Subgroups — C₁₁×#33716 #14610909

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#508	C₂	1	4	yes	maximal, complemented
2	C₁₁×#3147	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2251	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2250	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#135	—	2	2	no	—
7	C₂×C₁₁×#135	C₂²	1	4	yes	—
8	C₁₁×#532	—	2	2	no	—
9	C₁₁×#508	—	2	16	no	—
10	C₂×C₁₁×Q₃₂	C₂²	1	4	yes	—
11	C₂×C₁₁×SD₃₂	C₂²	1	8	yes	—
12	C₂×C₁₁×D₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
14	C₁₁×#495	—	2	2	no	—
15	C₁₁×#495	C₂²	1	4	yes	—
16	C₁₁×#494	C₂²	1	2	yes	—
17	C₁₁×#493	C₂²	1	2	yes	—
18	C₁₁×#492	—	2	2	no	—
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#346	C₂²	1	4	yes	—
21	C₂×C₁₁×#41	—	2	4	no	—
22	C₁₁×#135	—	2	16	no	—
23	C₁₁×#135	—	4	8	no	—
24	C₂×C₁₁×Q₁₆	—	2	2	no	—
25	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
26	C₂×C₁₁×SD₁₆	—	2	4	no	—
27	C₂×C₁₁×SD₁₆	—	2	4	no	—
28	C₂×C₁₁×D₈	—	2	2	no	—
29	C₂×C₁₁×D₈	C₂³	1	4	yes	—
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₁₁×C₄⋊Q₈	—	2	2	no	—
33	C₁₁×#127	—	2	2	no	—
34	C₁₁×#124	—	2	4	no	—
35	C₁₁×#121	—	4	4	no	—
36	C₄×D₄×C₁₁	—	4	4	no	—
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₁₁×Q₃₂	—	2	8	no	—
39	C₁₁×SD₃₂	—	2	16	no	—
40	C₁₁×D₁₆	—	2	8	no	—
41	C₂×C₁₁×C₁₆	D₄	1	8	yes	complemented
42	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
43	C₄×C₈×C₁₁	D₄	1	2	yes	—
44	C₄×C₈×C₁₁	C₂³	1	2	yes	—
45	#33716	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₁₁×#41	—	4	8	no	—
47	C₁₁×#41	—	4	8	no	—
48	C₂×Q₈×C₁₁	—	2	4	no	—
49	C₂×D₄×C₁₁	—	2	4	no	—
50	C₂×D₄×C₁₁	—	4	4	no	—
51	C₂×D₄×C₁₁	—	4	4	no	—
52	C₂²×C₄×C₁₁	—	4	4	no	—
53	C₂²×C₄×C₁₁	D₈	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₁₁×Q₁₆	—	2	8	no	—
56	C₁₁×Q₁₆	—	4	4	no	—
57	C₁₁×SD₁₆	—	4	8	no	—
58	C₁₁×SD₁₆	—	4	8	no	—
59	C₁₁×D₈	—	2	8	no	—
60	C₁₁×D₈	—	4	4	no	—
61	C₂×C₈×C₁₁	D₈	1	4	yes	—
62	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
65	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₁₁×C₂²⋊C₄	—	4	8	no	—
68	C₄²×C₁₁	D₈	1	2	yes	—
69	C₄²×C₁₁	C₂×D₄	1	2	yes	—
70	C₁₁×C₁₆	C₂×D₄	1	8	yes	—
71	C₂×#508	C₂×C₁₁	1	4	yes	complemented
72	#3147	C₂×C₁₁	1	2	yes	complemented
73	#2251	C₂×C₁₁	1	4	yes	complemented
74	#2250	C₂×C₁₁	1	4	yes	complemented
75	C₂×#346	C₂×C₁₁	1	1	yes	characteristic, complemented
76	C₂³×C₁₁	—	4	4	no	—
77	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
78	Q₈×C₁₁	—	4	4	no	—
79	Q₈×C₁₁	—	4	4	no	—
80	D₄×C₁₁	—	4	4	no	—
81	D₄×C₁₁	—	4	4	no	—
82	D₄×C₁₁	—	8	8	no	—
83	D₄×C₁₁	—	8	8	no	—
84	C₂×C₄×C₁₁	—	4	2	no	—
85	C₂×C₄×C₁₁	—	4	4	no	—
86	C₂×C₄×C₁₁	—	8	8	no	—
87	C₂×C₄×C₁₁	#127	1	2	yes	—
88	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
89	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
92	C₈×C₁₁	#127	1	2	yes	—
93	C₈×C₁₁	C₂×D₈	1	4	yes	—
94	C₈×C₁₁	C₂²×D₄	1	2	yes	—
95	C₂×#135	—	2	2	no	—
96	C₂×#135	C₂²×C₁₁	1	4	yes	—
97	#532	—	2	2	no	—
98	#508	—	2	16	no	—
99	C₂×Q₃₂	C₂²×C₁₁	1	4	yes	—
100	C₂×SD₃₂	C₂²×C₁₁	1	8	yes	—
101	C₂×D₁₆	C₂²×C₁₁	1	4	yes	—
102	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
103	#495	—	2	2	no	—
104	#495	C₂²×C₁₁	1	4	yes	—
105	#494	C₂²×C₁₁	1	2	yes	—
106	#493	C₂²×C₁₁	1	2	yes	—
107	#492	—	2	2	no	—
108	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
109	#346	C₂²×C₁₁	1	4	yes	—
110	C₂²×C₁₁	—	2	2	no	—
111	C₂²×C₁₁	—	8	4	no	—
112	C₂²×C₁₁	—	8	8	no	—
113	C₂²×C₁₁	#493	1	2	yes	—
114	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
115	C₄×C₁₁	—	2	4	no	—
