Subgroups — C₂×C₉×#493 #11767865

Order 1152.

1140 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₈	C₂	1	4	yes	maximal, complemented
2	C₂×C₉×#127	C₂	1	2	yes	maximal, complemented
3	C₉×#493	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#493	C₃	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₉	—	2	4	no	—
7	C₂²×D₄×C₉	C₂²	1	4	yes	—
8	C₂×C₉×D₈	—	2	16	no	—
9	C₂×C₉×D₈	C₂²	1	16	yes	complemented
10	C₂²×C₈×C₉	C₂²	1	2	yes	—
11	C₉×#127	—	2	4	no	—
12	C₉×#127	C₂²	1	8	yes	complemented
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₉	C₂²	1	4	yes	complemented
15	C₂²×C₃×D₈	C₂×C₃	1	4	yes	—
16	C₂×C₃×#127	C₂×C₃	1	2	yes	—
17	C₃×#493	C₂×C₃	1	8	yes	—
18	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
19	C₂⁴×C₉	—	2	4	no	—
20	C₂×D₄×C₉	—	2	16	no	—
21	C₂×D₄×C₉	—	2	4	no	—
22	C₂×D₄×C₉	—	2	16	no	—
23	C₂×D₄×C₉	—	4	16	no	—
24	C₂×D₄×C₉	C₂³	1	8	yes	—
25	C₂²×C₄×C₉	D₄	1	2	yes	—
26	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
27	C₉×D₈	—	2	32	no	—
28	C₂×C₈×C₉	D₄	1	8	yes	complemented
29	C₂×C₈×C₉	C₂³	1	4	yes	—
30	C₄²×C₉	D₄	1	2	yes	—
31	C₄²×C₉	C₂³	1	2	yes	—
32	C₂×#493	C₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²×C₃×D₄	—	2	4	no	—
34	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
35	C₂×C₃×D₈	—	2	16	no	—
36	C₂×C₃×D₈	C₂²×C₃	1	16	yes	—
37	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
38	C₃×#127	—	2	4	no	—
39	C₃×#127	C₂²×C₃	1	8	yes	—
40	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
42	C₂³×C₉	—	2	8	no	—
43	C₂³×C₉	—	4	8	no	—
44	C₂³×C₉	—	4	16	no	—
45	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
46	D₄×C₉	—	2	16	no	—
47	D₄×C₉	—	4	8	no	—
48	D₄×C₉	—	4	32	no	—
49	C₂×C₄×C₉	D₈	1	8	yes	complemented
50	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
52	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
53	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
54	C₈×C₉	C₂×D₄	1	8	yes	complemented
55	C₂²×D₈	C₂×C₉	1	4	yes	complemented
56	C₂×#127	C₂×C₉	1	2	yes	complemented
57	#493	C₂×C₉	1	8	yes	direct product factor
58	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic, complemented
59	C₂⁴×C₃	—	2	4	no	—
60	C₂×C₃×D₄	—	2	16	no	—
61	C₂×C₃×D₄	—	2	4	no	—
62	C₂×C₃×D₄	—	2	16	no	—
63	C₂×C₃×D₄	—	4	16	no	—
64	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
65	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
66	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
67	C₃×D₈	—	2	32	no	—
68	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
69	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
70	C₃×C₄²	C₃×D₄	1	2	yes	—
71	C₃×C₄²	C₂³×C₃	1	2	yes	—
72	C₂²×C₉	—	4	8	no	—
73	C₂²×C₉	—	4	16	no	—
74	C₂²×C₉	—	8	16	no	—
75	C₂²×C₉	#127	1	2	yes	—
76	C₂²×C₉	C₂×D₈	1	4	yes	—
77	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
78	C₄×C₉	#127	1	2	yes	—
79	C₄×C₉	C₂×D₈	1	8	yes	complemented
80	C₄×C₉	C₂²×D₄	1	2	yes	—
81	C₂²×D₄	—	2	4	no	—
82	C₂²×D₄	C₂²×C₉	1	4	yes	—
83	C₂×D₈	—	2	16	no	—
84	C₂×D₈	C₂²×C₉	1	16	yes	complemented
85	C₂²×C₈	C₂²×C₉	1	2	yes	—
86	#127	—	2	4	no	—
87	#127	C₂²×C₉	1	8	yes	complemented
88	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
89	C₄×C₈	C₂²×C₉	1	4	yes	complemented
90	C₂³×C₃	—	2	8	no	—
91	C₂³×C₃	—	4	8	no	—
92	C₂³×C₃	—	4	16	no	—
93	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
94	C₃×D₄	—	2	16	no	—
