Subgroups — #11782555

Order 1152.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588362	C₂	1	2	yes	maximal
2	#10588361	C₂	1	4	yes	maximal
3	C₈²×C₉	C₂	1	1	yes	maximal, characteristic
4	#68064	—	3	1	no	maximal
5	#63431	C₂²	1	4	yes	—
6	C₄×C₈×C₉	C₂²	1	2	yes	—
7	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
8	#63378	—	2	4	no	—
9	#63376	—	2	8	no	—
10	#4682	—	3	2	no	—
11	#4681	—	3	4	no	—
12	C₃×C₈²	D₃	1	1	yes	characteristic
13	C₂×Dic₁₈	—	2	4	no	—
14	C₂×C₈×C₉	D₄	1	4	yes	—
15	C₂×C₈×C₉	D₄	1	2	yes	—
16	C₄²×C₉	C₂³	1	1	yes	characteristic
17	C₄⋊Dic₉	—	2	4	no	—
18	C₄⋊Dic₉	—	2	4	no	—
19	#1710	—	9	1	no	Sylow
20	#869	—	3	4	no	—
21	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
22	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
23	#818	—	6	4	no	—
24	#816	—	6	8	no	—
25	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
26	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
27	C₂×Dic₉	—	4	4	no	—
28	Dic₁₈	—	4	8	no	—
29	C₈×C₉	—	2	4	no	—
30	C₈×C₉	Q₁₆	1	4	yes	—
31	#500	—	9	2	no	—
32	#487	—	9	4	no	—
33	C₈²	D₉	1	1	yes	characteristic
34	C₂×Dic₆	—	6	4	no	—
35	C₂×C₃×C₈	D₁₂	1	4	yes	—
36	C₂×C₃×C₈	D₁₂	1	2	yes	—
37	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
38	C₄⋊Dic₃	—	6	4	no	—
39	C₄⋊Dic₃	—	6	4	no	—
40	C₂²×C₉	#127	1	1	yes	characteristic
41	C₄×C₉	C₂×Q₁₆	1	2	yes	—
42	C₄×C₉	#135	1	4	yes	—
43	Dic₉	—	8	4	no	—
44	C₄⋊Q₈	—	9	4	no	—
45	#107	—	18	4	no	—
46	#103	—	18	8	no	—
47	C₄×C₈	C₂×D₉	1	2	yes	—
48	C₄×C₈	C₂×D₉	1	1	yes	characteristic
49	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
50	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
51	C₂×Dic₃	—	12	4	no	—
52	Dic₆	—	12	8	no	—
53	C₃×C₈	—	2	4	no	—
54	C₃×C₈	Dic₁₂	1	4	yes	—
55	C₂×C₉	#494	1	1	yes	characteristic
56	C₂×C₉	#495	1	2	yes	—
57	C₂×Q₈	—	18	4	no	—
58	C₂×C₈	D₃₆	1	4	yes	—
59	C₂×C₈	D₃₆	1	2	yes	—
60	C₄⋊C₄	—	18	4	no	—
61	C₄⋊C₄	—	18	4	no	—
62	C₄²	C₂²×D₉	1	1	yes	characteristic
63	C₂²×C₃	#874	1	1	yes	characteristic
64	C₃×C₄	#904	1	4	yes	—
65	C₃×C₄	C₂×Dic₁₂	1	2	yes	—
66	Dic₃	—	24	4	no	—
67	C₉	#1710	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	36	8	no	—
69	C₂×C₄	—	36	4	no	—
70	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
71	C₂×C₄	C₂×D₃₆	1	2	yes	—
72	C₈	—	2	4	no	—
73	C₈	Dic₃₆	1	4	yes	—
74	C₂×C₃	#4696	1	2	yes	—
75	C₂×C₃	#4699	1	1	yes	characteristic
76	C₂²	#63436	1	1	yes	characteristic
77	C₄	—	72	4	no	—
78	C₄	C₂×Dic₃₆	1	2	yes	—
79	C₄	#63467	1	4	yes	—
80	C₃	#68064	1	1	yes	characteristic
81	C₂	#10588365	1	1	yes	characteristic
82	C₂	#10588378	1	2	yes	—

	subgroup	G/H
center	C₂²	#63436
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₈²×C₉	C₂
socle, prime radical	C₂²×C₃	#874
hypercenter	C₈²	D₉
hypocenter	C₉	#1710
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
67. C₉	#1710	semidirect

Maximal subgroups

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

subgroup	index
#10588362	2
#10588361	2
C₈²×C₉	2
#68064	3