Subgroups — C₁₁×#23798 #14600991

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×D₈	C₂	1	4	yes	maximal, complemented
2	C₄×C₁₁×#127	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2093	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2011	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₁×D₈	C₂²	1	4	yes	—
7	C₂×C₁₁×#127	C₂²	1	2	yes	—
8	C₂×C₄×D₄×C₁₁	—	2	4	no	—
9	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
10	C₄×C₁₁×D₈	—	2	16	no	—
11	C₂×C₁₁×#107	C₂²	1	4	yes	—
12	C₂×C₁₁×#102	C₂²	1	8	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
14	C₁₁×#390	—	2	4	no	—
15	C₁₁×#390	C₂²	1	4	yes	—
16	C₁₁×#384	C₂²	1	2	yes	—
17	C₄³×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#336	C₂²	1	4	yes	—
19	C₂²×D₄×C₁₁	—	2	4	no	—
20	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₁	—	2	4	no	—
22	C₂×C₁₁×D₈	—	2	16	no	—
23	C₂×C₁₁×D₈	—	2	8	no	—
24	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
25	C₁₁×#127	—	2	8	no	—
26	C₄×D₄×C₁₁	—	2	16	no	—
27	C₄×D₄×C₁₁	—	4	16	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
29	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
30	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
31	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
32	C₂×C₄²×C₁₁	D₄	1	2	yes	—
33	C₂×C₄²×C₁₁	D₄	1	2	yes	—
34	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
35	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
36	C₁₁×#107	—	2	8	no	—
37	C₁₁×#102	—	2	16	no	—
38	C₄×C₈×C₁₁	D₄	1	8	yes	complemented
39	#23798	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁴×C₁₁	—	2	4	no	—
41	C₂×D₄×C₁₁	—	2	16	no	—
42	C₂×D₄×C₁₁	—	2	8	no	—
43	C₂×D₄×C₁₁	—	2	8	no	—
44	C₂×D₄×C₁₁	—	2	4	no	—
45	C₂×D₄×C₁₁	—	4	8	no	—
46	C₂×D₄×C₁₁	—	4	8	no	—
47	C₂×D₄×C₁₁	#41	1	8	yes	—
48	C₂²×C₄×C₁₁	—	2	4	no	—
49	C₂²×C₄×C₁₁	—	4	8	no	—
50	C₂²×C₄×C₁₁	—	4	16	no	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
55	C₁₁×D₈	—	2	32	no	—
56	C₂×C₈×C₁₁	—	2	8	no	—
57	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
58	C₁₁×C₄⋊C₄	—	2	8	no	—
59	C₁₁×C₄⋊C₄	—	4	8	no	—
60	C₁₁×C₂²⋊C₄	—	4	8	no	—
61	C₁₁×C₂²⋊C₄	—	4	16	no	—
62	C₄²×C₁₁	—	2	4	no	—
63	C₄²×C₁₁	—	4	2	no	—
64	C₄²×C₁₁	D₈	1	8	yes	complemented
65	C₄²×C₁₁	C₂×D₄	1	4	yes	—
66	C₂×C₄×D₈	C₂×C₁₁	1	4	yes	complemented
67	C₄×#127	C₂×C₁₁	1	2	yes	complemented
68	#2093	C₂×C₁₁	1	4	yes	complemented
69	#2011	C₂×C₁₁	1	4	yes	complemented
70	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
71	C₂³×C₁₁	—	2	8	no	—
72	C₂³×C₁₁	—	4	4	no	—
73	C₂³×C₁₁	—	4	4	no	—
74	C₂³×C₁₁	—	4	8	no	—
75	C₂³×C₁₁	—	4	8	no	—
76	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
77	D₄×C₁₁	—	2	16	no	—
78	D₄×C₁₁	—	4	32	no	—
79	D₄×C₁₁	—	4	8	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	—	4	4	no	—
84	C₂×C₄×C₁₁	—	4	8	no	—
85	C₂×C₄×C₁₁	—	8	16	no	—
86	C₂×C₄×C₁₁	#127	1	2	yes	—
87	C₂×C₄×C₁₁	#127	1	2	yes	—
88	C₂×C₄×C₁₁	C₂×D₈	1	8	yes	—
89	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
90	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
92	C₈×C₁₁	—	2	8	no	—
93	C₂²×D₈	C₂²×C₁₁	1	4	yes	—
94	C₂×#127	C₂²×C₁₁	1	2	yes	—
95	C₂×C₄×D₄	—	2	4	no	—
96	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
97	C₄×D₈	—	2	16	no	—
98	C₂×#107	C₂²×C₁₁	1	4	yes	—
99	C₂×#102	C₂²×C₁₁	1	8	yes	—
100	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
101	#390	—	2	4	no	—
102	#390	C₂²×C₁₁	1	4	yes	—
103	#384	C₂²×C₁₁	1	2	yes	—
104	C₄³	C₂²×C₁₁	1	1	yes	characteristic
105	#336	C₂²×C₁₁	1	4	yes	—
106	C₂²×C₁₁	—	4	16	no	—
107	C₂²×C₁₁	—	4	8	no	—
108	C₂²×C₁₁	—	8	8	no	—
109	C₂²×C₁₁	—	8	4	no	—
110	C₂²×C₁₁	—	8	4	no	—
111	C₂²×C₁₁	#525	1	2	yes	—
112	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
113	C₂²×C₁₁	C₂²×D₈	1	2	yes	—
114	C₂²×C₁₁	#575	1	2	yes	—
