Subgroups — C₂×C₉×#491 #11767855

Order 1152.

576 conjugacy classes of subgroups.

The subgroup lattice has 174 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×#125	C₂	1	1	yes	maximal, characteristic
3	C₉×#491	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#103	C₂	1	4	yes	maximal
5	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#491	C₃	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₉	C₂²	1	2	yes	—
9	C₉×C₄⋊Q₈	—	2	2	no	—
10	C₉×C₄⋊Q₈	C₂²	1	4	yes	—
11	C₉×#125	—	2	2	no	—
12	C₉×#125	C₂²	1	4	yes	—
13	C₂×C₉×C₄⋊C₄	—	2	2	no	—
14	C₂×C₉×C₄⋊C₄	—	2	2	no	—
15	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₉×#103	C₂²	1	16	yes	—
18	C₉×#97	C₂²	1	4	yes	—
19	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
21	C₃×#491	C₂×C₃	1	8	yes	—
22	C₂×C₃×#103	C₂×C₃	1	4	yes	—
23	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
24	C₂×Q₈×C₉	—	2	2	no	—
25	C₂×Q₈×C₉	—	2	8	no	—
26	C₂×Q₈×C₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₉	—	2	2	no	—
28	C₂²×C₄×C₉	—	2	2	no	—
29	C₂²×C₄×C₉	D₄	1	2	yes	—
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂×C₈×C₉	—	2	4	no	—
32	C₂×C₈×C₉	C₂³	1	4	yes	—
33	C₉×C₄⋊C₄	—	2	8	no	—
34	C₉×C₄⋊C₄	—	2	8	no	—
35	C₉×C₄⋊C₄	—	2	2	no	—
36	C₉×C₄⋊C₄	C₂³	1	4	yes	—
37	C₄²×C₉	D₄	1	2	yes	—
38	C₄²×C₉	C₂³	1	2	yes	—
39	C₂×#491	C₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
41	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
42	C₃×C₄⋊Q₈	—	2	2	no	—
43	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
44	C₃×#125	—	2	2	no	—
45	C₃×#125	C₂²×C₃	1	4	yes	—
46	C₂×C₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
49	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
50	C₃×#103	C₂²×C₃	1	16	yes	—
51	C₃×#97	C₂²×C₃	1	4	yes	—
52	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
53	Q₈×C₉	—	2	8	no	—
54	Q₈×C₉	—	4	4	no	—
55	C₂×C₄×C₉	—	2	4	no	—
56	C₂×C₄×C₉	—	2	4	no	—
57	C₂×C₄×C₉	—	2	4	no	—
58	C₂×C₄×C₉	—	4	4	no	—
59	C₂×C₄×C₉	—	4	4	no	—
60	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
61	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₉	#41	1	4	yes	—
63	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
64	C₈×C₉	—	2	4	no	—
65	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
66	C₂×#125	C₂×C₉	1	1	yes	characteristic
67	#491	C₂×C₉	1	8	yes	direct product factor
68	C₂×#103	C₂×C₉	1	4	yes	—
69	C₂×#97	C₂×C₉	1	1	yes	characteristic
70	C₂×C₃×Q₈	—	2	2	no	—
71	C₂×C₃×Q₈	—	2	8	no	—
72	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
73	C₂²×C₃×C₄	—	2	2	no	—
74	C₂²×C₃×C₄	—	2	2	no	—
75	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
76	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
77	C₂×C₃×C₈	—	2	4	no	—
78	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
79	C₃×C₄⋊C₄	—	2	8	no	—
80	C₃×C₄⋊C₄	—	2	8	no	—
81	C₃×C₄⋊C₄	—	2	2	no	—
82	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
83	C₃×C₄²	C₃×D₄	1	2	yes	—
84	C₃×C₄²	C₂³×C₃	1	2	yes	—
85	C₂²×C₉	#124	1	2	yes	—
86	C₂²×C₉	#137	1	4	yes	—
87	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
88	C₄×C₉	—	2	4	no	—
89	C₄×C₉	—	4	4	no	—
