Subgroups — C₉×#2388 #11767109

Order 1152.

1416 conjugacy classes of subgroups.

The subgroup lattice has 267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₉	C₂	1	3	yes	maximal, complemented
3	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#394	C₂	1	3	yes	maximal, complemented
5	C₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#392	C₂	1	3	yes	maximal, complemented
7	C₄×C₉×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
8	C₃×#2388	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	—	2	12	no	—
10	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₉	C₂²	1	3	yes	—
12	C₂²×D₄×C₉	C₂²	1	3	yes	—
13	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	3	yes	—
15	C₄×D₄×C₉	—	2	12	no	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	—
17	C₂×C₉×C₂²⋊C₄	C₂²	1	6	yes	—
18	C₂×C₉×C₂²⋊C₄	C₂²	1	3	yes	—
19	C₂×C₉×C₂²⋊C₄	C₂²	1	3	yes	—
20	C₂×C₄²×C₉	C₂²	1	3	yes	—
21	C₉×#95	C₂²	1	3	yes	—
22	C₉×#95	C₂²	1	3	yes	—
23	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×C₄×D₄	C₂×C₃	1	3	yes	—
25	C₃×#395	C₂×C₃	1	1	yes	characteristic
26	C₃×#394	C₂×C₃	1	3	yes	—
27	C₃×#393	C₂×C₃	1	1	yes	characteristic
28	C₃×#392	C₂×C₃	1	3	yes	—
29	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	3	yes	—
30	C₂⁴×C₉	C₂³	1	3	yes	—
31	C₂⁴×C₉	C₂³	1	1	yes	characteristic
32	C₉×#41	—	2	32	no	—
33	C₂×Q₈×C₉	—	2	6	no	—
34	C₂×D₄×C₉	—	2	6	no	—
35	C₂×D₄×C₉	—	2	12	no	—
36	C₂×D₄×C₉	—	2	6	no	—
37	C₂×D₄×C₉	—	2	6	no	—
38	C₂×D₄×C₉	—	2	6	no	—
39	C₂²×C₄×C₉	—	2	12	no	—
40	C₂²×C₄×C₉	—	2	6	no	—
41	C₂²×C₄×C₉	D₄	1	12	yes	complemented
42	C₂²×C₄×C₉	C₂³	1	3	yes	—
43	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₉	C₂³	1	3	yes	—
45	C₂²×C₄×C₉	C₂³	1	3	yes	—
46	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₉×C₄⋊C₄	—	2	6	no	—
48	C₉×C₂²⋊C₄	—	2	6	no	—
49	C₉×C₂²⋊C₄	—	2	6	no	—
50	C₉×C₂²⋊C₄	—	2	12	no	—
51	C₄²×C₉	—	2	6	no	—
52	#2388	C₉	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₃×#41	—	2	12	no	—
54	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
56	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
57	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
58	C₂³×C₃×C₄	C₂²×C₃	1	3	yes	—
59	C₃×C₄×D₄	—	2	12	no	—
60	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
61	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
62	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
63	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
64	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
65	C₃×#95	C₂²×C₃	1	3	yes	—
66	C₃×#95	C₂²×C₃	1	3	yes	—
67	C₂³×C₉	—	2	3	no	—
68	C₂³×C₉	—	2	6	no	—
69	C₂³×C₉	—	2	6	no	—
70	C₂³×C₉	—	2	3	no	—
71	C₂³×C₉	—	2	3	no	—
72	C₂³×C₉	—	2	3	no	—
73	C₂³×C₉	C₂×D₄	1	6	yes	—
74	C₂³×C₉	#41	1	2	yes	complemented
75	C₂³×C₉	C₂⁴	1	1	yes	characteristic
76	Q₈×C₉	—	2	8	no	—
77	D₄×C₉	—	2	24	no	—
78	D₄×C₉	—	2	24	no	—
79	C₂×C₄×C₉	—	2	3	no	—
80	C₂×C₄×C₉	—	2	6	no	—
81	C₂×C₄×C₉	—	2	3	no	—
82	C₂×C₄×C₉	—	2	24	no	—
83	C₂×C₄×C₉	—	2	3	no	—
84	C₂×C₄×C₉	—	2	3	no	—
85	C₂×C₄×C₉	—	2	6	no	—
86	C₂×C₄×C₉	—	4	4	no	—
87	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
