Subgroups — C₉×#2095 #11766816

Order 1152.

381 conjugacy classes of subgroups.

The subgroup lattice has 201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#107	C₂	1	2	yes	maximal
2	C₂×C₉×#103	C₂	1	2	yes	maximal
3	C₉×#391	C₂	1	1	yes	maximal, characteristic
4	C₉×#384	C₂	1	1	yes	maximal, characteristic
5	C₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₃×#2095	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₂×C₉×C₄⋊C₄	—	2	2	no	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₉×#107	—	2	4	no	—
14	C₉×#103	—	2	4	no	—
15	C₉×#95	—	2	2	no	—
16	C₂×C₃×#107	C₂×C₃	1	2	yes	—
17	C₂×C₃×#103	C₂×C₃	1	2	yes	—
18	C₃×#391	C₂×C₃	1	1	yes	characteristic
19	C₃×#384	C₂×C₃	1	1	yes	characteristic
20	C₃×#336	C₂×C₃	1	1	yes	characteristic
21	C₂×Q₈×C₉	—	2	1	no	—
22	C₂×Q₈×C₉	—	2	2	no	—
23	C₂×Q₈×C₉	—	2	2	no	—
24	C₂×Q₈×C₉	Q₈	1	2	yes	—
25	C₂²×C₄×C₉	—	2	1	no	—
26	C₂²×C₄×C₉	—	2	2	no	—
27	C₂²×C₄×C₉	—	2	1	no	—
28	C₂²×C₄×C₉	D₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₉	—	2	2	no	—
31	C₂×C₈×C₉	—	2	2	no	—
32	C₂×C₈×C₉	D₄	1	4	yes	—
33	C₉×C₄⋊C₄	—	2	2	no	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	—	4	4	no	—
37	C₄²×C₉	—	2	2	no	—
38	#2095	C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
41	C₂×C₃×C₄⋊C₄	—	2	2	no	—
42	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
43	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
44	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
45	C₃×#107	—	2	4	no	—
46	C₃×#103	—	2	4	no	—
47	C₃×#95	—	2	2	no	—
48	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
49	Q₈×C₉	—	2	4	no	—
50	Q₈×C₉	—	4	2	no	—
51	C₂×C₄×C₉	—	2	2	no	—
52	C₂×C₄×C₉	—	2	2	no	—
53	C₂×C₄×C₉	—	2	2	no	—
54	C₂×C₄×C₉	—	4	1	no	—
55	C₂×C₄×C₉	—	4	1	no	—
56	C₂×C₄×C₉	—	4	2	no	—
57	C₂×C₄×C₉	—	4	1	no	—
58	C₂×C₄×C₉	—	4	4	no	—
59	C₂×C₄×C₉	—	4	2	no	—
60	C₂×C₄×C₉	Q₁₆	1	4	yes	—
61	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₄×C₉	#41	1	2	yes	—
64	C₂×C₄×C₉	#41	1	1	yes	characteristic
65	C₈×C₉	—	2	4	no	—
66	C₂×#107	C₂×C₉	1	2	yes	—
67	C₂×#103	C₂×C₉	1	2	yes	—
68	#391	C₂×C₉	1	1	yes	characteristic
69	#384	C₂×C₉	1	1	yes	characteristic
70	#336	C₂×C₉	1	1	yes	characteristic
71	C₂×C₃×Q₈	—	2	1	no	—
72	C₂×C₃×Q₈	—	2	2	no	—
73	C₂×C₃×Q₈	—	2	2	no	—
74	C₂×C₃×Q₈	C₃×Q₈	1	2	yes	—
75	C₂²×C₃×C₄	—	2	1	no	—
76	C₂²×C₃×C₄	—	2	1	no	—
77	C₂²×C₃×C₄	—	2	2	no	—
78	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
79	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
80	C₂×C₃×C₈	—	2	2	no	—
81	C₂×C₃×C₈	—	2	2	no	—
82	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
83	C₃×C₄⋊C₄	—	2	2	no	—
84	C₃×C₄⋊C₄	—	2	2	no	—
85	C₃×C₄⋊C₄	—	2	2	no	—
86	C₃×C₄⋊C₄	—	4	4	no	—
87	C₃×C₄²	—	2	2	no	—
88	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂²×C₉	#123	1	1	yes	characteristic
90	C₂²×C₉	#127	1	1	yes	characteristic
91	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
92	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
93	C₄×C₉	—	2	4	no	—
94	C₄×C₉	—	4	2	no	—
95	C₄×C₉	—	8	2	no	—
96	C₄×C₉	—	8	1	no	—
97	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
98	C₄×C₉	#123	1	2	yes	—
99	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
100	C₂²×C₈	C₂²×C₉	1	2	yes	—
101	C₂×C₄⋊C₄	—	2	2	no	—
102	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