115	C₄×C₁₁	—	2	8	no	—
116	C₄×C₁₁	—	2	2	no	—
117	C₄×C₁₁	—	8	4	no	—
118	C₄×C₁₁	#493	1	4	yes	—
119	C₄×C₁₁	#525	1	4	yes	—
120	C₂²×D₄	—	2	4	no	—
121	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
122	C₂³×C₄	—	2	4	no	—
123	C₂×D₈	—	2	16	no	—
124	C₂×D₈	—	2	8	no	—
125	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
126	#127	—	2	8	no	—
127	C₄×D₄	—	2	16	no	—
128	C₄×D₄	—	4	16	no	—
129	C₂×C₄⋊C₄	—	2	4	no	—
130	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
131	C₂×C₂²⋊C₄	—	2	8	no	—
132	C₂×C₂²⋊C₄	—	2	4	no	—
133	C₂×C₄²	D₄×C₁₁	1	2	yes	—
134	C₂×C₄²	D₄×C₁₁	1	2	yes	—
135	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
136	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
137	#107	—	2	8	no	—
138	#102	—	2	16	no	—
139	C₄×C₈	D₄×C₁₁	1	8	yes	complemented
140	C₂×C₁₁	—	8	8	no	—
141	C₂×C₁₁	#2397	1	1	yes	characteristic
142	C₂×C₁₁	#3100	1	4	yes	—
143	C₂×C₁₁	C₂×#493	1	1	yes	characteristic
144	C₂×C₁₁	#3150	1	1	yes	characteristic
145	C₂⁴	—	2	4	no	—
146	C₂×D₄	—	2	16	no	—
147	C₂×D₄	—	2	8	no	—
148	C₂×D₄	—	2	8	no	—
149	C₂×D₄	—	2	4	no	—
150	C₂×D₄	—	4	8	no	—
151	C₂×D₄	—	4	8	no	—
152	C₂×D₄	C₁₁×#41	1	8	yes	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	4	8	no	—
155	C₂²×C₄	—	4	16	no	—
156	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
157	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
158	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
159	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
160	D₈	—	2	32	no	—
161	C₂×C₈	—	2	8	no	—
162	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
163	C₄⋊C₄	—	2	8	no	—
164	C₄⋊C₄	—	4	8	no	—
165	C₂²⋊C₄	—	4	8	no	—
166	C₂²⋊C₄	—	4	16	no	—
167	C₄²	—	2	4	no	—
168	C₄²	—	4	2	no	—
169	C₄²	C₁₁×D₈	1	8	yes	complemented
170	C₄²	C₂×D₄×C₁₁	1	4	yes	—
171	C₁₁	#23798	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	—	2	8	no	—
173	C₂³	—	4	4	no	—
174	C₂³	—	4	4	no	—
175	C₂³	—	4	8	no	—
176	C₂³	—	4	8	no	—
177	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
178	D₄	—	2	16	no	—
179	D₄	—	4	32	no	—
180	D₄	—	4	8	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	8	no	—
186	C₂×C₄	—	8	16	no	—
187	C₂×C₄	C₁₁×#127	1	2	yes	—
188	C₂×C₄	C₁₁×#127	1	2	yes	—
189	C₂×C₄	C₂×C₁₁×D₈	1	8	yes	—
190	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
191	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
192	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
193	C₈	—	2	8	no	—
194	C₂²	—	4	8	no	—
195	C₂²	—	4	16	no	—
196	C₂²	—	8	4	no	—
197	C₂²	—	8	8	no	—
198	C₂²	—	8	4	no	—
199	C₂²	C₁₁×#525	1	2	yes	—
200	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
201	C₂²	C₂²×C₁₁×D₈	1	2	yes	—
202	C₂²	C₁₁×#575	1	2	yes	—
203	C₄	—	2	2	no	—
204	C₄	—	2	8	no	—
205	C₄	—	8	4	no	—
206	C₄	C₁₁×#493	1	4	yes	—
207	C₄	C₁₁×#525	1	4	yes	—
208	C₂	—	8	8	no	—
209	C₂	C₁₁×#2397	1	1	yes	characteristic
210	C₂	C₁₁×#3100	1	4	yes	—
211	C₂	C₂×C₁₁×#493	1	1	yes	characteristic
212	C₂	C₁₁×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂³×C₁₁	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₁×D₈	C₂	semidirect
2. C₄×C₁₁×#127	C₂	semidirect
3. C₁₁×#2093	C₂	semidirect
4. C₁₁×#2011	C₂	semidirect
5. C₁₁×#1744	C₂	semidirect
38. C₄×C₈×C₁₁	D₄	semidirect
39. #23798	C₁₁	direct (N × H)
64. C₄²×C₁₁	D₈	semidirect
66. C₂×C₄×D₈	C₂×C₁₁	semidirect
67. C₄×#127	C₂×C₁₁	semidirect
68. #2093	C₂×C₁₁	semidirect
69. #2011	C₂×C₁₁	semidirect
70. #1744	C₂×C₁₁	semidirect
139. C₄×C₈	D₄×C₁₁	semidirect
169. C₄²	C₁₁×D₈	semidirect
171. C₁₁	#23798	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×C₄×C₁₁×D₈	2
C₄×C₁₁×#127	2
C₁₁×#2093	2
C₁₁×#2011	2
C₁₁×#1744	2
#23798	11

Subgroups — C11×#23798 #14600991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23798 #14600991