Subgroups — C₁₁×#3156 #13065994

Order 1408.

532 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#137	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#536	C₂	1	2	yes	maximal, complemented
5	C₁₁×#497	C₂	1	4	yes	maximal, complemented
6	C₁₁×#495	C₂	1	2	yes	maximal, complemented
7	C₁₁×#494	C₂	1	2	yes	maximal, complemented
8	C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#41	C₂²	1	2	yes	—
10	C₂²×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₁₁×#137	—	2	8	no	—
12	C₁₁×#135	—	2	4	no	—
13	C₂×C₁₁×Q₁₆	—	2	4	no	—
14	C₂×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
16	C₂×C₁₁×Q₁₆	C₂²	1	4	yes	—
17	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₁₁×SD₁₆	C₂²	1	4	yes	—
19	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₁₁×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×C₄⋊Q₈	C₂²	1	4	yes	—
24	C₁₁×#124	C₂²	1	4	yes	—
25	C₁₁×#123	—	2	4	no	—
26	C₁₁×C₂²⋊Q₈	—	2	4	no	—
27	C₁₁×#117	C₂²	1	1	yes	characteristic
28	C₁₁×#97	C₂²	1	2	yes	—
29	C₄×C₈×C₁₁	C₂²	1	2	yes	—
30	C₁₁×#41	—	2	4	no	—
31	C₁₁×#41	—	2	4	no	—
32	C₂×Q₈×C₁₁	—	2	2	no	—
33	C₂×Q₈×C₁₁	—	2	4	no	—
34	C₂×Q₈×C₁₁	—	2	4	no	—
35	C₂×Q₈×C₁₁	C₂³	1	4	yes	—
36	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
37	C₂×D₄×C₁₁	—	2	2	no	—
38	C₂×D₄×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₁	—	2	2	no	—
40	C₂²×C₄×C₁₁	—	2	2	no	—
41	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
42	C₁₁×Q₁₆	—	2	4	no	—
43	C₁₁×Q₁₆	—	2	4	no	—
44	C₁₁×Q₁₆	—	2	2	no	—
45	C₁₁×Q₁₆	—	2	8	no	—
46	C₁₁×SD₁₆	—	2	4	no	—
47	C₁₁×SD₁₆	—	2	8	no	—
48	C₁₁×D₈	—	2	2	no	—
49	C₁₁×M₁₆	D₄	1	4	yes	—
50	C₂×C₈×C₁₁	D₄	1	4	yes	—
51	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₁₁×C₄⋊C₄	—	2	8	no	—
55	C₁₁×C₄⋊C₄	D₄	1	2	yes	—
56	C₁₁×C₂²⋊C₄	—	2	8	no	—
57	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
58	C₄²×C₁₁	C₂³	1	2	yes	—
59	#3156	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₁₁	—	2	2	no	—
61	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
62	Q₈×C₁₁	—	2	4	no	—
63	Q₈×C₁₁	—	2	2	no	—
64	Q₈×C₁₁	—	2	4	no	—
65	Q₈×C₁₁	—	2	2	no	—
66	Q₈×C₁₁	—	4	4	no	—
67	D₄×C₁₁	—	2	2	no	—
68	D₄×C₁₁	—	2	2	no	—
69	D₄×C₁₁	—	4	4	no	—
70	C₂×C₄×C₁₁	—	2	4	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	4	4	no	—
73	C₂×C₄×C₁₁	—	4	4	no	—
74	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
75	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₈×C₁₁	C₂×D₄	1	2	yes	—
80	C₈×C₁₁	C₂×D₄	1	2	yes	—
81	C₈×C₁₁	C₂×D₄	1	4	yes	—
82	C₂×#137	C₂×C₁₁	1	2	yes	complemented
83	C₂×#135	C₂×C₁₁	1	1	yes	characteristic
84	C₂²×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
85	#536	C₂×C₁₁	1	2	yes	complemented
86	#497	C₂×C₁₁	1	4	yes	complemented
87	#495	C₂×C₁₁	1	2	yes	complemented
88	#494	C₂×C₁₁	1	2	yes	complemented
89	#405	C₂×C₁₁	1	1	yes	characteristic, complemented
90	C₂²×C₁₁	—	2	2	no	—
91	C₂²×C₁₁	—	4	2	no	—
92	C₂²×C₁₁	—	4	4	no	—
93	C₂²×C₁₁	#127	1	2	yes	—
94	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
95	C₄×C₁₁	—	2	4	no	—
96	C₄×C₁₁	—	4	2	no	—
97	C₄×C₁₁	—	4	4	no	—
98	C₄×C₁₁	#127	1	2	yes	—
99	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
101	C₂×#41	C₂²×C₁₁	1	2	yes	—
102	C₂²×Q₈	C₂²×C₁₁	1	2	yes	—
103	#137	—	2	8	no	—
104	#135	—	2	4	no	—
105	C₂×Q₁₆	—	2	4	no	—
106	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
107	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
