Subgroups — C₉×#2960 #11767681

Order 1152.

546 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	4	yes	maximal, complemented
3	C₈×Q₈×C₉	C₂	1	4	yes	maximal, complemented
4	C₉×#424	C₂	1	2	yes	maximal
5	C₉×#423	C₂	1	1	yes	maximal, characteristic
6	C₉×#405	C₂	1	2	yes	maximal
7	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
8	C₃×#2960	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₉×C₄⋊Q₈	C₄	1	2	yes	—
13	C₉×#125	C₄	1	2	yes	—
14	C₉×C₂²⋊Q₈	C₄	1	4	yes	—
15	C₄×Q₈×C₉	C₂²	1	4	yes	—
16	C₉×#117	C₂²	1	2	yes	—
17	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
18	C₉×C₄⋊C₈	C₂²	1	4	yes	—
19	C₉×C₄⋊C₈	C₂²	1	8	yes	—
20	C₉×#97	C₂²	1	4	yes	—
21	C₄×C₈×C₉	C₂²	1	2	yes	—
22	C₄×C₈×C₉	C₂²	1	2	yes	—
23	C₄×C₈×C₉	C₂²	1	4	yes	—
24	C₃×#533	C₂×C₃	1	1	yes	characteristic
25	C₃×#446	C₂×C₃	1	4	yes	—
26	C₃×C₈×Q₈	C₂×C₃	1	4	yes	—
27	C₃×#424	C₂×C₃	1	2	yes	—
28	C₃×#423	C₂×C₃	1	1	yes	characteristic
29	C₃×#405	C₂×C₃	1	2	yes	—
30	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
31	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
34	C₉×M₁₆	—	2	4	no	—
35	C₂×C₈×C₉	—	2	2	no	—
36	C₂×C₈×C₉	Q₈	1	4	yes	complemented
37	C₂×C₈×C₉	C₂³	1	2	yes	—
38	C₂×C₈×C₉	C₂³	1	4	yes	—
39	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
40	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
41	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
42	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
43	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
45	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
46	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₉	C₂³	1	2	yes	—
48	C₄²×C₉	C₂³	1	4	yes	—
49	#2960	C₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
51	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
53	C₃×C₄⋊Q₈	C₃×C₄	1	2	yes	—
54	C₃×#125	C₃×C₄	1	2	yes	—
55	C₃×C₂²⋊Q₈	C₃×C₄	1	4	yes	—
56	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
57	C₃×#117	C₂²×C₃	1	2	yes	—
58	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
59	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
60	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
61	C₃×#97	C₂²×C₃	1	4	yes	—
62	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
63	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
64	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
65	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
66	Q₈×C₉	—	2	8	no	—
67	C₂×C₄×C₉	—	2	4	no	—
68	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
70	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
73	C₂×C₄×C₉	#41	1	2	yes	—
74	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
75	C₈×C₉	—	2	2	no	—
76	C₈×C₉	—	2	4	no	—
77	C₈×C₉	C₂×Q₈	1	2	yes	—
78	C₈×C₉	C₂×Q₈	1	2	yes	—
79	#533	C₂×C₉	1	1	yes	characteristic
80	#446	C₂×C₉	1	4	yes	complemented
81	C₈×Q₈	C₂×C₉	1	4	yes	complemented
82	#424	C₂×C₉	1	2	yes	—
83	#423	C₂×C₉	1	1	yes	characteristic
84	#405	C₂×C₉	1	2	yes	—
85	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic
86	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
87	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
88	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
89	C₃×M₁₆	—	2	4	no	—
90	C₂×C₃×C₈	—	2	2	no	—
91	C₂×C₃×C₈	C₃×Q₈	1	4	yes	—
92	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
93	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
94	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
95	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
96	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
97	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
98	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
99	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
100	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
101	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
102	C₃×C₄²	C₂³×C₃	1	2	yes	—
103	C₃×C₄²	C₂³×C₃	1	4	yes	—
104	C₂²×C₉	—	2	2	no	—
105	C₂²×C₉	C₄×Q₈	1	2	yes	—
106	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
107	C₄×C₉	—	2	2	no	—
108	C₄×C₉	—	2	8	no	—
109	C₄×C₉	C₄×Q₈	1	2	yes	—
