Subgroups — C₂×C₉×#381 #11767000

Order 1152.

1716 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₉×#381	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#95	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×#381	C₃	1	1	yes	maximal, characteristic
6	C₂⁵×C₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₉	—	2	8	no	—
8	C₂³×C₄×C₉	C₄	1	8	yes	complemented
9	C₂³×C₄×C₉	C₂²	1	4	yes	—
10	C₂³×C₄×C₉	C₂²	1	2	yes	—
11	C₂³×C₄×C₉	C₂²	1	4	yes	—
12	C₂×C₉×C₂²⋊C₄	—	2	8	no	—
13	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	—
14	C₉×#95	C₂²	1	16	yes	complemented
15	C₂⁴×C₃×C₄	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
17	C₃×#381	C₂×C₃	1	8	yes	—
18	C₂×C₃×#95	C₂×C₃	1	4	yes	—
19	C₂⁴×C₉	—	2	8	no	—
20	C₂⁴×C₉	C₂×C₄	1	4	yes	—
21	C₂⁴×C₉	D₄	1	8	yes	—
22	C₂⁴×C₉	C₂³	1	2	yes	—
23	C₂⁴×C₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₉	—	2	32	no	—
25	C₂²×C₄×C₉	—	2	8	no	—
26	C₂²×C₄×C₉	—	2	16	no	—
27	C₂²×C₄×C₉	—	2	8	no	—
28	C₂²×C₄×C₉	—	2	16	no	—
29	C₂²×C₄×C₉	C₂×C₄	1	8	yes	—
30	C₂²×C₄×C₉	C₂×C₄	1	16	yes	complemented
31	C₂²×C₄×C₉	C₂³	1	8	yes	—
32	C₂²×C₄×C₉	C₂³	1	4	yes	—
33	C₉×C₂²⋊C₄	—	2	16	no	—
34	C₂×#381	C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
36	C₂³×C₃×C₄	—	2	8	no	—
37	C₂³×C₃×C₄	C₃×C₄	1	8	yes	—
38	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
39	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
40	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
41	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
42	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
43	C₃×#95	C₂²×C₃	1	16	yes	—
44	C₂³×C₉	—	2	16	no	—
45	C₂³×C₉	—	2	32	no	—
46	C₂³×C₉	—	2	8	no	—
47	C₂³×C₉	C₂²⋊C₄	1	16	yes	—
48	C₂³×C₉	C₂²×C₄	1	4	yes	—
49	C₂³×C₉	C₂²×C₄	1	2	yes	—
50	C₂³×C₉	C₂×D₄	1	8	yes	—
51	C₂³×C₉	C₂×D₄	1	4	yes	—
52	C₂³×C₉	#41	1	8	yes	—
53	C₂³×C₉	C₂⁴	1	1	yes	characteristic
54	C₂×C₄×C₉	—	2	16	no	—
55	C₂×C₄×C₉	—	2	32	no	—
56	C₂×C₄×C₉	—	2	8	no	—
57	C₂×C₄×C₉	—	2	8	no	—
58	C₂×C₄×C₉	—	2	16	no	—
59	C₂×C₄×C₉	—	4	16	no	—
60	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
61	C₂⁴×C₄	C₂×C₉	1	1	yes	characteristic
62	C₂²×C₂²⋊C₄	C₂×C₉	1	2	yes	—
63	#381	C₂×C₉	1	8	yes	direct product factor
64	C₂×#95	C₂×C₉	1	4	yes	complemented
65	C₂⁴×C₃	—	2	8	no	—
66	C₂⁴×C₃	C₂×C₃×C₄	1	4	yes	—
67	C₂⁴×C₃	C₃×D₄	1	8	yes	—
68	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
69	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
70	C₂²×C₃×C₄	—	2	32	no	—
71	C₂²×C₃×C₄	—	2	16	no	—
72	C₂²×C₃×C₄	—	2	8	no	—
73	C₂²×C₃×C₄	—	2	8	no	—
74	C₂²×C₃×C₄	—	2	16	no	—
75	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
76	C₂²×C₃×C₄	C₂×C₃×C₄	1	16	yes	—
77	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
78	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
79	C₃×C₂²⋊C₄	—	2	16	no	—
80	C₂²×C₉	—	2	8	no	—
81	C₂²×C₉	—	2	16	no	—
82	C₂²×C₉	—	2	32	no	—
83	C₂²×C₉	C₂×C₂²⋊C₄	1	8	yes	—
84	C₂²×C₉	C₂×C₂²⋊C₄	1	4	yes	—
85	C₂²×C₉	#117	1	8	yes	—
86	C₂²×C₉	#123	1	16	yes	—
87	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
88	C₂²×C₉	C₂²×D₄	1	2	yes	—
89	C₂²×C₉	C₂×#41	1	4	yes	—
90	C₄×C₉	—	2	8	no	—
91	C₄×C₉	—	4	8	no	—
92	C₂⁵	C₂²×C₉	1	1	yes	characteristic
93	C₂³×C₄	—	2	8	no	—
94	C₂³×C₄	C₄×C₉	1	8	yes	complemented
95	C₂³×C₄	C₂²×C₉	1	4	yes	—
96	C₂³×C₄	C₂²×C₉	1	2	yes	—
97	C₂³×C₄	C₂²×C₉	1	4	yes	—
98	C₂×C₂²⋊C₄	—	2	8	no	—
99	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	—
100	#95	C₂²×C₉	1	16	yes	complemented
101	C₂³×C₃	—	2	16	no	—
102	C₂³×C₃	—	2	32	no	—
103	C₂³×C₃	—	2	8	no	—
104	C₂³×C₃	C₃×C₂²⋊C₄	1	16	yes	—
105	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
