Subgroups — C₁₁×#9823 #14587016

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1990	C₂	1	2	yes	maximal
3	C₁₁×#1956	C₂	1	2	yes	maximal
4	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₁₁×#500	—	2	2	no	—
8	C₁₁×#500	C₄	1	4	yes	complemented
9	C₂×C₁₁×#107	—	2	2	no	—
10	C₂×C₁₁×#107	—	2	2	no	—
11	C₂×C₁₁×#103	—	2	4	no	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#384	C₂²	1	2	yes	—
16	C₁₁×#340	—	2	4	no	—
17	C₈²×C₁₁	—	2	2	no	—
18	C₂²×Q₈×C₁₁	—	2	2	no	—
19	C₂²×C₈×C₁₁	D₄	1	2	yes	—
20	C₂²×C₈×C₁₁	D₄	1	2	yes	—
21	C₂²×C₈×C₁₁	D₄	1	2	yes	—
22	C₁₁×C₄⋊Q₈	—	2	2	no	—
23	C₁₁×C₄⋊Q₈	—	2	2	no	—
24	C₁₁×C₄⋊Q₈	—	2	2	no	—
25	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₁₁×#107	—	2	8	no	—
33	C₁₁×#107	—	4	4	no	—
34	C₁₁×#103	—	4	8	no	—
35	C₄×C₈×C₁₁	—	2	1	no	—
36	C₄×C₈×C₁₁	—	2	1	no	—
37	C₄×C₈×C₁₁	—	2	1	no	—
38	C₄×C₈×C₁₁	—	2	1	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₁	D₄	1	2	yes	—
41	#9823	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×Q₈×C₁₁	—	2	4	no	—
43	C₂×Q₈×C₁₁	—	4	2	no	—
44	C₂×Q₈×C₁₁	—	4	4	no	—
45	C₂×Q₈×C₁₁	—	4	4	no	—
46	C₂²×C₄×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	2	2	no	—
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	—	2	2	no	—
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
56	C₂×C₈×C₁₁	D₈	1	4	yes	—
57	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
58	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
59	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
60	C₁₁×C₄⋊C₄	—	2	4	no	—
61	C₁₁×C₄⋊C₄	—	2	4	no	—
62	C₁₁×C₄⋊C₄	—	4	2	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	4	4	no	—
65	C₁₁×C₄⋊C₄	—	4	4	no	—
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₁	#41	1	1	yes	characteristic
70	C₄²×C₁₁	#41	1	1	yes	characteristic
71	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
72	#1990	C₂×C₁₁	1	2	yes	—
73	#1956	C₂×C₁₁	1	2	yes	—
74	#1845	C₂×C₁₁	1	1	yes	characteristic
75	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
76	C₂³×C₁₁	#127	1	1	yes	characteristic
77	Q₈×C₁₁	—	4	8	no	—
78	Q₈×C₁₁	—	8	4	no	—
79	C₂×C₄×C₁₁	—	4	4	no	—
80	C₂×C₄×C₁₁	—	8	2	no	—
81	C₂×C₄×C₁₁	—	8	2	no	—
82	C₂×C₄×C₁₁	—	8	2	no	—
83	C₂×C₄×C₁₁	—	8	2	no	—
84	C₂×C₄×C₁₁	—	8	2	no	—
85	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
92	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
93	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
94	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₁₁	#135	1	2	yes	—
96	C₂×C₄×C₁₁	#135	1	2	yes	—
97	C₈×C₁₁	—	2	4	no	—
98	C₈×C₁₁	—	2	4	no	—
99	C₈×C₁₁	#103	1	8	yes	complemented
100	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
101	#500	—	2	2	no	—
102	#500	C₄×C₁₁	1	4	yes	complemented
103	C₂×#107	—	2	2	no	—
104	C₂×#107	—	2	2	no	—
105	C₂×#103	—	2	4	no	—
106	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
107	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
108	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
109	#384	C₂²×C₁₁	1	2	yes	—
110	#340	—	2	4	no	—
111	C₈²	—	2	2	no	—
112	C₂²×C₁₁	#390	1	1	yes	characteristic
113	C₂²×C₁₁	#492	1	1	yes	characteristic
114	C₂²×C₁₁	#493	1	1	yes	characteristic
115	C₂²×C₁₁	#494	1	1	yes	characteristic
116	C₂²×C₁₁	#494	1	1	yes	characteristic
117	C₂²×C₁₁	#495	1	1	yes	characteristic
118	C₂²×C₁₁	#495	1	1	yes	characteristic
119	C₄×C₁₁	—	8	4	no	—
120	C₄×C₁₁	—	16	2	no	—
121	C₄×C₁₁	C₂×#103	1	2	yes	—
122	C₄×C₁₁	C₄×D₈	1	2	yes	—
123	C₄×C₁₁	C₄×Q₁₆	1	2	yes	—
124	C₄×C₁₁	#466	1	2	yes	—
125	C₄×C₁₁	#467	1	2	yes	—