103	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
104	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
105	#107	—	2	4	no	—
106	#103	—	2	4	no	—
107	#95	—	2	2	no	—
108	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
109	C₃×Q₈	—	2	4	no	—
110	C₃×Q₈	—	4	2	no	—
111	C₂×C₃×C₄	—	2	2	no	—
112	C₂×C₃×C₄	—	2	2	no	—
113	C₂×C₃×C₄	—	2	2	no	—
114	C₂×C₃×C₄	—	4	1	no	—
115	C₂×C₃×C₄	—	4	1	no	—
116	C₂×C₃×C₄	—	4	2	no	—
117	C₂×C₃×C₄	—	4	1	no	—
118	C₂×C₃×C₄	—	4	4	no	—
119	C₂×C₃×C₄	—	4	2	no	—
120	C₂×C₃×C₄	C₃×Q₁₆	1	4	yes	—
121	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
122	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
123	C₂×C₃×C₄	C₃×#41	1	2	yes	—
124	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
125	C₃×C₈	—	2	4	no	—
126	C₂×C₉	#399	1	1	yes	characteristic
127	C₂×C₉	#477	1	2	yes	—
128	C₂×C₉	#484	1	2	yes	—
129	C₂×C₉	#494	1	1	yes	characteristic
130	C₂×C₉	#496	1	1	yes	characteristic
131	C₂×Q₈	—	2	1	no	—
132	C₂×Q₈	—	2	2	no	—
133	C₂×Q₈	—	2	2	no	—
134	C₂×Q₈	Q₈×C₉	1	2	yes	—
135	C₂²×C₄	—	2	1	no	—
136	C₂²×C₄	—	2	1	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	D₄×C₉	1	2	yes	—
139	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	D₄×C₉	1	4	yes	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	—	4	4	no	—
147	C₄²	—	2	2	no	—
148	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
149	C₂²×C₃	C₃×#123	1	1	yes	characteristic
150	C₂²×C₃	C₃×#127	1	1	yes	characteristic
151	C₂²×C₃	C₂×C₃×Q₁₆	1	2	yes	—
152	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
153	C₃×C₄	—	2	4	no	—
154	C₃×C₄	—	4	2	no	—
155	C₃×C₄	—	8	2	no	—
156	C₃×C₄	—	8	1	no	—
157	C₃×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
158	C₃×C₄	C₃×#123	1	2	yes	—
159	C₉	#2095	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
161	Q₈	—	2	4	no	—
162	Q₈	—	4	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	4	1	no	—
167	C₂×C₄	—	4	1	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	1	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	C₉×Q₁₆	1	4	yes	—
173	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
174	C₂×C₄	C₂×Q₈×C₉	1	1	yes	characteristic
175	C₂×C₄	C₉×#41	1	2	yes	—
176	C₂×C₄	C₉×#41	1	1	yes	characteristic
177	C₈	—	2	4	no	—
178	C₂×C₃	C₃×#399	1	1	yes	characteristic
179	C₂×C₃	C₃×#477	1	2	yes	—
180	C₂×C₃	C₃×#484	1	2	yes	—
181	C₂×C₃	C₃×#494	1	1	yes	characteristic
182	C₂×C₃	C₃×#496	1	1	yes	characteristic
183	C₂²	C₉×C₂²⋊Q₈	1	1	yes	characteristic
184	C₂²	C₉×#123	1	1	yes	characteristic
185	C₂²	C₉×#127	1	1	yes	characteristic
186	C₂²	C₂×C₉×Q₁₆	1	2	yes	—
187	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
188	C₄	—	2	4	no	—
189	C₄	—	4	2	no	—
190	C₄	—	8	2	no	—
191	C₄	—	8	1	no	—
192	C₄	C₉×C₂²⋊Q₈	1	2	yes	—
193	C₄	C₉×#123	1	2	yes	—
194	C₃	C₃×#2095	1	1	yes	characteristic
195	C₂	C₉×#399	1	1	yes	characteristic
196	C₂	C₉×#477	1	2	yes	—
197	C₂	C₉×#484	1	2	yes	—
198	C₂	C₉×#494	1	1	yes	characteristic
199	C₂	C₉×#496	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
LCS	G ▷ C₂²×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
38. #2095	C₉	direct (N × H)
159. C₉	#2095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#107	2
C₂×C₉×#103	2
C₉×#391	2
C₉×#384	2
C₉×#336	2
C₃×#2095	3

Subgroups — C9×#2095 #11766816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2095 #11766816