Finite Group Databasebeta

← #7715669

Subgroups — #7715669

Order 512.

7832 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C211yesmaximal, characteristic, complemented
2C2×#3449C211yesmaximal, characteristic
3#51326C214yesmaximal, complemented
4#50867C214yesmaximal, complemented
5#50165C214yesmaximal, complemented
6#48773C214yesmaximal, complemented
7#46429C214yesmaximal, complemented
8#46426C214yesmaximal, complemented
9#46359C214yesmaximal, complemented
10#46358C214yesmaximal, complemented
11#39463C214yesmaximal, complemented
12#39343C214yesmaximal, complemented
13#37847C214yesmaximal, complemented
14#37651C214yesmaximal, complemented
15#37438C212yesmaximal, complemented
16#37375C212yesmaximal, complemented
17#37374C212yesmaximal, complemented
18#35310C212yesmaximal, complemented
19#35305C212yesmaximal, complemented
20#35305C212yesmaximal, complemented
21#34361C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C23×#41C2211yescharacteristic
24#3538—216no—
25C2×#563C2214yescomplemented
26C2×#552C2214yescomplemented
27C2×#551C2214yescomplemented
28C2×D4×Q8C2214yescomplemented
29C2×#544C2214yescomplemented
30C2×#541C2212yescomplemented
31C2×#539C2214yescomplemented
32#3449—216no—
33C2×#537C2212yes—
34C2×#537C2212yes—
35C2×#536C2212yes—
36C2×#536C2212yes—
37C2×#536C2212yes—
38C2×#536C2212yes—
39C2×#536C2212yescomplemented
40C2×#536C2212yescomplemented
41C2×#535C2212yes—
42C2×#535C2212yes—
43C2×#534C2212yes—
44C2×#534C2212yes—
45C2×#532C2214yes—
46C2×#525C2214yes—
47C2×#525C2211yescharacteristic
48C2×#525C2211yescharacteristic
49C2×#525C2211yescharacteristic
50C2×#525C2211yescharacteristic
51C22×C22⋊Q8C2212yescomplemented
52C22×C22⋊Q8C2212yescomplemented
53C22×#117C2211yescharacteristic
54#2857C2212yescomplemented
55#2851C2212yescomplemented
56#2848C2214yes—
57#2848C2214yescomplemented
58#2848C2214yescomplemented
59#2817C2214yescomplemented
60#2816C2214yescomplemented
61#2729C2218yescomplemented
62#2724C2214yescomplemented
63#2720C2218yescomplemented
64#2718C2218yescomplemented
65#2717C2214yescomplemented
66#2713C2218yescomplemented
67#2711C2218yescomplemented
68#2711C2218yescomplemented
69#2709C2218yescomplemented
70#2708C2218yescomplemented
71#2708C2218yescomplemented
72#2701C2218yescomplemented
73#2697C2218yescomplemented
74#2697C2214yescomplemented
75#2689C2218yescomplemented
76#2685C2218yescomplemented
77#2685C2218yescomplemented
78#2684C2214yescomplemented
79#2681C2218yescomplemented
80#2680C2218yescomplemented
81#2677C2218yescomplemented
82#2674C2218yescomplemented
83#2674C2218yescomplemented
84#2674C2218yescomplemented
85#2672C2218yescomplemented
86#2672C2218yescomplemented
87#2663C2218yescomplemented
88#2629C2212yescomplemented
89#2625C2214yescomplemented
90#2622C2218yescomplemented
91#2621C2212yescomplemented
92#2616C2214yes—
93#2616C2214yes—
94#2616C2214yescomplemented
95#2616C2214yescomplemented
96#2591C2214yescomplemented
97#2583C2214yescomplemented
98#2562C2214yescomplemented
99#2559C2218yescomplemented
100#2558C2218yescomplemented
101#2556C2218yescomplemented
102#2551C2218yescomplemented
103#2542C2214yescomplemented
104#2538C2214yescomplemented
105#2536C2214yescomplemented
106#2521C2218yescomplemented
107#2491C2218yescomplemented
108#2487C2214yescomplemented
109#2485C2214yescomplemented
110#2480C2218yes—
111#2478C2218yescomplemented