90	C₄×C₉	—	4	4	no	—
91	C₄×C₉	#124	1	2	yes	—
92	C₄×C₉	C₂×#41	1	2	yes	—
93	C₂²×Q₈	C₂²×C₉	1	2	yes	—
94	C₂²×C₈	C₂²×C₉	1	2	yes	—
95	C₄⋊Q₈	—	2	2	no	—
96	C₄⋊Q₈	C₂²×C₉	1	4	yes	—
97	#125	—	2	2	no	—
98	#125	C₂²×C₉	1	4	yes	—
99	C₂×C₄⋊C₄	—	2	2	no	—
100	C₂×C₄⋊C₄	—	2	2	no	—
101	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
102	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
103	#103	C₂²×C₉	1	16	yes	—
104	#97	C₂²×C₉	1	4	yes	—
105	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
106	C₃×Q₈	—	2	8	no	—
107	C₃×Q₈	—	4	4	no	—
108	C₂×C₃×C₄	—	2	4	no	—
109	C₂×C₃×C₄	—	2	4	no	—
110	C₂×C₃×C₄	—	2	4	no	—
111	C₂×C₃×C₄	—	4	4	no	—
112	C₂×C₃×C₄	—	4	4	no	—
113	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
114	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄	C₃×#41	1	4	yes	—
116	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
117	C₃×C₈	—	2	4	no	—
118	C₂×C₉	#491	1	4	yes	direct product factor
119	C₂×C₉	C₂×#124	1	1	yes	characteristic
120	C₂×C₉	C₂×#137	1	2	yes	—
121	C₂×Q₈	—	2	2	no	—
122	C₂×Q₈	—	2	8	no	—
123	C₂×Q₈	C₂³×C₉	1	4	yes	—
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	D₄×C₉	1	2	yes	—
127	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
128	C₂×C₈	—	2	4	no	—
129	C₂×C₈	C₂³×C₉	1	4	yes	—
130	C₄⋊C₄	—	2	8	no	—
131	C₄⋊C₄	—	2	8	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	C₂³×C₉	1	4	yes	—
134	C₄²	D₄×C₉	1	2	yes	—
135	C₄²	C₂³×C₉	1	2	yes	—
136	C₂²×C₃	C₃×#124	1	2	yes	—
137	C₂²×C₃	C₃×#137	1	4	yes	—
138	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
139	C₃×C₄	—	2	4	no	—
140	C₃×C₄	—	4	4	no	—
141	C₃×C₄	—	4	4	no	—
142	C₃×C₄	C₃×#124	1	2	yes	—
143	C₃×C₄	C₂×C₃×#41	1	2	yes	—
144	C₉	C₂×#491	1	1	yes	characteristic, direct product factor, Sylow
145	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
146	Q₈	—	2	8	no	—
147	Q₈	—	4	4	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	4	4	no	—
152	C₂×C₄	—	4	4	no	—
153	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
154	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
155	C₂×C₄	C₉×#41	1	4	yes	—
156	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
157	C₈	—	2	4	no	—
158	C₂×C₃	C₃×#491	1	4	yes	—
159	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
160	C₂×C₃	C₂×C₃×#137	1	2	yes	—
161	C₂²	C₉×#124	1	2	yes	—
162	C₂²	C₉×#137	1	4	yes	—
163	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
164	C₄	—	2	4	no	—
165	C₄	—	4	4	no	—
166	C₄	—	4	4	no	—
167	C₄	C₉×#124	1	2	yes	—
168	C₄	C₂×C₉×#41	1	2	yes	—
169	C₃	C₂×C₃×#491	1	1	yes	characteristic
170	C₂	C₉×#491	1	4	yes	direct product factor
171	C₂	C₂×C₉×#124	1	1	yes	characteristic
172	C₂	C₂×C₉×#137	1	2	yes	—

	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×#491	C₂	direct (N × H)
39. C₂×#491	C₉	direct (N × H)
67. #491	C₂×C₉	direct (N × H)
118. C₂×C₉	#491	direct (N × H)
144. C₉	C₂×#491	direct (N × H)
170. C₂	C₉×#491	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
C₂×C₉×#125	2
C₉×#491	2
C₂×C₉×#103	2
C₂×C₉×#97	2
C₂×C₃×#491	3

Subgroups — C2×C9×#491 #11767855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#491 #11767855