Subgroups — C₁₁×#11495 #14588688

Order 2816.

314 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×#446	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1322	C₂	1	4	yes	maximal
5	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
6	C₁₁×#446	—	2	1	no	—
7	C₁₁×#446	—	2	1	no	—
8	C₁₁×#446	—	2	1	no	—
9	C₁₁×#446	—	2	1	no	—
10	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₁×#97	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×C₄⋊C₁₆	—	2	1	no	—
15	C₁₁×C₄⋊C₁₆	—	2	1	no	—
16	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
17	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₁₁×#346	—	2	1	no	—
19	C₄×C₁₁×C₁₆	—	2	1	no	—
20	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₄×Q₈×C₁₁	—	2	1	no	—
25	C₄×Q₈×C₁₁	—	2	1	no	—
26	C₄×Q₈×C₁₁	—	2	1	no	—
27	C₄×Q₈×C₁₁	—	2	1	no	—
28	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₄	C₈	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₁₁×C₁₆	—	2	2	no	—
33	C₂×C₁₁×C₁₆	—	2	2	no	—
34	C₁₁×C₄⋊C₈	—	2	2	no	—
35	C₁₁×C₄⋊C₈	—	2	2	no	—
36	C₁₁×C₄⋊C₈	—	2	1	no	—
37	C₁₁×C₄⋊C₈	—	2	1	no	—
38	C₁₁×#97	—	2	2	no	—
39	C₁₁×#97	—	2	2	no	—
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	#11495	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×Q₈×C₁₁	—	2	1	no	—
46	C₂×Q₈×C₁₁	—	2	1	no	—
47	C₂×Q₈×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	—	2	2	no	—
55	C₂×C₈×C₁₁	—	4	1	no	—
56	C₂×C₈×C₁₁	—	4	2	no	—
57	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²⋊C₄	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	C₁₁×C₄⋊C₄	—	2	1	no	—
62	C₁₁×C₄⋊C₄	—	2	1	no	—
63	C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	—	2	2	no	—
67	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
70	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
71	C₁₁×C₁₆	—	4	2	no	—
72	C₁₁×C₁₆	—	4	2	no	—
73	C₂×#446	C₂×C₁₁	1	1	yes	characteristic
74	#2163	C₂×C₁₁	1	1	yes	characteristic
75	#2162	C₂×C₁₁	1	1	yes	characteristic
76	#1322	C₂×C₁₁	1	4	yes	—
77	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
78	Q₈×C₁₁	—	4	2	no	—
79	Q₈×C₁₁	—	4	2	no	—
80	C₂×C₄×C₁₁	—	2	2	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	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	4	2	no	—
88	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
94	C₈×C₁₁	—	2	1	no	—
95	C₈×C₁₁	—	2	1	no	—
96	C₈×C₁₁	—	2	1	no	—
97	C₈×C₁₁	—	4	2	no	—
98	C₈×C₁₁	#101	1	2	yes	—
99	C₂×C₄×Q₈	C₄×C₁₁	1	1	yes	characteristic
100	#446	—	2	1	no	—
101	#446	—	2	1	no	—
102	#446	—	2	1	no	—
103	#446	—	2	1	no	—
104	C₂×C₄⋊C₈	C₄×C₁₁	1	1	yes	characteristic
105	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
106	C₂×#97	C₄×C₁₁	1	2	yes	—
107	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
108	C₄⋊C₁₆	—	2	1	no	—
109	C₄⋊C₁₆	—	2	1	no	—
110	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
111	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
112	#346	—	2	1	no	—
113	C₄×C₁₆	—	2	1	no	—
114	C₂²×C₁₁	—	2	1	no	—
115	C₂²×C₁₁	—	2	1	no	—
116	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
117	C₂²×C₁₁	#504	1	2	yes	—
118	C₄×C₁₁	—	2	1	no	—
119	C₄×C₁₁	—	2	1	no	—
120	C₄×C₁₁	—	2	1	no	—
121	C₄×C₁₁	—	2	1	no	—
122	C₄×C₁₁	—	4	2	no	—
123	C₄×C₁₁	—	4	2	no	—
124	C₄×C₁₁	#349	1	2	yes	—
125	C₄×C₁₁	#410	1	1	yes	characteristic
126	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
127	C₂²×Q₈	C₈×C₁₁	1	1	yes	characteristic
128	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
129	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
130	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
131	C₄×Q₈	—	2	1	no	—
132	C₄×Q₈	—	2	1	no	—
133	C₄×Q₈	—	2	1	no	—
134	C₄×Q₈	—	2	1	no	—
135	C₂×C₄⋊C₄	C₈×C₁₁	1	1	yes	characteristic
136	C₂×C₄⋊C₄	C₈×C₁₁	1	2	yes	—
137	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
138	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	2	2	no	—
141	C₄⋊C₈	—	2	2	no	—
142	C₄⋊C₈	—	2	2	no	—
143	C₄⋊C₈	—	2	1	no	—
144	C₄⋊C₈	—	2	1	no	—
145	#97	—	2	2	no	—
146	#97	—	2	2	no	—
147	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
148	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
149	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
150	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
151	C₂×C₁₁	—	2	2	no	—
152	C₂×C₁₁	#1461	1	1	yes	characteristic
153	C₂×C₁₁	#2113	1	1	yes	characteristic
154	C₂×C₁₁	C₂×#349	1	1	yes	characteristic
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
159	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
160	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
161	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
162	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
170	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄²	—	2	2	no	—
176	C₄²	—	2	2	no	—
177	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
178	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
179	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
180	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
181	C₁₆	—	4	2	no	—
182	C₁₆	—	4	2	no	—
183	C₁₁	#11495	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
185	Q₈	—	4	2	no	—
186	Q₈	—	4	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
196	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
197	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
198	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
199	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
201	C₈	—	2	1	no	—
202	C₈	—	2	1	no	—
203	C₈	—	2	1	no	—
204	C₈	—	4	2	no	—
205	C₈	C₁₁×#101	1	2	yes	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
209	C₂²	C₁₁×#504	1	2	yes	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	2	no	—
215	C₄	—	4	2	no	—
216	C₄	C₁₁×#349	1	2	yes	—
217	C₄	C₁₁×#410	1	1	yes	characteristic
218	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	C₁₁×#1461	1	1	yes	characteristic
221	C₂	C₁₁×#2113	1	1	yes	characteristic
222	C₂	C₂×C₁₁×#349	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₁	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
44. #11495	C₁₁	direct (N × H)
183. C₁₁	#11495	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×#446	2
C₁₁×#2163	2
C₁₁×#2162	2
C₁₁×#1322	2
#11495	11

Subgroups — C11×#11495 #14588688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11495 #14588688