Subgroups — C₂²×C₁₁×#490 #14637800

Order 2816.

2830 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#490	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×#102	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₁	—	2	2	no	—
7	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂×C₁₁×#127	—	2	6	no	—
10	C₂×C₁₁×#127	C₂²	1	12	yes	—
11	C₂×C₁₁×#125	—	2	6	no	—
12	C₂×C₁₁×#125	C₂²	1	12	yes	complemented
13	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
14	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#490	C₂²	1	64	yes	direct product factor
17	C₂×C₁₁×#102	C₂²	1	48	yes	complemented
18	C₂×C₁₁×#97	C₂²	1	12	yes	complemented
19	C₂⁵×C₁₁	—	2	2	no	—
20	C₂²×D₄×C₁₁	—	2	6	no	—
21	C₂²×D₄×C₁₁	—	2	24	no	—
22	C₂²×D₄×C₁₁	—	2	16	no	—
23	C₂²×D₄×C₁₁	—	4	16	no	—
24	C₂²×D₄×C₁₁	C₂³	1	12	yes	—
25	C₂³×C₄×C₁₁	—	2	2	no	—
26	C₂³×C₄×C₁₁	D₄	1	2	yes	—
27	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	—	2	8	no	—
29	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
30	C₁₁×#127	—	2	24	no	—
31	C₁₁×#127	C₂³	1	16	yes	—
32	C₁₁×#125	—	2	24	no	—
33	C₁₁×#125	C₂³	1	16	yes	complemented
34	C₂×C₁₁×C₄⋊C₄	—	2	24	no	—
35	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
36	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
37	C₂×C₄²×C₁₁	D₄	1	6	yes	—
38	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
39	C₁₁×#102	C₂³	1	64	yes	complemented
40	C₁₁×#97	C₂³	1	16	yes	complemented
41	C₂²×#490	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₁	—	2	12	no	—
43	C₂⁴×C₁₁	—	4	8	no	—
44	C₂⁴×C₁₁	—	4	16	no	—
45	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₂×D₄×C₁₁	—	2	12	no	—
47	C₂×D₄×C₁₁	—	2	32	no	—
48	C₂×D₄×C₁₁	—	2	48	no	—
49	C₂×D₄×C₁₁	—	4	96	no	—
50	C₂×D₄×C₁₁	—	4	24	no	—
51	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
52	C₂²×C₄×C₁₁	—	2	8	no	—
53	C₂²×C₄×C₁₁	—	2	12	no	—
54	C₂²×C₄×C₁₁	—	4	8	no	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
56	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
57	C₂²×C₄×C₁₁	#41	1	8	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
59	C₂×C₈×C₁₁	—	2	24	no	—
60	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
61	C₁₁×C₄⋊C₄	—	2	32	no	—
62	C₁₁×C₄⋊C₄	—	2	12	no	—
63	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
64	C₄²×C₁₁	C₂×D₄	1	12	yes	—
65	C₄²×C₁₁	C₂⁴	1	4	yes	—
66	C₂²×#127	C₂×C₁₁	1	1	yes	characteristic
67	C₂²×#125	C₂×C₁₁	1	1	yes	characteristic, complemented
68	C₂×#490	C₂×C₁₁	1	24	yes	direct product factor
69	C₂²×#102	C₂×C₁₁	1	4	yes	complemented
70	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
71	C₂³×C₁₁	—	2	8	no	—
72	C₂³×C₁₁	—	4	24	no	—
73	C₂³×C₁₁	—	4	48	no	—
74	C₂³×C₁₁	—	8	32	no	—
75	C₂³×C₁₁	#124	1	4	yes	—
76	C₂³×C₁₁	AGL(1,ℤ/8)	1	8	yes	—
77	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
78	D₄×C₁₁	—	2	16	no	—
79	D₄×C₁₁	—	4	64	no	—
80	D₄×C₁₁	—	4	24	no	—
81	C₂×C₄×C₁₁	—	2	24	no	—
82	C₂×C₄×C₁₁	—	2	8	no	—
83	C₂×C₄×C₁₁	—	4	24	no	—
84	C₂×C₄×C₁₁	#124	1	12	yes	—
85	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
86	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
87	C₂×C₄×C₁₁	C₂×#41	1	12	yes	—
88	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
89	C₈×C₁₁	—	2	8	no	—
90	C₂³×D₄	—	2	2	no	—
91	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
92	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
93	C₂×#127	—	2	6	no	—
94	C₂×#127	C₂²×C₁₁	1	12	yes	—
95	C₂×#125	—	2	6	no	—
96	C₂×#125	C₂²×C₁₁	1	12	yes	complemented
97	C₂²×C₄⋊C₄	—	2	2	no	—
98	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
99	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
100	#490	C₂²×C₁₁	1	64	yes	direct product factor
101	C₂×#102	C₂²×C₁₁	1	48	yes	complemented
102	C₂×#97	C₂²×C₁₁	1	12	yes	complemented
103	C₂²×C₁₁	—	4	8	no	—
104	C₂²×C₁₁	—	4	16	no	—
105	C₂²×C₁₁	—	8	48	no	—
106	C₂²×C₁₁	#490	1	16	yes	direct product factor
107	C₂²×C₁₁	C₂×#124	1	6	yes	—
108	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	12	yes	—
109	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
110	C₄×C₁₁	—	2	8	no	—
111	C₄×C₁₁	—	4	8	no	—
112	C₄×C₁₁	C₂×#124	1	6	yes	—