106	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
107	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
108	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
109	C₂³×C₃	C₃×#41	1	8	yes	—
110	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄	—	2	16	no	—
112	C₂×C₃×C₄	—	2	32	no	—
113	C₂×C₃×C₄	—	2	8	no	—
114	C₂×C₃×C₄	—	2	8	no	—
115	C₂×C₃×C₄	—	2	16	no	—
116	C₂×C₃×C₄	—	4	16	no	—
117	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
118	C₂×C₉	—	2	8	no	—
119	C₂×C₉	#381	1	8	yes	direct product factor
120	C₂×C₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₉	C₂×#117	1	2	yes	—
122	C₂×C₉	C₂×#123	1	4	yes	—
123	C₂⁴	—	2	8	no	—
124	C₂⁴	C₂×C₄×C₉	1	4	yes	—
125	C₂⁴	D₄×C₉	1	8	yes	—
126	C₂⁴	C₂³×C₉	1	2	yes	—
127	C₂⁴	C₂³×C₉	1	1	yes	characteristic
128	C₂²×C₄	—	2	32	no	—
129	C₂²×C₄	—	2	8	no	—
130	C₂²×C₄	—	2	16	no	—
131	C₂²×C₄	—	2	8	no	—
132	C₂²×C₄	—	2	16	no	—
133	C₂²×C₄	C₂×C₄×C₉	1	8	yes	—
134	C₂²×C₄	C₂×C₄×C₉	1	16	yes	complemented
135	C₂²×C₄	C₂³×C₉	1	8	yes	—
136	C₂²×C₄	C₂³×C₉	1	4	yes	—
137	C₂²⋊C₄	—	2	16	no	—
138	C₂²×C₃	—	2	32	no	—
139	C₂²×C₃	—	2	8	no	—
140	C₂²×C₃	—	2	16	no	—
141	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	8	yes	—
142	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	4	yes	—
143	C₂²×C₃	C₃×#117	1	8	yes	—
144	C₂²×C₃	C₃×#123	1	16	yes	—
145	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
146	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
147	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
148	C₃×C₄	—	2	8	no	—
149	C₃×C₄	—	4	8	no	—
150	C₉	C₂×#381	1	1	yes	characteristic, direct product factor, Sylow
151	C₂³	—	2	16	no	—
152	C₂³	—	2	32	no	—
153	C₂³	—	2	8	no	—
154	C₂³	C₉×C₂²⋊C₄	1	16	yes	—
155	C₂³	C₂²×C₄×C₉	1	4	yes	—
156	C₂³	C₂²×C₄×C₉	1	2	yes	—
157	C₂³	C₂×D₄×C₉	1	8	yes	—
158	C₂³	C₂×D₄×C₉	1	4	yes	—
159	C₂³	C₉×#41	1	8	yes	—
160	C₂³	C₂⁴×C₉	1	1	yes	characteristic
161	C₂×C₄	—	2	16	no	—
162	C₂×C₄	—	2	32	no	—
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	2	8	no	—
165	C₂×C₄	—	2	16	no	—
166	C₂×C₄	—	4	16	no	—
167	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
168	C₂×C₃	—	2	8	no	—
169	C₂×C₃	C₃×#381	1	8	yes	—
170	C₂×C₃	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₃	C₂×C₃×#117	1	2	yes	—
172	C₂×C₃	C₂×C₃×#123	1	4	yes	—
173	C₂²	—	2	16	no	—
174	C₂²	—	2	32	no	—
175	C₂²	—	2	8	no	—
176	C₂²	C₂×C₉×C₂²⋊C₄	1	8	yes	—
177	C₂²	C₂×C₉×C₂²⋊C₄	1	4	yes	—
178	C₂²	C₉×#117	1	8	yes	—
179	C₂²	C₉×#123	1	16	yes	—
180	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
181	C₂²	C₂²×D₄×C₉	1	2	yes	—
182	C₂²	C₂×C₉×#41	1	4	yes	—
183	C₄	—	2	8	no	—
184	C₄	—	4	8	no	—
185	C₃	C₂×C₃×#381	1	1	yes	characteristic
186	C₂	—	2	8	no	—
187	C₂	C₉×#381	1	8	yes	direct product factor
188	C₂	C₂²×C₉×C₂²⋊C₄	1	1	yes	characteristic
189	C₂	C₂×C₉×#117	1	2	yes	—
190	C₂	C₂×C₉×#123	1	4	yes	—

	subgroup	G/H
center	C₂⁴×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle	C₂⁴×C₃	C₂³×C₃
prime radical	C₂⁵×C₃	C₂²×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#381	C₂	direct (N × H)
4. C₂×C₉×#95	C₂	semidirect
8. C₂³×C₄×C₉	C₄	semidirect
14. C₉×#95	C₂²	semidirect
30. C₂²×C₄×C₉	C₂×C₄	semidirect
34. C₂×#381	C₉	direct (N × H)
63. #381	C₂×C₉	direct (N × H)
64. C₂×#95	C₂×C₉	semidirect
94. C₂³×C₄	C₄×C₉	semidirect
100. #95	C₂²×C₉	semidirect
119. C₂×C₉	#381	direct (N × H)
134. C₂²×C₄	C₂×C₄×C₉	semidirect
150. C₉	C₂×#381	direct (N × H)
187. C₂	C₉×#381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×C₉	2
C₂²×C₉×C₂²⋊C₄	2
C₉×#381	2
C₂×C₉×#95	2
C₂×C₃×#381	3

Subgroups — C2×C9×#381 #11767000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#381 #11767000