108	C₂×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
109	C₂×Q₁₆	C₂²×C₁₁	1	4	yes	—
110	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
111	C₂×SD₁₆	C₂²×C₁₁	1	4	yes	—
112	C₂×D₈	C₂²×C₁₁	1	1	yes	characteristic
113	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
114	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
115	C₄⋊Q₈	C₂²×C₁₁	1	4	yes	—
116	#124	C₂²×C₁₁	1	4	yes	—
117	#123	—	2	4	no	—
118	C₂²⋊Q₈	—	2	4	no	—
119	#117	C₂²×C₁₁	1	1	yes	characteristic
120	#97	C₂²×C₁₁	1	2	yes	—
121	C₄×C₈	C₂²×C₁₁	1	2	yes	—
122	C₂×C₁₁	—	2	2	no	—
123	C₂×C₁₁	—	8	2	no	—
124	C₂×C₁₁	C₂×#127	1	1	yes	characteristic
125	C₂×C₁₁	#578	1	2	yes	—
126	#41	—	2	4	no	—
127	#41	—	2	4	no	—
128	C₂×Q₈	—	2	2	no	—
129	C₂×Q₈	—	2	4	no	—
130	C₂×Q₈	—	2	4	no	—
131	C₂×Q₈	C₂³×C₁₁	1	4	yes	—
132	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
133	C₂×D₄	—	2	2	no	—
134	C₂×D₄	C₂³×C₁₁	1	2	yes	—
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
138	Q₁₆	—	2	4	no	—
139	Q₁₆	—	2	4	no	—
140	Q₁₆	—	2	2	no	—
141	Q₁₆	—	2	8	no	—
142	SD₁₆	—	2	4	no	—
143	SD₁₆	—	2	8	no	—
144	D₈	—	2	2	no	—
145	M₁₆	D₄×C₁₁	1	4	yes	—
146	C₂×C₈	D₄×C₁₁	1	4	yes	—
147	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
148	C₂×C₈	C₂³×C₁₁	1	2	yes	—
149	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
150	C₄⋊C₄	—	2	8	no	—
151	C₄⋊C₄	D₄×C₁₁	1	2	yes	—
152	C₂²⋊C₄	—	2	8	no	—
153	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
154	C₄²	C₂³×C₁₁	1	2	yes	—
155	C₁₁	#3156	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	—	2	2	no	—
157	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
158	Q₈	—	2	4	no	—
159	Q₈	—	2	2	no	—
160	Q₈	—	2	4	no	—
161	Q₈	—	2	2	no	—
162	Q₈	—	4	4	no	—
163	D₄	—	2	2	no	—
164	D₄	—	2	2	no	—
165	D₄	—	4	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	C₂×D₄×C₁₁	1	4	yes	—
171	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
172	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
173	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
174	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
175	C₈	C₂×D₄×C₁₁	1	2	yes	—
176	C₈	C₂×D₄×C₁₁	1	2	yes	—
177	C₈	C₂×D₄×C₁₁	1	4	yes	—
178	C₂²	—	2	2	no	—
179	C₂²	—	4	2	no	—
180	C₂²	—	4	4	no	—
181	C₂²	C₁₁×#127	1	2	yes	—
182	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
183	C₄	—	2	4	no	—
184	C₄	—	4	2	no	—
185	C₄	—	4	4	no	—
186	C₄	C₁₁×#127	1	2	yes	—
187	C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
188	C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
189	C₂	—	2	2	no	—
190	C₂	—	8	2	no	—
191	C₂	C₂×C₁₁×#127	1	1	yes	characteristic
192	C₂	C₁₁×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#137	C₂	semidirect
3. C₂²×C₁₁×Q₁₆	C₂	semidirect
4. C₁₁×#536	C₂	semidirect
5. C₁₁×#497	C₂	semidirect
6. C₁₁×#495	C₂	semidirect
7. C₁₁×#494	C₂	semidirect
8. C₁₁×#405	C₂	semidirect
59. #3156	C₁₁	direct (N × H)
82. C₂×#137	C₂×C₁₁	semidirect
84. C₂²×Q₁₆	C₂×C₁₁	semidirect
85. #536	C₂×C₁₁	semidirect
86. #497	C₂×C₁₁	semidirect
87. #495	C₂×C₁₁	semidirect
88. #494	C₂×C₁₁	semidirect
89. #405	C₂×C₁₁	semidirect
155. C₁₁	#3156	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×#137	2
C₂×C₁₁×#135	2
C₂²×C₁₁×Q₁₆	2
C₁₁×#536	2
C₁₁×#497	2
C₁₁×#495	2
C₁₁×#494	2
C₁₁×#405	2
#3156	11

Subgroups — C11×#3156 #13065994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3156 #13065994