112#2476C2218yescomplemented
113#2476C2218yescomplemented
114#2475C2218yescomplemented
115#2474C2218yescomplemented
116#2473C2218yescomplemented
117#2472C2218yescomplemented
118#2470C2218yescomplemented
119#2445C2218yescomplemented
120#2443C2218yescomplemented
121#2440C2218yescomplemented
122#2435C2214yes—
123#2435C2214yes—
124#2434C2214yescomplemented
125#2434C2214yescomplemented
126#2432C2214yes—
127#2432C2214yes—
128#2432C2214yescomplemented
129#2432C2214yescomplemented
130#2422C2218yescomplemented
131#2418C2218yescomplemented
132#2417C2214yescomplemented
133#2415C2214yescomplemented
134#2415C2214yescomplemented
135#2415C2214yescomplemented
136#2409C2214yescomplemented
137#2409C2214yescomplemented
138#2406C2214yes—
139#2406C2214yes—
140#2406C2214yescomplemented
141#2406C2214yescomplemented
142#2405C2214yes—
143#2405C2214yes—
144#2405C2214yescomplemented
145#2405C2214yescomplemented
146#2375C2214yescomplemented
147#2374C2214yescomplemented
148#2354C2214yescomplemented
149#2352C2214yescomplemented
150#2333C2214yescomplemented
151#2332C2214yescomplemented
152#2323C2214yescomplemented
153#2314C2212yescomplemented
154#2311C2212yes—
155#2311C2212yes—
156#2311C2212yescomplemented
157#2311C2212yescomplemented
158C4×C22⋊Q8C2214yescomplemented
159#2280C2212yescomplemented
160#2280C2212yescomplemented
161C22×#41—28no—
162C22×#41—28no—
163C22×#41—44no—
164C22×#41—44no—
165C22×#41—44no—
166C22×#41—44no—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C22×#41C2311yescharacteristic
171C22×#41C2312yes—
172C22×#41C2312yes—
173C22×#41C2311yescharacteristic
174C22×#41C2312yes—
175C22×#41C2311yescharacteristic
176C22×#41C2311yescharacteristic
177C23×Q8C2311yescharacteristic
178C23×Q8C2311yescharacteristic
179C23×Q8C2312yes—
180C23×Q8C2312yes—
181C23×D4C2311yescharacteristic
182C23×D4C2312yes—
183C23×D4C2311yescharacteristic
184C23×D4C2311yescharacteristic
185C23×D4C2311yescharacteristic
186C24×C4C2311yescharacteristic
187C24×C4C2312yes—
188C24×C4C2311yescharacteristic
189C24×C4C2311yescharacteristic
190#563—232no—
191#552—232no—
192#551—232no—
193D4×Q8—232no—
194#544—232no—
195#541—216no—
196#539—232no—
197#537—216no—
198#537—216no—
199#536—216no—
200#536—216no—
201#536—216no—
202#536—48no—
203#536—48no—
204#536—48no—
205#535—216no—
206#535—216no—
207#534—216no—
208#534—216no—
209#532—232no—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2318yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×#127C2314yes—
218C2×#126C2318yes—
219C2×#126C2318yes—
220C2×#125C2312yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#124C2314yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229#525—28no—
230#525—28no—
231#525—232no—
232#525—28no—
233#525D4116yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2312yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2312yes—
240C2×#123C2312yes—
241C2×#123C2318yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2312yes—
249C2×C22⋊Q8—216no—
250C2×C22⋊Q8—48no—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2318yes—
264C2×C22⋊Q8C2318yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#120C2312yes—
283C2×#120C2314yes—
284C2×#120C2312yes—
285C2×#120C2312yes—
286C2×#120C2314yes—
287C2×#120C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2318yes—
293C2×C4×D4C2314yes—
