Subgroups — C₉×#1367 #11766088

Order 1152.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×#1367	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₁₆	—	2	2	no	—
5	C₄×C₈×C₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₉	C₄	1	1	yes	characteristic
7	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊C₁₆	C₂×C₃	1	2	yes	—
9	C₃×C₈²	C₂×C₃	1	1	yes	characteristic
10	C₂×C₈×C₉	—	2	1	no	—
11	C₂×C₈×C₉	C₈	1	1	yes	characteristic
12	C₂×C₈×C₉	C₈	1	1	yes	characteristic
13	C₂×C₈×C₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
15	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×C₁₆	—	4	2	no	—
17	#1367	C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₁₆	—	2	2	no	—
19	C₃×C₄×C₈	C₃×C₄	1	1	yes	characteristic
20	C₃×C₄×C₈	C₃×C₄	1	1	yes	characteristic
21	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₉	M₁₆	1	1	yes	characteristic
25	C₈×C₉	—	2	2	no	—
26	C₈×C₉	—	2	1	no	—
27	C₈×C₉	—	2	1	no	—
28	C₈×C₉	C₁₆	1	2	yes	complemented
29	C₈×C₉	SD₁₆	1	2	yes	—
30	C₄⋊C₁₆	C₂×C₉	1	2	yes	—
31	C₈²	C₂×C₉	1	1	yes	characteristic
32	C₂×C₃×C₈	—	2	1	no	—
33	C₂×C₃×C₈	C₃×C₈	1	1	yes	characteristic
34	C₂×C₃×C₈	C₃×C₈	1	1	yes	characteristic
35	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
36	C₂×C₃×C₈	C₃×Q₈	1	1	yes	characteristic
37	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
38	C₃×C₁₆	—	4	2	no	—
39	C₂²×C₉	C₄⋊C₈	1	1	yes	characteristic
40	C₄×C₉	—	2	1	no	—
41	C₄×C₉	#106	1	1	yes	characteristic
42	C₄×C₉	#108	1	1	yes	characteristic
43	C₄×C₉	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₉	M₃₂	1	1	yes	characteristic
45	C₂×C₁₆	—	2	2	no	—
46	C₄×C₈	C₄×C₉	1	1	yes	characteristic
47	C₄×C₈	C₄×C₉	1	1	yes	characteristic
48	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
49	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
51	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
52	C₃×C₈	—	2	2	no	—
53	C₃×C₈	—	2	1	no	—
54	C₃×C₈	—	2	1	no	—
55	C₃×C₈	C₃×C₁₆	1	2	yes	—
56	C₃×C₈	C₃×SD₁₆	1	2	yes	—
57	C₂×C₉	#334	1	1	yes	characteristic
58	C₂×C₉	C₄⋊C₁₆	1	1	yes	characteristic
59	C₂×C₉	#364	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	C₈×C₉	1	1	yes	characteristic
62	C₂×C₈	C₈×C₉	1	1	yes	characteristic
63	C₂×C₈	D₄×C₉	1	1	yes	characteristic
64	C₂×C₈	Q₈×C₉	1	1	yes	characteristic
65	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
66	C₁₆	—	4	2	no	—
67	C₂²×C₃	C₃×C₄⋊C₈	1	1	yes	characteristic
68	C₃×C₄	—	2	1	no	—
69	C₃×C₄	C₃×#106	1	1	yes	characteristic
70	C₃×C₄	C₃×#108	1	1	yes	characteristic
71	C₃×C₄	C₂×C₃×C₁₆	1	1	yes	characteristic
72	C₃×C₄	C₃×M₃₂	1	1	yes	characteristic
73	C₉	#1367	1	1	yes	characteristic, direct product factor, Sylow
74	C₂×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄	C₂×C₈×C₉	1	1	yes	characteristic
76	C₂×C₄	C₉×M₁₆	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₈	—	2	1	no	—
79	C₈	—	2	1	no	—
80	C₈	C₉×C₁₆	1	2	yes	complemented
81	C₈	C₉×SD₁₆	1	2	yes	—
82	C₂×C₃	C₃×#334	1	1	yes	characteristic
83	C₂×C₃	C₃×C₄⋊C₁₆	1	1	yes	characteristic
84	C₂×C₃	C₃×#364	1	1	yes	characteristic
85	C₂²	C₉×C₄⋊C₈	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	C₉×#106	1	1	yes	characteristic
88	C₄	C₉×#108	1	1	yes	characteristic
89	C₄	C₂×C₉×C₁₆	1	1	yes	characteristic
90	C₄	C₉×M₃₂	1	1	yes	characteristic
91	C₃	C₃×#1367	1	1	yes	characteristic
92	C₂	C₉×#334	1	1	yes	characteristic
93	C₂	C₉×C₄⋊C₁₆	1	1	yes	characteristic
94	C₂	C₉×#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₉	D₄
commutator	C₄	C₂×C₉×C₁₆
Frattini, cosocle	C₃×C₄×C₈	C₂²×C₃
socle, prime radical	C₂²×C₃	C₃×C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₉ ◁ C₄×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
17. #1367	C₉	direct (N × H)
28. C₈×C₉	C₁₆	semidirect
73. C₉	#1367	direct (N × H)
80. C₈	C₉×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₄⋊C₁₆	2
C₈²×C₉	2
C₃×#1367	3

Subgroups — C9×#1367 #11766088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1367 #11766088