Subgroups — D₁₁×#446 #13077539

Order 1408.

400 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622637	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	D₁₁×C₄⋊C₈	C₂	1	2	yes	maximal
6	#10622444	C₂	1	1	yes	maximal, characteristic, complemented
7	#10622441	C₂	1	2	yes	maximal, complemented
8	D₁₁×#97	C₂	1	2	yes	maximal
9	#10622314	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
11	#10622292	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₁₁	C₄	1	1	yes	characteristic
13	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	Q₈×Dic₁₁	C₄	1	1	yes	characteristic
15	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₁₁	C₂²	1	2	yes	—
17	C₂×C₈×D₁₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×D₁₁	C₄	1	2	yes	—
19	C₄⋊C₄×D₁₁	C₄	1	1	yes	characteristic
20	#66940	C₄	1	1	yes	characteristic
21	#66940	C₄	1	2	yes	—
22	C₄²×D₁₁	C₂²	1	1	yes	characteristic
23	C₄²×D₁₁	C₂²	1	2	yes	—
24	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
25	C₄×Dic₂₂	C₂²	1	2	yes	—
26	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
27	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₁×#97	C₂²	1	2	yes	—
29	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	#66879	C₂²	1	2	yes	—
31	#66879	C₂²	1	2	yes	—
32	Dic₁₁⋊C₈	C₂²	1	2	yes	—
33	Dic₁₁⋊C₈	C₂²	1	2	yes	—
34	Dic₁₁⋊C₈	C₂²	1	2	yes	—
35	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
37	C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
38	C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
39	#66867	C₂²	1	2	yes	—
40	C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	Q₈×D₁₁	—	2	4	no	—
43	C₂×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₁₁	C₂×C₄	1	2	yes	—
45	C₂×C₄×D₁₁	C₂×C₄	1	2	yes	—
46	C₂×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
48	C₂×Dic₂₂	C₂×C₄	1	2	yes	—
49	C₂×Dic₂₂	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₂³	1	2	yes	—
52	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₄²×C₁₁	C₂³	1	2	yes	—
57	C₄⋊Dic₁₁	C₂×C₄	1	2	yes	—
58	C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
59	Dic₁₁⋊C₄	C₂×C₄	1	2	yes	—
60	Dic₁₁⋊C₄	C₂×C₄	1	2	yes	—
61	Dic₁₁⋊C₄	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₁	C₂×C₄	1	2	yes	—
63	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₁	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
67	C₄×Dic₁₁	C₂³	1	2	yes	—
68	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
70	C₂×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
71	C₈×D₁₁	—	2	2	no	—
72	C₈×D₁₁	—	2	4	no	—
73	C₈×D₁₁	Q₈	1	4	yes	complemented
74	C₂×#446	—	11	1	no	maximal, Sylow
75	C₂²×D₁₁	C₂²×C₄	1	1	yes	characteristic
76	Q₈×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
82	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
84	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
85	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₄×D₁₁	—	2	4	no	—
88	C₄×D₁₁	—	2	2	no	—
89	C₄×D₁₁	—	2	4	no	—
90	C₄×D₁₁	M₁₆	1	4	yes	—
91	C₄×D₁₁	C₂×Q₈	1	2	yes	—
92	C₄×D₁₁	#41	1	2	yes	—
93	Dic₂₂	—	2	2	no	—
94	Dic₂₂	—	2	4	no	—
95	C₈×C₁₁	—	2	1	no	—
96	C₈×C₁₁	—	2	2	no	—
97	C₈×C₁₁	C₂×Q₈	1	2	yes	complemented
98	C₁₁⋊C₈	—	2	1	no	—
99	C₁₁⋊C₈	—	2	2	no	—
100	C₁₁⋊C₈	C₂×Q₈	1	2	yes	complemented
101	C₂×C₄×Q₈	—	11	1	no	—
102	#446	—	11	1	no	—
103	#446	—	11	2	no	—
104	#446	—	11	1	no	—
105	#446	—	11	2	no	—
106	#446	—	11	1	no	—
107	#446	D₁₁	1	1	yes	characteristic, direct product factor
108	C₂×C₄⋊C₈	—	11	1	no	—
109	C₂×C₄⋊C₈	—	11	2	no	—
110	C₂×#97	—	11	2	no	—
111	C₂×C₄×C₈	—	11	1	no	—
112	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
113	C₂×D₁₁	C₄×Q₈	1	2	yes	—
114	C₂×D₁₁	C₂×M₁₆	1	2	yes	—
115	C₂×D₁₁	#131	1	2	yes	—
116	C₄×C₁₁	—	2	2	no	—
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	2	2	no	—
119	C₄×C₁₁	C₂×M₁₆	1	2	yes	—
120	C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
121	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
122	Dic₁₁	—	2	2	no	—
123	Dic₁₁	—	2	1	no	—
124	Dic₁₁	—	2	2	no	—
125	Dic₁₁	C₄×Q₈	1	2	yes	—
126	Dic₁₁	C₂×M₁₆	1	2	yes	—
127	C₂²×Q₈	—	11	1	no	—