294C2×#117—28no—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2318yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C42C2312yes—
314#400C2318yes—
315#400C2318yes—
316#400C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C2318yes—
320#398C2318yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#397C2318yes—
326#397C2318yes—
327#397C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2318yes—
336#395C2318yes—
337#395C2318yes—
338#395C2318yes—
339#395C2318yes—
340#395C2318yes—
341#395C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#393C2318yes—
361#393C2318yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2318yes—
373#390C2318yes—
374#390C2318yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#384C2312yes—
431#384C2318yes—
432#382C2312yes—
433#381C2314yes—
434#381C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2318yes—
444#380C2314yes—
445#380C2318yes—
446#379C2318yes—
447#379C2318yes—
448#379C2318yes—
449#379C2314yes—
450#379C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C25C2411yescharacteristic
461C25C2412yes—
462C25C2411yescharacteristic
463C25C2411yescharacteristic
464C2×#41—24no—
465C2×#41—28no—
466C2×#41—24no—
467C2×#41—28no—
468C2×#41—24no—
469C2×#41—28no—
470C2×#41—28no—
471C2×#41—28no—
472C2×#41—28no—
473C2×#41—28no—
474C2×#41—28no—
475C2×#41—28no—
476C2×#41—42no—
477C2×#41—44no—
478C2×#41—42no—
479C2×#41—44no—
480C2×#41—44no—
481C2×#41—42no—
482C2×#41—42no—
483C2×#41—44no—
484C2×#41—42no—
485C2×#41—42no—
486C2×#41—44no—
487C2×#41—42no—
488C2×#41—44no—
489C2×#41—42no—
490C2×#41—44no—
491C2×#41—44no—
492C2×#41—44no—
493C2×#41—464no—
494C2×#41—464no—
495C2×#41C2×D418yes—
496C22×Q8—24no—
497C22×Q8—24no—
498C22×Q8—28no—
499C22×Q8—28no—
500C22×Q8—42no—
501C22×Q8—42no—
502C22×Q8—42no—
503C22×Q8—42no—
504C22×Q8—44no—
505C22×Q8—44no—
506C22×Q8—44no—
507C22×Q8—44no—
508C22×Q8C2414yes—
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×Q8C2414yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—28no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—42no—
522C22×D4—42no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—44no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—44no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2412yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2411yescharacteristic
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—24no—
551C23×C4—28no—
552C23×C4—24no—
553C23×C4—28no—
554C23×C4—42no—
555C23×C4—42no—
556C23×C4—44no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4C2×D418yes—
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2414yes—
576C23×C4C2414yes—
577C23×C4C2412yes—
578C23×C4C2411yescharacteristic
579C23×C4C2414yes—
580C23×C4C2412yes—
581C23×C4C2411yescharacteristic
582C4⋊Q8—216no—
583C4⋊Q8—216no—
584C4⋊Q8—232no—
585C4⋊Q8—28no—
586C4⋊Q8—48no—
587C4⋊Q8—48no—
588C4⋊Q8—48no—
589#127—216no—
590#126—232no—
591#126—232no—
592#125—232no—
593#125—232no—
594#125—28no—
595#124—216no—
596#124—216no—
597#124—216no—
598#124—48no—
599#124—48no—
600#124—48no—
601#123—28no—
602#123—216no—
603#123—216no—
604#123—232no—
605#123—28no—
606#123—216no—
607#123—216no—
608#123—28no—
609#123—48no—
610#123—48no—
611#123—48no—
612#123—48no—
613#123—48no—
614#123—48no—
615#123C2×D4116yes—
616C22⋊Q8—28no—
617C22⋊Q8—216no—
618C22⋊Q8—216no—
619C22⋊Q8—216no—
620C22⋊Q8—216no—
621C22⋊Q8—28no—
622C22⋊Q8—216no—
623C22⋊Q8—216no—
624C22⋊Q8—216no—
