2676C2218yes—
68#2674C2218yes—
69#2630C2218yes—
70#2629C2214yes—
71#2629C2214yes—
72#2627C2218yes—
73#2621C2212yes—
74#2621C2214yes—
75#2621C2212yes—
76#2618C2214yes—
77#2582C2214yes—
78#2582C2214yes—
79#2579C2218yes—
80#2565C2214yes—
81#2565C2214yes—
82#2551C2214yes—
83#2550C2214yes—
84#2547C2212yes—
85#2547C2214yes—
86#2546C2212yes—
87#2543C2214yes—
88#2538C2214yes—
89#2538C2214yes—
90#2537C2214yes—
91#2536C2212yes—
92#2535C2214yes—
93#2535C2214yes—
94#2535C2212yes—
95#2499C2214yes—
96#2499C2214yes—
97#2492C2214yes—
98#2489C2214yes—
99#2486C2214yes—
100#2478C2218yes—
101#2476C2218yes—
102#2466C2218yes—
103#2456C2218yes—
104#2453C2214yes—
105#2451C2214yes—
106#2450C2218yes—
107#2449C2218yes—
108#2447C2214yes—
109#2447C2214yes—
110#2447C2214yes—
111#2446C2214yes—
112#2442C2214yes—
113#2440C2214yes—
114#2440C2214yes—
115#2439C2214yes—
116#2438C2218yes—
117#2438C2218yes—
118#2434C2214yes—
119#2432C2214yes—
120#2429C2214yes—
121#2427C2214yes—
122#2427C2218yes—
123#2427C2214yes—
124#2427C2214yes—
125#2425C2218yes—
126#2422C2214yes—
127#2422C2214yes—
128#2421C2214yes—
129#2420C2214yes—
130#2420C2214yes—
131#2420C2214yes—
132#2417C2214yes—
133#2417C2214yes—
134#2417C2214yes—
135#2417C2214yes—
136#2417C2218yes—
137#2417C2214yes—
138#2415C2214yes—
139#2413C2218yes—
140#2409C2214yes—
141#2407C2214yes—
142#2407C2214yes—
143#2407C2214yes—
144#2399C2211yescharacteristic
145#2398C2212yes—
146#2397C2211yescharacteristic
147#2396C2212yes—
148#2396C2212yes—
149#2395C2212yes—
150#2395C2212yes—
151#2392C2211yescharacteristic
152#2392C2214yes—
153#2392C2212yes—
154#2392C2212yes—
155#2392C2211yescharacteristic
156#2392C2212yes—
157C2×#398C2214yes—
158#2388C2212yes—
159#2388C2212yes—
160#2362C2214yes—
161#2361C2214yes—
162#2361C2214yes—
163#2360C2214yes—
164#2354C2214yes—
165#2352C2214yes—
166#2351C2212yes—
167#2349C2214yes—
168#2349C2212yes—
169D4×C4⋊C4C2214yes—
170D4×C4⋊C4C2214yes—
171D4×C4⋊C4C2214yes—
172Q8×C22⋊C4C2214yes—
173#2339C2214yes—
174#2339C2214yes—
175#2339C2214yes—
176#2327C2212yes—
177#2327C2212yes—
178#2326C2212yes—
179#2326C2212yes—
180#2316C2214yes—
181#2311C2214yes—
182#2311C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#127C2211yescharacteristic
186C4×#127C2211yescharacteristic
187C2×#384C2211yescharacteristic
188C42×D4C2211yescharacteristic
189C42×D4C2211yescharacteristic
190C42×D4C2212yes—
191C4×#117C2211yescharacteristic
192C22×#41C2312yes—
193C22×#41C2314yes—
194C22×#41C2314yes—
195C22×#41C2312yes—
196C23×Q8C2314yes—
197#556—232no—
198#555—232no—
199#554—232no—
200#553—232no—
201#553—232no—
202D4×Q8—48no—
203#548—232no—
204#548—232no—
205#547—232no—
206#547—48no—
207#542—232no—
208#542—232no—
209#537—232no—
210#533—216no—
211#533—216no—
212#532—216no—
213#532—216no—
214#532D4116yescomplemented
215C2×C4⋊Q8—216no—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#126C2318yes—
227C2×#126C2318yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#124C2318yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#124C2318yes—
234C2×#124C2312yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2318yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2318yes—
255C2×#121C2318yes—
256C2×#121C2318yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259#520—232no—
260#520—48no—
261C4×#41—216no—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2318yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×#117C2314yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2318yes—
304C2×#117C2311yescharacteristic
305C2×#117C2314yes—
306C22×C4⋊C4C2318yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2314yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C42C2312yes—
314C22×C42C2312yes—
315C22×C42C2311yescharacteristic
316#400C2318yes—
317#400C2318yes—
318#400C2312yes—
319#400C2312yes—
320#399C2312yes—
321#399C2312yes—
322#398C2318yes—
323#398C2314yes—
324#398C2314yes—
325#398C2318yes—
