Subgroups — C₁₁×#33741 #14610934

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3177	C₂	1	2	yes	maximal
2	C₁₁×#2253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2245	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2219	C₂	1	2	yes	maximal
6	C₁₁×#2216	C₂	1	2	yes	maximal
7	C₁₁×#2176	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₁×Q₃₂	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#541	—	2	2	no	—
11	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
12	C₂×C₁₁×Q₃₂	C₂²	1	2	yes	—
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#499	C₂²	1	2	yes	—
16	C₁₁×#494	C₂²	1	2	yes	—
17	C₁₁×#491	—	2	2	no	—
18	C₁₁×#470	—	2	2	no	—
19	C₁₁×#467	C₂²	1	4	yes	—
20	C₁₁×#441	—	2	2	no	—
21	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
22	C₁₁×#405	C₂²	1	1	yes	characteristic
23	C₁₁×#367	C₂²	1	2	yes	—
24	C₁₁×#366	C₂²	1	2	yes	—
25	C₁₁×#358	C₂²	1	4	yes	—
26	C₁₁×#358	C₂²	1	4	yes	—
27	C₁₁×#346	C₂²	1	1	yes	characteristic
28	C₁₁×#346	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×Q₁₆	—	2	2	no	—
32	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
33	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	C₁₁×C₄⋊Q₈	—	2	2	no	—
36	C₁₁×#126	—	4	4	no	—
37	C₁₁×#125	—	2	2	no	—
38	C₁₁×#125	—	4	4	no	—
39	C₁₁×C₂²⋊Q₈	—	2	4	no	—
40	C₄×Q₈×C₁₁	—	2	4	no	—
41	C₁₁×#117	D₄	1	1	yes	characteristic
42	C₁₁×Q₃₂	—	2	4	no	—
43	C₁₁×Q₃₂	—	2	4	no	—
44	C₁₁×M₃₂	—	2	2	no	—
45	C₂×C₁₁×C₁₆	—	2	2	no	—
46	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
50	C₁₁×#107	C₂³	1	4	yes	—
51	C₁₁×#106	—	2	2	no	—
52	C₁₁×#103	—	2	4	no	—
53	C₁₁×#103	—	2	4	no	—
54	C₁₁×#97	D₄	1	1	yes	characteristic
55	C₁₁×#97	D₄	1	1	yes	characteristic
56	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	#33741	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂×Q₈×C₁₁	—	2	4	no	—
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₁₁×Q₁₆	—	2	4	no	—
62	C₁₁×Q₁₆	—	2	4	no	—
63	C₁₁×Q₁₆	—	4	4	no	—
64	C₁₁×M₁₆	—	2	2	no	—
65	C₂×C₈×C₁₁	—	2	1	no	—
66	C₂×C₈×C₁₁	—	2	1	no	—
67	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
71	C₁₁×C₄⋊C₄	—	2	4	no	—
72	C₁₁×C₄⋊C₄	—	4	4	no	—
73	C₁₁×C₄⋊C₄	—	4	4	no	—
74	C₁₁×C₄⋊C₄	—	4	4	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
77	C₁₁×C₂²⋊C₄	—	4	4	no	—
78	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
79	C₄²×C₁₁	—	4	4	no	—
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₁₁×C₁₆	—	2	1	no	—
83	C₁₁×C₁₆	—	2	1	no	—
84	C₁₁×C₁₆	#41	1	2	yes	—
85	C₁₁×C₁₆	#41	1	2	yes	—
86	#3177	C₂×C₁₁	1	2	yes	—
87	#2253	C₂×C₁₁	1	1	yes	characteristic, complemented
88	#2247	C₂×C₁₁	1	1	yes	characteristic, complemented
89	#2245	C₂×C₁₁	1	2	yes	complemented
90	#2219	C₂×C₁₁	1	2	yes	—
91	#2216	C₂×C₁₁	1	2	yes	—
92	#2176	C₂×C₁₁	1	2	yes	complemented
93	C₄×Q₃₂	C₂×C₁₁	1	2	yes	complemented
94	#2108	C₂×C₁₁	1	1	yes	characteristic
95	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
96	Q₈×C₁₁	—	4	4	no	—
97	Q₈×C₁₁	—	4	4	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	4	4	no	—
101	C₂×C₄×C₁₁	—	4	4	no	—
102	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
103	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
106	C₈×C₁₁	—	2	1	no	—
107	C₈×C₁₁	—	2	1	no	—
108	C₈×C₁₁	#135	1	2	yes	—
109	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
110	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
111	#541	—	2	2	no	—
112	C₂×Q₃₂	C₂²×C₁₁	1	2	yes	—
113	C₂×Q₃₂	C₂²×C₁₁	1	2	yes	—
114	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
115	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
116	#499	C₂²×C₁₁	1	2	yes	—
117	#494	C₂²×C₁₁	1	2	yes	—
118	#491	—	2	2	no	—
119	#470	—	2	2	no	—
120	#467	C₂²×C₁₁	1	4	yes	—
121	#441	—	2	2	no	—
122	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	—
123	#405	C₂²×C₁₁	1	1	yes	characteristic
124	#367	C₂²×C₁₁	1	2	yes	—
125	#366	C₂²×C₁₁	1	2	yes	—
