Subgroups — #11772663

Order 1152.

102 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	#10590132	C₂	1	1	yes	maximal, characteristic
3	C₃⋊D₃×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₈×#157	C₄	1	1	yes	characteristic
5	#63764	C₄	1	1	yes	characteristic
6	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	#63540	C₄	1	2	yes	complemented
8	C₃²×C₃₂	C₄	1	1	yes	characteristic, complemented
9	C₃⋊(C₃⋊C₃₂)	C₄	1	1	yes	characteristic, complemented
10	D₃×C₃₂	—	6	2	no	—
11	C₄×#157	C₈	1	1	yes	characteristic
12	#3787	C₈	1	1	yes	characteristic
13	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
14	#3708	C₈	1	2	yes	—
15	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	1	yes	characteristic
17	#1397	—	9	1	no	maximal, Sylow
18	D₃×C₁₆	—	6	2	no	—
19	C₃×C₃₂	—	2	2	no	—
20	C₃⋊C₃₂	—	6	2	no	—
21	C₂×#157	C₁₆	1	2	yes	—
22	C₄×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
23	#622	C₁₆	1	2	yes	—
24	C₃²×C₈	C₄²	1	1	yes	characteristic
25	C₃⋊(C₃⋊C₈)	C₂×C₈	1	1	yes	characteristic
26	C₂×C₃₂	—	9	1	no	—
27	C₂×C₃₂	—	9	1	no	—
28	C₄×C₁₆	—	9	1	no	—
29	D₃×C₈	—	6	2	no	—
30	C₃×C₁₆	—	2	2	no	—
31	C₃⋊C₁₆	—	6	2	no	—
32	C₂×C₃⋊D₃	C₂×C₁₆	1	1	yes	characteristic
33	#157	—	2	2	no	—
34	C₃²×C₄	C₄×C₈	1	1	yes	characteristic
35	C₃⋊Dic₃	C₂×C₁₆	1	1	yes	characteristic
36	C₂×C₁₆	—	9	1	no	—
37	C₂×C₁₆	—	9	1	no	—
38	C₄×C₈	—	9	1	no	—
39	C₃₂	—	9	2	no	—
40	C₃₂	—	9	1	no	—
41	C₃₂	#157	1	1	yes	characteristic, complemented
42	C₄×D₃	—	6	2	no	—
43	C₃×C₈	—	2	2	no	—
44	C₃⋊C₈	—	6	2	no	—
45	C₂×C₃²	C₄×C₁₆	1	1	yes	characteristic
46	C₃⋊D₃	M₆₄	1	2	yes	—
47	C₂×C₈	—	9	1	no	—
48	C₂×C₈	—	9	1	no	—
49	C₄²	—	9	1	no	—
50	C₁₆	—	9	2	no	—
51	C₁₆	—	9	1	no	—
52	C₁₆	C₂×#157	1	1	yes	characteristic
53	C₂×D₃	—	6	2	no	—
54	C₃×C₄	—	2	2	no	—
55	Dic₃	—	6	2	no	—
56	C₃²	#1397	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	9	1	no	—
58	C₂×C₄	—	9	2	no	—
59	C₈	—	9	2	no	—
60	C₈	—	9	1	no	—
61	C₈	C₄×#157	1	1	yes	characteristic
62	C₂×C₃	—	2	2	no	—
63	D₃	—	6	4	no	—
64	C₂²	—	9	1	no	—
65	C₄	—	9	1	no	—
66	C₄	—	18	2	no	—
67	C₄	C₈×#157	1	1	yes	characteristic
68	C₃	—	2	2	no	—
69	C₂	—	9	2	no	—
70	C₂	C₁₆×#157	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂×#157
commutator, socle	C₂×C₃²	C₄×C₁₆
Fitting	C₃²×C₃₂	C₄
prime radical	C₂×C₃⋊D₃	C₂×C₁₆
cosocle	C₁₆×C₃⋊D₃	C₂²
hypercenter	C₃₂	#157
hypocenter	C₃²	#1397
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #63540	C₄	semidirect
8. C₃²×C₃₂	C₄	semidirect
9. C₃⋊(C₃⋊C₃₂)	C₄	semidirect
41. C₃₂	#157	semidirect
56. C₃²	#1397	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
#10590132	2
C₃⋊D₃×C₃₂	2
#1397	9