326#398C2318yes—
327#398C2318yes—
328#398C2318yes—
329#398C2314yes—
330#398C2311yescharacteristic
331#398C2312yes—
332#398C2311yescharacteristic
333#398C2318yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2318yes—
339#397C2314yes—
340#397C2318yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2318yes—
345#397C2318yes—
346#397C2312yes—
347#397C2311yescharacteristic
348#397C2311yescharacteristic
349#397C2312yes—
350#397C2312yes—
351#397C2314yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#396C2312yes—
356#396C2318yes—
357#396C2318yes—
358#396C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2312yes—
362#396C2312yes—
363#396C2312yes—
364#395C2318yes—
365#395C2318yes—
366#395C2312yes—
367#395C2312yes—
368#395C2318yes—
369#394C2311yescharacteristic
370#394C2314yes—
371#394C2312yes—
372#394C2318yes—
373#394C2318yes—
374#394C2312yes—
375#394C2312yes—
376#394C2312yes—
377#394C2312yes—
378#394C2312yes—
379#394C2312yes—
380#394C2311yescharacteristic
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#393C2312yes—
385#393C2312yes—
386#393C2318yes—
387#392C2318yes—
388#392C2312yes—
389#392C2311yescharacteristic
390#392C2311yescharacteristic
391#392C2312yes—
392#392C2312yes—
393#392C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2318yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2318yes—
408#391C2318yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#390C2314yes—
413#390C2318yes—
414#389C2314yes—
415#389C2314yes—
416#389C2318yes—
417#389C2318yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2318yes—
427#389C2318yes—
428#389C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2318yes—
432#388C2318yes—
433#388C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2314yes—
464#384C2314yes—
465#384C2312yes—
466#384C2314yes—
467#382C2314yes—
468#382C2314yes—
469#382C2312yes—
470#382C2312yes—
471#382C2314yes—
472#381C2318yes—
473#381C2318yes—
474#381C2318yes—
475#380C2318yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2318yes—
481#380C2318yes—
482#380C2314yes—
483#380C2314yes—
484#380C2318yes—
485#380C2314yes—
486#380C2314yes—
487#380C2318yes—
488#380C2314yes—
489#380C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517#376C2311yescharacteristic
518#376C2311yescharacteristic
519C2×#95C2318yes—
520C2×#95C2314yes—
521C43C2311yescharacteristic
522C43C2311yescharacteristic
523C2×#41—216no—
524C2×#41—216no—
525C2×#41—28no—
526C2×#41—28no—
527C2×#41—216no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—48no—
532C2×#41—48no—
533C2×#41—48no—
534C2×#41C2×D4116yes—
535C22×Q8—216no—
536C22×Q8—48no—
537C22×Q8—48no—
538C22×Q8C2414yes—
539C22×Q8C2414yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2418yes—
543C22×D4C2411yescharacteristic
544C22×D4C2418yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C22×D4C2411yescharacteristic
551C22×D4C2412yes—
552C22×D4C2418yes—
553C22×D4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2418yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2412yes—
563C23×C4C2414yes—
564C23×C4C2418yes—
565C23×C4C2418yes—
566C23×C4C2414yes—
567C23×C4C2414yes—
568C23×C4C2414yes—
569C4⋊Q8—216no—
570C4⋊Q8—216no—
571C4⋊Q8—216no—
572C4⋊Q8—28no—
573C4⋊Q8—28no—
574C4⋊Q8—28no—
575C4⋊Q8—48no—
576C4⋊Q8—44no—
577C4⋊Q8C2×D418yes—
578#127C2×D418yes—
579#126—232no—
580#126—232no—
581#125—216no—
582#125—216no—
583#124—216no—
584#124—216no—
585#124—232no—
586#124—232no—
587#124C2×D4116yes—
588#123—232no—
589#123—232no—
590#123—416no—
591C22⋊Q8—216no—
592C22⋊Q8—216no—
593C22⋊Q8—216no—
594C22⋊Q8—232no—
595C22⋊Q8—216no—
596C22⋊Q8—232no—
597C22⋊Q8—232no—
598C22⋊Q8—416no—
599C22⋊Q8—48no—
600C22⋊Q8—48no—
601C22⋊Q8—48no—
602C22⋊Q8—48no—
603#121—216no—
604#121—216no—
605#121—216no—
606#121—216no—
607#121—232no—
608#121—232no—
609#121—232no—
610#121—48no—
611#121C2×D4132yes—
612C4×Q8—216no—
613C4×Q8—216no—
614C4×Q8—28no—
615C4×Q8—28no—
616C4×Q8—216no—
