Subgroups — C₁₁×#23378 #14600571

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#126	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1940	C₂	1	3	yes	maximal, complemented
3	C₁₁×#1924	C₂	1	3	yes	maximal
4	C₁₁×#1917	C₂	1	3	yes	maximal, complemented
5	C₁₁×#1851	C₂	1	3	yes	maximal
6	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#126	C₄	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	3	yes	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	3	yes	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	3	yes	—
13	C₂×C₁₁×C₂²⋊C₈	C₂²	1	3	yes	—
14	C₂×C₁₁×#97	C₂²	1	3	yes	—
15	C₁₁×#388	C₄	1	3	yes	—
16	C₁₁×#387	C₄	1	3	yes	—
17	C₁₁×#383	C₄	1	1	yes	characteristic
18	C₄×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
19	C₄×C₁₁×C₂²⋊C₄	C₂²	1	3	yes	—
20	C₄³×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#336	C₂²	1	3	yes	—
22	C₁₁×#336	C₂²	1	3	yes	—
23	C₁₁×#336	C₂²	1	3	yes	—
24	C₁₁×#336	C₂²	1	3	yes	—
25	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₁₁×M₁₆	—	4	3	no	—
27	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
31	C₁₁×#126	—	2	4	no	—
32	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	3	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	3	yes	—
34	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	3	yes	—
35	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	3	yes	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
40	C₁₁×C₄⋊C₈	—	4	3	no	—
41	C₁₁×C₄⋊C₈	—	4	3	no	—
42	C₁₁×C₄⋊C₈	—	4	3	no	—
43	C₁₁×C₂²⋊C₈	—	4	3	no	—
44	C₁₁×#97	—	4	3	no	—
45	C₁₁×#95	C₂×C₄	1	3	yes	—
46	C₁₁×#95	C₂×C₄	1	3	yes	—
47	C₁₁×#95	C₂×C₄	1	3	yes	—
48	C₁₁×#95	C₂×C₄	1	3	yes	—
49	#23378	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	—	2	3	no	—
52	C₂²×C₄×C₁₁	—	2	3	no	—
53	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
59	C₁₁×M₁₆	—	4	4	no	—
60	C₂×C₈×C₁₁	—	2	3	no	—
61	C₂×C₈×C₁₁	—	2	3	no	—
62	C₂×C₈×C₁₁	—	2	3	no	—
63	C₂×C₈×C₁₁	—	2	3	no	—
64	C₂×C₈×C₁₁	—	2	3	no	—
65	C₂×C₈×C₁₁	—	2	3	no	—
66	C₂×C₈×C₁₁	—	2	6	no	—
67	C₁₁×C₄⋊C₄	—	2	6	no	—
68	C₁₁×C₄⋊C₄	—	4	3	no	—
69	C₁₁×C₂²⋊C₄	—	2	6	no	—
70	C₁₁×C₂²⋊C₄	—	4	3	no	—
71	C₄²×C₁₁	—	2	3	no	—
72	C₄²×C₁₁	—	2	3	no	—
73	C₄²×C₁₁	—	2	3	no	—
74	C₄²×C₁₁	—	2	3	no	—
75	C₄²×C₁₁	—	4	3	no	—
76	C₄²×C₁₁	M₁₆	1	4	yes	complemented
77	C₄×#126	C₂×C₁₁	1	1	yes	characteristic
78	#1940	C₂×C₁₁	1	3	yes	complemented
79	#1924	C₂×C₁₁	1	3	yes	—
80	#1917	C₂×C₁₁	1	3	yes	complemented
81	#1851	C₂×C₁₁	1	3	yes	—
82	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
83	#1839	C₂×C₁₁	1	1	yes	characteristic, complemented
84	C₂³×C₁₁	—	2	3	no	—
85	C₂³×C₁₁	—	2	1	no	—
86	C₂³×C₁₁	—	2	3	no	—
