Subgroups — #11773076

Order 1152.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10590141	C₂	1	1	yes	maximal, characteristic
2	#10590139	C₂	1	1	yes	maximal, characteristic
3	#10589313	C₂	1	1	yes	maximal, characteristic
4	#63771	—	2	1	no	—
5	#63769	—	2	1	no	—
6	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃²×C₃₂	C₄	1	1	yes	characteristic, complemented
8	C₃⋊(C₃⋊C₃₂)	C₄	1	1	yes	characteristic, complemented
9	#4447	—	6	2	no	—
10	C₄⋊#157	—	4	1	no	—
11	#3788	—	4	1	no	—
12	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
13	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
15	#1426	—	9	1	no	maximal, Sylow
16	D₃×C₁₆	—	6	2	no	—
17	C₃×C₃₂	—	2	2	no	—
18	C₃⋊C₃₂	—	6	2	no	—
19	C₂×#157	—	8	1	no	—
20	C₄×C₃⋊D₃	D₈	1	1	yes	characteristic
21	#622	—	8	1	no	—
22	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	Q₁₆	1	1	yes	characteristic
24	M₆₄	—	9	1	no	—
25	#368	—	9	1	no	—
26	#367	—	9	1	no	—
27	D₃×C₈	—	6	2	no	—
28	C₃×C₁₆	—	2	2	no	—
29	C₃⋊C₁₆	—	6	2	no	—
30	C₂×C₃⋊D₃	SD₃₂	1	1	yes	characteristic
31	#157	—	16	1	no	—
32	C₃²×C₄	#107	1	1	yes	characteristic
33	C₃⋊Dic₃	SD₃₂	1	1	yes	characteristic
34	C₂×C₁₆	—	9	1	no	—
35	#108	—	18	1	no	—
36	#107	—	18	1	no	—
37	C₃₂	—	9	1	no	—
38	C₃₂	#157	1	1	yes	characteristic, complemented
39	C₄×D₃	—	6	2	no	—
40	C₃×C₈	—	2	2	no	—
41	C₃⋊C₈	—	6	2	no	—
42	C₂×C₃²	#367	1	1	yes	characteristic
43	C₃⋊D₃	—	2	1	no	—
44	M₁₆	—	36	1	no	—
45	C₂×C₈	—	9	1	no	—
46	C₄⋊C₄	—	36	1	no	—
47	C₁₆	—	9	1	no	—
48	C₁₆	C₂×#157	1	1	yes	characteristic
49	C₂×D₃	—	6	2	no	—
50	C₃×C₄	—	2	2	no	—
51	Dic₃	—	6	2	no	—
52	C₃²	#1426	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄	—	9	1	no	—
54	C₂×C₄	—	72	1	no	—
55	C₈	—	9	1	no	—
56	C₈	—	72	1	no	—
57	C₈	C₄⋊#157	1	1	yes	characteristic
58	C₂×C₃	—	2	2	no	—
59	D₃	—	12	2	no	—
60	C₂²	—	9	1	no	—
61	C₄	—	9	1	no	—
62	C₄	—	144	1	no	—
63	C₄	#63769	1	1	yes	characteristic
64	C₃	—	2	2	no	—
65	C₂	—	18	1	no	—
66	C₂	#10590139	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10590139
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₁₆	C₂×#157
Fitting	C₃²×C₃₂	C₄
socle	C₂×C₃²	#367
prime radical	C₂×C₃⋊D₃	SD₃₂
cosocle	C₁₆×C₃⋊D₃	C₂²
hypercenter	C₃₂	#157
hypocenter	C₃²	#1426
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
7. C₃²×C₃₂	C₄	semidirect
8. C₃⋊(C₃⋊C₃₂)	C₄	semidirect
38. C₃₂	#157	semidirect
52. C₃²	#1426	semidirect

Maximal subgroups

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

subgroup	index
#10590141	2
#10590139	2
#10589313	2
#1426	9