617C4×Q8—216no—
618C4×Q8—28no—
619C4×Q8—44no—
620C4×D4—216no—
621C4×D4—216no—
622C4×D4—216no—
623C4×D4—216no—
624C4×D4—28no—
625C4×D4—28no—
626C4×D4—28no—
627C4×D4—28no—
628C4×D4—232no—
629C4×D4—28no—
630C4×D4—28no—
631C4×D4—232no—
632C4×D4—28no—
633C4×D4—28no—
634C4×D4—28no—
635C4×D4—24no—
636C4×D4—24no—
637C4×D4—48no—
638C4×D4—48no—
639C4×D4—48no—
640C4×D4—44no—
641C4×D4—48no—
642C4×D4—44no—
643C4×D4—44no—
644C4×D4—44no—
645C4×D4—48no—
646C4×D4C2×D4132yes—
647#117—28no—
648#117—216no—
649#117—216no—
650#117—232no—
651#117—28no—
652#117—28no—
653#117—24no—
654#117—42no—
655#117—48no—
656C2×C4⋊C4—232no—
657C2×C4⋊C4—216no—
658C2×C4⋊C4—216no—
659C2×C4⋊C4—48no—
660C2×C4⋊C4—48no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4—48no—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2411yescharacteristic
708C2×C22⋊C4C2411yescharacteristic
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2412yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2418yes—
741C2×C42—28no—
742C2×C42—28no—
743C2×C42C2×D418yes—
744C2×C42C2412yes—
745C2×C42C2418yes—
746C2×C42C2418yes—
747C2×C42C2412yes—
748C2×C42C2411yescharacteristic
749C2×C42C2414yes—
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#95C2411yescharacteristic
766#95C2412yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2412yes—
773#95C2412yes—
774#95C2412yes—
775#95C2412yes—
776#95C2411yescharacteristic
777#95C2412yes—
778#95C2411yescharacteristic
779#95C2412yes—
780#95C2412yes—
781#95C2412yes—
782#95C2411yescharacteristic
783#95C2412yes—
784#95C2412yes—
785#95C2412yes—
786#95C2412yes—
787#95C2412yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791#95C2418yes—
792#95C2414yes—
793#95C2418yes—
794#95C2418yes—
795#95C2418yes—
796#95C2418yes—
797#95C2418yes—
798#95C2418yes—
799#95C2418yes—
800C24C2512yes—
801C24C2511yescharacteristic
802C24C2514yes—
803C24C2512yes—
804#41—432no—
805#41—432no—
806#41—464no—
807#41—832no—
808C2×Q8—24no—
809C2×Q8—28no—
810C2×Q8—28no—
811C2×Q8—216no—
812C2×Q8—24no—
813C2×Q8—28no—
814C2×Q8—24no—
815C2×Q8—28no—
816C2×Q8—24no—
817C2×Q8—28no—
818C2×Q8—28no—
819C2×Q8—42no—
820C2×Q8—48no—
821C2×Q8—48no—
822C2×Q8—832no—
823C2×Q8C22×D418yes—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—216no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—216no—
832C2×D4—216no—
833C2×D4—24no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—28no—
838C2×D4—24no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—44no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—42no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—48no—
852C2×D4C22×D4116yes—
853C2×D4C22×D418yes—
854C2×D4C22×D4116yes—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—216no—
862C22×C4—216no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—216no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—216no—
880C22×C4—28no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4C22×D418yes—
894C22×C4C22×D414yes—
895C22×C4C22×D4116yes—
896C22×C42−1+418yes—
897C22×C4C2512yes—
898C22×C4C2511yescharacteristic
899C22×C4C2512yes—
900C22×C4C2511yescharacteristic
901C22×C4C2512yes—
902C22×C4C2518yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2518yes—
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2512yes—
916C22×C4C2511yescharacteristic
917C22×C4C2512yes—
918C4⋊C4—24no—
919C4⋊C4—216no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—216no—
923C4⋊C4—216no—
924C4⋊C4—216no—
925C4⋊C4—24no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—28no—
932C4⋊C4—216no—
933C4⋊C4—216no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—24no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—28no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—44no—
948C4⋊C4—48no—
949C4⋊C4—44no—
950C4⋊C4—48no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—48no—
956C4⋊C4—48no—
957C4⋊C4—48no—
958C4⋊C4—48no—
959C4⋊C4C22×D4116yes—
960C22⋊C4—216no—
