Subgroups — C₉×#1811 #11766532

Order 1152.

408 conjugacy classes of subgroups.

The subgroup lattice has 177 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#108	C₂	1	2	yes	maximal, complemented
3	C₉×#407	C₂	1	2	yes	maximal
4	C₉×#341	C₂	1	2	yes	maximal, complemented
5	C₃×#1811	C₃	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₉×M₁₆	—	2	4	no	—
8	C₂×C₉×M₁₆	C₄	1	4	yes	—
9	C₂×C₉×M₁₆	C₂²	1	4	yes	—
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₉×#108	—	2	4	no	—
13	C₉×C₂²⋊C₈	—	2	4	no	—
14	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic
15	C₂×C₃×#108	C₂×C₃	1	2	yes	—
16	C₃×#407	C₂×C₃	1	2	yes	—
17	C₃×#341	C₂×C₃	1	2	yes	—
18	C₂⁴×C₉	Q₈	1	1	yes	characteristic
19	C₂²×C₄×C₉	—	2	2	no	—
20	C₂²×C₄×C₉	—	2	2	no	—
21	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₉	D₄	1	2	yes	—
23	C₂²×C₄×C₉	Q₈	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₉×M₁₆	—	2	8	no	—
26	C₉×M₁₆	—	2	4	no	—
27	C₉×M₁₆	—	2	4	no	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	—	2	4	no	—
30	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₉	D₄	1	4	yes	—
33	#1811	C₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
35	C₂×C₃×M₁₆	—	2	4	no	—
36	C₂×C₃×M₁₆	C₃×C₄	1	4	yes	—
37	C₂×C₃×M₁₆	C₂²×C₃	1	4	yes	—
38	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
39	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₃×#108	—	2	4	no	—
41	C₃×C₂²⋊C₈	—	2	4	no	—
42	C₂³×C₉	—	2	2	no	—
43	C₂³×C₉	—	4	2	no	—
44	C₂³×C₉	C₄⋊C₄	1	2	yes	—
45	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₉	—	2	2	no	—
47	C₂×C₄×C₉	—	2	2	no	—
48	C₂×C₄×C₉	—	2	2	no	—
49	C₂×C₄×C₉	—	2	4	no	—
50	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
51	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₉	#41	1	2	yes	—
55	C₈×C₉	—	2	2	no	—
56	C₈×C₉	—	4	4	no	—
57	C₈×C₉	C₂²⋊C₄	1	4	yes	—
58	C₂²×M₁₆	C₂×C₉	1	1	yes	characteristic
59	C₂×#108	C₂×C₉	1	2	yes	complemented
60	#407	C₂×C₉	1	2	yes	—
61	#341	C₂×C₉	1	2	yes	complemented
62	C₂⁴×C₃	C₃×Q₈	1	1	yes	characteristic
63	C₂²×C₃×C₄	—	2	2	no	—
64	C₂²×C₃×C₄	—	2	2	no	—
65	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
66	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
67	C₂²×C₃×C₄	C₃×Q₈	1	1	yes	characteristic
68	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₃×M₁₆	—	2	8	no	—
70	C₃×M₁₆	—	2	4	no	—
71	C₃×M₁₆	—	2	4	no	—
72	C₂×C₃×C₈	—	2	2	no	—
73	C₂×C₃×C₈	—	2	4	no	—
74	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
75	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
76	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
77	C₂²×C₉	—	2	2	no	—
78	C₂²×C₉	—	2	2	no	—
79	C₂²×C₉	—	2	4	no	—
80	C₂²×C₉	—	4	4	no	—
81	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
83	C₄×C₉	—	2	2	no	—
84	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₄×C₉	#117	1	1	yes	characteristic
86	C₄×C₉	#121	1	2	yes	—
87	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
88	C₂×M₁₆	—	2	4	no	—
89	C₂×M₁₆	C₄×C₉	1	4	yes	—
90	C₂×M₁₆	C₂²×C₉	1	4	yes	—
91	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
