Subgroups — C₉×#3142 #11767863

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#491	C₂	1	2	yes	maximal, complemented
4	C₉×#490	C₂	1	2	yes	maximal, complemented
5	C₉×#488	C₂	1	4	yes	maximal, complemented
6	C₉×#417	C₂	1	4	yes	maximal, complemented
7	C₄×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3142	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	C₂²	1	2	yes	—
10	C₂×C₉×M₁₆	C₂²	1	2	yes	—
11	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₉×#127	C₂²	1	1	yes	characteristic
13	C₉×#125	—	2	2	no	—
14	C₉×#125	C₂²	1	2	yes	—
15	C₉×#125	C₂²	1	2	yes	—
16	C₉×#124	C₂²	1	2	yes	—
17	C₉×#121	—	2	2	no	—
18	C₄×D₄×C₉	—	2	2	no	—
19	C₂×C₉×C₄⋊C₄	—	2	2	no	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₉×#103	C₂²	1	8	yes	—
23	C₉×#102	C₂²	1	8	yes	—
24	C₉×#97	C₂²	1	2	yes	—
25	C₄×C₈×C₉	C₂²	1	2	yes	—
26	C₃×#532	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
28	C₃×#491	C₂×C₃	1	2	yes	—
29	C₃×#490	C₂×C₃	1	2	yes	—
30	C₃×#488	C₂×C₃	1	4	yes	—
31	C₃×#417	C₂×C₃	1	4	yes	—
32	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic
33	C₉×#41	—	2	8	no	—
34	C₂×Q₈×C₉	C₂³	1	2	yes	—
35	C₂×D₄×C₉	—	2	2	no	—
36	C₂×D₄×C₉	—	2	2	no	—
37	C₂×D₄×C₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₉	—	2	2	no	—
39	C₂²×C₄×C₉	—	2	2	no	—
40	C₂²×C₄×C₉	D₄	1	2	yes	—
41	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
42	C₉×M₁₆	—	2	4	no	—
43	C₂×C₈×C₉	C₂³	1	4	yes	—
44	C₉×C₄⋊C₄	—	2	4	no	—
45	C₉×C₄⋊C₄	—	2	4	no	—
46	C₉×C₄⋊C₄	—	2	2	no	—
47	C₉×C₄⋊C₄	—	2	2	no	—
48	C₉×C₄⋊C₄	C₂³	1	4	yes	—
49	C₉×C₂²⋊C₄	—	2	4	no	—
50	C₄²×C₉	D₄	1	2	yes	—
51	C₄²×C₉	C₂³	1	1	yes	characteristic
52	C₄²×C₉	C₂³	1	1	yes	characteristic
53	#3142	C₉	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
55	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
56	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
57	C₃×#127	C₂²×C₃	1	1	yes	characteristic
58	C₃×#125	—	2	2	no	—
59	C₃×#125	C₂²×C₃	1	2	yes	—
60	C₃×#125	C₂²×C₃	1	2	yes	—
61	C₃×#124	C₂²×C₃	1	2	yes	—
62	C₃×#121	—	2	2	no	—
63	C₃×C₄×D₄	—	2	2	no	—
64	C₂×C₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
67	C₃×#103	C₂²×C₃	1	8	yes	—
68	C₃×#102	C₂²×C₃	1	8	yes	—
69	C₃×#97	C₂²×C₃	1	2	yes	—
70	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
71	C₂³×C₉	—	2	2	no	—
72	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
73	Q₈×C₉	—	2	4	no	—
74	D₄×C₉	—	2	4	no	—
75	D₄×C₉	—	4	4	no	—
76	D₄×C₉	—	4	4	no	—
77	C₂×C₄×C₉	—	2	2	no	—
78	C₂×C₄×C₉	—	2	4	no	—
79	C₂×C₄×C₉	—	4	2	no	—
80	C₂×C₄×C₉	—	4	4	no	—
81	C₂×C₄×C₉	—	4	4	no	—
82	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
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	4	yes	—
86	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
87	C₈×C₉	—	2	4	no	—
88	#532	C₂×C₉	1	1	yes	characteristic
89	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
90	#491	C₂×C₉	1	2	yes	complemented
91	#490	C₂×C₉	1	2	yes	complemented
92	#488	C₂×C₉	1	4	yes	complemented
93	#417	C₂×C₉	1	4	yes	complemented
94	C₄×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
95	C₃×#41	—	2	8	no	—
96	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
97	C₂×C₃×D₄	—	2	2	no	—
98	C₂×C₃×D₄	—	2	2	no	—
99	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
100	C₂²×C₃×C₄	—	2	2	no	—
101	C₂²×C₃×C₄	—	2	2	no	—
102	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
103	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
104	C₃×M₁₆	—	2	4	no	—
105	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
106	C₃×C₄⋊C₄	—	2	4	no	—
107	C₃×C₄⋊C₄	—	2	4	no	—
108	C₃×C₄⋊C₄	—	2	2	no	—
109	C₃×C₄⋊C₄	—	2	2	no	—
110	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
111	C₃×C₂²⋊C₄	—	2	4	no	—
112	C₃×C₄²	C₃×D₄	1	2	yes	—
113	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
114	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
115	C₂²×C₉	—	2	2	no	—
116	C₂²×C₉	—	4	2	no	—
117	C₂²×C₉	—	4	4	no	—
118	C₂²×C₉	#124	1	2	yes	—
119	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
