Subgroups — C₉×#1911 #11766632

Order 1152.

543 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	C₉×#535	C₂	1	1	yes	maximal, characteristic
2	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₃×#1911	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	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₉×#127	C₄	1	2	yes	complemented
11	C₉×#124	C₄	1	2	yes	complemented
12	C₉×#121	—	2	2	no	—
13	C₉×#120	—	2	2	no	—
14	C₄×D₄×C₉	—	2	4	no	—
15	C₉×#117	C₂²	1	1	yes	characteristic
16	C₉×#117	C₂²	1	2	yes	—
17	C₂×C₉×C₂²⋊C₄	—	2	2	no	—
18	C₉×#104	—	2	4	no	—
19	C₉×#100	—	2	2	no	—
20	C₃×#535	C₂×C₃	1	1	yes	characteristic
21	C₃×#518	C₂×C₃	1	1	yes	characteristic
22	C₃×#421	C₂×C₃	1	2	yes	—
23	C₂×C₃×#100	C₂×C₃	1	1	yes	characteristic
24	C₃×H(3,ℤ/4)	C₂×C₃	1	2	yes	—
25	C₂⁴×C₉	D₄	1	2	yes	—
26	C₉×#41	—	2	2	no	—
27	C₉×#41	—	2	2	no	—
28	C₂×Q₈×C₉	C₂×C₄	1	1	yes	characteristic, complemented
29	C₂×D₄×C₉	—	2	1	no	—
30	C₂×D₄×C₉	—	2	4	no	—
31	C₂×D₄×C₉	—	2	2	no	—
32	C₂×D₄×C₉	—	2	2	no	—
33	C₂×D₄×C₉	C₂×C₄	1	2	yes	—
34	C₂×D₄×C₉	C₂×C₄	1	1	yes	characteristic, complemented
35	C₂×D₄×C₉	D₄	1	2	yes	—
36	C₂²×C₄×C₉	—	2	4	no	—
37	C₂²×C₄×C₉	—	2	1	no	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×M₁₆	—	2	2	no	—
40	C₉×M₁₆	—	2	2	no	—
41	C₂×C₈×C₉	—	2	2	no	—
42	C₉×C₄⋊C₄	—	2	2	no	—
43	C₉×C₄⋊C₄	—	2	1	no	—
44	C₉×C₂²⋊C₄	—	2	4	no	—
45	C₉×C₂²⋊C₄	—	2	4	no	—
46	C₉×C₂²⋊C₄	—	2	2	no	—
47	C₉×C₂²⋊C₄	—	2	1	no	—
48	C₄²×C₉	C₂×C₄	1	2	yes	complemented
49	C₄²×C₉	D₄	1	4	yes	complemented
50	#1911	C₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
54	C₃×#127	C₃×C₄	1	2	yes	—
55	C₃×#124	C₃×C₄	1	2	yes	—
56	C₃×#121	—	2	2	no	—
57	C₃×#120	—	2	2	no	—
58	C₃×C₄×D₄	—	2	4	no	—
59	C₃×#117	C₂²×C₃	1	1	yes	characteristic
60	C₃×#117	C₂²×C₃	1	2	yes	—
61	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
62	C₃×#104	—	2	4	no	—
63	C₃×#100	—	2	2	no	—
64	C₂³×C₉	—	2	2	no	—
65	C₂³×C₉	—	2	2	no	—
66	C₂³×C₉	—	2	1	no	—
67	C₂³×C₉	—	8	2	no	—
68	C₂³×C₉	C₂²⋊C₄	1	4	yes	—
69	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
70	Q₈×C₉	—	2	2	no	—
71	D₄×C₉	—	2	4	no	—
72	D₄×C₉	—	2	2	no	—
73	D₄×C₉	—	2	4	no	—
74	D₄×C₉	—	4	1	no	—
75	D₄×C₉	—	4	1	no	—
76	D₄×C₉	—	8	4	no	—
77	C₂×C₄×C₉	—	2	2	no	—
78	C₂×C₄×C₉	—	2	1	no	—
79	C₂×C₄×C₉	—	2	4	no	—
80	C₂×C₄×C₉	—	4	2	no	—
81	C₂×C₄×C₉	—	8	4	no	—
82	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₉	#41	1	2	yes	—
86	C₈×C₉	—	4	2	no	—
87	#535	C₂×C₉	1	1	yes	characteristic
88	#518	C₂×C₉	1	1	yes	characteristic, complemented
89	#421	C₂×C₉	1	2	yes	complemented
90	C₂×#100	C₂×C₉	1	1	yes	characteristic, complemented
91	H(3,ℤ/4)	C₂×C₉	1	2	yes	complemented
92	C₂⁴×C₃	C₃×D₄	1	2	yes	—
93	C₃×#41	—	2	2	no	—
94	C₃×#41	—	2	2	no	—
95	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
96	C₂×C₃×D₄	—	2	1	no	—
97	C₂×C₃×D₄	—	2	4	no	—
98	C₂×C₃×D₄	—	2	2	no	—
99	C₂×C₃×D₄	—	2	2	no	—