116	C₄×C₁₁	—	8	4	no	—
117	C₄×C₁₁	#493	1	2	yes	—
118	C₄×C₁₁	C₂×#127	1	1	yes	characteristic
119	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
120	C₂×#41	—	2	4	no	—
121	#135	—	2	16	no	—
122	#135	—	4	8	no	—
123	C₂×Q₁₆	—	2	2	no	—
124	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
125	C₂×SD₁₆	—	2	4	no	—
126	C₂×SD₁₆	—	2	4	no	—
127	C₂×D₈	—	2	2	no	—
128	C₂×D₈	C₂³×C₁₁	1	4	yes	—
129	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
130	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
131	C₄⋊Q₈	—	2	2	no	—
132	#127	—	2	2	no	—
133	#124	—	2	4	no	—
134	#121	—	4	4	no	—
135	C₄×D₄	—	4	4	no	—
136	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
137	Q₃₂	—	2	8	no	—
138	SD₃₂	—	2	16	no	—
139	D₁₆	—	2	8	no	—
140	C₂×C₁₆	D₄×C₁₁	1	8	yes	complemented
141	C₂×C₁₆	C₂³×C₁₁	1	4	yes	—
142	C₄×C₈	D₄×C₁₁	1	2	yes	—
143	C₄×C₈	C₂³×C₁₁	1	2	yes	—
144	C₂×C₁₁	—	2	2	no	—
145	C₂×C₁₁	—	16	4	no	—
146	C₂×C₁₁	C₂×#493	1	1	yes	characteristic
147	C₂×C₁₁	#3414	1	2	yes	—
148	#41	—	4	8	no	—
149	#41	—	4	8	no	—
150	C₂×Q₈	—	2	4	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	4	4	no	—
153	C₂×D₄	—	4	4	no	—
154	C₂²×C₄	—	4	4	no	—
155	C₂²×C₄	C₁₁×D₈	1	2	yes	—
156	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
157	Q₁₆	—	2	8	no	—
158	Q₁₆	—	4	4	no	—
159	SD₁₆	—	4	8	no	—
160	SD₁₆	—	4	8	no	—
161	D₈	—	2	8	no	—
162	D₈	—	4	4	no	—
163	C₂×C₈	C₁₁×D₈	1	4	yes	—
164	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
165	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
166	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
167	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
168	C₄⋊C₄	—	4	4	no	—
169	C₂²⋊C₄	—	4	8	no	—
170	C₄²	C₁₁×D₈	1	2	yes	—
171	C₄²	C₂×D₄×C₁₁	1	2	yes	—
172	C₁₆	C₂×D₄×C₁₁	1	8	yes	—
173	C₁₁	#33716	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	—	4	4	no	—
175	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
176	Q₈	—	4	4	no	—
177	Q₈	—	4	4	no	—
178	D₄	—	4	4	no	—
179	D₄	—	4	4	no	—
180	D₄	—	8	8	no	—
181	D₄	—	8	8	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	8	8	no	—
185	C₂×C₄	C₁₁×#127	1	2	yes	—
186	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
187	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
188	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
189	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
190	C₈	C₁₁×#127	1	2	yes	—
191	C₈	C₂×C₁₁×D₈	1	4	yes	—
192	C₈	C₂²×D₄×C₁₁	1	2	yes	—
193	C₂²	—	2	2	no	—
194	C₂²	—	8	8	no	—
195	C₂²	—	8	4	no	—
196	C₂²	C₁₁×#493	1	2	yes	—
197	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
198	C₄	—	2	4	no	—
199	C₄	—	8	4	no	—
200	C₄	C₁₁×#493	1	2	yes	—
201	C₄	C₂×C₁₁×#127	1	1	yes	characteristic
202	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
203	C₂	—	2	2	no	—
204	C₂	—	16	4	no	—
205	C₂	C₂×C₁₁×#493	1	1	yes	characteristic
206	C₂	C₁₁×#3414	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#508	C₂	semidirect
2. C₁₁×#3147	C₂	semidirect
3. C₁₁×#2251	C₂	semidirect
4. C₁₁×#2250	C₂	semidirect
5. C₂×C₁₁×#346	C₂	semidirect
41. C₂×C₁₁×C₁₆	D₄	semidirect
45. #33716	C₁₁	direct (N × H)
71. C₂×#508	C₂×C₁₁	semidirect
72. #3147	C₂×C₁₁	semidirect
73. #2251	C₂×C₁₁	semidirect
74. #2250	C₂×C₁₁	semidirect
75. C₂×#346	C₂×C₁₁	semidirect
140. C₂×C₁₆	D₄×C₁₁	semidirect
173. C₁₁	#33716	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×#508	2
C₁₁×#3147	2
C₁₁×#2251	2
C₁₁×#2250	2
C₂×C₁₁×#346	2
#33716	11

Subgroups — C11×#33716 #14610909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33716 #14610909