Subgroups — C₁₁×#20825 #14598018

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2283	C₂	1	2	yes	maximal
3	C₁₁×#1846	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1835	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1809	C₂	1	4	yes	maximal
6	C₁₁×#1776	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#107	C₂²	1	4	yes	—
10	C₂×C₁₁×#106	C₂²	1	4	yes	—
11	C₄×C₁₁×M₁₆	C₄	1	8	yes	complemented
12	C₂×C₁₁×#97	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#383	—	2	2	no	—
16	C₁₁×#382	C₂²	1	4	yes	—
17	C₁₁×#381	—	2	2	no	—
18	C₁₁×#380	C₂²	1	4	yes	—
19	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
20	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
21	C₁₁×#376	—	2	2	no	—
22	C₁₁×#340	C₂²	1	8	yes	—
23	C₂³×C₄×C₁₁	D₄	1	2	yes	—
24	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂×C₁₁×M₁₆	—	2	4	no	—
26	C₂×C₁₁×M₁₆	—	2	4	no	—
27	C₂×C₁₁×M₁₆	C₂×C₄	1	8	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
30	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
31	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
32	C₂×C₄²×C₁₁	—	2	4	no	—
33	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
34	C₂×C₄²×C₁₁	D₄	1	2	yes	—
35	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
38	C₁₁×#107	—	2	8	no	—
39	C₁₁×#106	—	2	8	no	—
40	C₁₁×#97	C₂×C₄	1	8	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
43	C₁₁×#95	—	2	4	no	—
44	C₁₁×#95	—	2	4	no	—
45	C₁₁×#95	—	2	4	no	—
46	C₁₁×#95	—	2	4	no	—
47	#20825	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	—	2	2	no	—
51	C₂²×C₄×C₁₁	—	2	8	no	—
52	C₂²×C₄×C₁₁	—	4	4	no	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	8	yes	—
54	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
59	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
60	C₁₁×M₁₆	—	2	16	no	—
61	C₂×C₈×C₁₁	—	2	2	no	—
62	C₂×C₈×C₁₁	—	2	2	no	—
63	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₁₁	#41	1	4	yes	—
66	C₂×C₈×C₁₁	#41	1	4	yes	—
67	C₁₁×C₄⋊C₄	—	2	8	no	—
68	C₁₁×C₄⋊C₄	—	2	8	no	—
69	C₁₁×C₂²⋊C₄	—	4	8	no	—
70	C₄²×C₁₁	—	4	8	no	—
71	C₄²×C₁₁	C₄⋊C₄	1	8	yes	—
72	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
73	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
74	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
75	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
76	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic
77	#2283	C₂×C₁₁	1	2	yes	—
78	#1846	C₂×C₁₁	1	2	yes	complemented
79	#1835	C₂×C₁₁	1	2	yes	complemented
80	#1809	C₂×C₁₁	1	4	yes	—
81	#1776	C₂×C₁₁	1	4	yes	complemented
82	C₂³×C₁₁	—	2	2	no	—
83	C₂³×C₁₁	—	2	4	no	—
84	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
85	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	4	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	4	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	4	8	no	—
93	C₂×C₄×C₁₁	—	4	8	no	—
94	C₂×C₄×C₁₁	—	4	8	no	—
95	C₂×C₄×C₁₁	—	4	8	no	—
96	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
98	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
99	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
103	C₈×C₁₁	—	2	4	no	—
104	C₈×C₁₁	#117	1	8	yes	—
105	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
106	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
107	C₂×#107	C₂²×C₁₁	1	4	yes	—
108	C₂×#106	C₂²×C₁₁	1	4	yes	—
109	C₄×M₁₆	C₄×C₁₁	1	8	yes	complemented
110	C₂×#97	C₂²×C₁₁	1	2	yes	—
111	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
113	#383	—	2	2	no	—
114	#382	C₂²×C₁₁	1	4	yes	—
115	#381	—	2	2	no	—
116	#380	C₂²×C₁₁	1	4	yes	—
117	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
118	C₄×C₂²⋊C₄	—	2	2	no	—
119	#376	—	2	2	no	—
120	#340	C₂²×C₁₁	1	8	yes	—
121	C₂²×C₁₁	—	2	4	no	—
122	C₂²×C₁₁	—	2	2	no	—
123	C₂²×C₁₁	—	4	4	no	—
124	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₁₁	#532	1	2	yes	—
126	C₂²×C₁₁	#575	1	4	yes	—
127	C₄×C₁₁	—	2	4	no	—
128	C₄×C₁₁	—	2	4	no	—
129	C₄×C₁₁	—	2	2	no	—
130	C₄×C₁₁	—	8	8	no	—
