Subgroups — C₁₁×#33748 #14610941

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3169	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2246	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2240	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2218	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2177	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#532	—	2	2	no	—
9	C₂×C₁₁×D₁₆	C₂²	1	4	yes	—
10	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
11	C₁₁×#500	C₂²	1	2	yes	—
12	C₁₁×#493	C₂²	1	2	yes	—
13	C₁₁×#486	—	2	2	no	—
14	C₁₁×#466	—	2	2	no	—
15	C₁₁×#466	C₂²	1	4	yes	—
16	C₄×C₁₁×D₈	—	2	2	no	—
17	C₄×C₁₁×D₈	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#367	C₂²	1	4	yes	—
20	C₁₁×#357	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×#41	—	4	2	no	—
25	C₂×C₁₁×D₈	—	2	2	no	—
26	C₂×C₁₁×D₈	C₂³	1	4	yes	—
27	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×C₄⋊Q₈	—	2	2	no	—
30	C₁₁×#127	—	2	2	no	—
31	C₁₁×#124	—	4	2	no	—
32	C₁₁×#121	—	2	4	no	—
33	C₁₁×#121	—	4	2	no	—
34	C₄×D₄×C₁₁	—	2	4	no	—
35	C₄×D₄×C₁₁	—	4	2	no	—
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₁₁×D₁₆	—	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×#102	—	2	4	no	—
44	C₁₁×#102	—	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	#33748	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₁₁×#41	—	8	8	no	—
51	C₂×Q₈×C₁₁	—	4	2	no	—
52	C₂×D₄×C₁₁	—	2	4	no	—
53	C₂×D₄×C₁₁	—	4	4	no	—
54	C₂×D₄×C₁₁	—	4	2	no	—
55	C₂×D₄×C₁₁	—	4	2	no	—
56	C₂²×C₄×C₁₁	—	4	4	no	—
57	C₂²×C₄×C₁₁	D₈	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₁₁×D₈	—	2	8	no	—
60	C₁₁×D₈	—	4	4	no	—
61	C₂×C₈×C₁₁	—	2	2	no	—
62	C₂×C₈×C₁₁	—	2	2	no	—
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
67	C₁₁×C₄⋊C₄	—	2	4	no	—
68	C₁₁×C₄⋊C₄	—	4	2	no	—
69	C₁₁×C₂²⋊C₄	—	4	4	no	—
70	C₁₁×C₂²⋊C₄	—	4	4	no	—
71	C₄²×C₁₁	D₈	1	2	yes	—
72	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₁₁×C₁₆	—	2	2	no	—
75	C₁₁×C₁₆	#41	1	4	yes	complemented
76	#3169	C₂×C₁₁	1	2	yes	complemented
77	#2254	C₂×C₁₁	1	1	yes	characteristic, complemented
78	#2246	C₂×C₁₁	1	1	yes	characteristic, complemented
79	#2240	C₂×C₁₁	1	2	yes	complemented
80	#2218	C₂×C₁₁	1	4	yes	complemented
81	#2177	C₂×C₁₁	1	4	yes	complemented
82	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
83	C₂³×C₁₁	—	4	4	no	—
84	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
85	Q₈×C₁₁	—	8	4	no	—
86	D₄×C₁₁	—	4	4	no	—
87	D₄×C₁₁	—	4	4	no	—
88	D₄×C₁₁	—	8	8	no	—
89	D₄×C₁₁	—	8	4	no	—
90	D₄×C₁₁	—	8	4	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	4	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	8	8	no	—
96	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
99	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	C₈×C₁₁	—	2	1	no	—
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	#135	1	2	yes	—
103	C₈×C₁₁	C₂×#41	1	2	yes	—
104	#532	—	2	2	no	—
105	C₂×D₁₆	C₂²×C₁₁	1	4	yes	—
106	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
107	#500	C₂²×C₁₁	1	2	yes	—
108	#493	C₂²×C₁₁	1	2	yes	—
109	#486	—	2	2	no	—
110	#466	—	2	2	no	—
111	#466	C₂²×C₁₁	1	4	yes	—
112	C₄×D₈	—	2	2	no	—
113	C₄×D₈	C₂²×C₁₁	1	4	yes	—
114	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
115	#367	C₂²×C₁₁	1	4	yes	—
116	#357	C₂²×C₁₁	1	8	yes	—
117	#346	C₂²×C₁₁	1	2	yes	—
118	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
119	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
120	C₂²×C₁₁	—	2	2	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	8	4	no	—
123	C₂²×C₁₁	—	8	4	no	—
124	C₂²×C₁₁	—	8	4	no	—
125	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
126	C₄×C₁₁	—	2	2	no	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	8	4	no	—
129	C₄×C₁₁	#509	1	4	yes	—
