Subgroups — C₁₁×#3206 #13066044

Order 1408.

428 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#492	C₂	1	2	yes	maximal, complemented
4	C₁₁×#487	C₂	1	2	yes	maximal, complemented
5	C₁₁×#461	C₂	1	4	yes	maximal, complemented
6	C₁₁×#448	C₂	1	4	yes	maximal, complemented
7	C₁₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#41	—	2	1	no	—
9	C₂²×Q₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₁₁×SD₁₆	C₂²	1	8	yes	—
11	C₁₁×C₄⋊Q₈	—	2	1	no	—
12	C₁₁×C₄⋊Q₈	—	2	1	no	—
13	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₁₁×#127	C₂²	1	1	yes	characteristic
17	C₁₁×#124	—	2	1	no	—
18	C₁₁×#121	—	2	1	no	—
19	C₁₁×#121	C₂²	1	2	yes	—
20	C₄×D₄×C₁₁	—	2	1	no	—
21	C₄×D₄×C₁₁	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
23	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
24	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
25	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₁×#103	C₂²	1	8	yes	—
27	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₄×C₈×C₁₁	C₂²	1	2	yes	—
29	C₁₁×#41	—	4	4	no	—
30	C₂×Q₈×C₁₁	—	2	1	no	—
31	C₂×Q₈×C₁₁	—	2	2	no	—
32	C₂×Q₈×C₁₁	—	4	4	no	—
33	C₂×Q₈×C₁₁	C₂³	1	4	yes	—
34	C₂×D₄×C₁₁	—	2	2	no	—
35	C₂×D₄×C₁₁	—	2	1	no	—
36	C₂×D₄×C₁₁	—	2	1	no	—
37	C₂×D₄×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₁	—	2	2	no	—
39	C₂²×C₄×C₁₁	—	2	2	no	—
40	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×SD₁₆	—	4	8	no	—
44	C₂×C₈×C₁₁	C₂³	1	4	yes	—
45	C₁₁×C₄⋊C₄	—	2	2	no	—
46	C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₁₁×C₄⋊C₄	—	2	2	no	—
48	C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₁₁×C₄⋊C₄	—	2	1	no	—
50	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
51	C₁₁×C₂²⋊C₄	—	2	2	no	—
52	C₁₁×C₂²⋊C₄	—	2	2	no	—
53	C₄²×C₁₁	D₄	1	1	yes	characteristic
54	C₄²×C₁₁	D₄	1	1	yes	characteristic
55	C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	#3206	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₁₁	—	2	2	no	—
59	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
60	Q₈×C₁₁	—	2	8	no	—
61	Q₈×C₁₁	—	4	4	no	—
62	Q₈×C₁₁	—	4	2	no	—
63	D₄×C₁₁	—	2	4	no	—
64	D₄×C₁₁	—	4	4	no	—
65	D₄×C₁₁	—	4	2	no	—
66	D₄×C₁₁	—	4	2	no	—
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	—	2	2	no	—
70	C₂×C₄×C₁₁	—	2	4	no	—
71	C₂×C₄×C₁₁	—	4	4	no	—
72	C₂×C₄×C₁₁	—	4	4	no	—
73	C₂×C₄×C₁₁	SD₁₆	1	4	yes	complemented
74	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
80	C₈×C₁₁	—	2	4	no	—
81	#532	C₂×C₁₁	1	1	yes	characteristic
82	C₂×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
83	#492	C₂×C₁₁	1	2	yes	complemented
84	#487	C₂×C₁₁	1	2	yes	complemented
85	#461	C₂×C₁₁	1	4	yes	complemented
86	#448	C₂×C₁₁	1	4	yes	complemented
87	#431	C₂×C₁₁	1	1	yes	characteristic, complemented
88	C₂²×C₁₁	—	2	1	no	—
89	C₂²×C₁₁	—	2	1	no	—
90	C₂²×C₁₁	—	4	2	no	—
91	C₂²×C₁₁	—	4	2	no	—
92	C₂²×C₁₁	—	4	2	no	—
93	C₂²×C₁₁	C₂×SD₁₆	1	2	yes	—
94	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
95	C₄×C₁₁	—	2	1	no	—
96	C₄×C₁₁	—	2	1	no	—
97	C₄×C₁₁	—	4	4	no	—
98	C₄×C₁₁	—	4	2	no	—
99	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
100	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
101	C₄×C₁₁	#137	1	2	yes	—
102	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
103	C₂×#41	—	2	1	no	—
104	C₂²×Q₈	C₂²×C₁₁	1	2	yes	—
105	C₂×SD₁₆	C₂²×C₁₁	1	8	yes	—
106	C₄⋊Q₈	—	2	1	no	—
107	C₄⋊Q₈	—	2	1	no	—
108	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
109	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
110	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
111	#127	C₂²×C₁₁	1	1	yes	characteristic