88	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
89	C₂×C₄×C₉	#41	1	6	yes	complemented
90	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
91	C₂×C₄×D₄	C₂×C₉	1	3	yes	complemented
92	#395	C₂×C₉	1	1	yes	characteristic, complemented
93	#394	C₂×C₉	1	3	yes	complemented
94	#393	C₂×C₉	1	1	yes	characteristic, complemented
95	#392	C₂×C₉	1	3	yes	complemented
96	C₄×C₂²⋊C₄	C₂×C₉	1	3	yes	complemented
97	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
98	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
99	C₃×#41	—	2	32	no	—
100	C₂×C₃×Q₈	—	2	6	no	—
101	C₂×C₃×D₄	—	2	6	no	—
102	C₂×C₃×D₄	—	2	12	no	—
103	C₂×C₃×D₄	—	2	6	no	—
104	C₂×C₃×D₄	—	2	6	no	—
105	C₂×C₃×D₄	—	2	6	no	—
106	C₂²×C₃×C₄	—	2	12	no	—
107	C₂²×C₃×C₄	—	2	6	no	—
108	C₂²×C₃×C₄	C₃×D₄	1	12	yes	—
109	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
110	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
112	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
113	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
114	C₃×C₄⋊C₄	—	2	6	no	—
115	C₃×C₂²⋊C₄	—	2	6	no	—
116	C₃×C₂²⋊C₄	—	2	6	no	—
117	C₃×C₂²⋊C₄	—	2	12	no	—
118	C₃×C₄²	—	2	6	no	—
119	C₂²×C₉	—	2	6	no	—
120	C₂²×C₉	—	2	6	no	—
121	C₂²×C₉	—	2	6	no	—
122	C₂²×C₉	—	2	6	no	—
123	C₂²×C₉	—	4	1	no	—
124	C₂²×C₉	—	4	6	no	—
125	C₂²×C₉	—	4	3	no	—
126	C₂²×C₉	—	4	6	no	—
127	C₂²×C₉	C₂²×D₄	1	3	yes	—
128	C₂²×C₉	C₂×#41	1	1	yes	characteristic
129	C₂²×C₉	C₂×#41	1	3	yes	—
130	C₄×C₉	—	2	6	no	—
131	C₄×C₉	—	2	6	no	—
132	C₄×C₉	—	4	1	no	—
133	C₄×C₉	—	4	3	no	—
134	C₄×C₉	#120	1	4	yes	—
135	C₂×#41	—	2	12	no	—
136	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
137	C₂²×D₄	C₂²×C₉	1	3	yes	—
138	C₂²×D₄	C₂²×C₉	1	3	yes	—
139	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
140	C₂³×C₄	C₂²×C₉	1	3	yes	—
141	C₄×D₄	—	2	12	no	—
142	C₂×C₄⋊C₄	C₂²×C₉	1	3	yes	—
143	C₂×C₂²⋊C₄	C₂²×C₉	1	3	yes	—
144	C₂×C₂²⋊C₄	C₂²×C₉	1	3	yes	—
145	C₂×C₂²⋊C₄	C₂²×C₉	1	6	yes	—
146	C₂×C₄²	C₂²×C₉	1	3	yes	—
147	#95	C₂²×C₉	1	3	yes	—
148	#95	C₂²×C₉	1	3	yes	—
149	C₂³×C₃	—	2	3	no	—
150	C₂³×C₃	—	2	6	no	—
151	C₂³×C₃	—	2	6	no	—
152	C₂³×C₃	—	2	3	no	—
153	C₂³×C₃	—	2	3	no	—
154	C₂³×C₃	—	2	3	no	—
155	C₂³×C₃	C₂×C₃×D₄	1	6	yes	—
156	C₂³×C₃	C₃×#41	1	2	yes	—
157	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
158	C₃×Q₈	—	2	8	no	—
159	C₃×D₄	—	2	24	no	—
160	C₃×D₄	—	2	24	no	—
161	C₂×C₃×C₄	—	2	3	no	—
162	C₂×C₃×C₄	—	2	6	no	—
163	C₂×C₃×C₄	—	2	3	no	—
164	C₂×C₃×C₄	—	2	24	no	—
165	C₂×C₃×C₄	—	2	3	no	—
166	C₂×C₃×C₄	—	2	3	no	—
167	C₂×C₃×C₄	—	2	6	no	—
168	C₂×C₃×C₄	—	4	4	no	—
169	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
170	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
171	C₂×C₃×C₄	C₃×#41	1	6	yes	—
172	C₂×C₉	—	4	6	no	—
173	C₂×C₉	—	4	2	no	—
174	C₂×C₉	C₂×#120	1	1	yes	characteristic
175	C₂×C₉	#525	1	3	yes	—
176	C₂×C₉	#532	1	3	yes	—
177	C₂⁴	C₂³×C₉	1	3	yes	—
178	C₂⁴	C₂³×C₉	1	1	yes	characteristic
179	#41	—	2	32	no	—
180	C₂×Q₈	—	2	6	no	—
181	C₂×D₄	—	2	6	no	—
182	C₂×D₄	—	2	12	no	—
183	C₂×D₄	—	2	6	no	—
184	C₂×D₄	—	2	6	no	—
185	C₂×D₄	—	2	6	no	—
186	C₂²×C₄	—	2	12	no	—
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	D₄×C₉	1	12	yes	complemented