128	C₂²×C₈	—	11	1	no	—
129	C₂²×C₈	—	11	1	no	—
130	C₂²×C₈	—	11	2	no	—
131	C₄×Q₈	—	11	1	no	—
132	C₄×Q₈	—	11	2	no	—
133	C₄×Q₈	—	11	1	no	—
134	C₄×Q₈	—	11	2	no	—
135	C₄×Q₈	—	11	1	no	—
136	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
137	C₂×C₄⋊C₄	—	11	1	no	—
138	C₂×C₄⋊C₄	—	11	2	no	—
139	C₂×C₄²	—	11	1	no	—
140	C₂×C₄²	—	11	2	no	—
141	C₄⋊C₈	—	11	2	no	—
142	C₄⋊C₈	—	11	2	no	—
143	C₄⋊C₈	—	11	2	no	—
144	C₄⋊C₈	—	11	1	no	—
145	C₄⋊C₈	—	11	2	no	—
146	C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
147	C₄⋊C₈	C₂×D₁₁	1	2	yes	—
148	#97	—	11	2	no	—
149	#97	—	11	2	no	—
150	#97	—	11	2	no	—
151	#97	C₂×D₁₁	1	2	yes	—
152	C₄×C₈	—	11	1	no	—
153	C₄×C₈	—	11	1	no	—
154	C₄×C₈	—	11	1	no	—
155	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
156	C₂×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
157	C₂×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
158	C₂×C₁₁	C₂×#131	1	1	yes	characteristic
159	D₁₁	#446	1	4	yes	direct product factor
160	C₂×Q₈	—	11	2	no	—
161	C₂×Q₈	—	11	1	no	—
162	C₂×Q₈	—	22	4	no	—
163	C₂×Q₈	C₄×D₁₁	1	1	yes	characteristic
164	C₂²×C₄	—	11	1	no	—
165	C₂²×C₄	—	11	1	no	—
166	C₂²×C₄	—	11	1	no	—
167	C₂²×C₄	—	11	2	no	—
168	C₂²×C₄	—	11	2	no	—
169	C₂×C₈	—	11	1	no	—
170	C₂×C₈	—	11	4	no	—
171	C₂×C₈	—	11	1	no	—
172	C₂×C₈	—	11	2	no	—
173	C₂×C₈	—	22	2	no	—
174	C₂×C₈	—	22	4	no	—
175	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
176	C₂×C₈	C₂²×D₁₁	1	2	yes	—
177	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
178	C₄⋊C₄	—	11	2	no	—
179	C₄⋊C₄	—	11	2	no	—
180	C₄⋊C₄	—	11	2	no	—
181	C₄⋊C₄	—	11	2	no	—
182	C₄⋊C₄	—	11	1	no	—
183	C₄⋊C₄	C₄×D₁₁	1	2	yes	—
184	C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
185	C₄²	—	11	1	no	—
186	C₄²	—	11	2	no	—
187	C₄²	—	11	1	no	—
188	C₄²	—	11	2	no	—
189	C₄²	—	11	1	no	—
190	C₄²	—	11	2	no	—
191	C₄²	C₂²×D₁₁	1	1	yes	characteristic
192	C₄²	C₂²×D₁₁	1	2	yes	—
193	C₁₁	C₂×#446	1	1	yes	characteristic, complemented, Sylow
194	C₂³	—	11	1	no	—
195	Q₈	—	2	2	no	—
196	Q₈	—	22	4	no	—
197	Q₈	—	22	2	no	—
198	C₂×C₄	—	11	1	no	—
199	C₂×C₄	—	11	1	no	—
200	C₂×C₄	—	11	4	no	—
201	C₂×C₄	—	11	2	no	—
202	C₂×C₄	—	11	2	no	—
203	C₂×C₄	—	11	1	no	—
204	C₂×C₄	—	11	2	no	—
205	C₂×C₄	—	11	2	no	—
206	C₂×C₄	—	22	4	no	—
207	C₂×C₄	—	22	2	no	—
208	C₂×C₄	—	22	4	no	—
209	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
210	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
211	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
212	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
213	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
214	C₈	—	2	1	no	—
215	C₈	—	2	2	no	—
216	C₈	—	11	2	no	—
217	C₈	—	22	1	no	—
218	C₈	—	22	2	no	—
219	C₈	Q₈×D₁₁	1	2	yes	complemented
220	C₂²	—	11	2	no	—
221	C₂²	—	11	2	no	—
222	C₂²	—	11	2	no	—
223	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	2	no	—
227	C₄	—	11	2	no	—
228	C₄	—	11	2	no	—
229	C₄	—	22	2	no	—
230	C₄	—	22	1	no	—
231	C₄	—	22	2	no	—
232	C₄	M₁₆×D₁₁	1	2	yes	—
233	C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
234	C₄	#41×D₁₁	1	1	yes	characteristic
235	C₂	—	11	4	no	—
236	C₂	C₄×Q₈×D₁₁	1	1	yes	characteristic
237	C₂	C₂×M₁₆×D₁₁	1	1	yes	characteristic
238	C₂	D₁₁×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#446	C₂
prime radical	C₂²×D₁₁	C₂²×C₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#446	D₁₁
hypocenter	C₁₁	C₂×#446
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₁₁×#446	C₂	semidirect
3. #10622637	C₂	semidirect
6. #10622444	C₂	semidirect
7. #10622441	C₂	semidirect
9. #10622314	C₂	semidirect
11. #10622292	C₂	semidirect
73. C₈×D₁₁	Q₈	semidirect
97. C₈×C₁₁	C₂×Q₈	semidirect
100. C₁₁⋊C₈	C₂×Q₈	semidirect
107. #446	D₁₁	direct (N × H)
159. D₁₁	#446	direct (N × H)
193. C₁₁	C₂×#446	semidirect
219. C₈	Q₈×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×D₁₁	2
C₁₁×#446	2
#10622637	2
D₁₁×C₄⋊C₈	2
#10622444	2
#10622441	2
D₁₁×#97	2
#10622314	2
C₄×C₈×D₁₁	2
#10622292	2
C₂×#446	11

Subgroups — D11×#446 #13077539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#446 #13077539