625C22⋊Q8—216no—
626C22⋊Q8—28no—
627C22⋊Q8—216no—
628C22⋊Q8—232no—
629C22⋊Q8—232no—
630C22⋊Q8—48no—
631C22⋊Q8—48no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8—48no—
635C22⋊Q8—48no—
636C22⋊Q8C2×D4116yes—
637#121—28no—
638#121—216no—
639#121—216no—
640#121—28no—
641#121—28no—
642#121—216no—
643#121—216no—
644#121—216no—
645#121—216no—
646#121C2×D4116yes—
647#120—28no—
648#120—28no—
649#120—216no—
650#120—216no—
651#120—28no—
652#120C2×D4116yes—
653C4×Q8—216no—
654C4×D4—232no—
655C4×D4—216no—
656C4×D4—216no—
657C4×D4—216no—
658C4×D4C2×D4132yes—
659#117—24no—
660#117—28no—
661#117—28no—
662#117—28no—
663#117—232no—
664#117—28no—
665#117—44no—
666#117—44no—
667#117—44no—
668#117C2×D418yes—
669C2×C4⋊C4—216no—
670C2×C4⋊C4—28no—
671C2×C4⋊C4—28no—
672C2×C4⋊C4—44no—
673C2×C4⋊C4—48no—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2418yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2418yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C22⋊C4—216no—
702C2×C22⋊C4—28no—
703C2×C22⋊C4—48no—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C42—28no—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2418yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2418yes—
746C2×C42C2412yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—24no—
768C24—24no—
769C24—22no—
770C24—41no—
771C24—41no—
772C24—42no—
773C24—41no—
774C24—41no—
775C24—44no—
776C24—44no—
777C24—44no—
778C24—44no—
779C24—44no—
780C24C22×D414yes—
781C24C2512yes—
782C24C2512yes—
783C24C2511yescharacteristic
784C24C2512yes—
785C24C2512yes—
786C24C2511yescharacteristic
787C24C2511yescharacteristic
788#41—416no—
789#41—432no—
790#41—432no—
791#41—432no—
792#41—432no—
793#41—432no—
794#41—432no—
795#41—416no—
796#41—416no—
797#41—416no—
798C2×Q8—28no—
799C2×Q8—24no—
800C2×Q8—22no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—28no—
804C2×Q8—28no—
805C2×Q8—28no—
806C2×Q8—28no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—41no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—41no—
814C2×Q8—42no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—44no—
818C2×Q8—44no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×Q8—416no—
822C2×Q8—416no—
823C2×Q8—816no—
824C2×Q8—816no—
825C2×Q8C22×D414yes—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—24no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—28no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—42no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—416no—
869C2×D4—416no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—416no—
877C2×D4—432no—
878C2×D4—416no—
879C2×D4C22×D4116yes—
880C2×D4C22×D418yes—
881C2×D4C22×D414yes—
882C22×C4—232no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—22no—
905C22×C4—24no—
906C22×C4—28no—
907C22×C4—28no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—416no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—48no—
933C22×C4—432no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—416no—
943C22×C4C22×D418yes—
944C22×C4C22×D414yes—
945C22×C4C22×D418yes—
946C22×C4C22×D418yes—
947C22×C4C22×D414yes—
948C22×C4H(5,𝔽2)14yes—
949C22×C4H(5,𝔽2)14yes—
950C22×C4C2518yes—
951C22×C4C2514yes—
952C22×C4C2518yes—
953C22×C4C2518yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2518yes—
957C22×C4C2511yescharacteristic
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—216no—
