Subgroups — C₁₁×#11962 #14589155

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1362	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₁×Q₁₆	—	2	1	no	—
6	C₂²×C₁₁×Q₁₆	C₄	1	2	yes	—
7	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
8	C₁₁×#494	—	2	1	no	—
9	C₁₁×#494	—	2	1	no	—
10	C₁₁×#494	C₄	1	2	yes	—
11	C₁₁×#494	C₂²	1	2	yes	—
12	C₁₁×#423	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
15	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
16	C₄×C₁₁×C₁₆	—	2	1	no	—
17	C₁₁×#335	—	2	1	no	—
18	C₁₁×#335	C₂²	1	2	yes	—
19	C₂²×Q₈×C₁₁	—	2	2	no	—
20	C₂×C₁₁×Q₁₆	—	2	2	no	—
21	C₂×C₁₁×Q₁₆	—	2	2	no	—
22	C₂×C₁₁×Q₁₆	—	2	2	no	—
23	C₂×C₁₁×Q₁₆	—	4	4	no	—
24	C₂×C₁₁×Q₁₆	—	4	4	no	—
25	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
26	C₂×C₁₁×M₁₆	—	4	1	no	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
29	C₁₁×C₄⋊Q₈	—	2	2	no	—
30	C₁₁×C₄⋊Q₈	—	2	2	no	—
31	C₁₁×C₄⋊Q₈	—	4	1	no	—
32	C₁₁×C₄⋊Q₈	—	4	1	no	—
33	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
34	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₁₁×C₁₆	—	2	2	no	—
37	C₁₁×C₄⋊C₈	—	2	2	no	—
38	C₁₁×C₄⋊C₈	—	4	1	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	#11962	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₁	—	2	4	no	—
45	C₂×Q₈×C₁₁	—	4	4	no	—
46	C₂×Q₈×C₁₁	—	4	4	no	—
47	C₂×Q₈×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	—	4	2	no	—
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
52	C₁₁×Q₁₆	—	4	4	no	—
53	C₁₁×Q₁₆	—	4	4	no	—
54	C₁₁×Q₁₆	—	4	4	no	—
55	C₁₁×Q₁₆	—	4	4	no	—
56	C₁₁×M₁₆	—	8	2	no	—
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	—	4	2	no	—
60	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₁₁×C₄⋊C₄	—	4	2	no	—
67	C₁₁×C₄⋊C₄	—	4	2	no	—
68	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	D₈	1	1	yes	characteristic
70	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
71	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₁₁×C₁₆	—	4	2	no	—
73	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
74	#2162	C₂×C₁₁	1	1	yes	characteristic
75	#1567	C₂×C₁₁	1	1	yes	characteristic
76	#1362	C₂×C₁₁	1	4	yes	complemented
77	C₂³×C₁₁	#102	1	1	yes	characteristic
78	Q₈×C₁₁	—	4	4	no	—
79	Q₈×C₁₁	—	4	4	no	—
80	Q₈×C₁₁	—	8	4	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	1	no	—
83	C₂×C₄×C₁₁	—	2	1	no	—
84	C₂×C₄×C₁₁	—	4	4	no	—
85	C₂×C₄×C₁₁	—	8	4	no	—
86	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
88	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
89	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
90	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
94	C₈×C₁₁	—	2	1	no	—
95	C₈×C₁₁	—	2	1	no	—
96	C₈×C₁₁	—	8	2	no	—
97	C₈×C₁₁	#100	1	2	yes	—
98	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
99	C₂²×Q₁₆	—	2	1	no	—
100	C₂²×Q₁₆	C₄×C₁₁	1	2	yes	—
101	C₂×C₄⋊Q₈	—	2	1	no	—
102	#494	—	2	1	no	—
103	#494	—	2	1	no	—
104	#494	C₄×C₁₁	1	2	yes	—
105	#494	C₂²×C₁₁	1	2	yes	—
106	#423	—	2	1	no	—
107	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
108	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
109	C₂²⋊C₁₆	—	2	1	no	—
110	C₄×C₁₆	—	2	1	no	—
111	#335	—	2	1	no	—
112	#335	C₂²×C₁₁	1	2	yes	—
113	C₂²×C₁₁	—	2	1	no	—
114	C₂²×C₁₁	—	2	1	no	—
115	C₂²×C₁₁	#358	1	2	yes	—
116	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	2	1	no	—
119	C₄×C₁₁	—	8	4	no	—
120	C₄×C₁₁	#358	1	2	yes	—
121	C₄×C₁₁	#362	1	2	yes	—
122	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
123	C₄×C₁₁	#418	1	1	yes	characteristic
124	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
125	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
126	C₂²×Q₈	—	2	2	no	—
127	C₂×Q₁₆	—	2	2	no	—
128	C₂×Q₁₆	—	2	2	no	—
129	C₂×Q₁₆	—	2	2	no	—
130	C₂×Q₁₆	—	4	4	no	—
131	C₂×Q₁₆	—	4	4	no	—
132	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
133	C₂×M₁₆	—	4	1	no	—
134	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
135	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	—	4	1	no	—
139	C₄⋊Q₈	—	4	1	no	—
140	C₂×C₄⋊C₄	—	4	1	no	—
141	C₂×C₄⋊C₄	—	4	1	no	—
142	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
143	C₂×C₁₆	—	2	2	no	—
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	4	1	no	—
146	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
147	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
148	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
149	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
150	C₂×C₁₁	—	2	2	no	—
151	C₂×C₁₁	#1545	1	1	yes	characteristic
152	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
153	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	4	4	no	—
156	C₂×Q₈	—	4	4	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
161	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
162	Q₁₆	—	4	4	no	—
163	Q₁₆	—	4	4	no	—
164	Q₁₆	—	4	4	no	—
165	Q₁₆	—	4	4	no	—
166	M₁₆	—	8	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
173	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
179	C₄²	C₁₁×D₈	1	1	yes	characteristic
180	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
181	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
182	C₁₆	—	4	2	no	—
183	C₁₁	#11962	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₁₁×#102	1	1	yes	characteristic
185	Q₈	—	4	4	no	—
186	Q₈	—	4	4	no	—
187	Q₈	—	8	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	8	4	no	—
193	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
194	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
195	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
196	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
197	C₂×C₄	C₁₁×Q₃₂	1	2	yes	—
198	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
200	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
201	C₈	—	2	1	no	—
202	C₈	—	2	1	no	—
203	C₈	—	8	2	no	—
204	C₈	C₁₁×#100	1	2	yes	—
205	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₁₁×#358	1	2	yes	—
209	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	8	4	no	—
213	C₄	C₁₁×#358	1	2	yes	—
214	C₄	C₁₁×#362	1	2	yes	—
215	C₄	C₂×C₁₁×#100	1	1	yes	characteristic
216	C₄	C₁₁×#418	1	1	yes	characteristic
217	C₄	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
218	C₄	C₂×C₁₁×Q₃₂	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	C₁₁×#1545	1	1	yes	characteristic
221	C₂	C₂×C₁₁×#358	1	1	yes	characteristic
222	C₂	C₂×C₁₁×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#102
LCS	G ▷ C₂×C₈ ▷ C₂×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
4. C₁₁×#1362	C₂	semidirect
43. #11962	C₁₁	direct (N × H)
76. #1362	C₂×C₁₁	semidirect
183. C₁₁	#11962	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×#494	2
C₁₁×#2162	2
C₁₁×#1567	2
C₁₁×#1362	2
#11962	11

Subgroups — C11×#11962 #14589155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11962 #14589155