Subgroups — #11773018

Order 1152.

76 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	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	#63540	—	2	2	no	—
7	C₄×#157	C₈	1	1	yes	characteristic
8	#3787	C₈	1	1	yes	characteristic
9	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
10	#3708	—	2	1	no	—
11	C₃²×C₁₆	Q₈	1	1	yes	characteristic
12	C₃⋊(C₃⋊C₁₆)	D₄	1	1	yes	characteristic
13	C₄⋊C₃₂	—	9	1	no	maximal, Sylow
14	D₃×C₁₆	—	12	1	no	—
15	C₂×#157	C₁₆	1	1	yes	characteristic
16	C₂×#157	C₁₆	1	1	yes	characteristic
17	C₄×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
18	#622	—	2	1	no	—
19	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
20	C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
21	C₂×C₃₂	—	9	2	no	—
22	C₄×C₁₆	—	9	1	no	—
23	D₃×C₈	—	12	1	no	—
24	C₃×C₁₆	—	4	1	no	—
25	C₃⋊C₁₆	—	12	1	no	—
26	C₂×C₃⋊D₃	C₂×C₁₆	1	1	yes	characteristic
27	#157	—	2	1	no	—
28	#157	C₃₂	1	2	yes	complemented
29	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
30	C₃⋊Dic₃	M₃₂	1	1	yes	characteristic
31	C₂×C₁₆	—	9	1	no	—
32	C₂×C₁₆	—	9	1	no	—
33	C₄×C₈	—	9	1	no	—
34	C₃₂	—	18	2	no	—
35	C₄×D₃	—	12	1	no	—
36	C₃×C₈	—	4	1	no	—
37	C₃⋊C₈	—	12	1	no	—
38	C₂×C₃²	C₄⋊C₁₆	1	1	yes	characteristic
39	C₃⋊D₃	C₂×C₃₂	1	1	yes	characteristic
40	C₃⋊D₃	M₆₄	1	1	yes	characteristic
41	C₂×C₈	—	9	1	no	—
42	C₂×C₈	—	9	1	no	—
43	C₄²	—	9	1	no	—
44	C₁₆	—	9	1	no	—
45	C₁₆	—	18	1	no	—
46	C₁₆	PSU(3,𝔽₂)	1	1	yes	characteristic
47	C₂×D₃	—	12	1	no	—
48	C₃×C₄	—	4	1	no	—
49	Dic₃	—	12	1	no	—
50	C₃²	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₄	—	9	1	no	—
52	C₂×C₄	—	9	1	no	—
53	C₂×C₄	—	9	1	no	—
54	C₈	—	9	1	no	—
55	C₈	—	18	1	no	—
56	C₈	#3777	1	1	yes	characteristic
57	C₂×C₃	—	4	1	no	—
58	D₃	—	12	1	no	—
59	D₃	—	12	1	no	—
60	C₂²	—	9	1	no	—
61	C₄	—	9	2	no	—
62	C₄	—	9	1	no	—
63	C₄	—	18	1	no	—
64	C₄	#63744	1	1	yes	characteristic
65	C₃	—	4	1	no	—
66	C₂	—	9	1	no	—
67	C₂	—	9	1	no	—
68	C₂	#10590082	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	PSU(3,𝔽₂)
commutator	C₃⋊D₃	C₂×C₃₂
Fitting	C₃²×C₁₆	Q₈
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
28. #157	C₃₂	semidirect
50. 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
#10590132	2
C₄⋊C₃₂	9