Subgroups — C₂×C₉×#488 #11767851

Order 1152.

618 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂×C₃×D₄
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#125	C₂	semidirect
3. C₉×#488	C₂	direct (N × H)
4. C₂×C₉×#103	C₂	semidirect
6. C₂×C₄×C₈×C₉	C₂	semidirect
12. C₉×#125	C₂²	semidirect
19. C₉×#103	C₂²	semidirect
21. C₄×C₈×C₉	C₂²	semidirect
47. C₂×#488	C₉	direct (N × H)
80. C₂×#125	C₂×C₉	semidirect
82. #488	C₂×C₉	direct (N × H)
83. C₂×#103	C₂×C₉	semidirect
85. C₂×C₄×C₈	C₂×C₉	semidirect
120. #125	C₂²×C₉	semidirect
127. #103	C₂²×C₉	semidirect
129. C₄×C₈	C₂²×C₉	semidirect
149. C₂×C₉	#488	direct (N × H)
182. C₉	C₂×#488	direct (N × H)
218. C₂	C₉×#488	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#125	2
C₂×C₉×#124	2
C₉×#488	2
C₂×C₉×#103	2
C₂×C₉×#102	2
C₂×C₄×C₈×C₉	2
C₂×C₃×#488	3

Subgroups — C2×C9×#488 #11767851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#488 #11767851