Subgroups — #11773048

Order 1152.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#10589370	C₂	1	2	yes	maximal
3	#67592	—	3	4	no	maximal
4	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
5	#63645	—	2	2	no	—
6	C₃²×C₃₂	C₄	1	2	yes	complemented
7	C₂×C₃×C₃₂	D₃	1	4	yes	—
8	#4504	—	3	8	no	—
9	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
10	C₄⋊(C₃⋊Dic₃)	—	4	2	no	—
11	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₁₆	Q₈	1	1	yes	characteristic
13	#1424	—	9	1	no	Sylow
14	C₂×C₃×C₁₆	C₂×D₃	1	4	yes	—
15	#818	—	6	8	no	—
16	C₃×C₃₂	Dic₃	1	8	yes	complemented
17	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
18	C₂×C₃⋊Dic₃	—	8	2	no	—
19	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
20	C₃²×C₈	Q₁₆	1	1	yes	characteristic
21	C₂×C₃₂	C₃⋊D₃	1	1	yes	characteristic
22	#366	—	9	2	no	—
23	C₂×C₃×C₈	D₁₂	1	4	yes	—
24	C₄⋊Dic₃	—	12	8	no	—
25	C₃×C₁₆	Dic₆	1	4	yes	—
26	C₃×C₁₆	C₂×Dic₃	1	4	yes	—
27	C₂²×C₃²	D₁₆	1	1	yes	characteristic
28	C₃²×C₄	#107	1	1	yes	characteristic
29	C₃²×C₄	Q₃₂	1	1	yes	characteristic
30	C₃⋊Dic₃	—	16	2	no	—
31	C₂×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
32	#107	—	18	2	no	—
33	C₃₂	C₃⋊Dic₃	1	2	yes	complemented
34	C₂×C₃×C₄	D₂₄	1	4	yes	—
35	C₂×Dic₃	—	24	8	no	—
36	C₃×C₈	Dic₁₂	1	4	yes	—
37	C₃×C₈	C₄⋊Dic₃	1	4	yes	—
38	C₂×C₃²	#366	1	1	yes	characteristic
39	C₂×C₃²	SD₆₄	1	2	yes	—
40	C₂×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
41	C₄⋊C₄	—	36	2	no	—
42	C₁₆	#634	1	1	yes	characteristic
43	C₁₆	C₂×C₃⋊Dic₃	1	1	yes	characteristic
44	C₂²×C₃	D₄₈	1	4	yes	—
45	C₃×C₄	Dic₂₄	1	4	yes	—
46	C₃×C₄	#818	1	4	yes	—
47	Dic₃	—	48	8	no	—
48	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄	—	72	2	no	—
50	C₂×C₄	#3745	1	1	yes	characteristic
51	C₈	#3746	1	1	yes	characteristic
52	C₈	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
53	C₂×C₃	#4449	1	8	yes	—
54	C₂×C₃	#4504	1	4	yes	—
55	C₂²	#63626	1	1	yes	characteristic
56	C₄	—	144	2	no	—
57	C₄	#63628	1	1	yes	characteristic
58	C₄	#63645	1	1	yes	characteristic
59	C₃	#67592	1	4	yes	complemented
60	C₂	#10589315	1	2	yes	—
61	C₂	#10589370	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63626
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×C₃⋊D₃
Fitting	C₂×C₃²×C₃₂	C₂
socle, prime radical	C₂²×C₃²	D₁₆
cosocle	C₂×C₃²×C₁₆	C₂²
hypercenter	C₂×C₃₂	C₃⋊D₃
hypocenter	C₃²	#1424
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. C₃²×C₃₂	C₄	semidirect
16. C₃×C₃₂	Dic₃	semidirect
33. C₃₂	C₃⋊Dic₃	semidirect
48. C₃²	#1424	semidirect
59. C₃	#67592	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₃₂	2
#10589370	2
#67592	3