Subgroups — #11857069

Order 1152.

1908 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63436	C₂	1	14	yes	maximal, complemented
2	C₄³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#73318	—	3	1	no	maximal
4	C₂²×D₃₆	C₂²	1	28	yes	—
5	C₂×C₄²×C₉	C₂²	1	7	yes	—
6	#63436	—	2	56	no	—
7	C₂×#874	—	3	14	no	—
8	C₃×C₄³	D₃	1	1	yes	characteristic
9	C₂³×D₉	C₂³	1	8	yes	—
10	C₂²×C₄×C₉	C₂³	1	7	yes	—
11	C₂×D₃₆	—	2	168	no	—
12	C₄²×C₉	D₄	1	28	yes	complemented
13	#2867	—	9	1	no	Sylow
14	C₂²×D₁₂	—	3	28	no	—
15	C₂×C₃×C₄²	C₂×D₃	1	7	yes	—
16	#874	—	6	56	no	—
17	C₂³×C₉	C₂⁴	1	1	yes	characteristic
18	C₂²×D₉	—	2	56	no	—
19	C₂×C₄×C₉	C₂×D₄	1	42	yes	—
20	D₃₆	—	4	112	no	—
21	C₂×#127	—	9	14	no	—
22	C₄³	D₉	1	1	yes	characteristic, complemented
23	C₂³×D₃	—	3	8	no	—
24	C₂²×C₃×C₄	C₂²×D₃	1	7	yes	—
25	C₂×D₁₂	—	6	168	no	—
26	C₃×C₄²	D₁₂	1	28	yes	—
27	C₂²×C₉	C₂²×D₄	1	7	yes	—
28	C₂×D₉	—	4	56	no	—
29	C₄×C₉	#127	1	28	yes	complemented
30	C₂²×D₄	—	9	28	no	—
31	#127	—	18	56	no	—
32	C₂×C₄²	C₂×D₉	1	7	yes	—
33	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
34	C₂²×D₃	—	6	56	no	—
35	C₂×C₃×C₄	C₂×D₁₂	1	42	yes	—
36	D₁₂	—	12	112	no	—
37	C₂×C₉	C₂×#127	1	7	yes	—
38	D₉	—	8	8	no	—
39	C₂⁴	—	9	8	no	—
40	C₂×D₄	—	18	168	no	—
41	C₂²×C₄	C₂²×D₉	1	7	yes	—
42	C₄²	D₃₆	1	28	yes	complemented
43	C₂²×C₃	C₂²×D₁₂	1	7	yes	—
44	C₂×D₃	—	12	56	no	—
45	C₃×C₄	#874	1	28	yes	—
46	C₉	#2867	1	1	yes	characteristic, complemented, Sylow
47	C₂³	—	18	56	no	—
48	C₂³	C₂³×D₉	1	1	yes	characteristic
49	D₄	—	36	112	no	—
50	C₂×C₄	C₂×D₃₆	1	42	yes	—
51	C₂×C₃	C₂×#874	1	7	yes	—
52	D₃	—	24	8	no	—
53	C₂²	—	36	56	no	—
54	C₂²	C₂²×D₃₆	1	7	yes	—
55	C₄	#63436	1	28	yes	complemented
56	C₃	#73318	1	1	yes	characteristic
57	C₂	—	72	8	no	—
58	C₂	C₂×#63436	1	7	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂³×C₉	C₂⁴
Frattini, socle	C₂³×C₃	C₂³×D₃
Fitting	C₄³×C₉	C₂
hypercenter	C₄³	D₉
hypocenter	C₉	#2867
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
1. C₂×#63436	C₂	semidirect
2. C₄³×C₉	C₂	semidirect
12. C₄²×C₉	D₄	semidirect
22. C₄³	D₉	semidirect
29. C₄×C₉	#127	semidirect
42. C₄²	D₃₆	semidirect
46. C₉	#2867	semidirect
55. C₄	#63436	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63436	2
C₄³×C₉	2
#73318	3