87	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₁	—	2	3	no	—
89	C₂×C₄×C₁₁	—	2	3	no	—
90	C₂×C₄×C₁₁	—	2	3	no	—
91	C₂×C₄×C₁₁	—	2	3	no	—
92	C₂×C₄×C₁₁	—	2	3	no	—
93	C₂×C₄×C₁₁	—	2	3	no	—
94	C₂×C₄×C₁₁	—	2	3	no	—
95	C₂×C₄×C₁₁	—	2	3	no	—
96	C₂×C₄×C₁₁	—	2	3	no	—
97	C₂×C₄×C₁₁	—	2	3	no	—
98	C₂×C₄×C₁₁	—	2	3	no	—
99	C₂×C₄×C₁₁	—	2	3	no	—
100	C₂×C₄×C₁₁	—	4	1	no	—
101	C₂×C₄×C₁₁	—	4	3	no	—
102	C₂×C₄×C₁₁	C₂×M₁₆	1	6	yes	—
103	C₂×C₄×C₁₁	H(5,𝔽₂)	1	3	yes	—
104	C₂×C₄×C₁₁	2₋¹⁺⁴	1	3	yes	—
105	C₈×C₁₁	—	4	3	no	—
106	C₈×C₁₁	—	4	1	no	—
107	C₈×C₁₁	—	4	1	no	—
108	C₈×C₁₁	—	4	3	no	—
109	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
110	C₂×#126	C₄×C₁₁	1	1	yes	characteristic
111	C₂×C₄⋊C₈	C₂²×C₁₁	1	3	yes	—
112	C₂×C₄⋊C₈	C₂²×C₁₁	1	3	yes	—
113	C₂×C₄⋊C₈	C₂²×C₁₁	1	3	yes	—
114	C₂×C₂²⋊C₈	C₂²×C₁₁	1	3	yes	—
115	C₂×#97	C₂²×C₁₁	1	3	yes	—
116	#388	C₄×C₁₁	1	3	yes	—
117	#387	C₄×C₁₁	1	3	yes	—
118	#383	C₄×C₁₁	1	1	yes	characteristic
119	C₄×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
120	C₄×C₂²⋊C₄	C₂²×C₁₁	1	3	yes	—
121	C₄³	C₂²×C₁₁	1	1	yes	characteristic
122	#336	C₂²×C₁₁	1	3	yes	—
123	#336	C₂²×C₁₁	1	3	yes	—
124	#336	C₂²×C₁₁	1	3	yes	—
125	#336	C₂²×C₁₁	1	3	yes	—
126	C₂²×C₁₁	—	4	1	no	—
127	C₂²×C₁₁	—	4	3	no	—
128	C₂²×C₁₁	—	4	3	no	—
129	C₂²×C₁₁	#520	1	3	yes	—
130	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
131	C₂²×C₁₁	#568	1	3	yes	—
132	C₄×C₁₁	—	2	6	no	—
133	C₄×C₁₁	—	4	1	no	—
134	C₄×C₁₁	—	4	3	no	—
135	C₄×C₁₁	—	4	3	no	—
136	C₄×C₁₁	—	4	3	no	—
137	C₄×C₁₁	#560	1	1	yes	characteristic
138	C₄×C₁₁	#563	1	3	yes	—
139	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
140	C₂×M₁₆	—	4	3	no	—
141	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
142	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
143	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
144	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
145	#126	—	2	4	no	—
146	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
147	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
148	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
149	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
150	C₂×C₄²	C₂×C₄×C₁₁	1	3	yes	—
151	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
152	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
153	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
154	C₄⋊C₈	—	4	3	no	—
155	C₄⋊C₈	—	4	3	no	—
156	C₄⋊C₈	—	4	3	no	—
157	C₂²⋊C₈	—	4	3	no	—
158	#97	—	4	3	no	—
159	#95	C₂×C₄×C₁₁	1	3	yes	—
160	#95	C₂×C₄×C₁₁	1	3	yes	—
161	#95	C₂×C₄×C₁₁	1	3	yes	—
162	#95	C₂×C₄×C₁₁	1	3	yes	—
163	C₂×C₁₁	—	8	1	no	—
164	C₂×C₁₁	#2383	1	1	yes	characteristic
165	C₂×C₁₁	#2989	1	3	yes	—
166	C₂×C₁₁	#2995	1	3	yes	—
