Subgroups — D₁₁×#475 #13078377

Order 1408.

416 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622707	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622633	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₁×#106	C₂	1	2	yes	maximal
7	#10622467	C₂	1	2	yes	maximal, complemented
8	#10622464	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
10	D₁₁×#103	C₂	1	2	yes	maximal
11	#10622404	C₂	1	2	yes	maximal, complemented
12	C₂×Q₈×D₁₁	—	2	1	no	—
13	C₂×Q₈×D₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
16	Q₈×Dic₁₁	C₂²	1	1	yes	characteristic
17	#66997	—	2	1	no	—
18	C₂×C₈×D₁₁	C₂²	1	2	yes	—
19	C₄⋊C₄×D₁₁	—	2	1	no	—
20	C₄⋊C₄×D₁₁	—	2	1	no	—
21	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×D₁₁	C₂²	1	2	yes	—
23	#66941	—	2	1	no	—
24	#66941	C₂²	1	2	yes	—
25	#66940	—	2	1	no	—
26	#66940	C₂²	1	1	yes	characteristic
27	C₄²×D₁₁	—	2	1	no	—
28	C₄²×D₁₁	C₂²	1	1	yes	characteristic
29	#66922	C₂²	1	1	yes	characteristic
30	C₄×Dic₂₂	—	2	1	no	—
31	C₄×Dic₂₂	C₂²	1	1	yes	characteristic
32	C₁₁×#106	C₂²	1	2	yes	—
33	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₁×#103	C₂²	1	2	yes	—
35	#66899	C₂²	1	2	yes	—
36	#66881	C₂²	1	2	yes	—
37	#66880	C₂²	1	2	yes	—
38	Dic₁₁⋊C₈	C₂²	1	2	yes	—
39	#66874	C₂²	1	2	yes	—
40	#66872	C₂²	1	2	yes	—
41	#66872	C₂²	1	2	yes	—
42	C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₁	—	2	1	no	—
44	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
45	Q₈×D₁₁	—	2	2	no	—
46	Q₈×D₁₁	—	4	4	no	—
47	Q₈×D₁₁	Q₈	1	4	yes	complemented
48	C₂×C₄×D₁₁	—	2	1	no	—
49	C₂×C₄×D₁₁	—	2	1	no	—
50	C₂×C₄×D₁₁	—	2	2	no	—
51	C₂×C₄×D₁₁	D₄	1	1	yes	characteristic
52	C₂×C₄×D₁₁	D₄	1	1	yes	characteristic
53	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
54	C₂×Dic₂₂	—	2	1	no	—
55	C₂×Dic₂₂	—	2	2	no	—
56	C₂×Dic₂₂	—	2	1	no	—
57	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂³	1	2	yes	—
59	C₁₁×C₄⋊C₄	—	2	1	no	—
60	C₁₁×C₄⋊C₄	—	2	1	no	—
61	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
63	C₄²×C₁₁	—	2	1	no	—
64	C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₄⋊Dic₁₁	—	2	1	no	—
66	C₄⋊Dic₁₁	—	2	1	no	—
67	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
68	C₄⋊Dic₁₁	C₂³	1	2	yes	—
69	Dic₁₁⋊C₄	—	2	1	no	—
70	Dic₁₁⋊C₄	—	2	1	no	—
71	Dic₁₁⋊C₄	—	2	2	no	—
72	Dic₁₁⋊C₄	—	2	2	no	—
73	Dic₁₁⋊C₄	—	2	1	no	—
74	C₄×Dic₁₁	—	2	1	no	—
75	C₄×Dic₁₁	—	2	1	no	—
76	C₄×Dic₁₁	—	2	1	no	—
77	C₄×Dic₁₁	D₄	1	1	yes	characteristic
78	C₄×Dic₁₁	D₄	1	1	yes	characteristic
79	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
80	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
81	C₈×D₁₁	—	2	4	no	—
82	C₂×#475	—	11	1	no	maximal, Sylow
83	C₂²×D₁₁	C₂×D₄	1	1	yes	characteristic
84	Q₈×C₁₁	—	2	1	no	—
85	Q₈×C₁₁	—	4	2	no	—
86	Q₈×C₁₁	C₂×Q₈	1	2	yes	complemented
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
93	C₂×Dic₁₁	—	2	1	no	—
94	C₂×Dic₁₁	—	2	1	no	—
