Subgroups — C₉×#99 #63401

Order 288.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₃×#99	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₉	C₄	1	1	yes	characteristic, complemented
5	C₂³×C₉	C₂²	1	1	yes	characteristic
6	D₄×C₉	—	2	2	no	—
7	C₂×C₄×C₉	—	2	2	no	—
8	C₂×C₄×C₉	C₄	1	1	yes	characteristic, complemented
9	C₂×C₃×D₄	C₂×C₃	1	1	yes	characteristic
10	C₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
11	C₂²×C₉	—	2	1	no	—
12	C₂²×C₉	—	4	1	no	—
13	C₂²×C₉	—	4	1	no	—
14	C₂²×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₉	D₄	1	2	yes	—
16	C₄×C₉	—	2	1	no	—
17	C₄×C₉	—	4	2	no	—
18	#99	C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³×C₃	C₃×C₄	1	1	yes	characteristic
20	C₂³×C₃	C₂²×C₃	1	1	yes	characteristic
21	C₃×D₄	—	2	2	no	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	C₃×C₄	1	1	yes	characteristic
24	C₂×C₉	—	2	2	no	—
25	C₂×C₉	—	2	1	no	—
26	C₂×C₉	—	4	1	no	—
27	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×D₄	C₂×C₉	1	1	yes	characteristic
29	C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
30	C₂²×C₃	—	2	1	no	—
31	C₂²×C₃	—	4	1	no	—
32	C₂²×C₃	—	4	1	no	—
33	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
34	C₂²×C₃	C₃×D₄	1	2	yes	—
35	C₃×C₄	—	2	1	no	—
36	C₃×C₄	—	4	2	no	—
37	C₉	#99	1	1	yes	characteristic, direct product factor, Sylow
38	C₂³	C₄×C₉	1	1	yes	characteristic, complemented
39	C₂³	C₂²×C₉	1	1	yes	characteristic
40	D₄	—	2	2	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	C₄×C₉	1	1	yes	characteristic, complemented
43	C₂×C₃	—	2	2	no	—
44	C₂×C₃	—	2	1	no	—
45	C₂×C₃	—	4	1	no	—
46	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
47	C₂²	—	2	1	no	—
48	C₂²	—	4	1	no	—
49	C₂²	—	4	1	no	—
50	C₂²	C₂×C₄×C₉	1	1	yes	characteristic
51	C₂²	D₄×C₉	1	2	yes	—
52	C₄	—	2	1	no	—
53	C₄	—	4	2	no	—
54	C₃	C₃×#99	1	1	yes	characteristic
55	C₂	—	2	2	no	—
56	C₂	—	2	1	no	—
57	C₂	—	4	1	no	—
58	C₂	C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂²×C₃
socle	C₂×C₃	C₃×C₂²⋊C₄
prime radical	C₂×C₃×D₄	C₂×C₃
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₂²⋊C₄	C₂	semidirect
4. C₂³×C₉	C₄	semidirect
8. C₂×C₄×C₉	C₄	semidirect
18. #99	C₉	direct (N × H)
29. C₂²⋊C₄	C₂×C₉	semidirect
37. C₉	#99	direct (N × H)
38. C₂³	C₄×C₉	semidirect
42. C₂×C₄	C₄×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₉	2
C₉×C₂²⋊C₄	2
C₃×#99	3

Subgroups — C9×#99 #63401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#99 #63401