Subgroups — C₁₁×#20831 #14598024

Order 2816.

758 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	C₁₁×#2920	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1848	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1837	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1811	C₂	1	4	yes	maximal
6	C₁₁×#1778	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#432	—	2	4	no	—
10	C₁₁×#431	—	2	4	no	—
11	C₂×C₁₁×#108	C₂²	1	8	yes	—
12	C₁₁×#423	C₂²	1	4	yes	—
13	C₁₁×#407	C₂²	1	4	yes	—
14	C₄×C₁₁×M₁₆	C₄	1	4	yes	—
15	C₄×C₁₁×M₁₆	C₄	1	4	yes	—
16	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
17	C₂×C₁₁×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#341	C₂²	1	8	yes	—
21	C₂³×C₄×C₁₁	Q₈	1	2	yes	—
22	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	—	2	8	no	—
24	C₂×C₁₁×M₁₆	C₂×C₄	1	8	yes	—
25	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	D₄	1	4	yes	—
31	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₁₁×#108	—	2	16	no	—
35	C₁₁×C₄⋊C₈	—	2	8	no	—
36	C₁₁×C₂²⋊C₈	—	2	8	no	—
37	C₁₁×#97	—	2	4	no	—
38	C₁₁×#97	C₂×C₄	1	8	yes	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
44	#20831	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	—	2	4	no	—
47	C₂²×C₄×C₁₁	—	4	4	no	—
48	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
49	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
56	C₁₁×M₁₆	—	2	16	no	—
57	C₁₁×M₁₆	—	2	16	no	—
58	C₂×C₈×C₁₁	—	2	8	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
61	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
62	C₂×C₈×C₁₁	#41	1	8	yes	—
63	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
64	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
65	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
68	C₄²×C₁₁	C₂×D₄	1	2	yes	—
69	C₄²×C₁₁	C₂×D₄	1	2	yes	—
70	#2920	C₂×C₁₁	1	2	yes	—
71	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic
72	#1848	C₂×C₁₁	1	2	yes	complemented
73	#1837	C₂×C₁₁	1	2	yes	complemented
74	#1811	C₂×C₁₁	1	4	yes	—
75	#1778	C₂×C₁₁	1	4	yes	complemented
76	C₂³×C₁₁	—	2	2	no	—
77	C₂³×C₁₁	—	4	2	no	—
78	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
79	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	—	2	2	no	—
81	C₂×C₄×C₁₁	—	2	4	no	—
82	C₂×C₄×C₁₁	—	2	4	no	—
83	C₂×C₄×C₁₁	—	2	8	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	4	4	no	—
86	C₂×C₄×C₁₁	—	4	2	no	—
87	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
89	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
90	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
94	C₈×C₁₁	—	2	4	no	—
95	C₈×C₁₁	—	4	8	no	—
96	C₈×C₁₁	#117	1	8	yes	—
97	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
98	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
99	#432	—	2	4	no	—
100	#431	—	2	4	no	—
101	C₂×#108	C₂²×C₁₁	1	8	yes	—
102	#423	C₂²×C₁₁	1	4	yes	—
103	#407	C₂²×C₁₁	1	4	yes	—
104	C₄×M₁₆	C₄×C₁₁	1	4	yes	—
105	C₄×M₁₆	C₄×C₁₁	1	4	yes	—
106	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
107	C₂×#97	C₂²×C₁₁	1	2	yes	—
108	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	#341	C₂²×C₁₁	1	8	yes	—
111	C₂²×C₁₁	—	2	2	no	—
112	C₂²×C₁₁	—	2	4	no	—
113	C₂²×C₁₁	—	2	2	no	—
114	C₂²×C₁₁	—	4	4	no	—
115	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₁₁	#533	1	2	yes	—
117	C₄×C₁₁	—	2	4	no	—
118	C₄×C₁₁	—	2	2	no	—
119	C₄×C₁₁	—	2	2	no	—
120	C₄×C₁₁	#430	1	4	yes	—
121	C₄×C₁₁	C₂×#117	1	2	yes	—
122	C₄×C₁₁	#532	1	2	yes	—
123	C₂³×C₄	Q₈×C₁₁	1	2	yes	—
124	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
125	C₂×M₁₆	—	2	8	no	—
126	C₂×M₁₆	C₂×C₄×C₁₁	1	8	yes	—
127	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
128	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
129	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
130	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
131	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
132	C₂×C₄²	D₄×C₁₁	1	4	yes	—
133	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
134	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
135	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
136	#108	—	2	16	no	—
137	C₄⋊C₈	—	2	8	no	—
138	C₂²⋊C₈	—	2	8	no	—
139	#97	—	2	4	no	—
140	#97	C₂×C₄×C₁₁	1	8	yes	—
141	C₄×C₈	—	2	4	no	—
142	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
143	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
144	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
145	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
146	C₂×C₁₁	—	2	2	no	—
147	C₂×C₁₁	—	4	2	no	—
148	C₂×C₁₁	#2285	1	1	yes	characteristic
149	C₂×C₁₁	C₂×#430	1	2	yes	—
150	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	—	4	4	no	—
153	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
154	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
155	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
156	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
157	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
158	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
159	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
160	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
161	M₁₆	—	2	16	no	—
162	M₁₆	—	2	16	no	—
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	—	2	8	no	—
165	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
166	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
167	C₂×C₈	C₁₁×#41	1	8	yes	—
168	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
169	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
170	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
171	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
172	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
173	C₄²	C₂×D₄×C₁₁	1	2	yes	—
174	C₄²	C₂×D₄×C₁₁	1	2	yes	—
175	C₁₁	#20831	1	1	yes	characteristic, direct product factor, Sylow
176	C₂³	—	2	2	no	—
177	C₂³	—	4	2	no	—
178	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
179	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	8	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
188	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
189	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
190	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
191	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
192	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
194	C₈	—	2	4	no	—
195	C₈	—	4	8	no	—
196	C₈	C₁₁×#117	1	8	yes	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	4	no	—
199	C₂²	—	2	2	no	—
200	C₂²	—	4	4	no	—
201	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
202	C₂²	C₁₁×#533	1	2	yes	—
203	C₄	—	2	4	no	—
204	C₄	—	2	2	no	—
205	C₄	—	2	2	no	—
206	C₄	C₁₁×#430	1	4	yes	—
207	C₄	C₂×C₁₁×#117	1	2	yes	—
208	C₄	C₁₁×#532	1	2	yes	—
209	C₂	—	2	2	no	—
210	C₂	—	4	2	no	—
211	C₂	C₁₁×#2285	1	1	yes	characteristic
212	C₂	C₂×C₁₁×#430	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1848	C₂	semidirect
4. C₁₁×#1837	C₂	semidirect
6. C₁₁×#1778	C₂	semidirect
44. #20831	C₁₁	direct (N × H)
72. #1848	C₂×C₁₁	semidirect
73. #1837	C₂×C₁₁	semidirect
75. #1778	C₂×C₁₁	semidirect
175. C₁₁	#20831	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×#2920	2
C₂×C₄×C₁₁×M₁₆	2
C₁₁×#1848	2
C₁₁×#1837	2
C₁₁×#1811	2
C₁₁×#1778	2
#20831	11

Subgroups — C11×#20831 #14598024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#20831 #14598024