126	C₄×C₁₁	#487	1	2	yes	—
127	C₂²×Q₈	—	2	2	no	—
128	C₂²×C₈	D₄×C₁₁	1	2	yes	—
129	C₂²×C₈	D₄×C₁₁	1	2	yes	—
130	C₂²×C₈	D₄×C₁₁	1	2	yes	—
131	C₄⋊Q₈	—	2	2	no	—
132	C₄⋊Q₈	—	2	2	no	—
133	C₄⋊Q₈	—	2	2	no	—
134	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	2	2	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
141	#107	—	2	8	no	—
142	#107	—	4	4	no	—
143	#103	—	4	8	no	—
144	C₄×C₈	—	2	1	no	—
145	C₄×C₈	—	2	1	no	—
146	C₄×C₈	—	2	1	no	—
147	C₄×C₈	—	2	1	no	—
148	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
149	C₄×C₈	D₄×C₁₁	1	2	yes	—
150	C₂×C₁₁	#1706	1	1	yes	characteristic
151	C₂×C₁₁	#1707	1	1	yes	characteristic
152	C₂×C₁₁	#1710	1	1	yes	characteristic
153	C₂×C₁₁	#1713	1	1	yes	characteristic
154	C₂×C₁₁	#1956	1	1	yes	characteristic
155	C₂×C₁₁	#1969	1	1	yes	characteristic
156	C₂×C₁₁	#1970	1	1	yes	characteristic
157	C₂×Q₈	—	2	4	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	4	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
171	C₂×C₈	C₁₁×D₈	1	4	yes	—
172	C₂×C₈	C₁₁×SD₁₆	1	4	yes	—
173	C₂×C₈	C₁₁×Q₁₆	1	4	yes	—
174	C₂×C₈	C₁₁×Q₁₆	1	4	yes	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	4	no	—
180	C₄⋊C₄	—	4	4	no	—
181	C₄⋊C₄	—	4	4	no	—
182	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
183	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
184	C₄²	C₁₁×#41	1	1	yes	characteristic
185	C₄²	C₁₁×#41	1	1	yes	characteristic
186	C₁₁	#9823	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³	C₁₁×#127	1	1	yes	characteristic
188	Q₈	—	4	8	no	—
189	Q₈	—	8	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	2	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
198	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
199	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
200	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
201	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
202	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
203	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
204	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
205	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
206	C₂×C₄	C₁₁×#135	1	2	yes	—
207	C₂×C₄	C₁₁×#135	1	2	yes	—
208	C₈	—	2	4	no	—
209	C₈	—	2	4	no	—
210	C₈	C₁₁×#103	1	8	yes	complemented
211	C₂²	C₁₁×#390	1	1	yes	characteristic
212	C₂²	C₁₁×#492	1	1	yes	characteristic
213	C₂²	C₁₁×#493	1	1	yes	characteristic
214	C₂²	C₁₁×#494	1	1	yes	characteristic
215	C₂²	C₁₁×#494	1	1	yes	characteristic
216	C₂²	C₁₁×#495	1	1	yes	characteristic
217	C₂²	C₁₁×#495	1	1	yes	characteristic
218	C₄	—	8	4	no	—
219	C₄	—	16	2	no	—
220	C₄	C₂×C₁₁×#103	1	2	yes	—
221	C₄	C₄×C₁₁×D₈	1	2	yes	—
222	C₄	C₄×C₁₁×Q₁₆	1	2	yes	—
223	C₄	C₁₁×#466	1	2	yes	—
224	C₄	C₁₁×#467	1	2	yes	—
225	C₄	C₁₁×#487	1	2	yes	—
226	C₂	C₁₁×#1706	1	1	yes	characteristic
227	C₂	C₁₁×#1707	1	1	yes	characteristic
228	C₂	C₁₁×#1710	1	1	yes	characteristic
229	C₂	C₁₁×#1713	1	1	yes	characteristic
230	C₂	C₁₁×#1956	1	1	yes	characteristic
231	C₂	C₁₁×#1969	1	1	yes	characteristic
232	C₂	C₁₁×#1970	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#127
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₁×#500	C₄	semidirect
41. #9823	C₁₁	direct (N × H)
99. C₈×C₁₁	#103	semidirect
102. #500	C₄×C₁₁	semidirect
186. C₁₁	#9823	direct (N × H)
210. C₈	C₁₁×#103	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#500	2
C₁₁×#1990	2
C₁₁×#1956	2
C₁₁×#1845	2
C₂×C₈²×C₁₁	2
#9823	11

Subgroups — C11×#9823 #14587016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#9823 #14587016