126	#358	C₂²×C₁₁	1	4	yes	—
127	#358	C₂²×C₁₁	1	4	yes	—
128	#346	C₂²×C₁₁	1	1	yes	characteristic
129	#346	C₂²×C₁₁	1	1	yes	characteristic
130	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
131	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
132	C₂²×C₁₁	—	2	2	no	—
133	C₂²×C₁₁	—	2	1	no	—
134	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	2	2	no	—
137	C₄×C₁₁	—	2	1	no	—
138	C₄×C₁₁	—	8	4	no	—
139	C₄×C₁₁	—	8	4	no	—
140	C₄×C₁₁	#532	1	1	yes	characteristic
141	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
144	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
145	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
146	C₄⋊Q₈	—	2	2	no	—
147	#126	—	4	4	no	—
148	#125	—	2	2	no	—
149	#125	—	4	4	no	—
150	C₂²⋊Q₈	—	2	4	no	—
151	C₄×Q₈	—	2	4	no	—
152	#117	D₄×C₁₁	1	1	yes	characteristic
153	Q₃₂	—	2	4	no	—
154	Q₃₂	—	2	4	no	—
155	M₃₂	—	2	2	no	—
156	C₂×C₁₆	—	2	2	no	—
157	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
158	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
159	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
160	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
161	#107	C₂³×C₁₁	1	4	yes	—
162	#106	—	2	2	no	—
163	#103	—	2	4	no	—
164	#103	—	2	4	no	—
165	#97	D₄×C₁₁	1	1	yes	characteristic
166	#97	D₄×C₁₁	1	1	yes	characteristic
167	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
168	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
169	C₂×C₁₁	—	4	1	no	—
170	C₂×C₁₁	#3169	1	1	yes	characteristic
171	C₂×C₁₁	#3417	1	2	yes	—
172	C₂×Q₈	—	2	4	no	—
173	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
174	Q₁₆	—	2	4	no	—
175	Q₁₆	—	2	4	no	—
176	Q₁₆	—	4	4	no	—
177	M₁₆	—	2	2	no	—
178	C₂×C₈	—	2	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
182	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
183	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	4	4	no	—
186	C₄⋊C₄	—	4	4	no	—
187	C₄⋊C₄	—	4	4	no	—
188	C₄⋊C₄	—	4	4	no	—
189	C₄⋊C₄	C₁₁×D₈	1	2	yes	—
190	C₂²⋊C₄	—	4	4	no	—
191	C₂²⋊C₄	C₁₁×D₈	1	2	yes	—
192	C₄²	—	4	4	no	—
193	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
194	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
195	C₁₆	—	2	1	no	—
196	C₁₆	—	2	1	no	—
197	C₁₆	C₁₁×#41	1	2	yes	—
198	C₁₆	C₁₁×#41	1	2	yes	—
199	C₁₁	#33741	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
201	Q₈	—	4	4	no	—
202	Q₈	—	4	4	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
208	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
209	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
210	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
211	C₈	—	2	1	no	—
212	C₈	—	2	1	no	—
213	C₈	C₁₁×#135	1	2	yes	—
214	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
215	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
216	C₂²	—	2	2	no	—
217	C₂²	—	2	1	no	—
218	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	1	no	—
222	C₄	—	8	4	no	—
223	C₄	—	8	4	no	—
224	C₄	C₁₁×#532	1	1	yes	characteristic
225	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
226	C₂	—	4	1	no	—
227	C₂	C₁₁×#3169	1	1	yes	characteristic
228	C₂	C₁₁×#3417	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 ◁ C₁₁×#117 ◁ C₁₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2253	C₂	semidirect
3. C₁₁×#2247	C₂	semidirect
4. C₁₁×#2245	C₂	semidirect
7. C₁₁×#2176	C₂	semidirect
8. C₄×C₁₁×Q₃₂	C₂	semidirect
58. #33741	C₁₁	direct (N × H)
87. #2253	C₂×C₁₁	semidirect
88. #2247	C₂×C₁₁	semidirect
89. #2245	C₂×C₁₁	semidirect
92. #2176	C₂×C₁₁	semidirect
93. C₄×Q₃₂	C₂×C₁₁	semidirect
199. C₁₁	#33741	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×#3177	2
C₁₁×#2253	2
C₁₁×#2247	2
C₁₁×#2245	2
C₁₁×#2219	2
C₁₁×#2216	2
C₁₁×#2176	2
C₄×C₁₁×Q₃₂	2
C₁₁×#2108	2
#33741	11

Subgroups — C11×#33741 #14610934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33741 #14610934