Subgroups — C₁₁×#3373 #13066211

Order 1408.

384 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#489	C₂	1	2	yes	maximal, complemented
4	C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#476	C₂	1	2	yes	maximal, complemented
6	C₁₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#463	C₂	1	2	yes	maximal, complemented
8	C₁₁×#459	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#442	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₁	—	2	1	no	—
13	C₂×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×D₈	C₂²	1	2	yes	—
15	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₁₁×#127	C₂²	1	1	yes	characteristic
18	C₁₁×#124	—	2	1	no	—
19	C₁₁×#124	C₂²	1	2	yes	—
20	C₁₁×#123	—	2	2	no	—
21	C₁₁×C₂²⋊Q₈	—	2	1	no	—
22	C₁₁×C₂²⋊Q₈	—	2	2	no	—
23	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₁₁	—	2	1	no	—
26	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₁₁	C₂²	1	2	yes	—
28	C₄×D₄×C₁₁	C₂²	1	2	yes	—
29	C₁₁×#106	C₂²	1	1	yes	characteristic
30	C₁₁×#106	C₂²	1	2	yes	—
31	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
33	C₁₁×#103	C₂²	1	1	yes	characteristic
34	C₁₁×#103	C₂²	1	2	yes	—
35	C₁₁×#102	C₂²	1	2	yes	—
36	C₁₁×#102	C₂²	1	2	yes	—
37	C₁₁×#102	C₂²	1	1	yes	characteristic
38	C₁₁×#102	C₂²	1	2	yes	—
39	C₁₁×#97	C₂²	1	2	yes	—
40	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₁₁	—	2	2	no	—
42	C₂×Q₈×C₁₁	—	2	1	no	—
43	C₂×Q₈×C₁₁	—	4	4	no	—
44	C₂×Q₈×C₁₁	D₄	1	1	yes	characteristic
45	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₁₁	—	2	1	no	—
47	C₂×D₄×C₁₁	—	2	1	no	—
48	C₂×D₄×C₁₁	C₂³	1	2	yes	—
49	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	—	2	2	no	—
51	C₂²×C₄×C₁₁	—	2	1	no	—
52	C₂²×C₄×C₁₁	—	2	2	no	—
53	C₁₁×SD₁₆	—	2	2	no	—
54	C₁₁×D₈	—	2	4	no	—
55	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂³	1	2	yes	—
58	C₁₁×C₄⋊C₄	—	2	1	no	—
59	C₁₁×C₄⋊C₄	—	2	2	no	—
60	C₁₁×C₄⋊C₄	—	2	1	no	—
61	C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	D₄	1	2	yes	—
63	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
64	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₁₁×C₂²⋊C₄	—	2	2	no	—
67	C₁₁×C₂²⋊C₄	—	2	2	no	—
68	C₁₁×C₂²⋊C₄	—	2	1	no	—
69	C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₄²×C₁₁	—	2	1	no	—
72	C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₄²×C₁₁	C₂³	1	2	yes	—
74	#3373	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂³×C₁₁	—	2	1	no	—
76	C₂³×C₁₁	—	2	2	no	—
77	Q₈×C₁₁	—	2	2	no	—
78	Q₈×C₁₁	—	2	1	no	—
79	Q₈×C₁₁	—	2	1	no	—
80	Q₈×C₁₁	—	4	4	no	—
81	Q₈×C₁₁	—	4	2	no	—
82	D₄×C₁₁	—	2	2	no	—
83	D₄×C₁₁	—	2	1	no	—
84	D₄×C₁₁	—	2	2	no	—
85	D₄×C₁₁	—	4	2	no	—
86	D₄×C₁₁	—	8	1	no	—
87	D₄×C₁₁	#41	1	2	yes	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	4	4	no	—
93	C₂×C₄×C₁₁	—	4	2	no	—
94	C₂×C₄×C₁₁	—	8	2	no	—
95	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
96	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₈×C₁₁	—	2	2	no	—
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	—	2	1	no	—
103	#559	C₂×C₁₁	1	1	yes	characteristic, complemented
104	D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
105	#489	C₂×C₁₁	1	2	yes	complemented
106	#486	C₂×C₁₁	1	1	yes	characteristic, complemented
107	#476	C₂×C₁₁	1	2	yes	complemented
108	#475	C₂×C₁₁	1	1	yes	characteristic, complemented
109	#463	C₂×C₁₁	1	2	yes	complemented
110	#459	C₂×C₁₁	1	1	yes	characteristic
111	#446	C₂×C₁₁	1	1	yes	characteristic, complemented
112	#442	C₂×C₁₁	1	2	yes	complemented
113	C₄×SD₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
114	C₂²×C₁₁	—	2	2	no	—
115	C₂²×C₁₁	—	4	1	no	—
116	C₂²×C₁₁	—	4	1	no	—
117	C₂²×C₁₁	—	4	2	no	—
118	C₂²×C₁₁	—	4	2	no	—
119	C₂²×C₁₁	—	4	2	no	—
120	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
121	C₄×C₁₁	—	2	2	no	—
122	C₄×C₁₁	—	2	2	no	—
123	C₄×C₁₁	—	2	1	no	—
124	C₄×C₁₁	—	4	1	no	—
125	C₄×C₁₁	—	4	2	no	—
126	C₄×C₁₁	—	4	1	no	—
127	C₄×C₁₁	—	4	1	no	—
128	C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
129	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
130	C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
131	C₂²×Q₈	—	2	1	no	—
132	C₂×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
133	C₂×D₈	C₂²×C₁₁	1	2	yes	—