167	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
168	C₂²×C₄	—	2	3	no	—
169	C₂²×C₄	—	2	3	no	—
170	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
171	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
173	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
174	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
175	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
176	M₁₆	—	4	4	no	—
177	C₂×C₈	—	2	3	no	—
178	C₂×C₈	—	2	3	no	—
179	C₂×C₈	—	2	3	no	—
180	C₂×C₈	—	2	3	no	—
181	C₂×C₈	—	2	3	no	—
182	C₂×C₈	—	2	3	no	—
183	C₂×C₈	—	2	6	no	—
184	C₄⋊C₄	—	2	6	no	—
185	C₄⋊C₄	—	4	3	no	—
186	C₂²⋊C₄	—	2	6	no	—
187	C₂²⋊C₄	—	4	3	no	—
188	C₄²	—	2	3	no	—
189	C₄²	—	2	3	no	—
190	C₄²	—	2	3	no	—
191	C₄²	—	2	3	no	—
192	C₄²	—	4	3	no	—
193	C₄²	C₁₁×M₁₆	1	4	yes	complemented
194	C₁₁	#23378	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	—	2	3	no	—
196	C₂³	—	2	1	no	—
197	C₂³	—	2	3	no	—
198	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
199	C₂×C₄	—	2	3	no	—
200	C₂×C₄	—	2	3	no	—
201	C₂×C₄	—	2	3	no	—
202	C₂×C₄	—	2	3	no	—
203	C₂×C₄	—	2	3	no	—
204	C₂×C₄	—	2	3	no	—
205	C₂×C₄	—	2	3	no	—
206	C₂×C₄	—	2	3	no	—
207	C₂×C₄	—	2	3	no	—
208	C₂×C₄	—	2	3	no	—
209	C₂×C₄	—	2	3	no	—
210	C₂×C₄	—	2	3	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	3	no	—
213	C₂×C₄	C₂×C₁₁×M₁₆	1	6	yes	—
214	C₂×C₄	C₁₁×H(5,𝔽₂)	1	3	yes	—
215	C₂×C₄	C₁₁×2₋¹⁺⁴	1	3	yes	—
216	C₈	—	4	1	no	—
217	C₈	—	4	1	no	—
218	C₈	—	4	3	no	—
219	C₈	—	4	3	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	3	no	—
222	C₂²	—	4	3	no	—
223	C₂²	C₁₁×#520	1	3	yes	—
224	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
225	C₂²	C₁₁×#568	1	3	yes	—
226	C₄	—	2	6	no	—
227	C₄	—	4	1	no	—
228	C₄	—	4	3	no	—
229	C₄	—	4	3	no	—
230	C₄	—	4	3	no	—
231	C₄	C₁₁×#560	1	1	yes	characteristic
232	C₄	C₁₁×#563	1	3	yes	—
233	C₂	—	8	1	no	—
234	C₂	C₁₁×#2383	1	1	yes	characteristic
235	C₂	C₁₁×#2989	1	3	yes	—
236	C₂	C₁₁×#2995	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂³×C₄
prime radical	C₂⁴×C₁₁	C₂²×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
2. C₁₁×#1940	C₂	semidirect
4. C₁₁×#1917	C₂	semidirect
6. C₁₁×#1842	C₂	semidirect
7. C₁₁×#1839	C₂	semidirect
49. #23378	C₁₁	direct (N × H)
76. C₄²×C₁₁	M₁₆	semidirect
78. #1940	C₂×C₁₁	semidirect
80. #1917	C₂×C₁₁	semidirect
82. #1842	C₂×C₁₁	semidirect
83. #1839	C₂×C₁₁	semidirect
193. C₄²	C₁₁×M₁₆	semidirect
194. C₁₁	#23378	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×#126	2
C₁₁×#1940	2
C₁₁×#1924	2
C₁₁×#1917	2
C₁₁×#1851	2
C₁₁×#1842	2
C₁₁×#1839	2
#23378	11

Subgroups — C11×#23378 #14600571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23378 #14600571