961C22⋊C4—24no—
962C22⋊C4—24no—
963C22⋊C4—216no—
964C22⋊C4—216no—
965C22⋊C4—216no—
966C22⋊C4—216no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—216no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—28no—
977C22⋊C4—24no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—42no—
982C22⋊C4—44no—
983C22⋊C4—48no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—48no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4C22×D4132yes—
996C42—24no—
997C42—24no—
998C42—24no—
999C42—24no—
1000C42—24no—
1001C42—24no—
1002C42—216no—
1003C42—216no—
1004C42—22no—
1005C42—28no—
1006C42—24no—
1007C42—24no—
1008C42—22no—
1009C42—22no—
1010C42—24no—
1011C42—24no—
1012C42—44no—
1013C42C22×D414yes—
1014C42C22×D418yes—
1015C42C22×D414yes—
1016C42H(5,𝔽2)14yes—
1017C23—22no—
1018C23—21no—
1019C23—22no—
1020C23—24no—
1021C23—22no—
1022C23—22no—
1023C23—28no—
1024C23—22no—
1025C23—21no—
1026C23—28no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23C23×D412yes—
1039C23C23×D418yes—
1040C23C2×2−1+414yes—
1041C23C2611yescharacteristic
1042Q8—216no—
1043Q8—48no—
1044Q8—416no—
1045Q8—416no—
1046Q8—816no—
1047D4—28no—
1048D4—232no—
1049D4—216no—
1050D4—416no—
1051D4—48no—
1052D4—48no—
1053D4—44no—
1054D4—48no—
1055D4—432no—
1056D4—48no—
1057D4—816no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—216no—
1069C2×C4—216no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—28no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—28no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—28no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—28no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—28no—
1106C2×C4—416no—
1107C2×C4—432no—
1108C2×C4—48no—
1109C2×C4—48no—
1110C2×C4—48no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—88no—
1114C2×C4—816no—
1115C2×C4—816no—
1116C2×C4—164no—
1117C2×C4—164no—
1118C2×C4C23×D414yes—
1119C2×C4C23×D418yes—
1120C2×C4C23×D412yes—
1121C2×C4C23×D414yes—
1122C2×C4C23×D412yes—
1123C2×C4C2×H(5,𝔽2)12yes—
1124C2×C4C2×H(5,𝔽2)12yes—
1125C2×C4C2×H(5,𝔽2)12yes—
1126C2×C4C2×2−1+414yes—
1127C2×C4C2×2−1+414yes—
1128C2×C4#58514yes—
1129C2×C4#58512yes—
1130C22—22no—
1131C22—28no—
1132C22—24no—
1133C22—24no—
1134C22—216no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—41no—
1140C22—44no—
1141C22—44no—
1142C22—41no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—48no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22C24×D411yescharacteristic
1155C22C22×H(5,𝔽2)11yescharacteristic
1156C22C22×2−1+412yes—
1157C22C2×#58511yescharacteristic
1158C22C2×#58512yes—
1159C4—22no—
1160C4—28no—
1161C4—24no—
1162C4—24no—
1163C4—22no—
1164C4—22no—
1165C4—42no—
1166C4—42no—
1167C4—48no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—48no—
1172C4—41no—
1173C4—44no—
1174C4—44no—
1175C4—41no—
1176C4—42no—
1177C4—42no—
1178C4#348918yes—
1179C4#349614yes—
1180C2—42no—
1181C2—48no—
1182C2—44no—
1183C2—82no—
1184C2C2×#349611yescharacteristic
1185C2C2×#348912yes—
1186C2#6283311yescharacteristic
1187C2#6283611yescharacteristic
1188C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3511C2semidirect
2. #45429C2semidirect
3. #45307C2semidirect
4. #45267C2semidirect
5. #45107C2semidirect
6. #45104C2semidirect
7. #44890C2semidirect
8. #44885C2semidirect
9. #42926C2semidirect
10. #42442C2semidirect
11. #42440C2semidirect
12. #36151C2semidirect
13. #36149C2semidirect
14. #36149C2semidirect
15. #36129C2semidirect
16. #36127C2semidirect
17. D4×C4⋊Q8C2semidirect
18. #36020C2semidirect
19. #35806C2semidirect
20. #35763C2semidirect
21. #35737C2semidirect
22. #35322C2semidirect
23. #35280C2semidirect
24. #34547C2semidirect
25. #34207C2semidirect
214. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#454292
#453072
#452672
#451072
#451042
#448902
#448852
#429262
#424422
#424402
#361512
#361492
#361292
#361272
D4×C4⋊Q82
#360202
#358062
#357632
#357372
#353222
#352802
#345472
#342072