Subgroups — C₉×#836 #11720496

Order 864.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#208	C₂	1	2	yes	maximal
3	C₃×#836	C₃	1	1	yes	maximal, characteristic
4	C₉×#101	—	3	1	no	maximal
5	C₃×Q₈×C₉	—	2	2	no	—
6	C₂×C₃×C₄×C₉	C₄	1	2	yes	—
7	C₂×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₉×C₃⋊C₈	—	2	2	no	—
9	C₂×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₃×#208	C₂×C₃	1	2	yes	—
11	C₂×Q₈×C₉	—	2	1	no	—
12	C₂×Q₈×C₉	D₃	1	1	yes	characteristic
13	C₉×M₁₆	—	3	2	no	—
14	C₂²×C₃×C₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₉	—	2	2	no	—
16	C₃×C₄×C₉	D₄	1	2	yes	—
17	C₃×#101	—	3	1	no	—
18	#836	C₉	1	1	yes	characteristic, direct product factor
19	C₃²×Q₈	—	2	2	no	—
20	C₂×C₃²×C₄	C₃×C₄	1	2	yes	—
21	C₂×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₃×C₃⋊C₈	—	2	2	no	—
23	Q₈×C₉	—	2	4	no	—
24	Q₈×C₉	—	2	2	no	—
25	C₂×C₄×C₉	—	2	2	no	—
26	C₂×C₄×C₉	—	2	1	no	—
27	C₂×C₄×C₉	Dic₃	1	2	yes	—
28	C₂×C₄×C₉	C₂×D₃	1	1	yes	characteristic
29	C₈×C₉	—	6	2	no	—
30	C₂×C₃×C₉	—	2	1	no	—
31	C₂×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₃×Q₈	—	2	1	no	—
33	C₂×C₃×Q₈	C₂×C₉	1	1	yes	characteristic
34	C₂×C₃×Q₈	C₃×D₃	1	1	yes	characteristic
35	C₃×M₁₆	—	3	2	no	—
36	#208	C₂×C₉	1	2	yes	—
37	C₂²×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
38	C₃²×C₄	—	2	2	no	—
39	C₃²×C₄	C₃×D₄	1	2	yes	—
40	C₂²×C₉	—	2	1	no	—
41	C₂²×C₉	C₂×Dic₃	1	1	yes	characteristic
42	C₄×C₉	—	2	4	no	—
43	C₄×C₉	—	2	2	no	—
44	C₄×C₉	—	2	2	no	—
45	C₄×C₉	#67	1	2	yes	—
46	#101	—	3	1	no	Sylow
47	C₃×C₉	#101	1	1	yes	characteristic, complemented, Sylow
48	C₃×Q₈	—	2	4	no	—
49	C₃×Q₈	—	2	2	no	—
50	C₃×Q₈	—	2	2	no	—
51	C₂×C₃×C₄	—	2	2	no	—
52	C₂×C₃×C₄	—	2	1	no	—
53	C₂×C₃×C₄	C₄×C₉	1	2	yes	—
54	C₂×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
55	C₂×C₃×C₄	C₃×Dic₃	1	2	yes	—
56	C₂×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
57	C₃×C₈	—	6	2	no	—
58	C₃⋊C₈	—	2	2	no	—
59	C₂×C₃²	—	2	1	no	—
60	C₂×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₉	—	2	2	no	—
62	C₂×C₉	—	2	1	no	—
63	C₂×C₉	—	2	1	no	—
64	C₂×C₉	#217	1	1	yes	characteristic
65	C₂×Q₈	D₃×C₉	1	1	yes	characteristic
66	M₁₆	—	3	2	no	—
67	C₂²×C₃	—	2	1	no	—
68	C₂²×C₃	C₂×C₄×C₉	1	1	yes	characteristic
69	C₂²×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
70	C₃×C₄	—	2	4	no	—
71	C₃×C₄	—	2	2	no	—
72	C₃×C₄	—	2	2	no	—
73	C₃×C₄	—	2	2	no	—
74	C₃×C₄	D₄×C₉	1	2	yes	—
75	C₃×C₄	C₃×#67	1	2	yes	—
76	C₃²	C₃×#101	1	1	yes	characteristic
77	C₉	—	2	1	no	—
78	C₉	#836	1	1	yes	characteristic, direct product factor
79	Q₈	—	2	2	no	—
80	C₂×C₄	C₉×Dic₃	1	2	yes	—
81	C₂×C₄	C₂×D₃×C₉	1	1	yes	characteristic
82	C₈	—	6	2	no	—
83	C₂×C₃	—	2	2	no	—
84	C₂×C₃	—	2	1	no	—
85	C₂×C₃	—	2	1	no	—
86	C₂×C₃	—	2	1	no	—
87	C₂×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃	C₃×#217	1	1	yes	characteristic
89	C₂²	C₂×C₉×Dic₃	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	C₉×#67	1	2	yes	—
92	C₃	—	2	1	no	—
93	C₃	C₉×#101	1	1	yes	characteristic, complemented
94	C₃	C₃×#836	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	C₉×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#217
commutator	C₂²×C₃	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₃×Q₈×C₉	C₂
socle	C₂×C₃²	C₃×C₂²⋊C₄
prime radical	C₂²×C₃²	C₂×C₃×C₄
cosocle	C₂×C₃²×C₄	C₂²×C₃
hypercenter	C₂×Q₈×C₉	D₃
hypocenter	C₃	C₉×#101
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₂×Q₈×C₉

Complements

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

N	H ≅ G/N	type
18. #836	C₉	direct (N × H)
47. C₃×C₉	#101	semidirect
78. C₉	#836	direct (N × H)
93. C₃	C₉×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₉	2
C₉×#208	2
C₃×#836	3
C₉×#101	3

Subgroups — C9×#836 #11720496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#836 #11720496