Subgroups — D₁₁×#2252 #14909247

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×#500	C₂	1	2	yes	maximal
2	#13070891	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070890	C₂	1	4	yes	maximal, complemented
4	#13070889	C₂	1	2	yes	maximal, complemented
5	D₁₁×#366	C₂	1	4	yes	maximal
6	C₄×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#2252	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₁×C₄⋊Q₈	—	2	2	no	—
9	C₁₁×#500	C₂²	1	2	yes	—
10	#10622691	—	2	2	no	—
11	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
12	D₁₁×#107	—	2	2	no	—
13	D₁₁×#107	C₂²	1	4	yes	—
14	#10622487	—	2	2	no	—
15	#10622487	C₂²	1	4	yes	—
16	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
17	#10622295	C₂²	1	2	yes	—
18	C₁₁×#366	C₂²	1	4	yes	—
19	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
20	#10622142	C₂²	1	4	yes	—
21	C₁₆×Dic₁₁	C₂²	1	2	yes	—
22	#10622127	C₂²	1	8	yes	—
23	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₁₁	—	4	2	no	—
25	C₁₁×C₄⋊Q₈	—	2	2	no	—
26	#66997	—	4	2	no	—
27	C₂×C₈×D₁₁	D₄	1	1	yes	characteristic
28	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×D₁₁	—	2	4	no	—
30	C₄⋊C₄×D₁₁	—	4	2	no	—
31	#66941	—	2	4	no	—
32	#66941	—	4	2	no	—
33	C₄²×D₁₁	D₄	1	1	yes	characteristic
34	#66922	—	2	2	no	—
35	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
36	C₁₁×#107	—	2	2	no	—
37	C₁₁×#107	C₂³	1	4	yes	—
38	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	#66882	—	2	2	no	—
40	#66882	C₂³	1	4	yes	—
41	C₈×Dic₁₁	D₄	1	1	yes	characteristic
42	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
43	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
44	#66871	—	2	4	no	—
45	#66871	—	2	4	no	—
46	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
47	C₁₆×D₁₁	Q₈	1	8	yes	complemented
48	C₂×#2252	—	11	1	no	maximal, Sylow
49	C₂×Q₈×C₁₁	—	4	2	no	—
50	Q₈×D₁₁	—	8	8	no	—
51	C₂×C₄×D₁₁	—	4	4	no	—
52	C₂×C₄×D₁₁	D₈	1	1	yes	characteristic
53	C₂×C₄×D₁₁	D₈	1	1	yes	characteristic
54	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₂₂	—	4	4	no	—
56	C₂×Dic₂₂	—	4	2	no	—
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
59	C₁₁×C₄⋊C₄	—	2	4	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₄⋊Dic₁₁	—	2	4	no	—
63	C₄⋊Dic₁₁	—	4	2	no	—
64	Dic₁₁⋊C₄	—	4	4	no	—
65	Dic₁₁⋊C₄	—	4	4	no	—
66	C₄×Dic₁₁	D₈	1	1	yes	characteristic
67	C₄×Dic₁₁	D₈	1	1	yes	characteristic
68	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
70	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
71	C₈×D₁₁	Q₁₆	1	4	yes	—
72	C₈×D₁₁	C₂×Q₈	1	4	yes	—
73	C₁₁×C₁₆	C₂×Q₈	1	4	yes	complemented
74	C₁₁⋊C₁₆	C₂×Q₈	1	4	yes	complemented
75	C₂×#500	—	11	2	no	—
76	#2252	—	11	2	no	—
77	#2252	—	11	4	no	—
78	#2252	—	11	1	no	—
79	#2252	D₁₁	1	1	yes	characteristic, direct product factor
80	C₂×#366	—	11	4	no	—
81	C₂×C₄×C₁₆	—	11	1	no	—
82	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
83	Q₈×C₁₁	—	8	4	no	—
84	C₂×C₄×C₁₁	—	4	4	no	—
85	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
88	C₂×Dic₁₁	—	4	4	no	—
89	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
90	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
91	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
92	C₄×D₁₁	—	8	8	no	—
93	C₄×D₁₁	D₁₆	1	4	yes	—
94	C₄×D₁₁	Q₃₂	1	4	yes	—
95	C₄×D₁₁	C₄⋊Q₈	1	2	yes	—
96	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
97	Dic₂₂	—	8	4	no	—
98	Dic₂₂	—	8	8	no	—
99	C₈×C₁₁	C₂×Q₁₆	1	2	yes	—
100	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
101	C₁₁⋊C₈	C₄⋊Q₈	1	2	yes	—
102	C₁₁⋊C₈	C₂×Q₁₆	1	2	yes	—
103	C₂×C₄⋊Q₈	—	22	2	no	—
104	C₂²×C₁₆	—	11	2	no	—
105	#500	—	11	4	no	—
106	#500	—	11	2	no	—
107	#500	—	22	2	no	—
108	#500	—	22	2	no	—
109	#500	C₂×D₁₁	1	2	yes	—
110	C₂×#107	—	11	4	no	—
111	C₂×#107	—	22	2	no	—
112	C₂×C₄×C₈	—	11	1	no	—
113	#366	—	11	4	no	—
114	#366	—	11	8	no	—
115	#366	C₂×D₁₁	1	4	yes	—
116	C₄×C₁₆	—	11	2	no	—
117	C₄×C₁₆	—	11	1	no	—
118	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
