Subgroups — C₁₁×#2562 #13065400

Order 1408.

532 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×C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#400	C₂	1	2	yes	maximal, complemented
4	C₁₁×#394	C₂	1	2	yes	maximal
5	C₁₁×#388	C₂	1	4	yes	maximal, complemented
6	C₁₁×#380	C₂	1	2	yes	maximal, complemented
7	C₁₁×#380	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₁₁	C₂²	1	2	yes	—
11	C₁₁×#125	—	2	4	no	—
12	C₄×D₄×C₁₁	—	2	4	no	—
13	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#95	C₂²	1	2	yes	—
25	C₁₁×#95	C₂²	1	4	yes	—
26	C₁₁×#95	C₂²	1	4	yes	—
27	C₂⁴×C₁₁	C₂³	1	2	yes	—
28	C₂×D₄×C₁₁	—	2	4	no	—
29	C₂×D₄×C₁₁	—	2	2	no	—
30	C₂²×C₄×C₁₁	—	2	4	no	—
31	C₂²×C₄×C₁₁	—	2	4	no	—
32	C₂²×C₄×C₁₁	—	2	4	no	—
33	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
35	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
40	C₁₁×C₄⋊C₄	—	2	2	no	—
41	C₁₁×C₄⋊C₄	—	2	4	no	—
42	C₁₁×C₄⋊C₄	—	2	4	no	—
43	C₁₁×C₄⋊C₄	—	2	2	no	—
44	C₁₁×C₄⋊C₄	—	2	2	no	—
45	C₁₁×C₄⋊C₄	—	2	4	no	—
46	C₁₁×C₂²⋊C₄	—	2	8	no	—
47	C₁₁×C₂²⋊C₄	—	2	4	no	—
48	C₁₁×C₂²⋊C₄	—	4	4	no	—
49	C₄²×C₁₁	—	4	2	no	—
50	C₄²×C₁₁	D₄	1	4	yes	—
51	#2562	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂³×C₁₁	—	2	2	no	—
53	C₂³×C₁₁	—	2	2	no	—
54	C₂³×C₁₁	—	2	2	no	—
55	C₂³×C₁₁	—	2	2	no	—
56	C₂³×C₁₁	—	2	2	no	—
57	C₂³×C₁₁	—	2	2	no	—
58	C₂³×C₁₁	#41	1	4	yes	—
59	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
60	D₄×C₁₁	—	2	8	no	—
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	2	2	no	—
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	—	2	4	no	—
68	C₂×C₄×C₁₁	—	2	4	no	—
69	C₂×C₄×C₁₁	—	2	4	no	—
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	4	8	no	—
76	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₁	#41	1	4	yes	—
80	C₂×#125	C₂×C₁₁	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
82	#400	C₂×C₁₁	1	2	yes	complemented
83	#394	C₂×C₁₁	1	2	yes	—
84	#388	C₂×C₁₁	1	4	yes	complemented
85	#380	C₂×C₁₁	1	2	yes	complemented
86	#380	C₂×C₁₁	1	2	yes	complemented
87	C₄×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
88	C₂²×C₁₁	—	2	4	no	—
89	C₂²×C₁₁	—	2	4	no	—
90	C₂²×C₁₁	—	2	4	no	—
91	C₂²×C₁₁	—	4	2	no	—
92	C₂²×C₁₁	—	4	2	no	—
93	C₂²×C₁₁	—	4	2	no	—
94	C₂²×C₁₁	—	4	2	no	—
95	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
96	C₂²×C₁₁	C₂×#41	1	2	yes	—
97	C₂²×C₁₁	C₂×#41	1	2	yes	—
98	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
99	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
100	C₄×C₁₁	—	2	2	no	—
101	C₄×C₁₁	—	2	2	no	—
102	C₄×C₁₁	—	4	2	no	—
103	C₄×C₁₁	—	4	2	no	—
104	C₄×C₁₁	—	4	2	no	—
105	C₄×C₁₁	—	4	4	no	—
106	C₄×C₁₁	#124	1	4	yes	—
107	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic
108	C₂³×C₄	C₂²×C₁₁	1	2	yes	—
109	#125	—	2	4	no	—
110	C₄×D₄	—	2	4	no	—
111	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
112	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
113	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
116	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
117	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
118	C₂×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
