Subgroups — C₉×#2076 #11766797

Order 1152.

384 conjugacy classes of subgroups.

The subgroup lattice has 237 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	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₉×#380	C₂	1	2	yes	maximal
4	C₉×#340	C₂	1	2	yes	maximal, complemented
5	C₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2076	C₃	1	1	yes	maximal, characteristic
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
13	C₉×#107	—	2	2	no	—
14	C₉×C₂²⋊C₈	—	2	2	no	—
15	C₉×#95	—	2	2	no	—
16	C₂×C₃×#107	C₂×C₃	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
18	C₃×#380	C₂×C₃	1	2	yes	—
19	C₃×#340	C₂×C₃	1	2	yes	—
20	C₃×#340	C₂×C₃	1	1	yes	characteristic
21	C₂⁴×C₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₉	—	2	1	no	—
23	C₂²×C₄×C₉	—	2	1	no	—
24	C₂²×C₄×C₉	—	2	2	no	—
25	C₂²×C₄×C₉	—	2	2	no	—
26	C₂²×C₄×C₉	—	2	2	no	—
27	C₂²×C₄×C₉	—	2	2	no	—
28	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₉	—	2	2	no	—
31	C₂×C₈×C₉	—	2	1	no	—
32	C₂×C₈×C₉	—	2	2	no	—
33	C₂×C₈×C₉	D₄	1	2	yes	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	—	2	2	no	—
37	C₉×C₄⋊C₄	—	2	2	no	—
38	C₉×C₂²⋊C₄	—	4	4	no	—
39	#2076	C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
42	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
43	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
44	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
46	C₃×#107	—	2	2	no	—
47	C₃×C₂²⋊C₈	—	2	2	no	—
48	C₃×#95	—	2	2	no	—
49	C₂³×C₉	—	2	1	no	—
50	C₂³×C₉	—	2	2	no	—
51	C₂³×C₉	—	2	1	no	—
52	C₂³×C₉	—	2	2	no	—
53	C₂³×C₉	Q₁₆	1	2	yes	—
54	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₉	—	2	1	no	—
56	C₂×C₄×C₉	—	2	2	no	—
57	C₂×C₄×C₉	—	4	1	no	—
58	C₂×C₄×C₉	—	4	1	no	—
59	C₂×C₄×C₉	—	4	2	no	—
60	C₂×C₄×C₉	—	4	2	no	—
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	—	4	2	no	—
63	C₂×C₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	4	2	no	—
65	C₂×C₄×C₉	—	4	2	no	—
66	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₉	#41	1	2	yes	—
68	C₂×C₄×C₉	#41	1	2	yes	—
69	C₂×C₄×C₉	#41	1	1	yes	characteristic
70	C₈×C₉	—	2	2	no	—
71	C₈×C₉	—	4	1	no	—
72	C₂×#107	C₂×C₉	1	1	yes	characteristic, complemented
73	C₂×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic
74	#380	C₂×C₉	1	2	yes	—
75	#340	C₂×C₉	1	1	yes	characteristic, complemented
76	#340	C₂×C₉	1	2	yes	complemented
77	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
78	C₂²×C₃×C₄	—	2	1	no	—
79	C₂²×C₃×C₄	—	2	1	no	—
80	C₂²×C₃×C₄	—	2	2	no	—
81	C₂²×C₃×C₄	—	2	2	no	—
82	C₂²×C₃×C₄	—	2	2	no	—
83	C₂²×C₃×C₄	—	2	2	no	—
84	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
85	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
86	C₂×C₃×C₈	—	2	2	no	—
87	C₂×C₃×C₈	—	2	1	no	—
88	C₂×C₃×C₈	—	2	2	no	—
89	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
90	C₃×C₄⋊C₄	—	2	2	no	—
91	C₃×C₄⋊C₄	—	2	2	no	—
92	C₃×C₄⋊C₄	—	2	2	no	—
93	C₃×C₄⋊C₄	—	2	2	no	—
94	C₃×C₂²⋊C₄	—	4	4	no	—
95	C₂²×C₉	—	2	2	no	—
96	C₂²×C₉	—	2	4	no	—
97	C₂²×C₉	—	4	1	no	—
98	C₂²×C₉	—	4	1	no	—
99	C₂²×C₉	—	4	2	no	—
100	C₂²×C₉	#121	1	1	yes	characteristic
101	C₂²×C₉	#123	1	2	yes	—
102	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
103	C₂²×C₉	#135	1	1	yes	characteristic
104	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
105	C₄×C₉	—	4	1	no	—
106	C₄×C₉	—	8	2	no	—
107	C₄×C₉	—	8	2	no	—
108	C₄×C₉	#123	1	1	yes	characteristic
109	C₄×C₉	#124	1	1	yes	characteristic
110	C₄×C₉	#126	1	2	yes	—
111	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
112	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
