Subgroups — C₉×#1914 #11766635

Order 1152.

510 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#100	C₂	1	2	yes	maximal, complemented
5	C₉×#344	C₂	1	2	yes	maximal, complemented
6	C₃×#1914	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×#41	C₂²	1	1	yes	characteristic
8	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
9	C₉×#131	—	2	4	no	—
10	C₂×C₉×M₁₆	—	2	2	no	—
11	C₂×C₉×M₁₆	C₂²	1	2	yes	—
12	C₂×C₉×M₁₆	C₂²	1	2	yes	—
13	C₉×#127	—	2	1	no	—
14	C₉×#124	—	2	1	no	—
15	C₉×#121	—	2	2	no	—
16	C₉×#120	C₄	1	4	yes	—
17	C₉×#117	C₂²	1	1	yes	characteristic
18	C₉×#101	—	2	1	no	—
19	C₉×#100	—	2	1	no	—
20	C₉×#100	—	2	4	no	—
21	C₃×#568	C₂×C₃	1	1	yes	characteristic
22	C₃×#535	C₂×C₃	1	1	yes	characteristic
23	C₃×#413	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#100	C₂×C₃	1	2	yes	—
25	C₃×#344	C₂×C₃	1	2	yes	—
26	C₂⁴×C₉	C₂×C₄	1	2	yes	—
27	C₉×#41	—	2	2	no	—
28	C₉×#41	—	2	2	no	—
29	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
30	C₂×D₄×C₉	—	2	4	no	—
31	C₂×D₄×C₉	—	2	1	no	—
32	C₂×D₄×C₉	—	2	1	no	—
33	C₂×D₄×C₉	—	2	2	no	—
34	C₂×D₄×C₉	—	2	2	no	—
35	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
36	C₂×D₄×C₉	D₄	1	1	yes	characteristic
37	C₂²×C₄×C₉	D₄	1	2	yes	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×M₁₆	—	2	4	no	—
40	C₉×M₁₆	—	2	2	no	—
41	C₉×M₁₆	—	2	2	no	—
42	C₉×M₁₆	—	2	2	no	—
43	C₉×M₁₆	D₄	1	4	yes	complemented
44	C₂×C₈×C₉	—	2	4	no	—
45	C₂×C₈×C₉	—	2	2	no	—
46	C₂×C₈×C₉	—	2	2	no	—
47	C₉×C₄⋊C₄	—	2	1	no	—
48	C₉×C₂²⋊C₄	—	2	4	no	—
49	C₉×C₂²⋊C₄	C₂×C₄	1	2	yes	—
50	C₄²×C₉	—	2	1	no	—
51	#1914	C₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
54	C₃×#131	—	2	4	no	—
55	C₂×C₃×M₁₆	—	2	2	no	—
56	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
57	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
58	C₃×#127	—	2	1	no	—
59	C₃×#124	—	2	1	no	—
60	C₃×#121	—	2	2	no	—
61	C₃×#120	C₃×C₄	1	4	yes	—
62	C₃×#117	C₂²×C₃	1	1	yes	characteristic
63	C₃×#101	—	2	1	no	—
64	C₃×#100	—	2	1	no	—
65	C₃×#100	—	2	4	no	—
66	C₂³×C₉	—	2	2	no	—
67	C₂³×C₉	—	2	4	no	—
68	C₂³×C₉	—	8	2	no	—
69	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
70	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
71	Q₈×C₉	—	2	2	no	—
72	D₄×C₉	—	2	4	no	—
73	D₄×C₉	—	2	2	no	—
74	D₄×C₉	—	4	1	no	—
75	D₄×C₉	—	4	2	no	—
76	D₄×C₉	—	4	1	no	—
77	D₄×C₉	—	8	4	no	—
78	C₂×C₄×C₉	—	2	2	no	—
79	C₂×C₄×C₉	—	2	2	no	—
80	C₂×C₄×C₉	—	2	2	no	—
81	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₉	#41	1	2	yes	—
86	C₈×C₉	—	2	4	no	—
87	C₈×C₉	—	4	2	no	—
88	#568	C₂×C₉	1	1	yes	characteristic, complemented
89	#535	C₂×C₉	1	1	yes	characteristic
90	#413	C₂×C₉	1	1	yes	characteristic, complemented
