Subgroups — C₁₁×#33749 #14610942

Order 2816.

504 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	C₁₁×#3170	C₂	1	2	yes	maximal
2	C₁₁×#2254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2241	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2219	C₂	1	4	yes	maximal
6	C₁₁×#2176	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#533	—	2	2	no	—
9	C₂×C₁₁×Q₃₂	C₂²	1	4	yes	—
10	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
11	C₁₁×#500	C₂²	1	2	yes	—
12	C₁₁×#494	C₂²	1	2	yes	—
13	C₁₁×#487	—	2	2	no	—
14	C₁₁×#467	—	2	2	no	—
15	C₁₁×#467	C₂²	1	4	yes	—
16	C₄×C₁₁×Q₁₆	—	2	2	no	—
17	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#367	C₂²	1	4	yes	—
20	C₁₁×#358	C₂²	1	8	yes	—
21	C₁₁×#346	C₂²	1	2	yes	—
22	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×Q₁₆	—	2	2	no	—
25	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₁₁×C₄⋊Q₈	—	2	2	no	—
29	C₁₁×C₄⋊Q₈	—	2	2	no	—
30	C₁₁×#125	—	4	2	no	—
31	C₁₁×C₂²⋊Q₈	—	2	4	no	—
32	C₁₁×C₂²⋊Q₈	—	4	2	no	—
33	C₄×Q₈×C₁₁	—	2	4	no	—
34	C₄×Q₈×C₁₁	—	4	2	no	—
35	C₁₁×#117	—	4	2	no	—
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₁₁×Q₃₂	—	2	8	no	—
38	C₁₁×M₃₂	—	2	4	no	—
39	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
40	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
41	C₁₁×#107	—	2	2	no	—
42	C₁₁×#107	C₂³	1	4	yes	—
43	C₁₁×#103	—	2	4	no	—
44	C₁₁×#103	—	2	4	no	—
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	#33749	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×Q₈×C₁₁	—	2	4	no	—
51	C₂×Q₈×C₁₁	—	4	2	no	—
52	C₂²×C₄×C₁₁	D₈	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₁₁×Q₁₆	—	2	8	no	—
55	C₁₁×Q₁₆	—	4	4	no	—
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₁₁×C₄⋊C₄	—	4	4	no	—
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₁₁×C₄⋊C₄	—	4	2	no	—
68	C₁₁×C₂²⋊C₄	—	4	4	no	—
69	C₄²×C₁₁	—	4	4	no	—
70	C₄²×C₁₁	D₈	1	2	yes	—
71	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₁₁×C₁₆	—	2	2	no	—
74	C₁₁×C₁₆	#41	1	4	yes	—
75	#3170	C₂×C₁₁	1	2	yes	—
76	#2254	C₂×C₁₁	1	1	yes	characteristic, complemented
77	#2247	C₂×C₁₁	1	1	yes	characteristic, complemented
78	#2241	C₂×C₁₁	1	2	yes	complemented
79	#2219	C₂×C₁₁	1	4	yes	—
80	#2176	C₂×C₁₁	1	4	yes	complemented
81	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic
82	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
83	Q₈×C₁₁	—	4	4	no	—
84	Q₈×C₁₁	—	4	4	no	—
85	Q₈×C₁₁	—	8	4	no	—
86	C₂×C₄×C₁₁	—	2	1	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	4	4	no	—
90	C₂×C₄×C₁₁	—	4	4	no	—
91	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
92	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
94	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
95	C₈×C₁₁	—	2	1	no	—
96	C₈×C₁₁	—	2	1	no	—
97	C₈×C₁₁	#135	1	2	yes	—
98	C₈×C₁₁	C₂×#41	1	2	yes	—
99	#533	—	2	2	no	—
100	C₂×Q₃₂	C₂²×C₁₁	1	4	yes	—
101	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
102	#500	C₂²×C₁₁	1	2	yes	—
103	#494	C₂²×C₁₁	1	2	yes	—
104	#487	—	2	2	no	—
105	#467	—	2	2	no	—
106	#467	C₂²×C₁₁	1	4	yes	—
107	C₄×Q₁₆	—	2	2	no	—
108	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	—
109	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	#367	C₂²×C₁₁	1	4	yes	—
111	#358	C₂²×C₁₁	1	8	yes	—
112	#346	C₂²×C₁₁	1	2	yes	—
113	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
114	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
115	C₂²×C₁₁	—	2	2	no	—