95	C₃×D₄	—	4	8	no	—
96	C₃×D₄	—	4	32	no	—
97	C₂×C₃×C₄	C₃×D₈	1	8	yes	—
98	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
100	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
101	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
102	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
103	C₂×C₉	—	8	8	no	—
104	C₂×C₉	#493	1	4	yes	direct product factor
105	C₂×C₉	C₂×#127	1	1	yes	characteristic
106	C₂×C₉	C₂²×D₈	1	2	yes	—
107	C₂⁴	—	2	4	no	—
108	C₂×D₄	—	2	16	no	—
109	C₂×D₄	—	2	4	no	—
110	C₂×D₄	—	2	16	no	—
111	C₂×D₄	—	4	16	no	—
112	C₂×D₄	C₂³×C₉	1	8	yes	—
113	C₂²×C₄	D₄×C₉	1	2	yes	—
114	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
115	D₈	—	2	32	no	—
116	C₂×C₈	D₄×C₉	1	8	yes	complemented
117	C₂×C₈	C₂³×C₉	1	4	yes	—
118	C₄²	D₄×C₉	1	2	yes	—
119	C₄²	C₂³×C₉	1	2	yes	—
120	C₂²×C₃	—	4	16	no	—
121	C₂²×C₃	—	4	8	no	—
122	C₂²×C₃	—	8	16	no	—
123	C₂²×C₃	C₃×#127	1	2	yes	—
124	C₂²×C₃	C₂×C₃×D₈	1	4	yes	—
125	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
126	C₃×C₄	C₃×#127	1	2	yes	—
127	C₃×C₄	C₂×C₃×D₈	1	8	yes	—
128	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
129	C₉	C₂×#493	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³	—	2	8	no	—
131	C₂³	—	4	8	no	—
132	C₂³	—	4	16	no	—
133	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
134	D₄	—	2	16	no	—
135	D₄	—	4	8	no	—
136	D₄	—	4	32	no	—
137	C₂×C₄	C₉×D₈	1	8	yes	complemented
138	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
139	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
140	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
141	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
142	C₈	C₂×D₄×C₉	1	8	yes	complemented
143	C₂×C₃	—	8	8	no	—
144	C₂×C₃	C₃×#493	1	4	yes	—
145	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
146	C₂×C₃	C₂²×C₃×D₈	1	2	yes	—
147	C₂²	—	4	8	no	—
148	C₂²	—	4	16	no	—
149	C₂²	—	8	16	no	—
150	C₂²	C₉×#127	1	2	yes	—
151	C₂²	C₂×C₉×D₈	1	4	yes	—
152	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
153	C₄	C₉×#127	1	2	yes	—
154	C₄	C₂×C₉×D₈	1	8	yes	complemented
155	C₄	C₂²×D₄×C₉	1	2	yes	—
156	C₃	C₂×C₃×#493	1	1	yes	characteristic
157	C₂	—	8	8	no	—
158	C₂	C₉×#493	1	4	yes	direct product factor
159	C₂	C₂×C₉×#127	1	1	yes	characteristic
160	C₂	C₂²×C₉×D₈	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂×C₃×#493	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×D₈	C₂	semidirect
2. C₂×C₉×#127	C₂	semidirect
3. C₉×#493	C₂	direct (N × H)
4. C₂×C₄×C₈×C₉	C₂	semidirect
9. C₂×C₉×D₈	C₂²	semidirect
12. C₉×#127	C₂²	semidirect
14. C₄×C₈×C₉	C₂²	semidirect
28. C₂×C₈×C₉	D₄	semidirect
32. C₂×#493	C₉	direct (N × H)
49. C₂×C₄×C₉	D₈	semidirect
54. C₈×C₉	C₂×D₄	semidirect
55. C₂²×D₈	C₂×C₉	semidirect
56. C₂×#127	C₂×C₉	semidirect
57. #493	C₂×C₉	direct (N × H)
58. C₂×C₄×C₈	C₂×C₉	semidirect
79. C₄×C₉	C₂×D₈	semidirect
84. C₂×D₈	C₂²×C₉	semidirect
87. #127	C₂²×C₉	semidirect
89. C₄×C₈	C₂²×C₉	semidirect
104. C₂×C₉	#493	direct (N × H)
116. C₂×C₈	D₄×C₉	semidirect
129. C₉	C₂×#493	direct (N × H)
137. C₂×C₄	C₉×D₈	semidirect
142. C₈	C₂×D₄×C₉	semidirect
154. C₄	C₂×C₉×D₈	semidirect
158. C₂	C₉×#493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×D₈	2
C₂×C₉×#127	2
C₉×#493	2
C₂×C₄×C₈×C₉	2
C₂×C₃×#493	3

Subgroups — C2×C9×#493 #11767865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#493 #11767865