Subgroups — #11773012

Order 1152.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63540	C₂	1	2	yes	maximal
2	C₁₆×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₁₆	C₄	1	1	yes	characteristic
4	C₈×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
6	#63540	—	2	2	no	—
7	Dic₃×C₁₆	—	6	2	no	—
8	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
9	C₄×C₃⋊Dic₃	C₈	1	1	yes	characteristic
10	C₂×C₃⋊(C₃⋊C₈)	C₈	1	1	yes	characteristic
11	C₃²×C₁₆	—	2	1	no	—
12	C₃⋊(C₃⋊C₁₆)	D₄	1	1	yes	characteristic
13	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
14	C₄⋊C₃₂	—	9	1	no	maximal, Sylow
15	C₂×C₃×C₁₆	—	2	2	no	—
16	C₈×Dic₃	—	6	2	no	—
17	C₂×C₃⋊C₁₆	—	6	2	no	—
18	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃⋊Dic₃	C₁₆	1	1	yes	characteristic
20	C₂×C₃⋊Dic₃	C₁₆	1	1	yes	characteristic
21	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
22	C₃²×C₈	M₁₆	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	—	2	1	no	—
24	C₂×C₃₂	—	9	2	no	—
25	C₄×C₁₆	—	9	1	no	—
26	C₂×C₃×C₈	—	2	2	no	—
27	C₄×Dic₃	—	6	2	no	—
28	C₂×C₃⋊C₈	—	6	2	no	—
29	C₃×C₁₆	—	2	4	no	—
30	C₃⋊C₁₆	—	6	2	no	—
31	C₃⋊C₁₆	—	6	2	no	—
32	C₂²×C₃²	C₂×C₁₆	1	1	yes	characteristic
33	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
34	C₃²×C₄	M₃₂	1	1	yes	characteristic
35	C₃⋊Dic₃	—	2	1	no	—
36	C₃⋊Dic₃	C₃₂	1	2	yes	complemented
37	C₂×C₁₆	—	9	1	no	—
38	C₂×C₁₆	#157	1	1	yes	characteristic
39	C₄×C₈	—	9	1	no	—
40	C₃₂	—	18	2	no	—
41	C₂×C₃×C₄	—	2	2	no	—
42	C₂×Dic₃	—	6	2	no	—
43	C₂×Dic₃	—	6	2	no	—
44	C₃×C₈	—	2	2	no	—
45	C₃×C₈	—	2	2	no	—
46	C₃⋊C₈	—	6	4	no	—
47	C₂×C₃²	C₄⋊C₁₆	1	1	yes	characteristic
48	C₂×C₃²	C₂×C₃₂	1	1	yes	characteristic
49	C₂×C₃²	M₆₄	1	1	yes	characteristic
50	C₂×C₈	—	9	1	no	—
51	C₂×C₈	C₂×#157	1	1	yes	characteristic
52	C₄²	—	9	1	no	—
53	C₁₆	—	2	1	no	—
54	C₁₆	—	9	1	no	—
55	C₁₆	—	9	1	no	—
56	C₂²×C₃	—	2	2	no	—
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	—	2	2	no	—
59	Dic₃	—	6	4	no	—
60	Dic₃	—	6	4	no	—
61	C₃²	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₄	—	9	1	no	—
63	C₂×C₄	—	9	1	no	—
64	C₂×C₄	#3787	1	1	yes	characteristic
65	C₈	—	18	1	no	—
66	C₈	C₄⋊#157	1	1	yes	characteristic
67	C₈	#3792	1	1	yes	characteristic
68	C₂×C₃	—	2	2	no	—
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	—	2	2	no	—
71	C₂²	#63764	1	1	yes	characteristic
72	C₄	—	9	2	no	—
73	C₄	—	18	1	no	—
74	C₄	#63765	1	1	yes	characteristic
75	C₄	#63779	1	1	yes	characteristic
76	C₃	—	2	2	no	—
77	C₂	#10590132	1	1	yes	characteristic
78	C₂	#10590133	1	1	yes	characteristic
79	C₂	#10590177	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#157
commutator	C₂×C₃²	C₂×C₃₂
Fitting	C₂×C₃²×C₁₆	C₄
socle, prime radical	C₂²×C₃²	C₂×C₁₆
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypercenter	C₂×C₁₆	#157
hypocenter	C₃²	C₄⋊C₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
36. C₃⋊Dic₃	C₃₂	semidirect
61. C₃²	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63540	2
C₁₆×C₃⋊Dic₃	2
C₄⋊C₃₂	9