110	C₄×C₉	#131	1	4	yes	—
111	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
112	C₄×C₉	C₂×#41	1	1	yes	characteristic
113	C₂×M₁₆	C₂²×C₉	1	2	yes	—
114	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
115	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
116	C₄⋊Q₈	C₄×C₉	1	2	yes	—
117	#125	C₄×C₉	1	2	yes	—
118	C₂²⋊Q₈	C₄×C₉	1	4	yes	—
119	C₄×Q₈	C₂²×C₉	1	4	yes	—
120	#117	C₂²×C₉	1	2	yes	—
121	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
122	C₄⋊C₈	C₂²×C₉	1	4	yes	—
123	C₄⋊C₈	C₂²×C₉	1	8	yes	—
124	#97	C₂²×C₉	1	4	yes	—
125	C₄×C₈	C₂²×C₉	1	2	yes	—
126	C₄×C₈	C₂²×C₉	1	2	yes	—
127	C₄×C₈	C₂²×C₉	1	4	yes	—
128	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
129	C₃×Q₈	—	2	8	no	—
130	C₂×C₃×C₄	—	2	4	no	—
131	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
132	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
133	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
135	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
136	C₂×C₃×C₄	C₃×#41	1	2	yes	—
137	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
138	C₃×C₈	—	2	2	no	—
139	C₃×C₈	—	2	4	no	—
140	C₃×C₈	C₂×C₃×Q₈	1	2	yes	—
141	C₃×C₈	C₂×C₃×Q₈	1	2	yes	—
142	C₂×C₉	—	2	2	no	—
143	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
144	C₂×C₉	C₂×#131	1	2	yes	—
145	C₂×Q₈	C₂×C₄×C₉	1	4	yes	—
146	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
147	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
148	M₁₆	—	2	4	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	Q₈×C₉	1	4	yes	complemented
151	C₂×C₈	C₂³×C₉	1	2	yes	—
152	C₂×C₈	C₂³×C₉	1	4	yes	—
153	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
154	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
155	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
156	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
157	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
158	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	—
159	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
160	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
161	C₄²	C₂³×C₉	1	2	yes	—
162	C₄²	C₂³×C₉	1	4	yes	—
163	C₂²×C₃	—	2	2	no	—
164	C₂²×C₃	C₃×C₄×Q₈	1	2	yes	—
165	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
166	C₃×C₄	—	2	2	no	—
167	C₃×C₄	—	2	8	no	—
168	C₃×C₄	C₃×C₄×Q₈	1	2	yes	—
169	C₃×C₄	C₃×#131	1	4	yes	—
170	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
171	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
172	C₉	#2960	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
174	Q₈	—	2	8	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
177	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
178	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
179	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
180	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
181	C₂×C₄	C₉×#41	1	2	yes	—
182	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	—	2	4	no	—
185	C₈	C₂×Q₈×C₉	1	2	yes	—
186	C₈	C₂×Q₈×C₉	1	2	yes	—
187	C₂×C₃	—	2	2	no	—
188	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
189	C₂×C₃	C₂×C₃×#131	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	C₄×Q₈×C₉	1	2	yes	—
192	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	2	8	no	—
195	C₄	C₄×Q₈×C₉	1	2	yes	—
196	C₄	C₉×#131	1	4	yes	—
197	C₄	C₂²×Q₈×C₉	1	1	yes	characteristic
198	C₄	C₂×C₉×#41	1	1	yes	characteristic
199	C₃	C₃×#2960	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	C₂×C₄×Q₈×C₉	1	1	yes	characteristic
202	C₂	C₂×C₉×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂³×C₃×C₄
prime radical	C₂³×C₃	C₂²×C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
3. C₈×Q₈×C₉	C₂	semidirect
36. C₂×C₈×C₉	Q₈	semidirect
49. #2960	C₉	direct (N × H)
80. #446	C₂×C₉	semidirect
81. C₈×Q₈	C₂×C₉	semidirect
150. C₂×C₈	Q₈×C₉	semidirect
172. C₉	#2960	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×#533	2
C₉×#446	2
C₈×Q₈×C₉	2
C₉×#424	2
C₉×#423	2
C₉×#405	2
C₂×C₄×C₈×C₉	2
C₃×#2960	3

Subgroups — C9×#2960 #11767681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2960 #11767681