95	C₂×Dic₁₁	—	2	2	no	—
96	C₂×Dic₁₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₁₁	C₂×D₄	1	1	yes	characteristic
99	C₄×D₁₁	—	2	4	no	—
100	C₄×D₁₁	—	2	2	no	—
101	C₄×D₁₁	—	4	4	no	—
102	C₄×D₁₁	—	4	2	no	—
103	C₄×D₁₁	SD₁₆	1	4	yes	—
104	C₄×D₁₁	C₂×Q₈	1	2	yes	—
105	C₄×D₁₁	#41	1	2	yes	—
106	Dic₂₂	—	2	1	no	—
107	Dic₂₂	—	2	4	no	—
108	Dic₂₂	—	4	2	no	—
109	Dic₂₂	—	4	4	no	—
110	Dic₂₂	C₂×Q₈	1	2	yes	complemented
111	C₈×C₁₁	—	2	2	no	—
112	C₁₁⋊C₈	—	2	2	no	—
113	C₂×C₄⋊Q₈	—	11	1	no	—
114	C₂×C₄×Q₈	—	11	1	no	—
115	#475	—	11	1	no	—
116	#475	—	11	1	no	—
117	#475	—	11	2	no	—
118	#475	—	11	1	no	—
119	#475	—	11	2	no	—
120	#475	D₁₁	1	1	yes	characteristic, direct product factor
121	C₂×#106	—	11	2	no	—
122	C₂×C₄⋊C₈	—	11	1	no	—
123	C₂×#103	—	11	2	no	—
124	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
125	C₂×D₁₁	C₂²⋊Q₈	1	2	yes	—
126	C₂×D₁₁	C₂×SD₁₆	1	2	yes	—
127	C₂×D₁₁	#137	1	2	yes	—
128	C₄×C₁₁	—	2	2	no	—
129	C₄×C₁₁	—	2	1	no	—
130	C₄×C₁₁	—	4	2	no	—
131	C₄×C₁₁	—	4	1	no	—
132	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
133	C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
134	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
135	Dic₁₁	—	2	2	no	—
136	Dic₁₁	—	2	1	no	—
137	Dic₁₁	—	4	2	no	—
138	Dic₁₁	—	4	1	no	—
139	Dic₁₁	C₂²⋊Q₈	1	2	yes	—
140	Dic₁₁	C₂×SD₁₆	1	2	yes	—
141	C₂²×Q₈	—	11	1	no	—
142	C₂²×Q₈	—	22	1	no	—
143	C₂²×C₈	—	11	2	no	—
144	C₄⋊Q₈	—	11	2	no	—
145	C₄⋊Q₈	—	11	1	no	—
146	C₄⋊Q₈	—	22	1	no	—
147	C₄⋊Q₈	—	22	1	no	—
148	C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
149	C₄×Q₈	—	11	1	no	—
150	C₄×Q₈	—	11	1	no	—
151	C₄×Q₈	—	11	1	no	—
152	C₄×Q₈	—	22	1	no	—
153	C₄×Q₈	—	22	1	no	—
154	C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
155	C₂×C₄⋊C₄	—	11	1	no	—
156	C₂×C₄⋊C₄	—	11	2	no	—
157	C₂×C₄⋊C₄	—	22	1	no	—
158	C₂×C₄⋊C₄	—	22	1	no	—
159	C₂×C₄²	—	11	1	no	—
160	C₂×C₄²	—	22	1	no	—
161	#106	—	11	2	no	—
162	#106	—	11	2	no	—
163	#106	—	11	2	no	—
164	#106	C₂×D₁₁	1	2	yes	—
165	C₄⋊C₈	—	11	2	no	—
166	C₄⋊C₈	—	11	1	no	—
167	C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
168	#103	—	11	2	no	—
169	#103	—	11	2	no	—
170	#103	—	11	2	no	—
171	#103	C₂×D₁₁	1	2	yes	—
172	C₂×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
174	C₂×C₁₁	C₂×#137	1	1	yes	characteristic
175	D₁₁	#475	1	4	yes	direct product factor
176	C₂×Q₈	—	2	1	no	—
177	C₂×Q₈	—	11	4	no	—
178	C₂×Q₈	—	11	1	no	—
179	C₂×Q₈	—	22	1	no	—
180	C₂×Q₈	—	22	2	no	—
181	C₂×Q₈	—	22	2	no	—
182	C₂×Q₈	—	22	1	no	—
183	C₂×Q₈	—	44	4	no	—
184	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
185	C₂²×C₄	—	11	1	no	—
186	C₂²×C₄	—	11	1	no	—
187	C₂²×C₄	—	11	1	no	—
188	C₂²×C₄	—	22	1	no	—
189	C₂²×C₄	—	22	1	no	—
190	C₂²×C₄	—	22	2	no	—
191	C₂×C₈	—	11	2	no	—
192	C₂×C₈	—	22	4	no	—
193	C₂×C₈	C₂²×D₁₁	1	2	yes	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	2	1	no	—
196	C₄⋊C₄	—	11	2	no	—
197	C₄⋊C₄	—	11	1	no	—