91	C₂×#100	C₂×C₉	1	2	yes	complemented
92	#344	C₂×C₉	1	2	yes	complemented
93	C₂⁴×C₃	C₂×C₃×C₄	1	2	yes	—
94	C₃×#41	—	2	2	no	—
95	C₃×#41	—	2	2	no	—
96	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
97	C₂×C₃×D₄	—	2	4	no	—
98	C₂×C₃×D₄	—	2	2	no	—
99	C₂×C₃×D₄	—	2	1	no	—
100	C₂×C₃×D₄	—	2	1	no	—
101	C₂×C₃×D₄	—	2	2	no	—
102	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
103	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
105	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
106	C₃×M₁₆	—	2	4	no	—
107	C₃×M₁₆	—	2	2	no	—
108	C₃×M₁₆	—	2	2	no	—
109	C₃×M₁₆	—	2	2	no	—
110	C₃×M₁₆	C₃×D₄	1	4	yes	—
111	C₂×C₃×C₈	—	2	4	no	—
112	C₂×C₃×C₈	—	2	2	no	—
113	C₂×C₃×C₈	—	2	2	no	—
114	C₃×C₄⋊C₄	—	2	1	no	—
115	C₃×C₂²⋊C₄	—	2	4	no	—
116	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
117	C₃×C₄²	—	2	1	no	—
118	C₂²×C₉	—	2	2	no	—
119	C₂²×C₉	—	4	1	no	—
120	C₂²×C₉	—	4	2	no	—
121	C₂²×C₉	—	4	4	no	—
122	C₂²×C₉	—	4	2	no	—
123	C₂²×C₉	—	8	4	no	—
124	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₉	C₄×D₄	1	2	yes	—
126	C₄×C₉	—	2	2	no	—
127	C₄×C₉	—	4	2	no	—
128	C₄×C₉	#120	1	1	yes	characteristic
129	C₄×C₉	#121	1	2	yes	—
130	C₄×C₉	#123	1	1	yes	characteristic
131	C₂×#41	C₂²×C₉	1	1	yes	characteristic
132	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
133	#131	—	2	4	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	C₂²×C₉	1	2	yes	—
136	C₂×M₁₆	C₂²×C₉	1	2	yes	—
137	#127	—	2	1	no	—
138	#124	—	2	1	no	—
139	#121	—	2	2	no	—
140	#120	C₄×C₉	1	4	yes	—
141	#117	C₂²×C₉	1	1	yes	characteristic
142	#101	—	2	1	no	—
143	#100	—	2	1	no	—
144	#100	—	2	4	no	—
145	C₂³×C₃	—	2	2	no	—
146	C₂³×C₃	—	2	4	no	—
147	C₂³×C₃	—	8	2	no	—
148	C₂³×C₃	C₃×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
150	C₃×Q₈	—	2	2	no	—
151	C₃×D₄	—	2	4	no	—
152	C₃×D₄	—	2	2	no	—
153	C₃×D₄	—	4	1	no	—
154	C₃×D₄	—	4	2	no	—
155	C₃×D₄	—	4	1	no	—
156	C₃×D₄	—	8	4	no	—
157	C₂×C₃×C₄	—	2	2	no	—
158	C₂×C₃×C₄	—	2	2	no	—
159	C₂×C₃×C₄	—	2	2	no	—
160	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
161	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
162	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄	C₃×#41	1	2	yes	—
165	C₃×C₈	—	2	4	no	—
166	C₃×C₈	—	4	2	no	—
167	C₂×C₉	—	2	1	no	—
168	C₂×C₉	—	2	2	no	—
169	C₂×C₉	—	4	2	no	—
170	C₂×C₉	—	8	2	no	—
171	C₂×C₉	#386	1	1	yes	characteristic
172	C₂⁴	C₂×C₄×C₉	1	2	yes	—
173	#41	—	2	2	no	—
174	#41	—	2	2	no	—
175	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
176	C₂×D₄	—	2	4	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	2	1	no	—
179	C₂×D₄	—	2	1	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
