Subgroups — C₁₁×#11498 #14588691

Order 2816.

292 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2960	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×#1323	C₂	1	4	yes	maximal
5	C₁₁×#533	C₄	1	1	yes	characteristic
6	C₁₁×#446	—	2	1	no	—
7	C₁₁×#446	—	2	1	no	—
8	C₈×Q₈×C₁₁	—	2	1	no	—
9	C₈×Q₈×C₁₁	—	2	1	no	—
10	C₁₁×#424	C₂²	1	2	yes	—
11	C₁₁×#423	C₄	1	1	yes	characteristic
12	C₁₁×#405	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	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
23	C₁₁×C₄⋊Q₈	C₈	1	1	yes	characteristic
24	C₁₁×C₄⋊Q₈	C₈	1	1	yes	characteristic
25	C₁₁×#125	C₈	1	2	yes	—
26	C₁₁×C₂²⋊Q₈	—	2	1	no	—
27	C₁₁×C₂²⋊Q₈	—	2	1	no	—
28	C₄×Q₈×C₁₁	—	2	1	no	—
29	C₄×Q₈×C₁₁	—	2	1	no	—
30	C₁₁×#117	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	C₄×C₈×C₁₁	—	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	#11498	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	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₁₁×M₁₆	—	4	2	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	2	2	no	—
53	C₂×C₈×C₁₁	—	4	1	no	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₁₁×C₄⋊C₄	—	2	2	no	—
60	C₁₁×C₄⋊C₄	—	2	1	no	—
61	C₁₁×C₄⋊C₄	—	2	1	no	—
62	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
63	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
64	C₁₁×C₂²⋊C₄	—	2	2	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
69	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
70	C₁₁×C₁₆	—	4	2	no	—
71	C₁₁×C₁₆	—	4	2	no	—
72	#2960	C₂×C₁₁	1	1	yes	characteristic
73	#2163	C₂×C₁₁	1	1	yes	characteristic
74	#2162	C₂×C₁₁	1	1	yes	characteristic
75	#1323	C₂×C₁₁	1	4	yes	—
76	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
77	Q₈×C₁₁	—	4	2	no	—
78	Q₈×C₁₁	—	4	2	no	—
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	—	2	1	no	—
81	C₂×C₄×C₁₁	—	2	1	no	—
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	4	1	no	—
85	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
91	C₈×C₁₁	—	2	1	no	—
92	C₈×C₁₁	—	2	1	no	—
93	C₈×C₁₁	—	2	1	no	—
94	C₈×C₁₁	—	4	2	no	—
95	C₈×C₁₁	#101	1	2	yes	—
96	#533	C₄×C₁₁	1	1	yes	characteristic
97	#446	—	2	1	no	—
98	#446	—	2	1	no	—
99	C₈×Q₈	—	2	1	no	—
100	C₈×Q₈	—	2	1	no	—
101	#424	C₂²×C₁₁	1	2	yes	—
102	#423	C₄×C₁₁	1	1	yes	characteristic
103	#405	C₄×C₁₁	1	2	yes	—
104	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
105	C₄⋊C₁₆	—	2	1	no	—
106	C₄⋊C₁₆	—	2	1	no	—
107	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
108	C₂²⋊C₁₆	C₂²×C₁₁	1	2	yes	—
109	#346	—	2	1	no	—
110	C₄×C₁₆	—	2	1	no	—
111	C₂²×C₁₁	—	2	1	no	—
112	C₂²×C₁₁	—	2	1	no	—
113	C₂²×C₁₁	—	2	1	no	—
114	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
115	C₄×C₁₁	—	2	1	no	—
116	C₄×C₁₁	—	2	1	no	—
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	2	1	no	—
119	C₄×C₁₁	—	4	2	no	—
120	C₄×C₁₁	—	4	2	no	—
121	C₄×C₁₁	#350	1	2	yes	—
122	C₄×C₁₁	#410	1	1	yes	characteristic
123	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
124	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
125	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
126	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
127	C₄⋊Q₈	C₈×C₁₁	1	1	yes	characteristic
128	C₄⋊Q₈	C₈×C₁₁	1	1	yes	characteristic
129	#125	C₈×C₁₁	1	2	yes	—
130	C₂²⋊Q₈	—	2	1	no	—
131	C₂²⋊Q₈	—	2	1	no	—
132	C₄×Q₈	—	2	1	no	—
133	C₄×Q₈	—	2	1	no	—
134	#117	C₂×C₄×C₁₁	1	2	yes	—
135	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
136	C₂×C₁₆	—	2	2	no	—
137	C₂×C₁₆	—	2	2	no	—
138	C₄⋊C₈	—	2	2	no	—
139	C₄⋊C₈	—	2	2	no	—
140	C₄⋊C₈	—	2	1	no	—
141	C₄⋊C₈	—	2	1	no	—
142	#97	—	2	2	no	—
143	C₄×C₈	—	2	2	no	—
144	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
145	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
146	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
147	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
148	C₂×C₁₁	—	4	1	no	—
149	C₂×C₁₁	#1461	1	1	yes	characteristic
150	C₂×C₁₁	C₂×#350	1	1	yes	characteristic
151	C₂×C₁₁	#2117	1	1	yes	characteristic
152	C₂×Q₈	—	2	1	no	—
153	C₂×Q₈	—	2	1	no	—
154	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
155	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
156	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
157	M₁₆	—	4	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	—	2	2	no	—
167	C₄⋊C₄	—	2	1	no	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
170	C₄⋊C₄	C₂×C₈×C₁₁	1	2	yes	—
171	C₂²⋊C₄	—	2	2	no	—
172	C₄²	—	2	2	no	—
173	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
174	C₄²	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
175	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
176	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
177	C₁₆	—	4	2	no	—
178	C₁₆	—	4	2	no	—
179	C₁₁	#11498	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	C₂×C₁₁×M₁₆	1	1	yes	characteristic
181	Q₈	—	4	2	no	—
182	Q₈	—	4	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
190	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
191	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
192	C₂×C₄	C₁₁×C₂²⋊C₈	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
195	C₈	—	2	1	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	4	2	no	—
199	C₈	C₁₁×#101	1	2	yes	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	4	2	no	—
209	C₄	—	4	2	no	—
210	C₄	C₁₁×#350	1	2	yes	—
211	C₄	C₁₁×#410	1	1	yes	characteristic
212	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
213	C₂	—	4	1	no	—
214	C₂	C₁₁×#1461	1	1	yes	characteristic
215	C₂	C₂×C₁₁×#350	1	1	yes	characteristic
216	C₂	C₁₁×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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. #11498	C₁₁	direct (N × H)
179. C₁₁	#11498	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×#2960	2
C₁₁×#2163	2
C₁₁×#2162	2
C₁₁×#1323	2
#11498	11

Subgroups — C11×#11498 #14588691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11498 #14588691