968C4⋊C4—216no—
969C4⋊C4—28no—
970C4⋊C4—216no—
971C4⋊C4—216no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—216no—
976C4⋊C4—216no—
977C4⋊C4—28no—
978C4⋊C4—216no—
979C4⋊C4—28no—
980C4⋊C4—216no—
981C4⋊C4—44no—
982C4⋊C4—48no—
983C4⋊C4—48no—
984C4⋊C4—48no—
985C4⋊C4—48no—
986C4⋊C4—48no—
987C4⋊C4—48no—
988C4⋊C4—48no—
989C4⋊C4C22×D418yes—
990C4⋊C4C22×D4116yes—
991C22⋊C4—24no—
992C22⋊C4—216no—
993C22⋊C4—216no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—216no—
998C22⋊C4—216no—
999C22⋊C4—216no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—48no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—48no—
1019C22⋊C4—48no—
1020C22⋊C4—48no—
1021C22⋊C4C22×D418yes—
1022C22⋊C4C22×D4116yes—
1023C22⋊C4C22×D4116yes—
1024C42—24no—
1025C42—28no—
1026C42—28no—
1027C42—216no—
1028C42—48no—
1029C42—44no—
1030C42—44no—
1031C42—44no—
1032C42C22×D418yes—
1033C23—28no—
1034C23—21no—
1035C23—21no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—24no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—44no—
1062C23—48no—
1063C23—48no—
1064C23—44no—
1065C23—48no—
1066C23—88no—
1067C23—84no—
1068C23—84no—
1069C23—84no—
1070C23—84no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—84no—
1075C23—88no—
1076C23—84no—
1077C23C23×D412yes—
1078C23C23×D414yes—
1079C23C23×D414yes—
1080C23C2×H(5,𝔽2)12yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2611yescharacteristic
1083Q8—44no—
1084Q8—48no—
1085Q8—48no—
1086Q8—48no—
1087Q8—44no—
1088Q8—416no—
1089Q8—88no—
1090Q8—88no—
1091D4—44no—
1092D4—48no—
1093D4—416no—
1094D4—48no—
1095D4—48no—
1096D4—48no—
1097D4—48no—
1098D4—48no—
1099D4—48no—
1100D4—44no—
1101D4—48no—
1102D4—48no—
1103D4—48no—
1104D4—48no—
1105D4—88no—
1106D4—88no—
1107D4—88no—
1108C2×C4—28no—
1109C2×C4—28no—
1110C2×C4—28no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—28no—
1124C2×C4—28no—
1125C2×C4—28no—
1126C2×C4—216no—
1127C2×C4—216no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—28no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—28no—
1142C2×C4—28no—
1143C2×C4—28no—
1144C2×C4—28no—
1145C2×C4—28no—
1146C2×C4—28no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—44no—
1150C2×C4—48no—
1151C2×C4—48no—
1152C2×C4—48no—
1153C2×C4—48no—
1154C2×C4—48no—
1155C2×C4—416no—
1156C2×C4—44no—
1157C2×C4—48no—
1158C2×C4—48no—
1159C2×C4—88no—
1160C2×C4—88no—
1161C2×C4—88no—
1162C2×C4—88no—
1163C2×C4C23×D418yes—
1164C2×C4C23×D414yes—
1165C2×C4C23×D414yes—
1166C2×C4C23×D412yes—
1167C2×C4C23×D412yes—
1168C2×C4C2×H(5,𝔽2)12yes—
1169C2×C4C2×H(5,𝔽2)12yes—
1170C2×C4C2×H(5,𝔽2)12yes—
1171C2×C4C2×H(5,𝔽2)12yes—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—28no—
1179C22—24no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—44no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22—44no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—44no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—88no—
1205C22—88no—
1206C22—816no—
1207C22—88no—
1208C22C24×D411yescharacteristic
1209C22C22×H(5,𝔽2)11yescharacteristic
1210C22C22×H(5,𝔽2)11yescharacteristic
1211C222−1+614yes—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—24no—
1216C4—24no—
1217C4—28no—
1218C4—42no—
1219C4—42no—
1220C4—48no—
1221C4—48no—
1222C4—44no—
1223C4—48no—
1224C4—48no—
1225C4#348414yes—
1226C2—42no—
1227C2—44no—
1228C2—44no—
1229C2—42no—
1230C2—42no—
1231C2—82no—
1232C2—82no—
