Subgroups — C₉⋊#401 #10588342

Order 576.

177 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#95	C₂	1	1	yes	maximal, characteristic
2	C₉⋊#95	C₂	1	3	yes	maximal
3	C₉⋊#95	C₂	1	3	yes	maximal
4	C₃⋊#401	—	3	1	no	maximal
5	C₂²×C₄×C₉	C₂²	1	3	yes	—
6	C₂²×Dic₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₉	C₂²	1	3	yes	—
8	C₃×#95	D₃	1	1	yes	characteristic
9	C₃⋊#95	—	3	3	no	—
10	C₃⋊#95	—	3	3	no	—
11	C₂³×C₉	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₉	—	2	3	no	—
13	C₂×C₄×C₉	—	2	6	no	—
14	C₂×Dic₉	—	2	3	no	—
15	C₂×Dic₉	—	2	3	no	—
16	C₂×Dic₉	—	2	3	no	—
17	C₂×Dic₉	—	2	3	no	—
18	#401	—	9	1	no	Sylow
19	C₂²×C₃×C₄	C₂×D₃	1	3	yes	—
20	C₂²×Dic₃	—	3	1	no	—
21	C₂²×Dic₃	—	3	3	no	—
22	C₂²×C₉	#41	1	3	yes	—
23	C₂²×C₉	#41	1	3	yes	—
24	C₂²×C₉	#41	1	1	yes	characteristic
25	C₄×C₉	—	4	3	no	—
26	Dic₉	—	4	1	no	—
27	Dic₉	—	4	3	no	—
28	#95	—	9	3	no	—
29	#95	—	9	3	no	—
30	#95	D₉	1	1	yes	characteristic
31	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
32	C₂×C₃×C₄	—	2	3	no	—
33	C₂×C₃×C₄	—	2	6	no	—
34	C₂×Dic₃	—	6	3	no	—
35	C₂×Dic₃	—	6	3	no	—
36	C₂×Dic₃	—	6	3	no	—
37	C₂×Dic₃	—	6	3	no	—
38	C₂×C₉	#126	1	1	yes	characteristic
39	C₂×C₉	#126	1	3	yes	—
40	C₂×C₉	#126	1	3	yes	—
41	C₂²×C₄	—	9	1	no	—
42	C₂²×C₄	—	9	3	no	—
43	C₂²×C₄	C₂×D₉	1	3	yes	—
44	C₂²×C₃	#235	1	3	yes	—
45	C₂²×C₃	#237	1	3	yes	—
46	C₂²×C₃	#239	1	1	yes	characteristic
47	C₃×C₄	—	4	3	no	—
48	Dic₃	—	12	1	no	—
49	Dic₃	—	12	3	no	—
50	C₉	#401	1	1	yes	characteristic, complemented, Sylow
51	C₂³	C₂²×D₉	1	1	yes	characteristic
52	C₂×C₄	—	2	3	no	—
53	C₂×C₄	—	2	6	no	—
54	C₂×C₄	—	18	3	no	—
55	C₂×C₄	—	18	3	no	—
56	C₂×C₄	—	18	3	no	—
57	C₂×C₄	—	18	3	no	—
58	C₂×C₃	#876	1	1	yes	characteristic
59	C₂×C₃	#879	1	3	yes	—
60	C₂×C₃	#898	1	3	yes	—
61	C₂²	#3697	1	3	yes	—
62	C₂²	#3699	1	3	yes	—
63	C₂²	#3701	1	1	yes	characteristic
64	C₄	—	4	3	no	—
65	C₄	—	36	1	no	—
66	C₄	—	36	3	no	—
67	C₃	C₃⋊#401	1	1	yes	characteristic
68	C₂	#63438	1	1	yes	characteristic
69	C₂	#63441	1	3	yes	—
70	C₂	#63460	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₉
commutator, cosocle	C₂³×C₉	C₂³
Frattini, socle, prime radical	C₂³×C₃	C₂²×D₃
Fitting	C₉×#95	C₂
hypercenter	#95	D₉
hypocenter	C₉	#401
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
50. C₉	#401	semidirect

Maximal subgroups

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

subgroup	index
C₉×#95	2
C₉⋊#95	2
C₃⋊#401	3

Subgroups — C9⋊#401 #10588342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#401 #10588342