198	C₄⋊C₄	—	22	1	no	—
199	C₄⋊C₄	—	22	2	no	—
200	C₄⋊C₄	—	22	1	no	—
201	C₄⋊C₄	—	22	1	no	—
202	C₄⋊C₄	—	22	2	no	—
203	C₄⋊C₄	—	22	1	no	—
204	C₄⋊C₄	—	22	1	no	—
205	C₄⋊C₄	C₂²×D₁₁	1	2	yes	—
206	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
207	C₄²	—	2	1	no	—
208	C₄²	—	11	1	no	—
209	C₄²	—	11	1	no	—
210	C₄²	—	11	1	no	—
211	C₄²	—	22	1	no	—
212	C₄²	—	22	1	no	—
213	C₄²	—	22	1	no	—
214	C₄²	C₂²×D₁₁	1	1	yes	characteristic
215	C₁₁	C₂×#475	1	1	yes	characteristic, complemented, Sylow
216	C₂³	—	11	1	no	—
217	Q₈	—	2	1	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	11	2	no	—
220	Q₈	—	22	4	no	—
221	Q₈	—	22	1	no	—
222	Q₈	—	44	4	no	—
223	Q₈	—	44	2	no	—
224	Q₈	Q₈×D₁₁	1	2	yes	complemented
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	11	1	no	—
229	C₂×C₄	—	11	1	no	—
230	C₂×C₄	—	11	4	no	—
231	C₂×C₄	—	11	2	no	—
232	C₂×C₄	—	11	2	no	—
233	C₂×C₄	—	11	1	no	—
234	C₂×C₄	—	22	2	no	—
235	C₂×C₄	—	22	4	no	—
236	C₂×C₄	—	22	1	no	—
237	C₂×C₄	—	22	1	no	—
238	C₂×C₄	—	22	2	no	—
239	C₂×C₄	—	44	4	no	—
240	C₂×C₄	—	44	2	no	—
241	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
242	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
243	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
244	C₈	—	2	2	no	—
245	C₈	—	22	2	no	—
246	C₂²	—	11	2	no	—
247	C₂²	—	11	2	no	—
248	C₂²	—	11	2	no	—
249	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	2	no	—
252	C₄	—	4	2	no	—
253	C₄	—	4	1	no	—
254	C₄	—	11	2	no	—
255	C₄	—	11	2	no	—
256	C₄	—	22	1	no	—
257	C₄	—	22	2	no	—
258	C₄	—	44	2	no	—
259	C₄	—	44	1	no	—
260	C₄	SD₁₆×D₁₁	1	2	yes	—
261	C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
262	C₄	#41×D₁₁	1	1	yes	characteristic
263	C₂	—	11	4	no	—
264	C₂	D₁₁×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂	C₂×SD₁₆×D₁₁	1	1	yes	characteristic
266	C₂	D₁₁×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₁
commutator, cosocle	C₂×C₄×C₁₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₁
Fitting	C₁₁×#475	C₂
socle	C₂²×C₁₁	C₂²×D₄
prime radical	C₂²×D₁₁	C₂×D₄
hypercenter	#475	D₁₁
hypocenter	C₁₁	C₂×#475
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

Complements

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

N	H ≅ G/N	type
3. C₁₁×#475	C₂	semidirect
4. #10622707	C₂	semidirect
5. #10622633	C₂	semidirect
7. #10622467	C₂	semidirect
8. #10622464	C₂	semidirect
11. #10622404	C₂	semidirect
47. Q₈×D₁₁	Q₈	semidirect
86. Q₈×C₁₁	C₂×Q₈	semidirect
110. Dic₂₂	C₂×Q₈	semidirect
120. #475	D₁₁	direct (N × H)
175. D₁₁	#475	direct (N × H)
215. C₁₁	C₂×#475	semidirect
224. Q₈	Q₈×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×C₄⋊Q₈	2
C₄×Q₈×D₁₁	2
C₁₁×#475	2
#10622707	2
#10622633	2
D₁₁×#106	2
#10622467	2
#10622464	2
D₁₁×C₄⋊C₈	2
D₁₁×#103	2
#10622404	2
C₂×#475	11

Subgroups — D11×#475 #13078377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#475 #13078377