182	C₂×D₄	D₄×C₉	1	1	yes	characteristic
183	C₂²×C₄	D₄×C₉	1	2	yes	—
184	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
185	M₁₆	—	2	4	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	2	2	no	—
189	M₁₆	D₄×C₉	1	4	yes	complemented
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₄⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	2	4	no	—
195	C₂²⋊C₄	C₂×C₄×C₉	1	2	yes	—
196	C₄²	—	2	1	no	—
197	C₂²×C₃	—	2	2	no	—
198	C₂²×C₃	—	4	1	no	—
199	C₂²×C₃	—	4	2	no	—
200	C₂²×C₃	—	4	4	no	—
201	C₂²×C₃	—	4	2	no	—
202	C₂²×C₃	—	8	4	no	—
203	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
205	C₃×C₄	—	2	2	no	—
206	C₃×C₄	—	4	2	no	—
207	C₃×C₄	C₃×#120	1	1	yes	characteristic
208	C₃×C₄	C₃×#121	1	2	yes	—
209	C₃×C₄	C₃×#123	1	1	yes	characteristic
210	C₉	#1914	1	1	yes	characteristic, direct product factor, Sylow
211	C₂³	—	2	2	no	—
212	C₂³	—	2	4	no	—
213	C₂³	—	8	2	no	—
214	C₂³	C₉×C₂²⋊C₄	1	2	yes	—
215	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
216	Q₈	—	2	2	no	—
217	D₄	—	2	4	no	—
218	D₄	—	2	2	no	—
219	D₄	—	4	1	no	—
220	D₄	—	4	2	no	—
221	D₄	—	4	1	no	—
222	D₄	—	8	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
228	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
229	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
230	C₂×C₄	C₉×#41	1	2	yes	—
231	C₈	—	2	4	no	—
232	C₈	—	4	2	no	—
233	C₂×C₃	—	2	1	no	—
234	C₂×C₃	—	2	2	no	—
235	C₂×C₃	—	4	2	no	—
236	C₂×C₃	—	8	2	no	—
237	C₂×C₃	C₃×#386	1	1	yes	characteristic
238	C₂²	—	2	2	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	4	no	—
244	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²	C₄×D₄×C₉	1	2	yes	—
246	C₄	—	2	2	no	—
247	C₄	—	4	2	no	—
248	C₄	C₉×#120	1	1	yes	characteristic
249	C₄	C₉×#121	1	2	yes	—
250	C₄	C₉×#123	1	1	yes	characteristic
251	C₃	C₃×#1914	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	2	no	—
254	C₂	—	4	2	no	—
255	C₂	—	8	2	no	—
256	C₂	C₉×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#386
commutator	C₂³	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#386
prime radical	C₃×#535	C₂×C₃
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#568	C₂	semidirect
3. C₉×#413	C₂	semidirect
4. C₂×C₉×#100	C₂	semidirect
5. C₉×#344	C₂	semidirect
43. C₉×M₁₆	D₄	semidirect
51. #1914	C₉	direct (N × H)
88. #568	C₂×C₉	semidirect
90. #413	C₂×C₉	semidirect
91. C₂×#100	C₂×C₉	semidirect
92. #344	C₂×C₉	semidirect
189. M₁₆	D₄×C₉	semidirect
210. C₉	#1914	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×#568	2
C₉×#535	2
C₉×#413	2
C₂×C₉×#100	2
C₉×#344	2
C₃×#1914	3

Subgroups — C9×#1914 #11766635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1914 #11766635