Subgroups — #11782588

Order 1152.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592394	C₂	1	6	yes	maximal, complemented
2	C₃²×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	#68062	—	3	4	no	maximal
4	C₂×#3745	—	2	12	no	—
5	#64083	C₂²	1	4	yes	—
6	C₃²×C₄×C₈	C₂²	1	3	yes	—
7	#4695	—	3	24	no	—
8	C₃×C₈²	D₃	1	4	yes	complemented
9	C₂×C₄⋊(C₃⋊D₃)	—	2	12	no	—
10	C₂×C₃²×C₈	D₄	1	6	yes	—
11	C₃²×C₄²	C₂³	1	1	yes	characteristic
12	#3745	—	4	24	no	—
13	#1712	—	9	1	no	Sylow
14	C₂×D₂₄	—	6	48	no	—
15	#874	—	3	16	no	—
16	C₃×C₄×C₈	C₂×D₃	1	12	yes	—
17	C₂²×C₃⋊D₃	—	4	4	no	—
18	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
19	C₄⋊(C₃⋊D₃)	—	4	24	no	—
20	C₃²×C₈	D₈	1	12	yes	complemented
21	#493	—	9	6	no	—
22	C₈²	C₃⋊D₃	1	1	yes	characteristic, complemented
23	C₂×D₁₂	—	6	48	no	—
24	C₂×C₃×C₈	D₁₂	1	24	yes	—
25	C₃×C₄²	C₂²×D₃	1	4	yes	—
26	D₂₄	—	12	96	no	—
27	C₂²×C₃²	#127	1	1	yes	characteristic
28	C₂×C₃⋊D₃	—	8	12	no	—
29	C₃²×C₄	C₂×D₈	1	6	yes	—
30	C₂×D₈	—	18	12	no	—
31	#127	—	9	4	no	—
32	C₄×C₈	C₂×C₃⋊D₃	1	3	yes	—
33	C₂²×D₃	—	12	16	no	—
34	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	—
35	D₁₂	—	12	96	no	—
36	C₃×C₈	D₂₄	1	48	yes	complemented
37	C₂×C₃²	#493	1	3	yes	—
38	C₃⋊D₃	—	16	4	no	—
39	C₂×D₄	—	18	12	no	—
40	D₈	—	36	24	no	—
41	C₂×C₈	C₄⋊(C₃⋊D₃)	1	6	yes	—
42	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
43	C₂²×C₃	#874	1	4	yes	—
44	C₂×D₃	—	24	48	no	—
45	C₃×C₄	C₂×D₂₄	1	24	yes	—
46	C₃²	#1712	1	1	yes	characteristic, complemented, Sylow
47	C₂³	—	36	4	no	—
48	D₄	—	36	24	no	—
49	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	3	yes	—
50	C₈	#3745	1	12	yes	complemented
51	C₂×C₃	#4695	1	12	yes	—
52	D₃	—	48	16	no	—
53	C₂²	—	72	12	no	—
54	C₂²	#64083	1	1	yes	characteristic
55	C₄	C₂×#3745	1	6	yes	—
56	C₃	#68062	1	4	yes	complemented
57	C₂	—	144	4	no	—
58	C₂	#10592394	1	3	yes	—

	subgroup	G/H
center	C₂²	#64083
commutator, cosocle	C₃²×C₄²	C₂³
Frattini	C₄²	C₂²×C₃⋊D₃
Fitting	C₃²×C₈²	C₂
socle	C₂²×C₃²	#127
hypercenter	C₈²	C₃⋊D₃
hypocenter	C₃²	#1712
LCS	G ▷ C₃²×C₄² ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #10592394	C₂	semidirect
2. C₃²×C₈²	C₂	semidirect
8. C₃×C₈²	D₃	semidirect
20. C₃²×C₈	D₈	semidirect
22. C₈²	C₃⋊D₃	semidirect
36. C₃×C₈	D₂₄	semidirect
46. C₃²	#1712	semidirect
50. C₈	#3745	semidirect
56. C₃	#68062	semidirect

Maximal subgroups

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

subgroup	index
#10592394	2
C₃²×C₈²	2
#68062	3