Subgroups — #11772202

Order 1152.

73 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593255	C₂	1	1	yes	maximal, characteristic
2	#10590083	C₂	1	1	yes	maximal, characteristic
3	#10590023	C₂	1	1	yes	maximal, characteristic
4	#64213	C₄	1	1	yes	characteristic
5	#64213	C₄	1	1	yes	characteristic
6	C₈×#157	C₂²	1	1	yes	characteristic
7	#63765	—	2	1	no	—
8	#63544	—	2	1	no	—
9	C₄×#157	Q₈	1	1	yes	characteristic
10	#3787	C₂×C₄	1	1	yes	characteristic
11	#3771	—	2	1	no	—
12	#3771	C₈	1	2	yes	—
13	C₈×C₃⋊D₃	D₄	1	1	yes	characteristic
14	#3708	—	4	1	no	—
15	C₃×C₃⋊C₁₆	—	4	1	no	—
16	#1369	—	9	1	no	maximal, Sylow
17	#798	—	12	1	no	—
18	C₂×#157	—	2	1	no	—
19	C₄×C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
20	#622	C₂×C₈	1	1	yes	characteristic
21	#622	M₁₆	1	1	yes	characteristic
22	C₃²×C₈	SD₁₆	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	SD₁₆	1	1	yes	characteristic
24	#364	—	9	1	no	—
25	#364	—	9	1	no	—
26	#346	—	9	1	no	—
27	D₃×C₈	—	12	1	no	—
28	C₃×C₁₆	—	12	1	no	—
29	C₃⋊C₁₆	—	4	1	no	—
30	C₂×C₃⋊D₃	#108	1	1	yes	characteristic
31	#157	—	4	1	no	—
32	C₃²×C₄	#106	1	1	yes	characteristic
33	C₃⋊Dic₃	C₄⋊C₈	1	1	yes	characteristic
34	M₃₂	—	18	1	no	—
35	M₃₂	—	18	1	no	—
36	C₂×C₁₆	—	9	1	no	—
37	C₂×C₁₆	—	9	1	no	—
38	C₄×C₈	—	9	1	no	—
39	C₄×D₃	—	12	1	no	—
40	C₃×C₈	—	4	1	no	—
41	C₃⋊C₈	—	12	1	no	—
42	C₂×C₃²	#334	1	1	yes	characteristic
43	C₃⋊D₃	—	2	1	no	—
44	C₂×C₈	—	9	1	no	—
45	C₂×C₈	—	9	1	no	—
46	C₄²	—	9	1	no	—
47	C₁₆	—	9	2	no	—
48	C₁₆	—	12	1	no	—
49	C₁₆	—	18	1	no	—
50	C₁₆	—	36	1	no	—
51	C₂×D₃	—	12	1	no	—
52	C₃×C₄	—	4	1	no	—
53	Dic₃	—	12	1	no	—
54	C₃²	#1369	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄	—	9	1	no	—
56	C₂×C₄	—	18	1	no	—
57	C₈	—	9	1	no	—
58	C₈	—	9	1	no	—
59	C₈	—	9	1	no	—
60	C₈	AΓL(1,𝔽₉)	1	1	yes	characteristic
61	C₂×C₃	—	4	1	no	—
62	D₃	—	24	1	no	—
63	C₂²	—	9	1	no	—
64	C₄	—	9	1	no	—
65	C₄	—	36	1	no	—
66	C₄	AGL(1,𝔽₉)⋊C₄	1	1	yes	characteristic
67	C₃	—	4	1	no	—
68	C₂	—	18	1	no	—
69	C₂	AGL(1,𝔽₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	AGL(1,𝔽₉)⋊C₄
commutator	#622	C₂×C₈
Frattini, hypercenter	C₈	AΓL(1,𝔽₉)
Fitting	C₃²×C₈	SD₁₆
socle	C₂×C₃²	#334
prime radical	C₂×C₃⋊D₃	#108
cosocle	C₈×#157	C₂²
hypocenter	C₃²	#1369
LCS	G ▷ #622 ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
54. C₃²	#1369	semidirect

Maximal subgroups

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

subgroup	index
#10593255	2
#10590083	2
#10590023	2
#1369	9