112	#124	—	2	1	no	—
113	#121	—	2	1	no	—
114	#121	C₂²×C₁₁	1	2	yes	—
115	C₄×D₄	—	2	1	no	—
116	C₄×D₄	C₂²×C₁₁	1	2	yes	—
117	C₂×C₄⋊C₄	—	2	1	no	—
118	C₂×C₄⋊C₄	—	2	1	no	—
119	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
120	C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
121	#103	C₂²×C₁₁	1	8	yes	—
122	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
123	C₄×C₈	C₂²×C₁₁	1	2	yes	—
124	C₂×C₁₁	—	2	2	no	—
125	C₂×C₁₁	—	8	2	no	—
126	C₂×C₁₁	#535	1	1	yes	characteristic
127	C₂×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
128	C₂×C₁₁	C₂×#137	1	1	yes	characteristic
129	#41	—	4	4	no	—
130	C₂×Q₈	—	2	1	no	—
131	C₂×Q₈	—	2	2	no	—
132	C₂×Q₈	—	4	4	no	—
133	C₂×Q₈	C₂³×C₁₁	1	4	yes	—
134	C₂×D₄	—	2	2	no	—
135	C₂×D₄	—	2	1	no	—
136	C₂×D₄	—	2	1	no	—
137	C₂×D₄	C₂³×C₁₁	1	2	yes	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
141	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
142	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
143	SD₁₆	—	4	8	no	—
144	C₂×C₈	C₂³×C₁₁	1	4	yes	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	—	2	2	no	—
147	C₄⋊C₄	—	2	2	no	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄⋊C₄	—	2	1	no	—
150	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
151	C₂²⋊C₄	—	2	2	no	—
152	C₂²⋊C₄	—	2	2	no	—
153	C₄²	D₄×C₁₁	1	1	yes	characteristic
154	C₄²	D₄×C₁₁	1	1	yes	characteristic
155	C₄²	C₂³×C₁₁	1	1	yes	characteristic
156	C₄²	C₂³×C₁₁	1	1	yes	characteristic
157	C₁₁	#3206	1	1	yes	characteristic, direct product factor, Sylow
158	C₂³	—	2	2	no	—
159	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
160	Q₈	—	2	8	no	—
161	Q₈	—	4	4	no	—
162	Q₈	—	4	2	no	—
163	D₄	—	2	4	no	—
164	D₄	—	4	4	no	—
165	D₄	—	4	2	no	—
166	D₄	—	4	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	C₁₁×SD₁₆	1	4	yes	complemented
174	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
175	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
176	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
177	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
178	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
179	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
180	C₈	—	2	4	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	2	1	no	—
183	C₂²	—	4	2	no	—
184	C₂²	—	4	2	no	—
185	C₂²	—	4	2	no	—
186	C₂²	C₂×C₁₁×SD₁₆	1	2	yes	—
187	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
188	C₄	—	2	1	no	—
189	C₄	—	2	1	no	—
190	C₄	—	4	4	no	—
191	C₄	—	4	2	no	—
192	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
193	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
194	C₄	C₁₁×#137	1	2	yes	—
195	C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
196	C₂	—	2	2	no	—
197	C₂	—	8	2	no	—
198	C₂	C₁₁×#535	1	1	yes	characteristic
199	C₂	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
200	C₂	C₂×C₁₁×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₄⋊Q₈	C₂	semidirect
3. C₁₁×#492	C₂	semidirect
4. C₁₁×#487	C₂	semidirect
5. C₁₁×#461	C₂	semidirect
6. C₁₁×#448	C₂	semidirect
7. C₁₁×#431	C₂	semidirect
57. #3206	C₁₁	direct (N × H)
73. C₂×C₄×C₁₁	SD₁₆	semidirect
82. C₂×C₄⋊Q₈	C₂×C₁₁	semidirect
83. #492	C₂×C₁₁	semidirect
84. #487	C₂×C₁₁	semidirect
85. #461	C₂×C₁₁	semidirect
86. #448	C₂×C₁₁	semidirect
87. #431	C₂×C₁₁	semidirect
157. C₁₁	#3206	direct (N × H)
173. C₂×C₄	C₁₁×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#532	2
C₂×C₁₁×C₄⋊Q₈	2
C₁₁×#492	2
C₁₁×#487	2
C₁₁×#461	2
C₁₁×#448	2
C₁₁×#431	2
#3206	11

Subgroups — C11×#3206 #13066044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3206 #13066044