120	C₄×C₉	—	2	2	no	—
121	C₄×C₉	—	2	2	no	—
122	C₄×C₉	—	4	2	no	—
123	C₄×C₉	—	4	4	no	—
124	C₄×C₉	#124	1	2	yes	—
125	C₄×C₉	C₂×#41	1	2	yes	—
126	C₂×#41	C₂²×C₉	1	2	yes	—
127	C₂×M₁₆	C₂²×C₉	1	2	yes	—
128	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
129	#127	C₂²×C₉	1	1	yes	characteristic
130	#125	—	2	2	no	—
131	#125	C₂²×C₉	1	2	yes	—
132	#125	C₂²×C₉	1	2	yes	—
133	#124	C₂²×C₉	1	2	yes	—
134	#121	—	2	2	no	—
135	C₄×D₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
138	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
139	#103	C₂²×C₉	1	8	yes	—
140	#102	C₂²×C₉	1	8	yes	—
141	#97	C₂²×C₉	1	2	yes	—
142	C₄×C₈	C₂²×C₉	1	2	yes	—
143	C₂³×C₃	—	2	2	no	—
144	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
145	C₃×Q₈	—	2	4	no	—
146	C₃×D₄	—	2	4	no	—
147	C₃×D₄	—	4	4	no	—
148	C₃×D₄	—	4	4	no	—
149	C₂×C₃×C₄	—	2	2	no	—
150	C₂×C₃×C₄	—	2	4	no	—
151	C₂×C₃×C₄	—	4	2	no	—
152	C₂×C₃×C₄	—	4	4	no	—
153	C₂×C₃×C₄	—	4	4	no	—
154	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
155	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
156	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄	C₃×#41	1	4	yes	—
158	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
159	C₃×C₈	—	2	4	no	—
160	C₂×C₉	—	2	2	no	—
161	C₂×C₉	—	8	2	no	—
162	C₂×C₉	C₂×#124	1	1	yes	characteristic
163	C₂×C₉	#575	1	2	yes	—
164	#41	—	2	8	no	—
165	C₂×Q₈	C₂³×C₉	1	2	yes	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	C₂³×C₉	1	2	yes	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	D₄×C₉	1	2	yes	—
172	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
173	M₁₆	—	2	4	no	—
174	C₂×C₈	C₂³×C₉	1	4	yes	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	C₂³×C₉	1	4	yes	—
180	C₂²⋊C₄	—	2	4	no	—
181	C₄²	D₄×C₉	1	2	yes	—
182	C₄²	C₂³×C₉	1	1	yes	characteristic
183	C₄²	C₂³×C₉	1	1	yes	characteristic
184	C₂²×C₃	—	2	2	no	—
185	C₂²×C₃	—	4	4	no	—
186	C₂²×C₃	—	4	2	no	—
187	C₂²×C₃	C₃×#124	1	2	yes	—
188	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
189	C₃×C₄	—	2	2	no	—
190	C₃×C₄	—	2	2	no	—
191	C₃×C₄	—	4	4	no	—
192	C₃×C₄	—	4	2	no	—
193	C₃×C₄	C₃×#124	1	2	yes	—
194	C₃×C₄	C₂×C₃×#41	1	2	yes	—
195	C₉	#3142	1	1	yes	characteristic, direct product factor, Sylow
196	C₂³	—	2	2	no	—
197	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
198	Q₈	—	2	4	no	—
199	D₄	—	2	4	no	—
200	D₄	—	4	4	no	—
201	D₄	—	4	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
208	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
209	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
210	C₂×C₄	C₉×#41	1	4	yes	—
211	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
212	C₈	—	2	4	no	—
213	C₂×C₃	—	2	2	no	—
214	C₂×C₃	—	8	2	no	—
215	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
216	C₂×C₃	C₃×#575	1	2	yes	—
217	C₂²	—	2	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	—	4	4	no	—
220	C₂²	C₉×#124	1	2	yes	—
221	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
222	C₄	—	2	2	no	—
223	C₄	—	2	2	no	—
224	C₄	—	4	2	no	—
225	C₄	—	4	4	no	—
226	C₄	C₉×#124	1	2	yes	—
227	C₄	C₂×C₉×#41	1	2	yes	—
228	C₃	C₃×#3142	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	—	8	2	no	—
231	C₂	C₂×C₉×#124	1	1	yes	characteristic
232	C₂	C₉×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#532	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×#125	C₂	semidirect
3. C₉×#491	C₂	semidirect
4. C₉×#490	C₂	semidirect
5. C₉×#488	C₂	semidirect
6. C₉×#417	C₂	semidirect
7. C₄×C₉×M₁₆	C₂	semidirect
53. #3142	C₉	direct (N × H)
89. C₂×#125	C₂×C₉	semidirect
90. #491	C₂×C₉	semidirect
91. #490	C₂×C₉	semidirect
92. #488	C₂×C₉	semidirect
93. #417	C₂×C₉	semidirect
94. C₄×M₁₆	C₂×C₉	semidirect
195. C₉	#3142	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×#532	2
C₂×C₉×#125	2
C₉×#491	2
C₉×#490	2
C₉×#488	2
C₉×#417	2
C₄×C₉×M₁₆	2
C₃×#3142	3

Subgroups — C9×#3142 #11767863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3142 #11767863