Subgroups — C₉×#124 #63526

Order 288.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#124	C₃	1	1	yes	maximal, characteristic
6	C₂³×C₉	C₂²	1	2	yes	—
7	Q₈×C₉	—	2	2	no	—
8	D₄×C₉	—	2	2	no	—
9	C₂×C₄×C₉	C₂²	1	2	yes	—
10	C₂×C₄×C₉	C₂²	1	2	yes	—
11	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃×D₄	C₂×C₃	1	1	yes	characteristic
14	C₃×C₂²⋊C₄	C₂×C₃	1	4	yes	—
15	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₉	—	2	2	no	—
17	C₂²×C₉	—	2	4	no	—
18	C₂²×C₉	C₂³	1	1	yes	characteristic
19	C₄×C₉	—	2	2	no	—
20	C₄×C₉	—	2	2	no	—
21	C₄×C₉	D₄	1	2	yes	—
22	#124	C₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂³×C₃	C₂²×C₃	1	2	yes	—
24	C₃×Q₈	—	2	2	no	—
25	C₃×D₄	—	2	2	no	—
26	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
27	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
28	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₉	—	4	2	no	—
30	C₂×C₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₉	#41	1	2	yes	—
32	C₂×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
33	C₂×D₄	C₂×C₉	1	1	yes	characteristic
34	C₂²⋊C₄	C₂×C₉	1	4	yes	complemented
35	C₄²	C₂×C₉	1	1	yes	characteristic, complemented
36	C₂²×C₃	—	2	2	no	—
37	C₂²×C₃	—	2	4	no	—
38	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
39	C₃×C₄	—	2	2	no	—
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	C₃×D₄	1	2	yes	—
42	C₉	#124	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³	C₂²×C₉	1	2	yes	—
44	Q₈	—	2	2	no	—
45	D₄	—	2	2	no	—
46	C₂×C₄	C₂²×C₉	1	2	yes	—
47	C₂×C₄	C₂²×C₉	1	2	yes	—
48	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
49	C₂×C₃	—	4	2	no	—
50	C₂×C₃	C₂×C₃×D₄	1	1	yes	characteristic
51	C₂×C₃	C₃×#41	1	2	yes	—
52	C₂²	—	2	2	no	—
53	C₂²	—	2	4	no	—
54	C₂²	C₂³×C₉	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	2	2	no	—
57	C₄	D₄×C₉	1	2	yes	—
58	C₃	C₃×#124	1	1	yes	characteristic
59	C₂	—	4	2	no	—
60	C₂	C₂×D₄×C₉	1	1	yes	characteristic
61	C₂	C₉×#41	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₉	C₂	semidirect
3. C₉×C₂²⋊C₄	C₂	semidirect
4. C₄²×C₉	C₂	semidirect
22. #124	C₉	direct (N × H)
32. C₂×Q₈	C₂×C₉	semidirect
34. C₂²⋊C₄	C₂×C₉	semidirect
35. C₄²	C₂×C₉	semidirect
42. C₉	#124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₉	2
C₂×D₄×C₉	2
C₉×C₂²⋊C₄	2
C₄²×C₉	2
C₃×#124	3

Subgroups — C9×#124 #63526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#124 #63526