Subgroups — C₉×#103 #63405

Order 288.

63 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
2	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₃	1	1	yes	maximal, characteristic
5	Q₈×C₉	—	2	1	no	—
6	Q₈×C₉	C₄	1	2	yes	complemented
7	C₂×C₄×C₉	—	2	1	no	—
8	C₂×C₄×C₉	—	2	1	no	—
9	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₈×C₉	—	2	1	no	—
11	C₂×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₉	D₄	1	1	yes	characteristic
15	C₄×C₉	—	2	2	no	—
16	C₄×C₉	—	4	1	no	—
17	C₄×C₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₉	D₄	1	1	yes	characteristic
19	#103	C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×Q₈	—	2	1	no	—
21	C₃×Q₈	C₃×C₄	1	2	yes	—
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	2	1	no	—
24	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
25	C₃×C₈	—	2	1	no	—
26	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₉	SD₁₆	1	1	yes	characteristic
28	C₂×C₉	Q₁₆	1	1	yes	characteristic
29	C₂×Q₈	C₂×C₉	1	1	yes	characteristic
30	C₂×C₈	C₂×C₉	1	1	yes	characteristic
31	C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
32	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
33	C₃×C₄	—	2	2	no	—
34	C₃×C₄	—	4	1	no	—
35	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
36	C₃×C₄	C₃×D₄	1	1	yes	characteristic
37	C₉	#103	1	1	yes	characteristic, direct product factor, Sylow
38	Q₈	—	2	1	no	—
39	Q₈	C₄×C₉	1	2	yes	complemented
40	C₂×C₄	—	2	1	no	—
41	C₂×C₄	—	2	1	no	—
42	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₃	C₃×SD₁₆	1	1	yes	characteristic
46	C₂×C₃	C₃×Q₁₆	1	1	yes	characteristic
47	C₂²	D₄×C₉	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	4	1	no	—
50	C₄	C₂×C₄×C₉	1	1	yes	characteristic
51	C₄	D₄×C₉	1	1	yes	characteristic
52	C₃	C₃×#103	1	1	yes	characteristic
53	C₂	C₉×C₂²⋊C₄	1	1	yes	characteristic
54	C₂	C₉×SD₁₆	1	1	yes	characteristic
55	C₂	C₉×Q₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. Q₈×C₉	C₄	semidirect
19. #103	C₉	direct (N × H)
37. C₉	#103	direct (N × H)
39. Q₈	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×Q₈×C₉	2
C₂×C₈×C₉	2
C₉×C₄⋊C₄	2
C₃×#103	3

Subgroups — C9×#103 #63405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#103 #63405