Subgroups — C₉×#2253 #11766974

Order 1152.

174 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#499	C₂	1	2	yes	maximal
2	C₉×#367	C₂	1	2	yes	maximal
3	C₉×#366	C₂	1	2	yes	maximal
4	C₄×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₃×#2253	C₃	1	1	yes	maximal, characteristic
6	C₉×#125	—	2	2	no	—
7	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
9	C₉×#107	C₂²	1	4	yes	—
10	C₉×#106	—	2	2	no	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₃×#499	C₂×C₃	1	2	yes	—
13	C₃×#367	C₂×C₃	1	2	yes	—
14	C₃×#366	C₂×C₃	1	2	yes	—
15	C₃×C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
16	C₂×C₈×C₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
18	C₉×C₄⋊C₄	—	2	4	no	—
19	C₉×C₄⋊C₄	—	4	4	no	—
20	C₄²×C₉	D₄	1	1	yes	characteristic
21	C₉×C₁₆	Q₈	1	2	yes	—
22	C₉×C₁₆	Q₈	1	2	yes	—
23	#2253	C₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×#125	—	2	2	no	—
25	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₃×C₁₆	C₂²×C₃	1	1	yes	characteristic
27	C₃×#107	C₂²×C₃	1	4	yes	—
28	C₃×#106	—	2	2	no	—
29	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
30	C₂×C₄×C₉	—	4	4	no	—
31	C₂×C₄×C₉	D₈	1	2	yes	—
32	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
33	C₈×C₉	Q₁₆	1	2	yes	—
34	C₈×C₉	C₂×Q₈	1	1	yes	characteristic
35	C₈×C₉	C₂×Q₈	1	1	yes	characteristic
36	#499	C₂×C₉	1	2	yes	—
37	#367	C₂×C₉	1	2	yes	—
38	#366	C₂×C₉	1	2	yes	—
39	C₄×C₁₆	C₂×C₉	1	1	yes	characteristic
40	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
41	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
42	C₃×C₄⋊C₄	—	2	4	no	—
43	C₃×C₄⋊C₄	—	4	4	no	—
44	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
45	C₃×C₁₆	C₃×Q₈	1	2	yes	—
46	C₃×C₁₆	C₃×Q₈	1	2	yes	—
47	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₉	—	2	2	no	—
49	C₄×C₉	—	8	4	no	—
50	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₉	C₂×Q₁₆	1	1	yes	characteristic
52	#125	—	2	2	no	—
53	C₂×C₁₆	C₂²×C₉	1	1	yes	characteristic
54	C₂×C₁₆	C₂²×C₉	1	1	yes	characteristic
55	#107	C₂²×C₉	1	4	yes	—
56	#106	—	2	2	no	—
57	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
58	C₂×C₃×C₄	—	4	4	no	—
59	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
60	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
61	C₃×C₈	C₃×Q₁₆	1	2	yes	—
62	C₃×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
63	C₃×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
64	C₂×C₉	#500	1	1	yes	characteristic
65	C₂×C₉	#508	1	2	yes	—
66	C₂×C₈	D₄×C₉	1	1	yes	characteristic
67	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	4	4	no	—
70	C₄²	D₄×C₉	1	1	yes	characteristic
71	C₁₆	Q₈×C₉	1	2	yes	—
72	C₁₆	Q₈×C₉	1	2	yes	—
73	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
74	C₃×C₄	—	2	2	no	—
75	C₃×C₄	—	8	4	no	—
76	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
77	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
78	C₉	#2253	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×C₄	—	4	4	no	—
80	C₂×C₄	C₉×D₈	1	2	yes	—
81	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
82	C₈	C₉×Q₁₆	1	2	yes	—
83	C₈	C₂×Q₈×C₉	1	1	yes	characteristic
84	C₈	C₂×Q₈×C₉	1	1	yes	characteristic
85	C₂×C₃	C₃×#500	1	1	yes	characteristic
86	C₂×C₃	C₃×#508	1	2	yes	—
87	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	8	4	no	—
90	C₄	C₉×C₄⋊Q₈	1	1	yes	characteristic
91	C₄	C₂×C₉×Q₁₆	1	1	yes	characteristic
92	C₃	C₃×#2253	1	1	yes	characteristic
93	C₂	C₉×#500	1	1	yes	characteristic
94	C₂	C₉×#508	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂×D₈
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂×C₃×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₄×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
23. #2253	C₉	direct (N × H)
78. C₉	#2253	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×#499	2
C₉×#367	2
C₉×#366	2
C₄×C₉×C₁₆	2
C₃×#2253	3

Subgroups — C9×#2253 #11766974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2253 #11766974