92	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
93	#108	—	2	4	no	—
94	C₂²⋊C₈	—	2	4	no	—
95	C₂³×C₃	—	2	2	no	—
96	C₂³×C₃	—	4	2	no	—
97	C₂³×C₃	C₃×C₄⋊C₄	1	2	yes	—
98	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
99	C₂×C₃×C₄	—	2	2	no	—
100	C₂×C₃×C₄	—	2	2	no	—
101	C₂×C₃×C₄	—	2	2	no	—
102	C₂×C₃×C₄	—	2	4	no	—
103	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
104	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
106	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄	C₃×#41	1	2	yes	—
108	C₃×C₈	—	2	2	no	—
109	C₃×C₈	—	4	4	no	—
110	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	—
111	C₂×C₉	—	2	2	no	—
112	C₂×C₉	—	4	2	no	—
113	C₂×C₉	#380	1	1	yes	characteristic
114	C₂×C₉	#430	1	2	yes	—
115	C₂⁴	Q₈×C₉	1	1	yes	characteristic
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
119	C₂²×C₄	D₄×C₉	1	2	yes	—
120	C₂²×C₄	Q₈×C₉	1	1	yes	characteristic
121	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
122	M₁₆	—	2	8	no	—
123	M₁₆	—	2	4	no	—
124	M₁₆	—	2	4	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	2	4	no	—
127	C₂×C₈	C₂×C₄×C₉	1	2	yes	—
128	C₂×C₈	C₂×C₄×C₉	1	2	yes	—
129	C₂×C₈	D₄×C₉	1	4	yes	—
130	C₂²×C₃	—	2	2	no	—
131	C₂²×C₃	—	2	2	no	—
132	C₂²×C₃	—	2	4	no	—
133	C₂²×C₃	—	4	4	no	—
134	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×C₃	C₃×C₂²⋊Q₈	1	2	yes	—
136	C₃×C₄	—	2	2	no	—
137	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
138	C₃×C₄	C₃×#117	1	1	yes	characteristic
139	C₃×C₄	C₃×#121	1	2	yes	—
140	C₉	#1811	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	—	2	2	no	—
142	C₂³	—	4	2	no	—
143	C₂³	C₉×C₄⋊C₄	1	2	yes	—
144	C₂³	C₂×Q₈×C₉	1	1	yes	characteristic
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	C₉×C₄⋊C₄	1	2	yes	—
150	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
151	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
152	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
153	C₂×C₄	C₉×#41	1	2	yes	—
154	C₈	—	2	2	no	—
155	C₈	—	4	4	no	—
156	C₈	C₉×C₂²⋊C₄	1	4	yes	—
157	C₂×C₃	—	2	2	no	—
158	C₂×C₃	—	4	2	no	—
159	C₂×C₃	C₃×#380	1	1	yes	characteristic
160	C₂×C₃	C₃×#430	1	2	yes	—
161	C₂²	—	2	2	no	—
162	C₂²	—	2	2	no	—
163	C₂²	—	2	4	no	—
164	C₂²	—	4	4	no	—
165	C₂²	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
166	C₂²	C₉×C₂²⋊Q₈	1	2	yes	—
167	C₄	—	2	2	no	—
168	C₄	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
169	C₄	C₉×#117	1	1	yes	characteristic
170	C₄	C₉×#121	1	2	yes	—
171	C₃	C₃×#1811	1	1	yes	characteristic
172	C₂	—	2	2	no	—
173	C₂	—	4	2	no	—
174	C₂	C₉×#380	1	1	yes	characteristic
175	C₂	C₉×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₄⋊C₄
prime radical	C₂⁴×C₃	C₃×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#108	C₂	semidirect
4. C₉×#341	C₂	semidirect
33. #1811	C₉	direct (N × H)
59. C₂×#108	C₂×C₉	semidirect
61. #341	C₂×C₉	semidirect
140. C₉	#1811	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×M₁₆	2
C₂×C₉×#108	2
C₉×#407	2
C₉×#341	2
C₃×#1811	3

Subgroups — C9×#1811 #11766532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1811 #11766532