Subgroups — #11773050

Order 1152.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590138	C₂	1	2	yes	maximal
2	C₃⋊D₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#63769	—	2	2	no	—
4	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃²×C₃₂	C₄	1	1	yes	characteristic, complemented
6	C₃⋊(C₃⋊C₃₂)	C₄	1	1	yes	characteristic, complemented
7	D₃×C₃₂	—	6	2	no	—
8	C₄⋊#157	—	4	2	no	—
9	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
10	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
12	#1424	—	9	1	no	maximal, Sylow
13	D₃×C₁₆	—	6	2	no	—
14	C₃×C₃₂	—	2	2	no	—
15	C₃⋊C₃₂	—	6	2	no	—
16	C₂×#157	—	8	2	no	—
17	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
18	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
19	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
20	C₂×C₃₂	—	9	1	no	—
21	#366	—	9	2	no	—
22	D₃×C₈	—	6	2	no	—
23	C₃×C₁₆	—	2	2	no	—
24	C₃⋊C₁₆	—	6	2	no	—
25	C₂×C₃⋊D₃	D₁₆	1	1	yes	characteristic
26	#157	—	16	2	no	—
27	C₃²×C₄	#107	1	1	yes	characteristic
28	C₃⋊Dic₃	Q₃₂	1	1	yes	characteristic
29	C₂×C₁₆	—	9	1	no	—
30	#107	—	18	2	no	—
31	C₃₂	—	9	1	no	—
32	C₃₂	#157	1	1	yes	characteristic, complemented
33	C₄×D₃	—	6	2	no	—
34	C₃×C₈	—	2	2	no	—
35	C₃⋊C₈	—	6	2	no	—
36	C₂×C₃²	#366	1	1	yes	characteristic
37	C₃⋊D₃	SD₆₄	1	2	yes	—
38	C₂×C₈	—	9	1	no	—
39	C₄⋊C₄	—	36	2	no	—
40	C₁₆	—	9	1	no	—
41	C₁₆	C₂×#157	1	1	yes	characteristic
42	C₂×D₃	—	6	2	no	—
43	C₃×C₄	—	2	2	no	—
44	Dic₃	—	6	2	no	—
45	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₄	—	9	1	no	—
47	C₂×C₄	—	72	2	no	—
48	C₈	—	9	1	no	—
49	C₈	C₄⋊#157	1	1	yes	characteristic
50	C₂×C₃	—	2	2	no	—
51	D₃	—	6	4	no	—
52	C₂²	—	9	1	no	—
53	C₄	—	9	1	no	—
54	C₄	—	144	2	no	—
55	C₄	#63769	1	1	yes	characteristic
56	C₃	—	2	2	no	—
57	C₂	—	9	2	no	—
58	C₂	#10590138	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10590138
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₁₆	C₂×#157
Fitting	C₃²×C₃₂	C₄
socle	C₂×C₃²	#366
prime radical	C₂×C₃⋊D₃	D₁₆
cosocle	C₁₆×C₃⋊D₃	C₂²
hypercenter	C₃₂	#157
hypocenter	C₃²	#1424
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃²×C₃₂	C₄	semidirect
6. C₃⋊(C₃⋊C₃₂)	C₄	semidirect
32. C₃₂	#157	semidirect
45. C₃²	#1424	semidirect

Maximal subgroups

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

subgroup	index
#10590138	2
C₃⋊D₃×C₃₂	2
#1424	9