Subgroups — C₉×#3147 #11767868

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 219 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#135	C₂	1	4	yes	maximal, complemented
2	C₉×#532	C₂	1	2	yes	maximal, complemented
3	C₉×#495	C₂	1	4	yes	maximal, complemented
4	C₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#492	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#3147	C₃	1	1	yes	maximal, characteristic
9	C₂×C₉×#41	C₂²	1	4	yes	—
10	C₉×#135	—	2	16	no	—
11	C₂×C₉×Q₁₆	C₂²	1	4	yes	—
12	C₂×C₉×SD₁₆	C₂²	1	8	yes	—
13	C₂×C₉×D₈	C₂²	1	4	yes	—
14	C₂²×C₈×C₉	C₂²	1	2	yes	—
15	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₉×#127	C₂²	1	2	yes	—
17	C₉×#124	C₂²	1	4	yes	—
18	C₉×#121	—	2	4	no	—
19	C₄×D₄×C₉	—	2	4	no	—
20	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₉	C₂²	1	2	yes	—
24	C₂×C₃×#135	C₂×C₃	1	4	yes	—
25	C₃×#532	C₂×C₃	1	2	yes	—
26	C₃×#495	C₂×C₃	1	4	yes	—
27	C₃×#494	C₂×C₃	1	1	yes	characteristic
28	C₃×#493	C₂×C₃	1	1	yes	characteristic
29	C₃×#492	C₂×C₃	1	2	yes	—
30	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
31	C₉×#41	—	2	16	no	—
32	C₂×Q₈×C₉	C₂³	1	4	yes	—
33	C₂×D₄×C₉	—	2	4	no	—
34	C₂×D₄×C₉	—	2	4	no	—
35	C₂×D₄×C₉	C₂³	1	4	yes	—
36	C₂²×C₄×C₉	—	2	4	no	—
37	C₂²×C₄×C₉	D₄	1	2	yes	—
38	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
39	C₉×Q₁₆	—	2	8	no	—
40	C₉×SD₁₆	—	2	16	no	—
41	C₉×D₈	—	2	8	no	—
42	C₂×C₈×C₉	D₄	1	8	yes	complemented
43	C₂×C₈×C₉	C₂³	1	2	yes	—
44	C₂×C₈×C₉	C₂³	1	2	yes	—
45	C₉×C₄⋊C₄	—	2	4	no	—
46	C₉×C₂²⋊C₄	—	2	8	no	—
47	C₄²×C₉	D₄	1	2	yes	—
48	C₄²×C₉	C₂³	1	1	yes	characteristic
49	C₄²×C₉	C₂³	1	1	yes	characteristic
50	#3147	C₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
52	C₃×#135	—	2	16	no	—
53	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	—
54	C₂×C₃×SD₁₆	C₂²×C₃	1	8	yes	—
55	C₂×C₃×D₈	C₂²×C₃	1	4	yes	—
56	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
57	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
58	C₃×#127	C₂²×C₃	1	2	yes	—
59	C₃×#124	C₂²×C₃	1	4	yes	—
60	C₃×#121	—	2	4	no	—
61	C₃×C₄×D₄	—	2	4	no	—
62	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
63	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
66	C₂³×C₉	—	2	4	no	—
67	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
68	Q₈×C₉	—	2	8	no	—
69	D₄×C₉	—	2	8	no	—
70	D₄×C₉	—	4	8	no	—
71	D₄×C₉	—	4	8	no	—
72	C₂×C₄×C₉	—	2	4	no	—
73	C₂×C₄×C₉	—	2	4	no	—
74	C₂×C₄×C₉	—	4	8	no	—
75	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
77	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
80	C₈×C₉	C₂×D₄	1	4	yes	—
81	C₈×C₉	C₂×D₄	1	4	yes	—
82	C₂×#135	C₂×C₉	1	4	yes	complemented
83	#532	C₂×C₉	1	2	yes	complemented
84	#495	C₂×C₉	1	4	yes	complemented
85	#494	C₂×C₉	1	1	yes	characteristic, complemented
86	#493	C₂×C₉	1	1	yes	characteristic, complemented
87	#492	C₂×C₉	1	2	yes	complemented
88	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic, complemented
89	C₃×#41	—	2	16	no	—
90	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
91	C₂×C₃×D₄	—	2	4	no	—
92	C₂×C₃×D₄	—	2	4	no	—
93	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
94	C₂²×C₃×C₄	—	2	4	no	—
95	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
96	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
97	C₃×Q₁₆	—	2	8	no	—
98	C₃×SD₁₆	—	2	16	no	—
99	C₃×D₈	—	2	8	no	—
100	C₂×C₃×C₈	C₃×D₄	1	8	yes	—
101	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
102	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
103	C₃×C₄⋊C₄	—	2	4	no	—
104	C₃×C₂²⋊C₄	—	2	8	no	—
105	C₃×C₄²	C₃×D₄	1	2	yes	—
106	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
107	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₉	—	2	2	no	—
109	C₂²×C₉	—	4	4	no	—
110	C₂²×C₉	—	4	8	no	—
111	C₂²×C₉	#127	1	2	yes	—
112	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
113	C₄×C₉	—	2	2	no	—
114	C₄×C₉	—	4	4	no	—
115	C₄×C₉	#127	1	2	yes	—
116	C₄×C₉	#135	1	4	yes	complemented
117	C₄×C₉	C₂²×D₄	1	2	yes	—
118	C₂×#41	C₂²×C₉	1	4	yes	—
119	#135	—	2	16	no	—
120	C₂×Q₁₆	C₂²×C₉	1	4	yes	—
121	C₂×SD₁₆	C₂²×C₉	1	8	yes	—
122	C₂×D₈	C₂²×C₉	1	4	yes	—