119	C₂×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
120	C₂×C₄²	C₂²×C₁₁	1	2	yes	—
121	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
122	#95	C₂²×C₁₁	1	2	yes	—
123	#95	C₂²×C₁₁	1	4	yes	—
124	#95	C₂²×C₁₁	1	4	yes	—
125	C₂×C₁₁	—	4	4	no	—
126	C₂×C₁₁	#525	1	1	yes	characteristic
127	C₂×C₁₁	C₂×#124	1	1	yes	characteristic
128	C₂×C₁₁	#537	1	1	yes	characteristic
129	C₂×C₁₁	#552	1	2	yes	—
130	C₂×C₁₁	#553	1	2	yes	—
131	C₂⁴	C₂³×C₁₁	1	2	yes	—
132	C₂×D₄	—	2	4	no	—
133	C₂×D₄	—	2	2	no	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	—	2	4	no	—
136	C₂²×C₄	—	2	4	no	—
137	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
138	C₂²×C₄	C₂³×C₁₁	1	4	yes	—
139	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
140	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
141	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
142	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
143	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	2	4	no	—
147	C₄⋊C₄	—	2	2	no	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄⋊C₄	—	2	4	no	—
150	C₂²⋊C₄	—	2	8	no	—
151	C₂²⋊C₄	—	2	4	no	—
152	C₂²⋊C₄	—	4	4	no	—
153	C₄²	—	4	2	no	—
154	C₄²	D₄×C₁₁	1	4	yes	—
155	C₁₁	#2562	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	—	2	2	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	—	2	2	no	—
162	C₂³	C₁₁×#41	1	4	yes	—
163	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
164	D₄	—	2	8	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	8	no	—
180	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
181	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
182	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
183	C₂×C₄	C₁₁×#41	1	4	yes	—
184	C₂²	—	2	4	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	2	4	no	—
187	C₂²	—	4	2	no	—
188	C₂²	—	4	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	2	no	—
191	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
192	C₂²	C₂×C₁₁×#41	1	2	yes	—
193	C₂²	C₂×C₁₁×#41	1	2	yes	—
194	C₂²	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
196	C₄	—	2	2	no	—
197	C₄	—	2	2	no	—
198	C₄	—	4	2	no	—
199	C₄	—	4	2	no	—
200	C₄	—	4	2	no	—
201	C₄	—	4	4	no	—
202	C₄	C₁₁×#124	1	4	yes	—
203	C₂	—	4	4	no	—
204	C₂	C₁₁×#525	1	1	yes	characteristic
205	C₂	C₂×C₁₁×#124	1	1	yes	characteristic
206	C₂	C₁₁×#537	1	1	yes	characteristic
207	C₂	C₁₁×#552	1	2	yes	—
208	C₂	C₁₁×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#125	C₂	semidirect
3. C₁₁×#400	C₂	semidirect
5. C₁₁×#388	C₂	semidirect
6. C₁₁×#380	C₂	semidirect
7. C₁₁×#380	C₂	semidirect
8. C₄×C₁₁×C₄⋊C₄	C₂	semidirect
51. #2562	C₁₁	direct (N × H)
80. C₂×#125	C₂×C₁₁	semidirect
82. #400	C₂×C₁₁	semidirect
84. #388	C₂×C₁₁	semidirect
85. #380	C₂×C₁₁	semidirect
86. #380	C₂×C₁₁	semidirect
87. C₄×C₄⋊C₄	C₂×C₁₁	semidirect
155. C₁₁	#2562	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×C₁₁×#125	2
C₂×C₄×D₄×C₁₁	2
C₁₁×#400	2
C₁₁×#394	2
C₁₁×#388	2
C₁₁×#380	2
C₄×C₁₁×C₄⋊C₄	2
#2562	11

Subgroups — C11×#2562 #13065400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2562 #13065400