Subgroups — C₉×#1283 #11766004

Order 1152.

240 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#1283	C₃	1	1	yes	maximal, characteristic
5	C₂×C₉×M₁₆	C₄	1	2	yes	—
6	C₂²×C₈×C₉	C₄	1	2	yes	—
7	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₉×C₄⋊C₈	—	2	1	no	—
9	C₉×C₄⋊C₈	—	2	1	no	—
10	C₉×C₄⋊C₈	—	2	1	no	—
11	C₉×C₂²⋊C₈	C₄	1	2	yes	—
12	C₉×#97	—	2	1	no	—
13	C₄×C₈×C₉	—	2	1	no	—
14	C₄×C₈×C₉	—	2	1	no	—
15	C₃×#431	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
17	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
21	C₉×M₁₆	—	2	2	no	—
22	C₉×M₁₆	C₈	1	4	yes	complemented
23	C₂×C₈×C₉	—	2	2	no	—
24	C₂×C₈×C₉	—	2	2	no	—
25	C₂×C₈×C₉	—	2	2	no	—
26	C₂×C₈×C₉	—	4	2	no	—
27	C₄²×C₉	D₄	1	1	yes	characteristic
28	C₄²×C₉	D₄	1	1	yes	characteristic
29	C₄²×C₉	D₄	1	1	yes	characteristic
30	C₄²×C₉	Q₈	1	1	yes	characteristic
31	#1283	C₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×M₁₆	C₃×C₄	1	2	yes	—
33	C₂²×C₃×C₈	C₃×C₄	1	2	yes	—
34	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
35	C₃×C₄⋊C₈	—	2	1	no	—
36	C₃×C₄⋊C₈	—	2	1	no	—
37	C₃×C₄⋊C₈	—	2	1	no	—
38	C₃×C₂²⋊C₈	C₃×C₄	1	2	yes	—
39	C₃×#97	—	2	1	no	—
40	C₃×C₄×C₈	—	2	1	no	—
41	C₃×C₄×C₈	—	2	1	no	—
42	C₂³×C₉	C₄²	1	1	yes	characteristic
43	C₂×C₄×C₉	—	2	1	no	—
44	C₂×C₄×C₉	—	2	1	no	—
45	C₂×C₄×C₉	—	4	1	no	—
46	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
53	C₂×C₄×C₉	M₁₆	1	2	yes	—
54	C₈×C₉	—	2	4	no	—
55	C₈×C₉	—	4	2	no	—
56	C₈×C₉	—	4	2	no	—
57	#431	C₂×C₉	1	1	yes	characteristic
58	C₂×C₄⋊C₈	C₂×C₉	1	1	yes	characteristic
59	C₄×M₁₆	C₂×C₉	1	1	yes	characteristic
60	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
61	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
62	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
63	C₃×M₁₆	—	2	2	no	—
64	C₃×M₁₆	C₃×C₈	1	4	yes	—
65	C₂×C₃×C₈	—	2	2	no	—
66	C₂×C₃×C₈	—	2	2	no	—
67	C₂×C₃×C₈	—	2	2	no	—
68	C₂×C₃×C₈	—	4	2	no	—
69	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
70	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
71	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
72	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
73	C₂²×C₉	—	2	1	no	—
74	C₂²×C₉	—	2	1	no	—
75	C₂²×C₉	#95	1	1	yes	characteristic
76	C₂²×C₉	C₄×C₈	1	1	yes	characteristic
77	C₂²×C₉	#97	1	1	yes	characteristic
78	C₄×C₉	—	2	1	no	—
79	C₄×C₉	—	2	1	no	—
80	C₄×C₉	—	2	1	no	—
81	C₄×C₉	C₂²⋊C₈	1	2	yes	—
82	C₄×C₉	#100	1	1	yes	characteristic
83	C₄×C₉	#101	1	1	yes	characteristic
84	C₄×C₉	C₄⋊C₈	1	2	yes	—
85	C₂×M₁₆	C₄×C₉	1	2	yes	—
86	C₂²×C₈	C₄×C₉	1	2	yes	—
87	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
88	C₄⋊C₈	—	2	1	no	—
89	C₄⋊C₈	—	2	1	no	—
90	C₄⋊C₈	—	2	1	no	—
91	C₂²⋊C₈	C₄×C₉	1	2	yes	—
92	#97	—	2	1	no	—
93	C₄×C₈	—	2	1	no	—
94	C₄×C₈	—	2	1	no	—
95	C₂³×C₃	C₃×C₄²	1	1	yes	characteristic
96	C₂×C₃×C₄	—	2	1	no	—
