Subgroups — C₁₁×#23372 #14600565

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#125	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1940	C₂	1	4	yes	maximal
3	C₁₁×#1917	C₂	1	4	yes	maximal
4	C₁₁×#1917	C₂	1	4	yes	maximal
5	C₁₁×#1831	C₂	1	2	yes	maximal
6	C₂×C₁₁×#125	C₄	1	1	yes	characteristic
7	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₁×#97	C₂²	1	4	yes	—
11	C₁₁×#389	C₄	1	2	yes	—
12	C₁₁×#387	C₄	1	4	yes	—
13	C₁₁×#382	C₄	1	1	yes	characteristic
14	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
16	C₄³×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#336	C₂²	1	4	yes	—
18	C₁₁×#336	C₂²	1	4	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₁₁×#336	C₂²	1	4	yes	—
21	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
22	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
23	C₁₁×#125	—	2	4	no	—
24	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
26	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
34	C₁₁×C₄⋊C₈	—	4	4	no	—
35	C₁₁×C₄⋊C₈	—	4	2	no	—
36	C₁₁×C₄⋊C₈	—	4	2	no	—
37	C₁₁×#97	—	4	4	no	—
38	C₁₁×#95	C₂×C₄	1	4	yes	—
39	C₁₁×#95	C₂×C₄	1	4	yes	—
40	C₁₁×#95	C₂×C₄	1	4	yes	—
41	#23372	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
44	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
46	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	—	2	4	no	—
53	C₂×C₈×C₁₁	—	2	4	no	—
54	C₂×C₈×C₁₁	—	2	4	no	—
55	C₁₁×C₄⋊C₄	—	2	8	no	—
56	C₁₁×C₄⋊C₄	—	2	4	no	—
57	C₁₁×C₄⋊C₄	—	4	2	no	—
58	C₁₁×C₄⋊C₄	—	4	4	no	—
59	C₄²×C₁₁	—	2	4	no	—
60	C₄²×C₁₁	—	2	2	no	—
61	C₄²×C₁₁	—	2	1	no	—
62	C₄²×C₁₁	—	2	1	no	—
63	C₄²×C₁₁	—	2	2	no	—
64	C₄²×C₁₁	—	2	4	no	—
65	C₄²×C₁₁	—	4	1	no	—
66	C₄²×C₁₁	—	4	2	no	—
67	C₄²×C₁₁	M₁₆	1	4	yes	—
68	C₄×#125	C₂×C₁₁	1	1	yes	characteristic
69	#1940	C₂×C₁₁	1	4	yes	—
70	#1917	C₂×C₁₁	1	4	yes	—
71	#1917	C₂×C₁₁	1	4	yes	—
72	#1831	C₂×C₁₁	1	2	yes	—
73	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	1	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	2	1	no	—
79	C₂×C₄×C₁₁	—	2	4	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	4	no	—
83	C₂×C₄×C₁₁	—	2	2	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	—	2	4	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
90	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
91	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
92	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
93	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
94	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
95	C₈×C₁₁	—	4	4	no	—
96	C₈×C₁₁	—	4	4	no	—
97	C₂×#125	C₄×C₁₁	1	1	yes	characteristic
98	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
99	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
100	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
101	C₂×#97	C₂²×C₁₁	1	4	yes	—
102	#389	C₄×C₁₁	1	2	yes	—
103	#387	C₄×C₁₁	1	4	yes	—
104	#382	C₄×C₁₁	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
106	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
107	C₄³	C₂²×C₁₁	1	1	yes	characteristic
108	#336	C₂²×C₁₁	1	4	yes	—
109	#336	C₂²×C₁₁	1	4	yes	—
110	#336	C₂²×C₁₁	1	4	yes	—
111	#336	C₂²×C₁₁	1	4	yes	—
112	C₂²×C₁₁	#519	1	1	yes	characteristic
113	C₂²×C₁₁	#520	1	2	yes	—
114	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
115	C₂²×C₁₁	#568	1	1	yes	characteristic
116	C₂²×C₁₁	#568	1	2	yes	—
117	C₄×C₁₁	—	2	2	no	—
118	C₄×C₁₁	—	2	4	no	—
119	C₄×C₁₁	—	4	1	no	—
120	C₄×C₁₁	—	4	4	no	—
121	C₄×C₁₁	—	4	2	no	—
122	C₄×C₁₁	—	4	4	no	—
123	C₄×C₁₁	#562	1	1	yes	characteristic
124	C₄×C₁₁	#563	1	2	yes	—
125	C₄×C₁₁	#564	1	1	yes	characteristic
126	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
127	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
128	#125	—	2	4	no	—
129	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
130	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
131	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
132	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
133	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
134	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
135	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
136	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
137	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
138	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
139	C₄⋊C₈	—	4	4	no	—
140	C₄⋊C₈	—	4	2	no	—
141	C₄⋊C₈	—	4	2	no	—
142	#97	—	4	4	no	—
143	#95	C₂×C₄×C₁₁	1	4	yes	—
144	#95	C₂×C₄×C₁₁	1	4	yes	—
145	#95	C₂×C₄×C₁₁	1	4	yes	—
146	C₂×C₁₁	#2382	1	1	yes	characteristic
147	C₂×C₁₁	#2983	1	1	yes	characteristic
148	C₂×C₁₁	#2987	1	1	yes	characteristic
149	C₂×C₁₁	#2989	1	2	yes	—
150	C₂×C₁₁	#2995	1	2	yes	—
151	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
152	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
153	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
154	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
155	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
156	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
157	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	4	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	4	no	—
168	C₄²	—	2	4	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	2	1	no	—
171	C₄²	—	2	1	no	—
172	C₄²	—	2	2	no	—
173	C₄²	—	2	4	no	—
174	C₄²	—	4	1	no	—
175	C₄²	—	4	2	no	—
176	C₄²	C₁₁×M₁₆	1	4	yes	—
177	C₁₁	#23372	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
195	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
196	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
200	C₈	—	4	4	no	—
201	C₈	—	4	4	no	—
202	C₂²	C₁₁×#519	1	1	yes	characteristic
203	C₂²	C₁₁×#520	1	2	yes	—
204	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
205	C₂²	C₁₁×#568	1	1	yes	characteristic
206	C₂²	C₁₁×#568	1	2	yes	—
207	C₄	—	2	2	no	—
208	C₄	—	2	4	no	—
209	C₄	—	4	1	no	—
210	C₄	—	4	4	no	—
211	C₄	—	4	2	no	—
212	C₄	—	4	4	no	—
213	C₄	C₁₁×#562	1	1	yes	characteristic
214	C₄	C₁₁×#563	1	2	yes	—
215	C₄	C₁₁×#564	1	1	yes	characteristic
216	C₂	C₁₁×#2382	1	1	yes	characteristic
217	C₂	C₁₁×#2983	1	1	yes	characteristic
218	C₂	C₁₁×#2987	1	1	yes	characteristic
219	C₂	C₁₁×#2989	1	2	yes	—
220	C₂	C₁₁×#2995	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle, prime radical	C₂³×C₁₁	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
41. #23372	C₁₁	direct (N × H)
177. C₁₁	#23372	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₁×#125	2
C₁₁×#1940	2
C₁₁×#1917	2
C₁₁×#1831	2
#23372	11

Subgroups — C11×#23372 #14600565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23372 #14600565