131	C₄×C₁₁	C₂×#117	1	2	yes	—
132	C₄×C₁₁	#533	1	1	yes	characteristic
133	C₄×C₁₁	#533	1	1	yes	characteristic
134	C₂³×C₄	D₄×C₁₁	1	2	yes	—
135	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
136	C₂×M₁₆	—	2	4	no	—
137	C₂×M₁₆	—	2	4	no	—
138	C₂×M₁₆	C₂×C₄×C₁₁	1	8	yes	—
139	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
140	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
141	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
142	C₂×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₄²	—	2	4	no	—
144	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
145	C₂×C₄²	D₄×C₁₁	1	2	yes	—
146	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
147	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
148	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
149	#107	—	2	8	no	—
150	#106	—	2	8	no	—
151	#97	C₂×C₄×C₁₁	1	8	yes	—
152	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
153	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
154	#95	—	2	4	no	—
155	#95	—	2	4	no	—
156	#95	—	2	4	no	—
157	#95	—	2	4	no	—
158	C₂×C₁₁	—	4	2	no	—
159	C₂×C₁₁	#2285	1	1	yes	characteristic
160	C₂×C₁₁	#2911	1	2	yes	—
161	C₂×C₁₁	#3183	1	4	yes	—
162	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	4	4	no	—
167	C₂²×C₄	C₁₁×C₄⋊C₄	1	8	yes	—
168	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
169	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
171	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
172	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
173	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
174	M₁₆	—	2	16	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
178	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
179	C₂×C₈	C₁₁×#41	1	4	yes	—
180	C₂×C₈	C₁₁×#41	1	4	yes	—
181	C₄⋊C₄	—	2	8	no	—
182	C₄⋊C₄	—	2	8	no	—
183	C₂²⋊C₄	—	4	8	no	—
184	C₄²	—	4	8	no	—
185	C₄²	C₁₁×C₄⋊C₄	1	8	yes	—
186	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
187	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
188	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
189	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
190	C₁₁	#20825	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³	—	2	2	no	—
192	C₂³	—	2	4	no	—
193	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
194	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	8	no	—
202	C₂×C₄	—	4	8	no	—
203	C₂×C₄	—	4	8	no	—
204	C₂×C₄	—	4	8	no	—
205	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
206	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
207	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
208	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
209	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
210	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
211	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
212	C₈	—	2	4	no	—
213	C₈	C₁₁×#117	1	8	yes	—
214	C₂²	—	2	4	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	4	4	no	—
217	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
218	C₂²	C₁₁×#532	1	2	yes	—
219	C₂²	C₁₁×#575	1	4	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	2	4	no	—
222	C₄	—	2	2	no	—
223	C₄	—	8	8	no	—
224	C₄	C₂×C₁₁×#117	1	2	yes	—
225	C₄	C₁₁×#533	1	1	yes	characteristic
226	C₄	C₁₁×#533	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	C₁₁×#2285	1	1	yes	characteristic
229	C₂	C₁₁×#2911	1	2	yes	—
230	C₂	C₁₁×#3183	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1846	C₂	semidirect
4. C₁₁×#1835	C₂	semidirect
6. C₁₁×#1776	C₂	semidirect
11. C₄×C₁₁×M₁₆	C₄	semidirect
47. #20825	C₁₁	direct (N × H)
78. #1846	C₂×C₁₁	semidirect
79. #1835	C₂×C₁₁	semidirect
81. #1776	C₂×C₁₁	semidirect
109. C₄×M₁₆	C₄×C₁₁	semidirect
190. C₁₁	#20825	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×M₁₆	2
C₁₁×#2283	2
C₁₁×#1846	2
C₁₁×#1835	2
C₁₁×#1809	2
C₁₁×#1776	2
#20825	11

Subgroups — C11×#20825 #14598018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#20825 #14598018