Subgroups — #10619530

Order 648.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#6195	—	3	1	no	maximal
5	#6192	—	3	1	no	maximal
6	C₂×C₉²	C₂²	1	1	yes	characteristic
7	C₉⋊D₉	—	2	1	no	—
8	C₉×D₉	—	2	1	no	—
9	C₂×C₃⋊D₉	—	3	1	no	—
10	C₂×C₃⋊D₉	—	3	1	no	—
11	C₂×C₃⋊D₉	—	6	1	no	—
12	C₂×D₃×C₉	—	3	1	no	—
13	C₂×C₃×D₉	D₃	1	1	yes	characteristic
14	C₉×Dic₃	—	3	1	no	—
15	C₃×Dic₉	D₃	1	1	yes	characteristic
16	C₉²	D₄	1	1	yes	characteristic, complemented, Sylow
17	#626	—	9	1	no	—
18	#611	—	9	1	no	—
19	D₃₆	—	9	1	no	—
20	C₂×C₃×C₉	—	2	1	no	—
21	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
23	C₃⋊D₉	—	6	2	no	—
24	C₃⋊D₉	—	6	1	no	—
25	C₃⋊D₉	—	6	1	no	—
26	D₃×C₉	—	6	1	no	—
27	C₃×D₉	—	2	1	no	—
28	C₂×C₃⋊D₃	—	9	1	no	—
29	C₂×C₃×D₃	—	3	1	no	—
30	C₃×Dic₃	—	3	1	no	—
31	C₂²×C₉	—	9	1	no	—
32	C₂×D₉	—	9	1	no	—
33	C₂×D₉	—	9	1	no	—
34	C₂×D₉	—	18	1	no	—
35	C₂×D₉	—	18	1	no	—
36	C₂×D₉	—	18	3	no	—
37	C₂×D₉	D₉	1	1	yes	characteristic, complemented
38	C₄×C₉	—	9	1	no	—
39	Dic₉	D₉	1	1	yes	characteristic, complemented
40	C₃×C₉	—	2	1	no	—
41	C₃×C₉	D₁₂	1	1	yes	characteristic
42	C₃×C₉	#67	1	1	yes	characteristic
43	#67	—	27	1	no	—
44	D₁₂	—	27	1	no	—
45	C₂×C₃²	D₃²	1	1	yes	characteristic
46	C₃⋊D₃	—	18	1	no	—
47	C₃×D₃	—	6	1	no	—
48	C₂×C₉	—	2	3	no	—
49	C₂×C₉	—	2	1	no	—
50	C₂×C₉	—	2	1	no	—
51	C₂×C₉	—	18	1	no	—
52	C₂×C₉	C₂×D₉	1	1	yes	characteristic
53	C₂×C₉	C₂×D₉	1	1	yes	characteristic
54	D₉	—	2	1	no	—
55	D₉	—	18	6	no	—
56	D₉	—	18	2	no	—
57	D₉	—	18	2	no	—
58	D₉	—	18	1	no	—
59	D₉	—	18	1	no	—
60	C₂²×C₃	—	9	1	no	—
61	C₂×D₃	—	3	1	no	—
62	C₂×D₃	—	27	1	no	—
63	C₂×D₃	—	27	1	no	—
64	C₂×D₃	—	54	1	no	—
65	C₃×C₄	—	9	1	no	—
66	Dic₃	—	3	1	no	—
67	C₃²	#626	1	1	yes	characteristic
68	C₉	—	2	3	no	—
69	C₉	—	2	1	no	—
70	C₉	—	2	1	no	—
71	C₉	D₃₆	1	1	yes	characteristic, complemented
72	C₉	#611	1	1	yes	characteristic, complemented
73	D₄	—	81	1	no	Sylow
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	18	1	no	—
76	C₂×C₃	D₃×D₉	1	1	yes	characteristic
77	C₂×C₃	D₃×D₉	1	1	yes	characteristic
78	D₃	—	6	1	no	—
79	D₃	—	54	2	no	—
80	D₃	—	54	1	no	—
81	D₃	—	54	1	no	—
82	C₂²	—	9	1	no	—
83	C₂²	—	81	1	no	—
84	C₄	—	9	1	no	—
85	C₃	—	2	1	no	—
86	C₃	#6192	1	1	yes	characteristic
87	C₃	#6195	1	1	yes	characteristic
88	C₂	—	18	1	no	—
89	C₂	—	162	1	no	—
90	C₂	D₉²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉²
commutator, Fitting, cosocle	C₂×C₉²	C₂²
Frattini, socle	C₂×C₃²	D₃²
hypocenter	C₉²	D₄
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₉⋊D₉	C₂	semidirect
2. C₂×C₉×D₉	C₂	semidirect
3. C₉×Dic₉	C₂	semidirect
16. C₉²	D₄	semidirect
37. C₂×D₉	D₉	semidirect
39. Dic₉	D₉	semidirect
71. C₉	D₃₆	semidirect
72. C₉	#611	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉⋊D₉	2
C₂×C₉×D₉	2
C₉×Dic₉	2
#6195	3
#6192	3