134	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
135	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
136	#127	C₂²×C₁₁	1	1	yes	characteristic
137	#124	—	2	1	no	—
138	#124	C₂²×C₁₁	1	2	yes	—
139	#123	—	2	2	no	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
143	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
144	C₄×D₄	—	2	1	no	—
145	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
146	C₄×D₄	C₂²×C₁₁	1	2	yes	—
147	C₄×D₄	C₂²×C₁₁	1	2	yes	—
148	#106	C₂²×C₁₁	1	1	yes	characteristic
149	#106	C₂²×C₁₁	1	2	yes	—
150	C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
151	C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
152	#103	C₂²×C₁₁	1	1	yes	characteristic
153	#103	C₂²×C₁₁	1	2	yes	—
154	#102	C₂²×C₁₁	1	1	yes	characteristic
155	#102	C₂²×C₁₁	1	2	yes	—
156	#102	C₂²×C₁₁	1	2	yes	—
157	#102	C₂²×C₁₁	1	2	yes	—
158	#97	C₂²×C₁₁	1	2	yes	—
159	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
160	C₂×C₁₁	—	4	2	no	—
161	C₂×C₁₁	—	8	2	no	—
162	C₂×C₁₁	#548	1	1	yes	characteristic
163	C₂×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₁₁	#577	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	4	4	no	—
168	C₂×Q₈	D₄×C₁₁	1	1	yes	characteristic
169	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
170	C₂×D₄	—	2	1	no	—
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	C₂³×C₁₁	1	2	yes	—
173	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	2	2	no	—
177	SD₁₆	—	2	2	no	—
178	D₈	—	2	4	no	—
179	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
180	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂³×C₁₁	1	2	yes	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
186	C₄⋊C₄	D₄×C₁₁	1	2	yes	—
187	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
188	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
189	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	2	no	—
192	C₂²⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	2	no	—
194	C₂²⋊C₄	—	2	2	no	—
195	C₄²	—	2	1	no	—
196	C₄²	C₂³×C₁₁	1	1	yes	characteristic
197	C₄²	C₂³×C₁₁	1	2	yes	—
198	C₁₁	#3373	1	1	yes	characteristic, direct product factor, Sylow
199	C₂³	—	2	1	no	—
200	C₂³	—	2	2	no	—
201	Q₈	—	2	2	no	—
202	Q₈	—	2	1	no	—
203	Q₈	—	2	1	no	—
204	Q₈	—	4	4	no	—
205	Q₈	—	4	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	2	1	no	—
208	D₄	—	2	2	no	—
209	D₄	—	4	2	no	—
210	D₄	—	8	1	no	—
211	D₄	C₁₁×#41	1	2	yes	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
220	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
221	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
222	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
223	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	2	no	—
231	C₂²	—	4	2	no	—
232	C₂²	—	4	2	no	—
233	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	1	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	1	no	—
240	C₄	—	4	1	no	—
241	C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
242	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
243	C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
244	C₂	—	4	2	no	—
245	C₂	—	8	2	no	—
246	C₂	C₁₁×#548	1	1	yes	characteristic
247	C₂	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂	C₁₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#559	C₂	semidirect
2. D₄×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#489	C₂	semidirect
4. C₁₁×#486	C₂	semidirect
5. C₁₁×#476	C₂	semidirect
6. C₁₁×#475	C₂	semidirect
7. C₁₁×#463	C₂	semidirect
9. C₁₁×#446	C₂	semidirect
10. C₁₁×#442	C₂	semidirect
11. C₄×C₁₁×SD₁₆	C₂	semidirect
74. #3373	C₁₁	direct (N × H)
103. #559	C₂×C₁₁	semidirect
104. D₄×Q₈	C₂×C₁₁	semidirect
105. #489	C₂×C₁₁	semidirect
106. #486	C₂×C₁₁	semidirect
107. #476	C₂×C₁₁	semidirect
108. #475	C₂×C₁₁	semidirect
109. #463	C₂×C₁₁	semidirect
111. #446	C₂×C₁₁	semidirect
112. #442	C₂×C₁₁	semidirect
113. C₄×SD₁₆	C₂×C₁₁	semidirect
198. C₁₁	#3373	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×#559	2
D₄×Q₈×C₁₁	2
C₁₁×#489	2
C₁₁×#486	2
C₁₁×#476	2
C₁₁×#475	2
C₁₁×#463	2
C₁₁×#459	2
C₁₁×#446	2
C₁₁×#442	2
C₄×C₁₁×SD₁₆	2
#3373	11

Subgroups — C11×#3373 #13066211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3373 #13066211