189	C₂²×C₄	C₂³×C₉	1	3	yes	—
190	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
191	C₂²×C₄	C₂³×C₉	1	3	yes	—
192	C₂²×C₄	C₂³×C₉	1	3	yes	—
193	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
194	C₄⋊C₄	—	2	6	no	—
195	C₂²⋊C₄	—	2	6	no	—
196	C₂²⋊C₄	—	2	6	no	—
197	C₂²⋊C₄	—	2	12	no	—
198	C₄²	—	2	6	no	—
199	C₂²×C₃	—	2	6	no	—
200	C₂²×C₃	—	2	6	no	—
201	C₂²×C₃	—	2	6	no	—
202	C₂²×C₃	—	2	6	no	—
203	C₂²×C₃	—	4	1	no	—
204	C₂²×C₃	—	4	6	no	—
205	C₂²×C₃	—	4	3	no	—
206	C₂²×C₃	—	4	6	no	—
207	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
208	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
209	C₂²×C₃	C₂×C₃×#41	1	3	yes	—
210	C₃×C₄	—	2	6	no	—
211	C₃×C₄	—	2	6	no	—
212	C₃×C₄	—	4	1	no	—
213	C₃×C₄	—	4	3	no	—
214	C₃×C₄	C₃×#120	1	4	yes	—
215	C₉	#2388	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	3	no	—
217	C₂³	—	2	6	no	—
218	C₂³	—	2	6	no	—
219	C₂³	—	2	3	no	—
220	C₂³	—	2	3	no	—
221	C₂³	—	2	3	no	—
222	C₂³	C₂×D₄×C₉	1	6	yes	—
223	C₂³	C₉×#41	1	2	yes	complemented
224	C₂³	C₂⁴×C₉	1	1	yes	characteristic
225	Q₈	—	2	8	no	—
226	D₄	—	2	24	no	—
227	D₄	—	2	24	no	—
228	C₂×C₄	—	2	3	no	—
229	C₂×C₄	—	2	6	no	—
230	C₂×C₄	—	2	3	no	—
231	C₂×C₄	—	2	24	no	—
232	C₂×C₄	—	2	3	no	—
233	C₂×C₄	—	2	3	no	—
234	C₂×C₄	—	2	6	no	—
235	C₂×C₄	—	4	4	no	—
236	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
237	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
238	C₂×C₄	C₉×#41	1	6	yes	complemented
239	C₂×C₃	—	4	6	no	—
240	C₂×C₃	—	4	2	no	—
241	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
242	C₂×C₃	C₃×#525	1	3	yes	—
243	C₂×C₃	C₃×#532	1	3	yes	—
244	C₂²	—	2	6	no	—
245	C₂²	—	2	6	no	—
246	C₂²	—	2	6	no	—
247	C₂²	—	2	6	no	—
248	C₂²	—	4	1	no	—
249	C₂²	—	4	6	no	—
250	C₂²	—	4	3	no	—
251	C₂²	—	4	6	no	—
252	C₂²	C₂²×D₄×C₉	1	3	yes	—
253	C₂²	C₂×C₉×#41	1	1	yes	characteristic
254	C₂²	C₂×C₉×#41	1	3	yes	—
255	C₄	—	2	6	no	—
256	C₄	—	2	6	no	—
257	C₄	—	4	1	no	—
258	C₄	—	4	3	no	—
259	C₄	C₉×#120	1	4	yes	—
260	C₃	C₃×#2388	1	1	yes	characteristic
261	C₂	—	4	6	no	—
262	C₂	—	4	2	no	—
263	C₂	C₂×C₉×#120	1	1	yes	characteristic
264	C₂	C₉×#525	1	3	yes	—
265	C₂	C₉×#532	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₃×#2388	C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#41	C₂	semidirect
2. C₂×C₄×D₄×C₉	C₂	semidirect
3. C₉×#395	C₂	semidirect
4. C₉×#394	C₂	semidirect
5. C₉×#393	C₂	semidirect
6. C₉×#392	C₂	semidirect
7. C₄×C₉×C₂²⋊C₄	C₂	semidirect
41. C₂²×C₄×C₉	D₄	semidirect
52. #2388	C₉	direct (N × H)
74. C₂³×C₉	#41	semidirect
89. C₂×C₄×C₉	#41	semidirect
90. C₂²×#41	C₂×C₉	semidirect
91. C₂×C₄×D₄	C₂×C₉	semidirect
92. #395	C₂×C₉	semidirect
93. #394	C₂×C₉	semidirect
94. #393	C₂×C₉	semidirect
95. #392	C₂×C₉	semidirect
96. C₄×C₂²⋊C₄	C₂×C₉	semidirect
188. C₂²×C₄	D₄×C₉	semidirect
215. C₉	#2388	direct (N × H)
223. C₂³	C₉×#41	semidirect
238. C₂×C₄	C₉×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×#41	2
C₂×C₄×D₄×C₉	2
C₉×#395	2
C₉×#394	2
C₉×#393	2
C₉×#392	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2388	3

Subgroups — C9×#2388 #11767109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2388 #11767109