113	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
116	C₂×C₂²⋊C₄	—	2	2	no	—
117	#107	—	2	2	no	—
118	C₂²⋊C₈	—	2	2	no	—
119	#95	—	2	2	no	—
120	C₂³×C₃	—	2	1	no	—
121	C₂³×C₃	—	2	2	no	—
122	C₂³×C₃	—	2	1	no	—
123	C₂³×C₃	—	2	2	no	—
124	C₂³×C₃	C₃×Q₁₆	1	2	yes	—
125	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄	—	2	1	no	—
127	C₂×C₃×C₄	—	2	2	no	—
128	C₂×C₃×C₄	—	4	1	no	—
129	C₂×C₃×C₄	—	4	1	no	—
130	C₂×C₃×C₄	—	4	2	no	—
131	C₂×C₃×C₄	—	4	2	no	—
132	C₂×C₃×C₄	—	4	2	no	—
133	C₂×C₃×C₄	—	4	2	no	—
134	C₂×C₃×C₄	—	4	2	no	—
135	C₂×C₃×C₄	—	4	2	no	—
136	C₂×C₃×C₄	—	4	2	no	—
137	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄	C₃×#41	1	2	yes	—
139	C₂×C₃×C₄	C₃×#41	1	2	yes	—
140	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
141	C₃×C₈	—	2	2	no	—
142	C₃×C₈	—	4	1	no	—
143	C₂×C₉	—	4	2	no	—
144	C₂×C₉	#397	1	1	yes	characteristic
145	C₂×C₉	#467	1	1	yes	characteristic
146	C₂×C₉	#469	1	1	yes	characteristic
147	C₂×C₉	#482	1	2	yes	—
148	C₂×C₉	#484	1	2	yes	—
149	C₂⁴	D₄×C₉	1	1	yes	characteristic
150	C₂²×C₄	—	2	1	no	—
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
157	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	D₄×C₉	1	2	yes	—
162	C₄⋊C₄	—	2	2	no	—
163	C₄⋊C₄	—	2	2	no	—
164	C₄⋊C₄	—	2	2	no	—
165	C₄⋊C₄	—	2	2	no	—
166	C₂²⋊C₄	—	4	4	no	—
167	C₂²×C₃	—	2	2	no	—
168	C₂²×C₃	—	2	4	no	—
169	C₂²×C₃	—	4	1	no	—
170	C₂²×C₃	—	4	1	no	—
171	C₂²×C₃	—	4	2	no	—
172	C₂²×C₃	C₃×#121	1	1	yes	characteristic
173	C₂²×C₃	C₃×#123	1	2	yes	—
174	C₂²×C₃	C₂×C₃×Q₁₆	1	1	yes	characteristic
175	C₂²×C₃	C₃×#135	1	1	yes	characteristic
176	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
177	C₃×C₄	—	4	1	no	—
178	C₃×C₄	—	8	2	no	—
179	C₃×C₄	—	8	2	no	—
180	C₃×C₄	C₃×#123	1	1	yes	characteristic
181	C₃×C₄	C₃×#124	1	1	yes	characteristic
182	C₃×C₄	C₃×#126	1	2	yes	—
183	C₉	#2076	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	—	2	1	no	—
185	C₂³	—	2	2	no	—
186	C₂³	—	2	1	no	—
187	C₂³	—	2	2	no	—
188	C₂³	C₉×Q₁₆	1	2	yes	—
189	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
202	C₂×C₄	C₉×#41	1	2	yes	—
203	C₂×C₄	C₉×#41	1	2	yes	—
204	C₂×C₄	C₉×#41	1	1	yes	characteristic
205	C₈	—	2	2	no	—
206	C₈	—	4	1	no	—
207	C₂×C₃	—	4	2	no	—
208	C₂×C₃	C₃×#397	1	1	yes	characteristic
209	C₂×C₃	C₃×#467	1	1	yes	characteristic
210	C₂×C₃	C₃×#469	1	1	yes	characteristic
211	C₂×C₃	C₃×#482	1	2	yes	—
212	C₂×C₃	C₃×#484	1	2	yes	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	1	no	—
216	C₂²	—	4	1	no	—
217	C₂²	—	4	2	no	—
218	C₂²	C₉×#121	1	1	yes	characteristic
219	C₂²	C₉×#123	1	2	yes	—
220	C₂²	C₂×C₉×Q₁₆	1	1	yes	characteristic
221	C₂²	C₉×#135	1	1	yes	characteristic
222	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	—
223	C₄	—	4	1	no	—
224	C₄	—	8	2	no	—
225	C₄	—	8	2	no	—
226	C₄	C₉×#123	1	1	yes	characteristic
227	C₄	C₉×#124	1	1	yes	characteristic
228	C₄	C₉×#126	1	2	yes	—
229	C₃	C₃×#2076	1	1	yes	characteristic
230	C₂	—	4	2	no	—
231	C₂	C₉×#397	1	1	yes	characteristic
232	C₂	C₉×#467	1	1	yes	characteristic
233	C₂	C₉×#469	1	1	yes	characteristic
234	C₂	C₉×#482	1	2	yes	—
235	C₂	C₉×#484	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#107	C₂	semidirect
4. C₉×#340	C₂	semidirect
5. C₉×#340	C₂	semidirect
39. #2076	C₉	direct (N × H)
72. C₂×#107	C₂×C₉	semidirect
75. #340	C₂×C₉	semidirect
76. #340	C₂×C₉	semidirect
183. C₉	#2076	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×C₂²⋊C₈	2
C₉×#380	2
C₉×#340	2
C₃×#2076	3

Subgroups — C9×#2076 #11766797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2076 #11766797