Subgroups — #11773054

Order 1152.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590138	C₂	1	2	yes	maximal
2	#10590132	C₂	1	1	yes	maximal, characteristic
3	#63769	—	2	2	no	—
4	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	#63540	C₄	1	2	yes	complemented
6	C₄⋊#157	—	4	2	no	—
7	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
8	C₃²×C₁₆	Q₈	1	1	yes	characteristic
9	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	1	yes	characteristic
10	#1424	—	9	1	no	maximal, Sylow
11	D₃×C₁₆	—	12	1	no	—
12	C₂×#157	—	8	2	no	—
13	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
14	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
15	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
16	C₂×C₃₂	—	9	1	no	—
17	#366	—	9	2	no	—
18	D₃×C₈	—	12	1	no	—
19	C₃×C₁₆	—	4	1	no	—
20	C₃⋊C₁₆	—	12	1	no	—
21	C₂×C₃⋊D₃	D₁₆	1	1	yes	characteristic
22	#157	—	16	2	no	—
23	C₃²×C₄	#107	1	1	yes	characteristic
24	C₃⋊Dic₃	Q₃₂	1	1	yes	characteristic
25	C₂×C₁₆	—	9	1	no	—
26	#107	—	18	2	no	—
27	C₃₂	—	9	2	no	—
28	C₄×D₃	—	12	1	no	—
29	C₃×C₈	—	4	1	no	—
30	C₃⋊C₈	—	12	1	no	—
31	C₂×C₃²	#366	1	1	yes	characteristic
32	C₃⋊D₃	SD₆₄	1	2	yes	—
33	C₂×C₈	—	9	1	no	—
34	C₄⋊C₄	—	36	2	no	—
35	C₁₆	—	9	1	no	—
36	C₁₆	PSU(3,𝔽₂)	1	1	yes	characteristic
37	C₂×D₃	—	12	1	no	—
38	C₃×C₄	—	4	1	no	—
39	Dic₃	—	12	1	no	—
40	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₄	—	9	1	no	—
42	C₂×C₄	—	72	2	no	—
43	C₈	—	9	1	no	—
44	C₈	#3777	1	1	yes	characteristic
45	C₂×C₃	—	4	1	no	—
46	D₃	—	12	2	no	—
47	C₂²	—	9	1	no	—
48	C₄	—	9	1	no	—
49	C₄	—	144	2	no	—
50	C₄	#63746	1	1	yes	characteristic
51	C₃	—	4	1	no	—
52	C₂	—	9	2	no	—
53	C₂	#10590085	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10590085
commutator	C₃⋊(C₃⋊C₁₆)	C₂×C₄
Frattini, hypercenter	C₁₆	PSU(3,𝔽₂)
Fitting	C₃²×C₁₆	Q₈
socle	C₂×C₃²	#366
prime radical	C₂×C₃⋊D₃	D₁₆
cosocle	C₁₆×C₃⋊D₃	C₂²
hypocenter	C₃²	#1424
LCS	G ▷ C₃⋊(C₃⋊C₁₆) ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
5. #63540	C₄	semidirect
40. 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
#10590132	2
#1424	9