Subgroups — C₉×#331 #10588255

Order 576.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₉×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₃×#331	C₃	1	1	yes	maximal, characteristic
4	C₂×D₄×C₉	—	2	2	no	—
5	C₂×D₄×C₉	C₄	1	2	yes	—
6	C₂×C₈×C₉	—	2	2	no	—
7	C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₃×#127	C₂×C₃	1	1	yes	characteristic
9	C₃×C₄⋊C₈	C₂×C₃	1	2	yes	—
10	C₂³×C₉	—	2	2	no	—
11	D₄×C₉	—	4	2	no	—
12	D₄×C₉	—	4	2	no	—
13	D₄×C₉	—	4	2	no	—
14	C₂×C₄×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₉	D₄	1	2	yes	—
16	C₈×C₉	—	4	2	no	—
17	#331	C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×D₄	—	2	2	no	—
19	C₂×C₃×D₄	C₃×C₄	1	2	yes	—
20	C₂×C₃×C₈	—	2	2	no	—
21	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
22	C₂²×C₉	—	4	2	no	—
23	C₂²×C₉	—	4	4	no	—
24	C₂²×C₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₄×C₉	—	2	1	no	—
26	C₄×C₉	D₈	1	2	yes	—
27	C₄×C₉	SD₁₆	1	2	yes	—
28	#127	C₂×C₉	1	1	yes	characteristic
29	C₄⋊C₈	C₂×C₉	1	2	yes	complemented
30	C₂³×C₃	—	2	2	no	—
31	C₃×D₄	—	4	2	no	—
32	C₃×D₄	—	4	2	no	—
33	C₃×D₄	—	4	2	no	—
34	C₂×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄	C₃×D₄	1	2	yes	—
36	C₃×C₈	—	4	2	no	—
37	C₂×C₉	—	8	2	no	—
38	C₂×C₉	#100	1	1	yes	characteristic
39	C₂×C₉	#102	1	2	yes	—
40	C₂×D₄	—	2	2	no	—
41	C₂×D₄	C₄×C₉	1	2	yes	—
42	C₂×C₈	—	2	2	no	—
43	C₄²	C₂²×C₉	1	1	yes	characteristic
44	C₂²×C₃	—	4	2	no	—
45	C₂²×C₃	—	4	4	no	—
46	C₂²×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
47	C₃×C₄	—	2	1	no	—
48	C₃×C₄	C₃×D₈	1	2	yes	—
49	C₃×C₄	C₃×SD₁₆	1	2	yes	—
50	C₉	#331	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³	—	2	2	no	—
52	D₄	—	4	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	4	2	no	—
55	C₂×C₄	C₂×C₄×C₉	1	1	yes	characteristic
56	C₂×C₄	D₄×C₉	1	2	yes	—
57	C₈	—	4	2	no	—
58	C₂×C₃	—	8	2	no	—
59	C₂×C₃	C₃×#100	1	1	yes	characteristic
60	C₂×C₃	C₃×#102	1	2	yes	—
61	C₂²	—	4	2	no	—
62	C₂²	—	4	4	no	—
63	C₂²	C₉×C₂²⋊C₄	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	C₉×D₈	1	2	yes	—
66	C₄	C₉×SD₁₆	1	2	yes	—
67	C₃	C₃×#331	1	1	yes	characteristic
68	C₂	—	8	2	no	—
69	C₂	C₉×#100	1	1	yes	characteristic
70	C₂	C₉×#102	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₉
Frattini, cosocle	C₃×C₄²	C₂²×C₃
socle	C₂²×C₃	C₃×C₂²⋊C₄
prime radical	C₃×#127	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₄⋊C₈	C₂	semidirect
17. #331	C₉	direct (N × H)
29. C₄⋊C₈	C₂×C₉	semidirect
50. C₉	#331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#127	2
C₉×C₄⋊C₈	2
C₃×#331	3

Subgroups — C9×#331 #10588255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#331 #10588255