113	C₄×C₁₁	C₂²×#41	1	2	yes	—
114	C₂⁵	—	2	2	no	—
115	C₂²×D₄	—	2	6	no	—
116	C₂²×D₄	—	2	24	no	—
117	C₂²×D₄	—	2	16	no	—
118	C₂²×D₄	—	4	16	no	—
119	C₂²×D₄	C₂³×C₁₁	1	12	yes	—
120	C₂³×C₄	—	2	2	no	—
121	C₂³×C₄	D₄×C₁₁	1	2	yes	—
122	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
123	C₂²×C₈	—	2	8	no	—
124	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
125	#127	—	2	24	no	—
126	#127	C₂³×C₁₁	1	16	yes	—
127	#125	—	2	24	no	—
128	#125	C₂³×C₁₁	1	16	yes	complemented
129	C₂×C₄⋊C₄	—	2	24	no	—
130	C₂×C₄⋊C₄	—	2	6	no	—
131	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
132	C₂×C₄²	D₄×C₁₁	1	6	yes	—
133	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
134	#102	C₂³×C₁₁	1	64	yes	complemented
135	#97	C₂³×C₁₁	1	16	yes	complemented
136	C₂×C₁₁	—	8	8	no	—
137	C₂×C₁₁	C₂×#490	1	12	yes	direct product factor
138	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
139	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	2	yes	—
140	C₂⁴	—	2	12	no	—
141	C₂⁴	—	4	8	no	—
142	C₂⁴	—	4	16	no	—
143	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
144	C₂×D₄	—	2	12	no	—
145	C₂×D₄	—	2	32	no	—
146	C₂×D₄	—	2	48	no	—
147	C₂×D₄	—	4	96	no	—
148	C₂×D₄	—	4	24	no	—
149	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
150	C₂²×C₄	—	2	8	no	—
151	C₂²×C₄	—	2	12	no	—
152	C₂²×C₄	—	4	8	no	—
153	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
154	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
155	C₂²×C₄	C₁₁×#41	1	8	yes	—
156	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
157	C₂×C₈	—	2	24	no	—
158	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
159	C₄⋊C₄	—	2	32	no	—
160	C₄⋊C₄	—	2	12	no	—
161	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
162	C₄²	C₂×D₄×C₁₁	1	12	yes	—
163	C₄²	C₂⁴×C₁₁	1	4	yes	—
164	C₁₁	C₂²×#490	1	1	yes	characteristic, direct product factor, Sylow
165	C₂³	—	2	8	no	—
166	C₂³	—	4	24	no	—
167	C₂³	—	4	48	no	—
168	C₂³	—	8	32	no	—
169	C₂³	C₁₁×#124	1	4	yes	—
170	C₂³	C₁₁×AGL(1,ℤ/8)	1	8	yes	—
171	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
172	D₄	—	2	16	no	—
173	D₄	—	4	64	no	—
174	D₄	—	4	24	no	—
175	C₂×C₄	—	2	24	no	—
176	C₂×C₄	—	2	8	no	—
177	C₂×C₄	—	4	24	no	—
178	C₂×C₄	C₁₁×#124	1	12	yes	—
179	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
180	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
181	C₂×C₄	C₂×C₁₁×#41	1	12	yes	—
182	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
183	C₈	—	2	8	no	—
184	C₂²	—	4	8	no	—
185	C₂²	—	4	16	no	—
186	C₂²	—	8	48	no	—
187	C₂²	C₁₁×#490	1	16	yes	direct product factor
188	C₂²	C₂×C₁₁×#124	1	6	yes	—
189	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	12	yes	—
190	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
191	C₄	—	2	8	no	—
192	C₄	—	4	8	no	—
193	C₄	C₂×C₁₁×#124	1	6	yes	—
194	C₄	C₂²×C₁₁×#41	1	2	yes	—
195	C₂	—	8	8	no	—
196	C₂	C₂×C₁₁×#490	1	12	yes	direct product factor
197	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
198	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×#125	C₂	semidirect
3. C₂×C₁₁×#490	C₂	direct (N × H)
4. C₂²×C₁₁×#102	C₂	semidirect
5. C₂²×C₁₁×#97	C₂	semidirect
12. C₂×C₁₁×#125	C₂²	semidirect
16. C₁₁×#490	C₂²	direct (N × H)
17. C₂×C₁₁×#102	C₂²	semidirect
18. C₂×C₁₁×#97	C₂²	semidirect
33. C₁₁×#125	C₂³	semidirect
39. C₁₁×#102	C₂³	semidirect
40. C₁₁×#97	C₂³	semidirect
41. C₂²×#490	C₁₁	direct (N × H)
67. C₂²×#125	C₂×C₁₁	semidirect
68. C₂×#490	C₂×C₁₁	direct (N × H)
69. C₂²×#102	C₂×C₁₁	semidirect
70. C₂²×#97	C₂×C₁₁	semidirect
96. C₂×#125	C₂²×C₁₁	semidirect
100. #490	C₂²×C₁₁	direct (N × H)
101. C₂×#102	C₂²×C₁₁	semidirect
102. C₂×#97	C₂²×C₁₁	semidirect
106. C₂²×C₁₁	#490	direct (N × H)
128. #125	C₂³×C₁₁	semidirect
134. #102	C₂³×C₁₁	semidirect
135. #97	C₂³×C₁₁	semidirect
137. C₂×C₁₁	C₂×#490	direct (N × H)
164. C₁₁	C₂²×#490	direct (N × H)
187. C₂²	C₁₁×#490	direct (N × H)
196. C₂	C₂×C₁₁×#490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#127	2
C₂²×C₁₁×#125	2
C₂×C₁₁×#490	2
C₂²×C₁₁×#102	2
C₂²×C₁₁×#97	2
C₂²×#490	11

Subgroups — C22×C11×#490 #14637800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#490 #14637800