116	C₂²×C₁₁	—	2	1	no	—
117	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
118	C₄×C₁₁	—	2	2	no	—
119	C₄×C₁₁	—	2	1	no	—
120	C₄×C₁₁	—	8	4	no	—
121	C₄×C₁₁	—	8	4	no	—
122	C₄×C₁₁	#510	1	4	yes	—
123	C₄×C₁₁	#532	1	1	yes	characteristic
124	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
125	C₂×Q₁₆	—	2	2	no	—
126	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
127	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
128	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
129	C₄⋊Q₈	—	2	2	no	—
130	C₄⋊Q₈	—	2	2	no	—
131	#125	—	4	2	no	—
132	C₂²⋊Q₈	—	2	4	no	—
133	C₂²⋊Q₈	—	4	2	no	—
134	C₄×Q₈	—	2	4	no	—
135	C₄×Q₈	—	4	2	no	—
136	#117	—	4	2	no	—
137	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
138	Q₃₂	—	2	8	no	—
139	M₃₂	—	2	4	no	—
140	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
141	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
142	#107	—	2	2	no	—
143	#107	C₂³×C₁₁	1	4	yes	—
144	#103	—	2	4	no	—
145	#103	—	2	4	no	—
146	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
147	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
148	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
149	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
150	C₂×C₁₁	—	4	1	no	—
151	C₂×C₁₁	#3169	1	1	yes	characteristic
152	C₂×C₁₁	C₂×#510	1	2	yes	—
153	C₂×Q₈	—	2	4	no	—
154	C₂×Q₈	—	4	2	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	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
162	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
163	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	4	no	—
169	C₄⋊C₄	—	4	4	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₂²⋊C₄	—	4	4	no	—
172	C₄²	—	4	4	no	—
173	C₄²	C₁₁×D₈	1	2	yes	—
174	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
175	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
176	C₁₆	—	2	2	no	—
177	C₁₆	C₁₁×#41	1	4	yes	—
178	C₁₁	#33749	1	1	yes	characteristic, direct product factor, Sylow
179	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
180	Q₈	—	4	4	no	—
181	Q₈	—	4	4	no	—
182	Q₈	—	8	4	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
189	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
190	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
191	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
192	C₈	—	2	1	no	—
193	C₈	—	2	1	no	—
194	C₈	C₁₁×#135	1	2	yes	—
195	C₈	C₂×C₁₁×#41	1	2	yes	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	1	no	—
198	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
199	C₄	—	2	2	no	—
200	C₄	—	2	1	no	—
201	C₄	—	8	4	no	—
202	C₄	—	8	4	no	—
203	C₄	C₁₁×#510	1	4	yes	—
204	C₄	C₁₁×#532	1	1	yes	characteristic
205	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
206	C₂	—	4	1	no	—
207	C₂	C₁₁×#3169	1	1	yes	characteristic
208	C₂	C₂×C₁₁×#510	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
2. C₁₁×#2254	C₂	semidirect
3. C₁₁×#2247	C₂	semidirect
4. C₁₁×#2241	C₂	semidirect
6. C₁₁×#2176	C₂	semidirect
49. #33749	C₁₁	direct (N × H)
76. #2254	C₂×C₁₁	semidirect
77. #2247	C₂×C₁₁	semidirect
78. #2241	C₂×C₁₁	semidirect
80. #2176	C₂×C₁₁	semidirect
178. C₁₁	#33749	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3170	2
C₁₁×#2254	2
C₁₁×#2247	2
C₁₁×#2241	2
C₁₁×#2219	2
C₁₁×#2176	2
C₄×C₁₁×M₃₂	2
#33749	11

Subgroups — C11×#33749 #14610942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33749 #14610942