97	C₂×C₃×C₄	—	2	1	no	—
98	C₂×C₃×C₄	—	4	1	no	—
99	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₃×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
106	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
107	C₃×C₈	—	2	4	no	—
108	C₃×C₈	—	4	2	no	—
109	C₃×C₈	—	4	2	no	—
110	C₂×C₉	—	2	1	no	—
111	C₂×C₉	—	2	1	no	—
112	C₂×C₉	#336	1	1	yes	characteristic
113	C₂×C₉	#343	1	1	yes	characteristic
114	C₂×C₉	#344	1	1	yes	characteristic
115	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
117	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
118	M₁₆	—	2	2	no	—
119	M₁₆	C₈×C₉	1	4	yes	complemented
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	2	2	no	—
123	C₂×C₈	—	4	2	no	—
124	C₄²	D₄×C₉	1	1	yes	characteristic
125	C₄²	D₄×C₉	1	1	yes	characteristic
126	C₄²	D₄×C₉	1	1	yes	characteristic
127	C₄²	Q₈×C₉	1	1	yes	characteristic
128	C₂²×C₃	—	2	1	no	—
129	C₂²×C₃	—	2	1	no	—
130	C₂²×C₃	C₃×#95	1	1	yes	characteristic
131	C₂²×C₃	C₃×C₄×C₈	1	1	yes	characteristic
132	C₂²×C₃	C₃×#97	1	1	yes	characteristic
133	C₃×C₄	—	2	1	no	—
134	C₃×C₄	—	2	1	no	—
135	C₃×C₄	—	2	1	no	—
136	C₃×C₄	C₃×C₂²⋊C₈	1	2	yes	—
137	C₃×C₄	C₃×#100	1	1	yes	characteristic
138	C₃×C₄	C₃×#101	1	1	yes	characteristic
139	C₃×C₄	C₃×C₄⋊C₈	1	2	yes	—
140	C₉	#1283	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	C₄²×C₉	1	1	yes	characteristic
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	1	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄	C₉×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄	C₂×C₈×C₉	1	2	yes	—
152	C₂×C₄	C₉×M₁₆	1	2	yes	—
153	C₈	—	2	4	no	—
154	C₈	—	4	2	no	—
155	C₈	—	4	2	no	—
156	C₂×C₃	—	2	1	no	—
157	C₂×C₃	—	2	1	no	—
158	C₂×C₃	C₃×#336	1	1	yes	characteristic
159	C₂×C₃	C₃×#343	1	1	yes	characteristic
160	C₂×C₃	C₃×#344	1	1	yes	characteristic
161	C₂²	—	2	1	no	—
162	C₂²	—	2	1	no	—
163	C₂²	C₉×#95	1	1	yes	characteristic
164	C₂²	C₄×C₈×C₉	1	1	yes	characteristic
165	C₂²	C₉×#97	1	1	yes	characteristic
166	C₄	—	2	1	no	—
167	C₄	—	2	1	no	—
168	C₄	—	2	1	no	—
169	C₄	C₉×C₂²⋊C₈	1	2	yes	—
170	C₄	C₉×#100	1	1	yes	characteristic
171	C₄	C₉×#101	1	1	yes	characteristic
172	C₄	C₉×C₄⋊C₈	1	2	yes	—
173	C₃	C₃×#1283	1	1	yes	characteristic
174	C₂	—	2	1	no	—
175	C₂	—	2	1	no	—
176	C₂	C₉×#336	1	1	yes	characteristic
177	C₂	C₉×#343	1	1	yes	characteristic
178	C₂	C₉×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²⋊C₄
commutator	C₂²	C₄×C₈×C₉
Frattini, cosocle	C₂×C₃×C₄²	C₂²×C₃
socle	C₂²×C₃	C₃×#95
prime radical	C₂³×C₃	C₃×C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₉×M₁₆	C₈	semidirect
31. #1283	C₉	direct (N × H)
119. M₁₆	C₈×C₉	semidirect
140. C₉	#1283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#431	2
C₂×C₉×C₄⋊C₈	2
C₄×C₉×M₁₆	2
C₃×#1283	3

Subgroups — C9×#1283 #11766004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1283 #11766004