Subgroups — #11857070

Order 1152.

3816 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64083	C₂	1	14	yes	maximal, complemented
2	C₃²×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
3	#73318	—	3	4	no	maximal
4	C₂²×C₄⋊(C₃⋊D₃)	C₂²	1	28	yes	—
5	C₂×C₃²×C₄²	C₂²	1	7	yes	—
6	#64083	—	2	56	no	—
7	C₂×#874	—	3	56	no	—
8	C₃×C₄³	D₃	1	4	yes	complemented
9	C₂³×C₃⋊D₃	C₂³	1	8	yes	—
10	C₂²×C₃²×C₄	C₂³	1	7	yes	—
11	C₂×C₄⋊(C₃⋊D₃)	—	2	168	no	—
12	C₃²×C₄²	D₄	1	28	yes	complemented
13	#2867	—	9	1	no	Sylow
14	C₂²×D₁₂	—	3	112	no	—
15	C₂×C₃×C₄²	C₂×D₃	1	28	yes	—
16	#874	—	6	224	no	—
17	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
18	C₂²×C₃⋊D₃	—	2	56	no	—
19	C₂×C₃²×C₄	C₂×D₄	1	42	yes	—
20	C₄⋊(C₃⋊D₃)	—	4	112	no	—
21	C₂×#127	—	9	14	no	—
22	C₄³	C₃⋊D₃	1	1	yes	characteristic, complemented
23	C₂³×D₃	—	3	32	no	—
24	C₂²×C₃×C₄	C₂²×D₃	1	28	yes	—
25	C₂×D₁₂	—	6	672	no	—
26	C₃×C₄²	D₁₂	1	112	yes	complemented
27	C₂²×C₃²	C₂²×D₄	1	7	yes	—
28	C₂×C₃⋊D₃	—	4	56	no	—
29	C₃²×C₄	#127	1	28	yes	complemented
30	C₂²×D₄	—	9	28	no	—
31	#127	—	18	56	no	—
32	C₂×C₄²	C₂×C₃⋊D₃	1	7	yes	—
33	C₂³×C₃	C₂³×D₃	1	4	yes	—
34	C₂²×D₃	—	6	224	no	—
35	C₂×C₃×C₄	C₂×D₁₂	1	168	yes	—
36	D₁₂	—	12	448	no	—
37	C₂×C₃²	C₂×#127	1	7	yes	—
38	C₃⋊D₃	—	8	8	no	—
39	C₂⁴	—	9	8	no	—
40	C₂×D₄	—	18	168	no	—
41	C₂²×C₄	C₂²×C₃⋊D₃	1	7	yes	—
42	C₄²	C₄⋊(C₃⋊D₃)	1	28	yes	complemented
43	C₂²×C₃	C₂²×D₁₂	1	28	yes	—
44	C₂×D₃	—	12	224	no	—
45	C₃×C₄	#874	1	112	yes	complemented
46	C₃²	#2867	1	1	yes	characteristic, complemented, Sylow
47	C₂³	—	18	56	no	—
48	C₂³	C₂³×C₃⋊D₃	1	1	yes	characteristic
49	D₄	—	36	112	no	—
50	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	42	yes	—
51	C₂×C₃	C₂×#874	1	28	yes	—
52	D₃	—	24	32	no	—
53	C₂²	—	36	56	no	—
54	C₂²	C₂²×C₄⋊(C₃⋊D₃)	1	7	yes	—
55	C₄	#64083	1	28	yes	complemented
56	C₃	#73318	1	4	yes	complemented
57	C₂	—	72	8	no	—
58	C₂	C₂×#64083	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×C₃⋊D₃
commutator, socle, cosocle	C₂³×C₃²	C₂⁴
Fitting	C₃²×C₄³	C₂
hypercenter	C₄³	C₃⋊D₃
hypocenter	C₃²	#2867
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
1. C₂×#64083	C₂	semidirect
2. C₃²×C₄³	C₂	semidirect
8. C₃×C₄³	D₃	semidirect
12. C₃²×C₄²	D₄	semidirect
22. C₄³	C₃⋊D₃	semidirect
26. C₃×C₄²	D₁₂	semidirect
29. C₃²×C₄	#127	semidirect
42. C₄²	C₄⋊(C₃⋊D₃)	semidirect
45. C₃×C₄	#874	semidirect
46. C₃²	#2867	semidirect
55. C₄	#64083	semidirect
56. C₃	#73318	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64083	2
C₃²×C₄³	2
#73318	3