119	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
120	C₂×D₁₁	#500	1	2	yes	—
121	C₂×D₁₁	C₂×D₁₆	1	2	yes	—
122	C₂×D₁₁	C₂×Q₃₂	1	2	yes	—
123	C₄×C₁₁	—	8	4	no	—
124	C₄×C₁₁	C₂×D₁₆	1	2	yes	—
125	C₄×C₁₁	C₂×Q₃₂	1	2	yes	—
126	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
127	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
128	Dic₁₁	—	8	4	no	—
129	Dic₁₁	#500	1	2	yes	—
130	Dic₁₁	C₂×D₁₆	1	2	yes	—
131	Dic₁₁	C₂×Q₃₂	1	2	yes	—
132	C₂²×Q₈	—	44	2	no	—
133	C₂²×C₈	—	11	1	no	—
134	C₂²×C₈	—	11	1	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	22	4	no	—
137	C₄⋊Q₈	—	22	2	no	—
138	C₄⋊Q₈	—	44	2	no	—
139	C₄⋊Q₈	—	44	2	no	—
140	C₂×C₄⋊C₄	—	22	4	no	—
141	C₂×C₄⋊C₄	—	44	2	no	—
142	C₂×C₄²	—	11	1	no	—
143	C₂×C₁₆	—	11	2	no	—
144	C₂×C₁₆	—	11	8	no	—
145	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
146	#107	—	2	2	no	—
147	#107	—	11	4	no	—
148	#107	—	22	4	no	—
149	#107	—	22	4	no	—
150	#107	—	22	2	no	—
151	#107	C₂²×D₁₁	1	4	yes	—
152	C₄×C₈	—	11	1	no	—
153	C₄×C₈	—	11	1	no	—
154	C₄×C₈	—	11	1	no	—
155	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
156	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
157	C₂×C₁₁	C₂²×D₁₆	1	1	yes	characteristic
158	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
159	D₁₁	#2252	1	4	yes	direct product factor
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	44	4	no	—
162	C₂×Q₈	—	44	2	no	—
163	C₂×Q₈	—	88	8	no	—
164	C₂²×C₄	—	11	1	no	—
165	C₂²×C₄	—	11	1	no	—
166	C₂²×C₄	—	11	1	no	—
167	C₂²×C₄	—	44	4	no	—
168	C₂×C₈	—	11	1	no	—
169	C₂×C₈	—	11	1	no	—
170	C₂×C₈	—	11	4	no	—
171	C₂×C₈	—	11	4	no	—
172	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
173	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	22	4	no	—
177	C₄⋊C₄	—	44	4	no	—
178	C₄⋊C₄	—	44	4	no	—
179	C₄⋊C₄	—	44	2	no	—
180	C₄²	—	11	1	no	—
181	C₄²	—	11	1	no	—
182	C₄²	—	11	1	no	—
183	C₄²	D₄×D₁₁	1	1	yes	characteristic
184	C₁₆	—	11	4	no	—
185	C₁₆	Q₈×D₁₁	1	4	yes	complemented
186	C₁₁	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
187	C₂³	—	11	1	no	—
188	Q₈	—	8	4	no	—
189	Q₈	—	88	8	no	—
190	Q₈	—	88	4	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	11	1	no	—
193	C₂×C₄	—	11	1	no	—
194	C₂×C₄	—	11	1	no	—
195	C₂×C₄	—	11	2	no	—
196	C₂×C₄	—	11	4	no	—
197	C₂×C₄	—	11	2	no	—
198	C₂×C₄	—	11	4	no	—
199	C₂×C₄	—	44	4	no	—
200	C₂×C₄	—	88	8	no	—
201	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
202	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
203	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
204	C₈	—	11	2	no	—
205	C₈	—	11	2	no	—
206	C₈	Q₁₆×D₁₁	1	2	yes	—
207	C₈	C₂×Q₈×D₁₁	1	2	yes	—
208	C₂²	—	11	2	no	—
209	C₂²	—	11	2	no	—
210	C₂²	—	11	2	no	—
211	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
212	C₄	—	8	4	no	—
213	C₄	—	11	2	no	—
214	C₄	—	11	2	no	—
215	C₄	—	11	2	no	—
216	C₄	—	88	4	no	—
217	C₄	D₁₁×D₁₆	1	2	yes	—
218	C₄	D₁₁×Q₃₂	1	2	yes	—
219	C₄	D₁₁×C₄⋊Q₈	1	1	yes	characteristic
220	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
221	C₂	—	11	4	no	—
222	C₂	D₁₁×#500	1	1	yes	characteristic
223	C₂	C₂×D₁₁×D₁₆	1	1	yes	characteristic
224	C₂	C₂×D₁₁×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2252	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	#2252	D₁₁
hypocenter	C₁₁	C₂×#2252
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

Complements

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

N	H ≅ G/N	type
2. #13070891	C₂	semidirect
3. #13070890	C₂	semidirect
4. #13070889	C₂	semidirect
7. C₁₁×#2252	C₂	semidirect
47. C₁₆×D₁₁	Q₈	semidirect
73. C₁₁×C₁₆	C₂×Q₈	semidirect
74. C₁₁⋊C₁₆	C₂×Q₈	semidirect
79. #2252	D₁₁	direct (N × H)
159. D₁₁	#2252	direct (N × H)
185. C₁₆	Q₈×D₁₁	semidirect
186. C₁₁	C₂×#2252	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×#500	2
#13070891	2
#13070890	2
#13070889	2
D₁₁×#366	2
C₄×C₁₆×D₁₁	2
C₁₁×#2252	2
C₂×#2252	11

Subgroups — D11×#2252 #14909247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#2252 #14909247