Subgroups — C₂×C₉×#487 #11767850

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₉×#487	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#103	C₂	1	4	yes	maximal
5	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#487	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	—	2	1	no	—
8	C₂²×Q₈×C₉	C₂²	1	2	yes	—
9	C₂²×C₈×C₉	C₂²	1	2	yes	—
10	C₉×C₄⋊Q₈	—	2	2	no	—
11	C₉×C₄⋊Q₈	—	2	2	no	—
12	C₉×C₄⋊Q₈	C₂²	1	4	yes	—
13	C₉×C₄⋊Q₈	C₂²	1	4	yes	—
14	C₂×C₉×C₄⋊C₄	—	2	1	no	—
15	C₂×C₉×C₄⋊C₄	—	2	1	no	—
16	C₂×C₉×C₄⋊C₄	—	2	1	no	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₉×#103	C₂²	1	16	yes	—
20	C₄×C₈×C₉	C₂²	1	4	yes	—
21	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
23	C₃×#487	C₂×C₃	1	8	yes	—
24	C₂×C₃×#103	C₂×C₃	1	4	yes	—
25	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
26	C₂×Q₈×C₉	—	2	2	no	—
27	C₂×Q₈×C₉	—	2	4	no	—
28	C₂×Q₈×C₉	—	2	8	no	—
29	C₂×Q₈×C₉	—	4	4	no	—
30	C₂×Q₈×C₉	C₂³	1	4	yes	—
31	C₂²×C₄×C₉	—	2	2	no	—
32	C₂²×C₄×C₉	—	2	2	no	—
33	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
34	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₉	—	2	4	no	—
37	C₂×C₈×C₉	C₂³	1	4	yes	—
38	C₉×C₄⋊C₄	—	2	4	no	—
39	C₉×C₄⋊C₄	—	2	4	no	—
40	C₉×C₄⋊C₄	—	2	4	no	—
41	C₉×C₄⋊C₄	—	2	2	no	—
42	C₉×C₄⋊C₄	C₂³	1	4	yes	—
43	C₄²×C₉	D₄	1	2	yes	—
44	C₄²×C₉	C₂³	1	2	yes	—
45	C₂×#487	C₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₃×Q₈	—	2	1	no	—
47	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
48	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
49	C₃×C₄⋊Q₈	—	2	2	no	—
50	C₃×C₄⋊Q₈	—	2	2	no	—
51	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
52	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
53	C₂×C₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
57	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
58	C₃×#103	C₂²×C₃	1	16	yes	—
59	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
60	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
61	Q₈×C₉	—	2	8	no	—
62	Q₈×C₉	—	4	4	no	—
63	Q₈×C₉	—	4	8	no	—
64	C₂×C₄×C₉	—	2	4	no	—
65	C₂×C₄×C₉	—	2	4	no	—
66	C₂×C₄×C₉	—	4	4	no	—
67	C₂×C₄×C₉	—	4	4	no	—
68	C₂×C₄×C₉	SD₁₆	1	4	yes	—
69	C₂×C₄×C₉	Q₁₆	1	4	yes	—
70	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₉	#41	1	4	yes	—
74	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
75	C₈×C₉	—	2	4	no	—
76	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
77	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
78	#487	C₂×C₉	1	8	yes	direct product factor
79	C₂×#103	C₂×C₉	1	4	yes	—
80	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic
81	C₂×C₃×Q₈	—	2	2	no	—
82	C₂×C₃×Q₈	—	2	4	no	—
83	C₂×C₃×Q₈	—	2	8	no	—
84	C₂×C₃×Q₈	—	4	4	no	—
85	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
86	C₂²×C₃×C₄	—	2	2	no	—
87	C₂²×C₃×C₄	—	2	2	no	—
88	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
89	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
90	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
91	C₂×C₃×C₈	—	2	4	no	—
92	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
93	C₃×C₄⋊C₄	—	2	4	no	—
94	C₃×C₄⋊C₄	—	2	4	no	—
95	C₃×C₄⋊C₄	—	2	4	no	—
96	C₃×C₄⋊C₄	—	2	2	no	—
97	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
98	C₃×C₄²	C₃×D₄	1	2	yes	—
99	C₃×C₄²	C₂³×C₃	1	2	yes	—
100	C₂²×C₉	#124	1	2	yes	—
101	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
102	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
103	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₉	—	4	4	no	—
105	C₄×C₉	—	4	4	no	—
106	C₄×C₉	#124	1	2	yes	—
107	C₄×C₉	C₂×SD₁₆	1	4	yes	—
108	C₄×C₉	C₂×Q₁₆	1	4	yes	—
109	C₄×C₉	C₂×#41	1	2	yes	—
110	C₂²×Q₈	—	2	1	no	—
111	C₂²×Q₈	C₂²×C₉	1	2	yes	—
