Subgroups — #11773059

Order 1152.

150 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	#10589372	C₂	1	2	yes	maximal
3	#67593	—	3	4	no	maximal
4	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
5	#63646	—	2	2	no	—
6	C₃²×C₃₂	C₄	1	2	yes	—
7	C₂×C₃×C₃₂	D₃	1	4	yes	—
8	#4506	—	3	8	no	—
9	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
10	#3748	—	4	2	no	—
11	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₁₆	Q₈	1	1	yes	characteristic
13	#1425	—	9	1	no	Sylow
14	C₂×C₃×C₁₆	C₂×D₃	1	4	yes	—
15	#819	—	6	8	no	—
16	C₃×C₃₂	Dic₃	1	8	yes	—
17	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
18	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
19	C₃²×C₈	Q₁₆	1	1	yes	characteristic
20	C₃⋊(C₃⋊C₈)	—	8	2	no	—
21	C₂×C₃₂	C₃⋊D₃	1	1	yes	characteristic
22	#368	—	9	2	no	—
23	C₂×C₃×C₈	D₁₂	1	4	yes	—
24	#208	—	12	8	no	—
25	C₃×C₁₆	Dic₆	1	4	yes	—
26	C₃×C₁₆	C₂×Dic₃	1	4	yes	—
27	C₂²×C₃²	Q₃₂	1	1	yes	characteristic
28	C₃²×C₄	#107	1	1	yes	characteristic
29	C₃²×C₄	D₁₆	1	1	yes	characteristic
30	C₂×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
31	#108	—	18	2	no	—
32	C₃₂	C₃⋊Dic₃	1	2	yes	—
33	C₂×C₃×C₄	D₂₄	1	4	yes	—
34	C₃×C₈	Dic₁₂	1	4	yes	—
35	C₃×C₈	C₄⋊Dic₃	1	4	yes	—
36	C₃⋊C₈	—	24	8	no	—
37	C₂×C₃²	—	2	1	no	—
38	C₂×C₃²	#366	1	1	yes	characteristic
39	M₁₆	—	36	2	no	—
40	C₂×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
41	C₁₆	#634	1	1	yes	characteristic
42	C₁₆	C₂×C₃⋊Dic₃	1	1	yes	characteristic
43	C₂²×C₃	Dic₂₄	1	4	yes	—
44	C₃×C₄	D₄₈	1	4	yes	—
45	C₃×C₄	#818	1	4	yes	—
46	C₃²	#1425	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	#3745	1	1	yes	characteristic
48	C₈	—	72	2	no	—
49	C₈	#3746	1	1	yes	characteristic
50	C₈	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
51	C₂×C₃	—	2	4	no	—
52	C₂×C₃	#4504	1	4	yes	—
53	C₂²	#63628	1	1	yes	characteristic
54	C₄	#63626	1	1	yes	characteristic
55	C₄	#63645	1	1	yes	characteristic
56	C₃	#67593	1	4	yes	complemented
57	C₂	—	2	1	no	—
58	C₂	#10589370	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#63626
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×C₃⋊D₃
Fitting	C₂×C₃²×C₃₂	C₂
socle	C₂×C₃²	#366
prime radical	C₂²×C₃²	Q₃₂
cosocle	C₂×C₃²×C₁₆	C₂²
hypercenter	C₂×C₃₂	C₃⋊D₃
hypocenter	C₃²	#1425
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
46. C₃²	#1425	semidirect
56. C₃	#67593	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
#10589372	2
#67593	3