130	C₄×C₁₁	#532	1	1	yes	characteristic
131	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
132	C₂×#41	—	4	2	no	—
133	C₂×D₈	—	2	2	no	—
134	C₂×D₈	C₂³×C₁₁	1	4	yes	—
135	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
136	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
137	C₄⋊Q₈	—	2	2	no	—
138	#127	—	2	2	no	—
139	#124	—	4	2	no	—
140	#121	—	2	4	no	—
141	#121	—	4	2	no	—
142	C₄×D₄	—	2	4	no	—
143	C₄×D₄	—	4	2	no	—
144	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
145	D₁₆	—	2	8	no	—
146	M₃₂	—	2	4	no	—
147	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
148	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
149	#107	—	2	2	no	—
150	#107	C₂³×C₁₁	1	4	yes	—
151	#102	—	2	4	no	—
152	#102	—	2	4	no	—
153	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
154	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
155	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
156	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
157	C₂×C₁₁	—	4	1	no	—
158	C₂×C₁₁	—	16	4	no	—
159	C₂×C₁₁	#3169	1	1	yes	characteristic
160	C₂×C₁₁	C₂×#509	1	2	yes	—
161	#41	—	8	8	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×D₄	—	2	4	no	—
164	C₂×D₄	—	4	4	no	—
165	C₂×D₄	—	4	2	no	—
166	C₂×D₄	—	4	2	no	—
167	C₂²×C₄	—	4	4	no	—
168	C₂²×C₄	C₁₁×D₈	1	2	yes	—
169	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
170	D₈	—	2	8	no	—
171	D₈	—	4	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
175	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
176	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
177	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	4	no	—
181	C₂²⋊C₄	—	4	4	no	—
182	C₄²	C₁₁×D₈	1	2	yes	—
183	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
184	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
185	C₁₆	—	2	2	no	—
186	C₁₆	C₁₁×#41	1	4	yes	complemented
187	C₁₁	#33748	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³	—	4	4	no	—
189	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
190	Q₈	—	8	4	no	—
191	D₄	—	4	4	no	—
192	D₄	—	4	4	no	—
193	D₄	—	8	8	no	—
194	D₄	—	8	4	no	—
195	D₄	—	8	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	8	8	no	—
201	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
202	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
203	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
204	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	C₁₁×#135	1	2	yes	—
208	C₈	C₂×C₁₁×#41	1	2	yes	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	8	4	no	—
212	C₂²	—	8	4	no	—
213	C₂²	—	8	4	no	—
214	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	1	no	—
217	C₄	—	8	4	no	—
218	C₄	C₁₁×#509	1	4	yes	—
219	C₄	C₁₁×#532	1	1	yes	characteristic
220	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
221	C₂	—	4	1	no	—
222	C₂	—	16	4	no	—
223	C₂	C₁₁×#3169	1	1	yes	characteristic
224	C₂	C₂×C₁₁×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
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
1. C₁₁×#3169	C₂	semidirect
2. C₁₁×#2254	C₂	semidirect
3. C₁₁×#2246	C₂	semidirect
4. C₁₁×#2240	C₂	semidirect
5. C₁₁×#2218	C₂	semidirect
6. C₁₁×#2177	C₂	semidirect
7. C₄×C₁₁×M₃₂	C₂	semidirect
49. #33748	C₁₁	direct (N × H)
75. C₁₁×C₁₆	#41	semidirect
76. #3169	C₂×C₁₁	semidirect
77. #2254	C₂×C₁₁	semidirect
78. #2246	C₂×C₁₁	semidirect
79. #2240	C₂×C₁₁	semidirect
80. #2218	C₂×C₁₁	semidirect
81. #2177	C₂×C₁₁	semidirect
82. C₄×M₃₂	C₂×C₁₁	semidirect
186. C₁₆	C₁₁×#41	semidirect
187. C₁₁	#33748	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×#3169	2
C₁₁×#2254	2
C₁₁×#2246	2
C₁₁×#2240	2
C₁₁×#2218	2
C₁₁×#2177	2
C₄×C₁₁×M₃₂	2
#33748	11

Subgroups — C11×#33748 #14610941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33748 #14610941