100	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
101	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
102	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
103	C₂²×C₃×C₄	—	2	4	no	—
104	C₂²×C₃×C₄	—	2	1	no	—
105	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
106	C₃×M₁₆	—	2	2	no	—
107	C₃×M₁₆	—	2	2	no	—
108	C₂×C₃×C₈	—	2	2	no	—
109	C₃×C₄⋊C₄	—	2	2	no	—
110	C₃×C₄⋊C₄	—	2	1	no	—
111	C₃×C₂²⋊C₄	—	2	4	no	—
112	C₃×C₂²⋊C₄	—	2	4	no	—
113	C₃×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
116	C₃×C₄²	C₃×D₄	1	4	yes	—
117	C₂²×C₉	—	2	4	no	—
118	C₂²×C₉	—	4	1	no	—
119	C₂²×C₉	—	4	4	no	—
120	C₂²×C₉	—	4	4	no	—
121	C₂²×C₉	—	4	2	no	—
122	C₂²×C₉	—	4	1	no	—
123	C₂²×C₉	—	8	2	no	—
124	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₉	#120	1	1	yes	characteristic
126	C₂²×C₉	#123	1	1	yes	characteristic
127	C₄×C₉	—	4	4	no	—
128	C₄×C₉	—	4	2	no	—
129	C₄×C₉	—	4	1	no	—
130	C₄×C₉	C₄×D₄	1	2	yes	—
131	C₄×C₉	#121	1	2	yes	—
132	C₂×#41	C₂²×C₉	1	1	yes	characteristic
133	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
134	C₂×M₁₆	C₂²×C₉	1	2	yes	—
135	#127	C₄×C₉	1	2	yes	complemented
136	#124	C₄×C₉	1	2	yes	complemented
137	#121	—	2	2	no	—
138	#120	—	2	2	no	—
139	C₄×D₄	—	2	4	no	—
140	#117	C₂²×C₉	1	1	yes	characteristic
141	#117	C₂²×C₉	1	2	yes	—
142	C₂×C₂²⋊C₄	—	2	2	no	—
143	#104	—	2	4	no	—
144	#100	—	2	2	no	—
145	C₂³×C₃	—	2	2	no	—
146	C₂³×C₃	—	2	2	no	—
147	C₂³×C₃	—	2	1	no	—
148	C₂³×C₃	—	8	2	no	—
149	C₂³×C₃	C₃×C₂²⋊C₄	1	4	yes	—
150	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
151	C₃×Q₈	—	2	2	no	—
152	C₃×D₄	—	2	4	no	—
153	C₃×D₄	—	2	2	no	—
154	C₃×D₄	—	2	4	no	—
155	C₃×D₄	—	4	1	no	—
156	C₃×D₄	—	4	1	no	—
157	C₃×D₄	—	8	4	no	—
158	C₂×C₃×C₄	—	2	2	no	—
159	C₂×C₃×C₄	—	2	1	no	—
160	C₂×C₃×C₄	—	2	4	no	—
161	C₂×C₃×C₄	—	4	2	no	—
162	C₂×C₃×C₄	—	8	4	no	—
163	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
164	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
165	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄	C₃×#41	1	2	yes	—
167	C₃×C₈	—	4	2	no	—
168	C₂×C₉	—	2	1	no	—
169	C₂×C₉	—	2	1	no	—
170	C₂×C₉	—	2	1	no	—
171	C₂×C₉	—	4	4	no	—
172	C₂×C₉	—	8	1	no	—
173	C₂×C₉	#386	1	1	yes	characteristic
174	C₂⁴	D₄×C₉	1	2	yes	—
175	#41	—	2	2	no	—
176	#41	—	2	2	no	—
177	C₂×Q₈	C₂×C₄×C₉	1	1	yes	characteristic, complemented
178	C₂×D₄	—	2	1	no	—
179	C₂×D₄	—	2	4	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	C₂×C₄×C₉	1	2	yes	—
183	C₂×D₄	C₂×C₄×C₉	1	1	yes	characteristic, complemented
184	C₂×D₄	D₄×C₉	1	2	yes	—
185	C₂²×C₄	—	2	4	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
188	M₁₆	—	2	2	no	—
189	M₁₆	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	4	no	—
194	C₂²⋊C₄	—	2	4	no	—
195	C₂²⋊C₄	—	2	2	no	—
196	C₂²⋊C₄	—	2	1	no	—
197	C₄²	C₂×C₄×C₉	1	2	yes	complemented
198	C₄²	D₄×C₉	1	4	yes	complemented
199	C₂²×C₃	—	2	4	no	—