1233C2C2×#348411yescharacteristic
1234C2#6285912yes—
1235C2#6288612yes—
1236C2#6288812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3449C2
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×#3538C2semidirect
3. #51326C2semidirect
4. #50867C2semidirect
5. #50165C2semidirect
6. #48773C2semidirect
7. #46429C2semidirect
8. #46426C2semidirect
9. #46359C2semidirect
10. #46358C2semidirect
11. #39463C2semidirect
12. #39343C2semidirect
13. #37847C2semidirect
14. #37651C2semidirect
15. #37438C2semidirect
16. #37375C2semidirect
17. #37374C2semidirect
18. #35310C2semidirect
19. #35305C2semidirect
20. #35305C2semidirect
21. #34361C2semidirect
25. C2×#563C22semidirect
26. C2×#552C22semidirect
27. C2×#551C22semidirect
28. C2×D4×Q8C22semidirect
29. C2×#544C22semidirect
30. C2×#541C22semidirect
31. C2×#539C22semidirect
39. C2×#536C22semidirect
40. C2×#536C22semidirect
51. C22×C22⋊Q8C22semidirect
52. C22×C22⋊Q8C22semidirect
54. #2857C22semidirect
55. #2851C22semidirect
57. #2848C22semidirect
58. #2848C22semidirect
59. #2817C22semidirect
60. #2816C22semidirect
61. #2729C22semidirect
62. #2724C22semidirect
63. #2720C22semidirect
64. #2718C22semidirect
65. #2717C22semidirect
66. #2713C22semidirect
67. #2711C22semidirect
68. #2711C22semidirect
69. #2709C22semidirect
70. #2708C22semidirect
71. #2708C22semidirect
72. #2701C22semidirect
73. #2697C22semidirect
74. #2697C22semidirect
75. #2689C22semidirect
76. #2685C22semidirect
77. #2685C22semidirect
78. #2684C22semidirect
79. #2681C22semidirect
80. #2680C22semidirect
81. #2677C22semidirect
82. #2674C22semidirect
83. #2674C22semidirect
84. #2674C22semidirect
85. #2672C22semidirect
86. #2672C22semidirect
87. #2663C22semidirect
88. #2629C22semidirect
89. #2625C22semidirect
90. #2622C22semidirect
91. #2621C22semidirect
94. #2616C22semidirect
95. #2616C22semidirect
96. #2591C22semidirect
97. #2583C22semidirect
98. #2562C22semidirect
99. #2559C22semidirect
100. #2558C22semidirect
101. #2556C22semidirect
102. #2551C22semidirect
103. #2542C22semidirect
104. #2538C22semidirect
105. #2536C22semidirect
106. #2521C22semidirect
107. #2491C22semidirect
108. #2487C22semidirect
109. #2485C22semidirect
111. #2478C22semidirect
112. #2476C22semidirect
113. #2476C22semidirect
114. #2475C22semidirect
115. #2474C22semidirect
116. #2473C22semidirect
117. #2472C22semidirect
118. #2470C22semidirect
119. #2445C22semidirect
120. #2443C22semidirect
121. #2440C22semidirect
124. #2434C22semidirect
125. #2434C22semidirect
128. #2432C22semidirect
129. #2432C22semidirect
130. #2422C22semidirect
131. #2418C22semidirect
132. #2417C22semidirect
133. #2415C22semidirect
134. #2415C22semidirect
135. #2415C22semidirect
136. #2409C22semidirect
137. #2409C22semidirect
140. #2406C22semidirect
141. #2406C22semidirect
144. #2405C22semidirect
145. #2405C22semidirect
146. #2375C22semidirect
147. #2374C22semidirect
148. #2354C22semidirect
149. #2352C22semidirect
150. #2333C22semidirect
151. #2332C22semidirect
152. #2323C22semidirect
153. #2314C22semidirect
156. #2311C22semidirect
157. #2311C22semidirect
158. C4×C22⋊Q8C22semidirect
159. #2280C22semidirect
160. #2280C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
C2×#34492
#513262
#508672
#501652
#487732
#464292
#464262
#463592
#463582
#394632
#393432
#378472
#376512
#374382
#373752
#373742
#353102
#353052
#343612