Subgroups — #11773017

Order 1152.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×#157	C₂	1	1	yes	maximal, characteristic
2	#10589067	C₂	1	2	yes	maximal
3	C₈×#157	C₄	1	1	yes	characteristic
4	#63764	C₄	1	1	yes	characteristic
5	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃×C₃⋊C₃₂	—	2	2	no	—
7	D₃×C₃₂	—	6	2	no	—
8	C₄×#157	C₈	1	1	yes	characteristic
9	#3787	C₈	1	1	yes	characteristic
10	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
11	#3708	—	2	1	no	—
12	C₃²×C₁₆	D₄	1	1	yes	characteristic
13	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
14	C₄⋊C₃₂	—	9	1	no	maximal, Sylow
15	D₃×C₁₆	—	6	2	no	—
16	C₃×C₃₂	—	6	2	no	—
17	C₃⋊C₃₂	—	2	2	no	—
18	C₂×#157	C₁₆	1	1	yes	characteristic
19	C₂×#157	C₁₆	1	1	yes	characteristic
20	C₄×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
21	#622	—	2	1	no	—
22	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
24	C₂×C₃₂	—	9	2	no	—
25	C₄×C₁₆	—	9	1	no	—
26	D₃×C₈	—	6	2	no	—
27	C₃×C₁₆	—	2	2	no	—
28	C₃⋊C₁₆	—	6	2	no	—
29	C₂×C₃⋊D₃	C₂×C₁₆	1	1	yes	characteristic
30	#157	—	2	1	no	—
31	#157	C₃₂	1	2	yes	complemented
32	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
33	C₃⋊Dic₃	M₃₂	1	1	yes	characteristic
34	C₂×C₁₆	—	9	1	no	—
35	C₂×C₁₆	—	9	1	no	—
36	C₄×C₈	—	9	1	no	—
37	C₃₂	—	6	2	no	—
38	C₄×D₃	—	6	2	no	—
39	C₃×C₈	—	2	2	no	—
40	C₃⋊C₈	—	6	2	no	—
41	C₂×C₃²	C₄⋊C₁₆	1	1	yes	characteristic
42	C₃⋊D₃	C₂×C₃₂	1	1	yes	characteristic
43	C₃⋊D₃	M₆₄	1	1	yes	characteristic
44	C₂×C₈	—	9	1	no	—
45	C₂×C₈	—	9	1	no	—
46	C₄²	—	9	1	no	—
47	C₁₆	—	9	1	no	—
48	C₁₆	—	18	1	no	—
49	C₁₆	GO⁺(4,𝔽₂)	1	1	yes	characteristic
50	C₂×D₃	—	6	2	no	—
51	C₃×C₄	—	2	2	no	—
52	Dic₃	—	6	2	no	—
53	C₃²	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₄	—	9	1	no	—
55	C₂×C₄	—	9	1	no	—
56	C₂×C₄	—	9	1	no	—
57	C₈	—	9	1	no	—
58	C₈	—	18	1	no	—
59	C₈	#3773	1	1	yes	characteristic
60	C₂×C₃	—	2	2	no	—
61	D₃	—	6	2	no	—
62	D₃	—	6	2	no	—
63	C₂²	—	9	1	no	—
64	C₄	—	9	2	no	—
65	C₄	—	9	1	no	—
66	C₄	—	18	1	no	—
67	C₄	#63732	1	1	yes	characteristic
68	C₃	—	2	2	no	—
69	C₂	—	9	1	no	—
70	C₂	—	9	1	no	—
71	C₂	#10590022	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	GO⁺(4,𝔽₂)
commutator	C₃⋊D₃	C₂×C₃₂
Fitting	C₃²×C₁₆	D₄
socle	C₂×C₃²	C₄⋊C₁₆
prime radical	C₂×C₃⋊D₃	C₂×C₁₆
cosocle	C₁₆×C₃⋊D₃	C₂²
hypocenter	C₃²	C₄⋊C₃₂
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
31. #157	C₃₂	semidirect
53. 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
C₁₆×#157	2
#10589067	2
C₄⋊C₃₂	9