Subgroups — C₉×#2252 #11766973

Order 1152.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#500	C₂	1	2	yes	maximal
2	C₉×#366	C₂	1	4	yes	maximal
3	C₄×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#2252	C₃	1	1	yes	maximal, characteristic
5	C₉×C₄⋊Q₈	—	2	2	no	—
6	C₂×C₉×C₁₆	C₂²	1	2	yes	—
7	C₉×#107	—	2	2	no	—
8	C₉×#107	C₂²	1	4	yes	—
9	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₃×#500	C₂×C₃	1	2	yes	—
11	C₃×#366	C₂×C₃	1	4	yes	—
12	C₃×C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
13	C₂×Q₈×C₉	—	4	2	no	—
14	C₂×C₈×C₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
16	C₉×C₄⋊C₄	—	2	4	no	—
17	C₉×C₄⋊C₄	—	4	2	no	—
18	C₄²×C₉	D₄	1	1	yes	characteristic
19	C₉×C₁₆	Q₈	1	4	yes	complemented
20	#2252	C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₄⋊Q₈	—	2	2	no	—
22	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	—
23	C₃×#107	—	2	2	no	—
24	C₃×#107	C₂²×C₃	1	4	yes	—
25	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
26	Q₈×C₉	—	8	4	no	—
27	C₂×C₄×C₉	—	4	4	no	—
28	C₂×C₄×C₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
31	C₈×C₉	Q₁₆	1	2	yes	—
32	C₈×C₉	C₂×Q₈	1	2	yes	—
33	#500	C₂×C₉	1	2	yes	—
34	#366	C₂×C₉	1	4	yes	—
35	C₄×C₁₆	C₂×C₉	1	1	yes	characteristic
36	C₂×C₃×Q₈	—	4	2	no	—
37	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
38	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
39	C₃×C₄⋊C₄	—	2	4	no	—
40	C₃×C₄⋊C₄	—	4	2	no	—
41	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
42	C₃×C₁₆	C₃×Q₈	1	4	yes	—
43	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
44	C₄×C₉	—	8	4	no	—
45	C₄×C₉	D₁₆	1	2	yes	—
46	C₄×C₉	Q₃₂	1	2	yes	—
47	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₉	C₂×Q₁₆	1	1	yes	characteristic
49	C₄⋊Q₈	—	2	2	no	—
50	C₂×C₁₆	C₂²×C₉	1	2	yes	—
51	#107	—	2	2	no	—
52	#107	C₂²×C₉	1	4	yes	—
53	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
54	C₃×Q₈	—	8	4	no	—
55	C₂×C₃×C₄	—	4	4	no	—
56	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
57	C₂×C₃×C₄	C₃×D₈	1	1	yes	characteristic
58	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
59	C₃×C₈	C₃×Q₁₆	1	2	yes	—
60	C₃×C₈	C₂×C₃×Q₈	1	2	yes	—
61	C₂×C₉	#500	1	1	yes	characteristic
62	C₂×C₉	C₂×D₁₆	1	1	yes	characteristic
63	C₂×C₉	C₂×Q₃₂	1	1	yes	characteristic
64	C₂×Q₈	—	4	2	no	—
65	C₂×C₈	D₄×C₉	1	1	yes	characteristic
66	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	—	4	2	no	—
69	C₄²	D₄×C₉	1	1	yes	characteristic
70	C₁₆	Q₈×C₉	1	4	yes	complemented
71	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
72	C₃×C₄	—	8	4	no	—
73	C₃×C₄	C₃×D₁₆	1	2	yes	—
74	C₃×C₄	C₃×Q₃₂	1	2	yes	—
75	C₃×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
76	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
77	C₉	#2252	1	1	yes	characteristic, direct product factor, Sylow
78	Q₈	—	8	4	no	—
79	C₂×C₄	—	4	4	no	—
80	C₂×C₄	C₉×D₈	1	1	yes	characteristic
81	C₂×C₄	C₉×D₈	1	1	yes	characteristic
82	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
83	C₈	C₉×Q₁₆	1	2	yes	—
84	C₈	C₂×Q₈×C₉	1	2	yes	—
85	C₂×C₃	C₃×#500	1	1	yes	characteristic
86	C₂×C₃	C₂×C₃×D₁₆	1	1	yes	characteristic
87	C₂×C₃	C₂×C₃×Q₃₂	1	1	yes	characteristic
88	C₂²	C₂×C₉×D₈	1	1	yes	characteristic
89	C₄	—	8	4	no	—
90	C₄	C₉×D₁₆	1	2	yes	—
91	C₄	C₉×Q₃₂	1	2	yes	—
92	C₄	C₉×C₄⋊Q₈	1	1	yes	characteristic
93	C₄	C₂×C₉×Q₁₆	1	1	yes	characteristic
94	C₃	C₃×#2252	1	1	yes	characteristic
95	C₂	C₉×#500	1	1	yes	characteristic
96	C₂	C₂×C₉×D₁₆	1	1	yes	characteristic
97	C₂	C₂×C₉×Q₃₂	1	1	yes	characteristic

	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
19. C₉×C₁₆	Q₈	semidirect
20. #2252	C₉	direct (N × H)
70. C₁₆	Q₈×C₉	semidirect
77. C₉	#2252	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×#500	2
C₉×#366	2
C₄×C₉×C₁₆	2
C₃×#2252	3

Subgroups — C9×#2252 #11766973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2252 #11766973