123	C₂²×C₈	C₂²×C₉	1	2	yes	—
124	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
125	#127	C₂²×C₉	1	2	yes	—
126	#124	C₂²×C₉	1	4	yes	—
127	#121	—	2	4	no	—
128	C₄×D₄	—	2	4	no	—
129	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
130	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
131	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
132	C₄×C₈	C₂²×C₉	1	2	yes	—
133	C₂³×C₃	—	2	4	no	—
134	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
135	C₃×Q₈	—	2	8	no	—
136	C₃×D₄	—	2	8	no	—
137	C₃×D₄	—	4	8	no	—
138	C₃×D₄	—	4	8	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	2	4	no	—
141	C₂×C₃×C₄	—	4	8	no	—
142	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
143	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
145	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
146	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
147	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
148	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
149	C₂×C₉	—	2	2	no	—
150	C₂×C₉	—	8	4	no	—
151	C₂×C₉	C₂×#127	1	1	yes	characteristic
152	C₂×C₉	C₂×#135	1	2	yes	—
153	#41	—	2	16	no	—
154	C₂×Q₈	C₂³×C₉	1	4	yes	—
155	C₂×D₄	—	2	4	no	—
156	C₂×D₄	—	2	4	no	—
157	C₂×D₄	C₂³×C₉	1	4	yes	—
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	D₄×C₉	1	2	yes	—
160	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
161	Q₁₆	—	2	8	no	—
162	SD₁₆	—	2	16	no	—
163	D₈	—	2	8	no	—
164	C₂×C₈	D₄×C₉	1	8	yes	complemented
165	C₂×C₈	C₂³×C₉	1	2	yes	—
166	C₂×C₈	C₂³×C₉	1	2	yes	—
167	C₄⋊C₄	—	2	4	no	—
168	C₂²⋊C₄	—	2	8	no	—
169	C₄²	D₄×C₉	1	2	yes	—
170	C₄²	C₂³×C₉	1	1	yes	characteristic
171	C₄²	C₂³×C₉	1	1	yes	characteristic
172	C₂²×C₃	—	2	2	no	—
173	C₂²×C₃	—	4	8	no	—
174	C₂²×C₃	—	4	4	no	—
175	C₂²×C₃	C₃×#127	1	2	yes	—
176	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
177	C₃×C₄	—	2	2	no	—
178	C₃×C₄	—	4	4	no	—
179	C₃×C₄	C₃×#127	1	2	yes	—
180	C₃×C₄	C₃×#135	1	4	yes	—
181	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
182	C₉	#3147	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³	—	2	4	no	—
184	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
185	Q₈	—	2	8	no	—
186	D₄	—	2	8	no	—
187	D₄	—	4	8	no	—
188	D₄	—	4	8	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	4	8	no	—
192	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
193	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
194	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
195	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
196	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
197	C₈	C₂×D₄×C₉	1	4	yes	—
198	C₈	C₂×D₄×C₉	1	4	yes	—
199	C₂×C₃	—	2	2	no	—
200	C₂×C₃	—	8	4	no	—
201	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
202	C₂×C₃	C₂×C₃×#135	1	2	yes	—
203	C₂²	—	2	2	no	—
204	C₂²	—	4	4	no	—
205	C₂²	—	4	8	no	—
206	C₂²	C₉×#127	1	2	yes	—
207	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
208	C₄	—	2	2	no	—
209	C₄	—	4	4	no	—
210	C₄	C₉×#127	1	2	yes	—
211	C₄	C₉×#135	1	4	yes	complemented
212	C₄	C₂²×D₄×C₉	1	2	yes	—
213	C₃	C₃×#3147	1	1	yes	characteristic
214	C₂	—	2	2	no	—
215	C₂	—	8	4	no	—
216	C₂	C₂×C₉×#127	1	1	yes	characteristic
217	C₂	C₂×C₉×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3147	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#135	C₂	semidirect
2. C₉×#532	C₂	semidirect
3. C₉×#495	C₂	semidirect
4. C₉×#494	C₂	semidirect
5. C₉×#493	C₂	semidirect
6. C₉×#492	C₂	semidirect
7. C₂×C₄×C₈×C₉	C₂	semidirect
42. C₂×C₈×C₉	D₄	semidirect
50. #3147	C₉	direct (N × H)
82. C₂×#135	C₂×C₉	semidirect
83. #532	C₂×C₉	semidirect
84. #495	C₂×C₉	semidirect
85. #494	C₂×C₉	semidirect
86. #493	C₂×C₉	semidirect
87. #492	C₂×C₉	semidirect
88. C₂×C₄×C₈	C₂×C₉	semidirect
116. C₄×C₉	#135	semidirect
164. C₂×C₈	D₄×C₉	semidirect
182. C₉	#3147	direct (N × H)
211. C₄	C₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#135	2
C₉×#532	2
C₉×#495	2
C₉×#494	2
C₉×#493	2
C₉×#492	2
C₂×C₄×C₈×C₉	2
C₃×#3147	3

Subgroups — C9×#3147 #11767868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3147 #11767868