112	C₂²×C₈	C₂²×C₉	1	2	yes	—
113	C₄⋊Q₈	—	2	2	no	—
114	C₄⋊Q₈	—	2	2	no	—
115	C₄⋊Q₈	C₂²×C₉	1	4	yes	—
116	C₄⋊Q₈	C₂²×C₉	1	4	yes	—
117	C₂×C₄⋊C₄	—	2	1	no	—
118	C₂×C₄⋊C₄	—	2	1	no	—
119	C₂×C₄⋊C₄	—	2	1	no	—
120	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
121	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
122	#103	C₂²×C₉	1	16	yes	—
123	C₄×C₈	C₂²×C₉	1	4	yes	—
124	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
125	C₃×Q₈	—	2	8	no	—
126	C₃×Q₈	—	4	4	no	—
127	C₃×Q₈	—	4	8	no	—
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	—	2	4	no	—
130	C₂×C₃×C₄	—	4	4	no	—
131	C₂×C₃×C₄	—	4	4	no	—
132	C₂×C₃×C₄	C₃×SD₁₆	1	4	yes	—
133	C₂×C₃×C₄	C₃×Q₁₆	1	4	yes	—
134	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
136	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
137	C₂×C₃×C₄	C₃×#41	1	4	yes	—
138	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
139	C₃×C₈	—	2	4	no	—
140	C₂×C₉	#487	1	4	yes	direct product factor
141	C₂×C₉	C₂×#124	1	1	yes	characteristic
142	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
143	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
144	C₂×Q₈	—	2	2	no	—
145	C₂×Q₈	—	2	4	no	—
146	C₂×Q₈	—	2	8	no	—
147	C₂×Q₈	—	4	4	no	—
148	C₂×Q₈	C₂³×C₉	1	4	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
152	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
153	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	C₂³×C₉	1	4	yes	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	2	4	no	—
159	C₄⋊C₄	—	2	2	no	—
160	C₄⋊C₄	C₂³×C₉	1	4	yes	—
161	C₄²	D₄×C₉	1	2	yes	—
162	C₄²	C₂³×C₉	1	2	yes	—
163	C₂²×C₃	C₃×#124	1	2	yes	—
164	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
165	C₂²×C₃	C₂×C₃×Q₁₆	1	2	yes	—
166	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
167	C₃×C₄	—	4	4	no	—
168	C₃×C₄	—	4	4	no	—
169	C₃×C₄	C₃×#124	1	2	yes	—
170	C₃×C₄	C₂×C₃×SD₁₆	1	4	yes	—
171	C₃×C₄	C₂×C₃×Q₁₆	1	4	yes	—
172	C₃×C₄	C₂×C₃×#41	1	2	yes	—
173	C₉	C₂×#487	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
175	Q₈	—	2	8	no	—
176	Q₈	—	4	4	no	—
177	Q₈	—	4	8	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	C₉×SD₁₆	1	4	yes	—
183	C₂×C₄	C₉×Q₁₆	1	4	yes	—
184	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
185	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
186	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
187	C₂×C₄	C₉×#41	1	4	yes	—
188	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
189	C₈	—	2	4	no	—
190	C₂×C₃	C₃×#487	1	4	yes	—
191	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
192	C₂×C₃	C₂²×C₃×SD₁₆	1	1	yes	characteristic
193	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
194	C₂²	C₉×#124	1	2	yes	—
195	C₂²	C₂×C₉×SD₁₆	1	2	yes	—
196	C₂²	C₂×C₉×Q₁₆	1	2	yes	—
197	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
198	C₄	—	4	4	no	—
199	C₄	—	4	4	no	—
200	C₄	C₉×#124	1	2	yes	—
201	C₄	C₂×C₉×SD₁₆	1	4	yes	—
202	C₄	C₂×C₉×Q₁₆	1	4	yes	—
203	C₄	C₂×C₉×#41	1	2	yes	—
204	C₃	C₂×C₃×#487	1	1	yes	characteristic
205	C₂	C₉×#487	1	4	yes	direct product factor
206	C₂	C₂×C₉×#124	1	1	yes	characteristic
207	C₂	C₂²×C₉×SD₁₆	1	1	yes	characteristic
208	C₂	C₂²×C₉×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle, prime radical	C₂³×C₃	C₂×C₃×D₄
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
3. C₉×#487	C₂	direct (N × H)
45. C₂×#487	C₉	direct (N × H)
78. #487	C₂×C₉	direct (N × H)
140. C₂×C₉	#487	direct (N × H)
173. C₉	C₂×#487	direct (N × H)
205. C₂	C₉×#487	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×C₄⋊Q₈	2
C₉×#487	2
C₂×C₉×#103	2
C₂×C₄×C₈×C₉	2
C₂×C₃×#487	3

Subgroups — C2×C9×#487 #11767850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#487 #11767850