Subgroups — #11773061

Order 1152.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590140	C₂	1	2	yes	maximal
2	C₃⋊D₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#63771	—	2	2	no	—
4	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃²×C₃₂	C₄	1	1	yes	characteristic
6	C₃⋊(C₃⋊C₃₂)	C₄	1	1	yes	characteristic
7	D₃×C₃₂	—	6	2	no	—
8	#3788	—	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	#1425	—	9	1	no	maximal, Sylow
13	D₃×C₁₆	—	6	2	no	—
14	C₃×C₃₂	—	2	2	no	—
15	C₃⋊C₃₂	—	6	2	no	—
16	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
17	#622	—	8	2	no	—
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	#368	—	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	Q₃₂	1	1	yes	characteristic
26	C₃²×C₄	#107	1	1	yes	characteristic
27	C₃⋊Dic₃	D₁₆	1	1	yes	characteristic
28	C₂×C₁₆	—	9	1	no	—
29	#108	—	18	2	no	—
30	C₃₂	—	9	1	no	—
31	C₃₂	#157	1	1	yes	characteristic
32	C₄×D₃	—	6	2	no	—
33	C₃×C₈	—	2	2	no	—
34	C₃⋊C₈	—	6	2	no	—
35	C₂×C₃²	#366	1	1	yes	characteristic
36	C₃⋊D₃	—	2	1	no	—
37	M₁₆	—	36	2	no	—
38	C₂×C₈	—	9	1	no	—
39	C₁₆	—	9	1	no	—
40	C₁₆	C₂×#157	1	1	yes	characteristic
41	C₂×D₃	—	6	2	no	—
42	C₃×C₄	—	2	2	no	—
43	Dic₃	—	6	2	no	—
44	C₃²	#1425	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄	—	9	1	no	—
46	C₈	—	9	1	no	—
47	C₈	—	72	2	no	—
48	C₈	C₄⋊#157	1	1	yes	characteristic
49	C₂×C₃	—	2	2	no	—
50	D₃	—	6	4	no	—
51	C₂²	—	9	1	no	—
52	C₄	—	9	1	no	—
53	C₄	#63769	1	1	yes	characteristic
54	C₃	—	2	2	no	—
55	C₂	—	18	1	no	—
56	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	Q₃₂
cosocle	C₁₆×C₃⋊D₃	C₂²
hypercenter	C₃₂	#157
hypocenter	C₃²	#1425
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
44. C₃²	#1425	semidirect

Maximal subgroups

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

subgroup	index
#10590140	2
C₃⋊D₃×C₃₂	2
#1425	9