200	C₂²×C₃	—	4	1	no	—
201	C₂²×C₃	—	4	4	no	—
202	C₂²×C₃	—	4	4	no	—
203	C₂²×C₃	—	4	2	no	—
204	C₂²×C₃	—	4	1	no	—
205	C₂²×C₃	—	8	2	no	—
206	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₃	C₃×#120	1	1	yes	characteristic
208	C₂²×C₃	C₃×#123	1	1	yes	characteristic
209	C₃×C₄	—	4	4	no	—
210	C₃×C₄	—	4	2	no	—
211	C₃×C₄	—	4	1	no	—
212	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
213	C₃×C₄	C₃×#121	1	2	yes	—
214	C₉	#1911	1	1	yes	characteristic, direct product factor, Sylow
215	C₂³	—	2	2	no	—
216	C₂³	—	2	2	no	—
217	C₂³	—	2	1	no	—
218	C₂³	—	8	2	no	—
219	C₂³	C₉×C₂²⋊C₄	1	4	yes	—
220	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
221	Q₈	—	2	2	no	—
222	D₄	—	2	4	no	—
223	D₄	—	2	2	no	—
224	D₄	—	2	4	no	—
225	D₄	—	4	1	no	—
226	D₄	—	4	1	no	—
227	D₄	—	8	4	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	8	4	no	—
233	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
234	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
235	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
236	C₂×C₄	C₉×#41	1	2	yes	—
237	C₈	—	4	2	no	—
238	C₂×C₃	—	2	1	no	—
239	C₂×C₃	—	2	1	no	—
240	C₂×C₃	—	2	1	no	—
241	C₂×C₃	—	4	4	no	—
242	C₂×C₃	—	8	1	no	—
243	C₂×C₃	C₃×#386	1	1	yes	characteristic
244	C₂²	—	2	4	no	—
245	C₂²	—	4	1	no	—
246	C₂²	—	4	4	no	—
247	C₂²	—	4	4	no	—
248	C₂²	—	4	2	no	—
249	C₂²	—	4	1	no	—
250	C₂²	—	8	2	no	—
251	C₂²	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²	C₉×#120	1	1	yes	characteristic
253	C₂²	C₉×#123	1	1	yes	characteristic
254	C₄	—	4	4	no	—
255	C₄	—	4	2	no	—
256	C₄	—	4	1	no	—
257	C₄	C₄×D₄×C₉	1	2	yes	—
258	C₄	C₉×#121	1	2	yes	—
259	C₃	C₃×#1911	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	—	2	1	no	—
263	C₂	—	4	4	no	—
264	C₂	—	8	1	no	—
265	C₂	C₉×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#386
commutator	C₂×C₄	C₂²×C₄×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#386
prime radical	C₃×#535	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ 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
2. C₉×#518	C₂	semidirect
3. C₉×#421	C₂	semidirect
4. C₂×C₉×#100	C₂	semidirect
5. C₉×H(3,ℤ/4)	C₂	semidirect
10. C₉×#127	C₄	semidirect
11. C₉×#124	C₄	semidirect
28. C₂×Q₈×C₉	C₂×C₄	semidirect
34. C₂×D₄×C₉	C₂×C₄	semidirect
48. C₄²×C₉	C₂×C₄	semidirect
49. C₄²×C₉	D₄	semidirect
50. #1911	C₉	direct (N × H)
88. #518	C₂×C₉	semidirect
89. #421	C₂×C₉	semidirect
90. C₂×#100	C₂×C₉	semidirect
91. H(3,ℤ/4)	C₂×C₉	semidirect
135. #127	C₄×C₉	semidirect
136. #124	C₄×C₉	semidirect
177. C₂×Q₈	C₂×C₄×C₉	semidirect
183. C₂×D₄	C₂×C₄×C₉	semidirect
197. C₄²	C₂×C₄×C₉	semidirect
198. C₄²	D₄×C₉	semidirect
214. C₉	#1911	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×#535	2
C₉×#518	2
C₉×#421	2
C₂×C₉×#100	2
C₉×H(3,ℤ/4)	2
C₃×#1911	3

Subgroups — C9×#1911 #11766632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1911 #11766632