Subgroups — C₁₁×#13203 #14590396

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#358	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×Q₁₆	—	2	1	no	—
6	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
7	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
8	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₁₁×#494	—	2	2	no	—
10	C₁₁×#494	C₄	1	4	yes	complemented
11	C₂×C₁₁×#107	—	2	1	no	—
12	C₂×C₁₁×#107	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#384	—	2	1	no	—
15	C₁₁×#358	—	2	8	no	—
16	C₄×C₁₁×C₁₆	—	2	2	no	—
17	C₂²×Q₈×C₁₁	—	2	2	no	—
18	C₂×C₁₁×Q₁₆	—	2	4	no	—
19	C₂×C₁₁×Q₁₆	—	2	4	no	—
20	C₂×C₁₁×Q₁₆	—	2	2	no	—
21	C₂×C₁₁×Q₁₆	—	2	4	no	—
22	C₂×C₁₁×Q₁₆	—	4	2	no	—
23	C₂×C₁₁×Q₁₆	—	4	2	no	—
24	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	—	2	4	no	—
28	C₁₁×C₄⋊Q₈	—	4	2	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
31	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₁₁×C₁₆	—	2	2	no	—
34	C₂×C₁₁×C₁₆	—	2	2	no	—
35	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
36	C₁₁×#107	—	2	4	no	—
37	C₁₁×#107	—	4	2	no	—
38	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₁	D₄	1	2	yes	—
40	#13203	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₁	—	2	4	no	—
42	C₂×Q₈×C₁₁	—	4	2	no	—
43	C₂×Q₈×C₁₁	—	4	2	no	—
44	C₂×Q₈×C₁₁	—	4	2	no	—
45	C₂×Q₈×C₁₁	—	4	2	no	—
46	C₂×Q₈×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	—	4	2	no	—
49	C₂²×C₄×C₁₁	D₈	1	2	yes	—
50	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
51	C₁₁×Q₁₆	—	2	8	no	—
52	C₁₁×Q₁₆	—	4	8	no	—
53	C₁₁×Q₁₆	—	4	4	no	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₁	D₈	1	2	yes	—
56	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₁	#41	1	2	yes	—
61	C₁₁×C₄⋊C₄	—	4	8	no	—
62	C₁₁×C₄⋊C₄	—	4	2	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	8	4	no	—
65	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₁₁	SD₁₆	1	2	yes	—
67	C₁₁×C₁₆	—	2	4	no	—
68	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
69	C₂×#358	C₂×C₁₁	1	4	yes	—
70	C₂×C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic
71	#1845	C₂×C₁₁	1	1	yes	characteristic
72	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₁₁	—	4	4	no	—
74	Q₈×C₁₁	—	4	4	no	—
75	Q₈×C₁₁	—	8	2	no	—
76	Q₈×C₁₁	—	8	2	no	—
77	C₂×C₄×C₁₁	—	4	4	no	—
78	C₂×C₄×C₁₁	—	8	2	no	—
79	C₂×C₄×C₁₁	—	8	2	no	—
80	C₂×C₄×C₁₁	—	8	2	no	—
81	C₂×C₄×C₁₁	—	8	4	no	—
82	C₂×C₄×C₁₁	#102	1	4	yes	—
83	C₂×C₄×C₁₁	SD₃₂	1	4	yes	—
84	C₂×C₄×C₁₁	Q₃₂	1	4	yes	—
85	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
91	C₈×C₁₁	#102	1	4	yes	—
92	C₈×C₁₁	C₄×D₄	1	2	yes	—
93	C₈×C₁₁	#121	1	2	yes	—
94	C₂²×Q₁₆	—	2	1	no	—
95	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
96	C₂×C₄⋊Q₈	—	2	1	no	—
97	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
98	#494	—	2	2	no	—
99	#494	C₄×C₁₁	1	4	yes	complemented
100	C₂×#107	—	2	1	no	—
101	C₂×#107	C₂²×C₁₁	1	2	yes	—
102	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
103	#384	—	2	1	no	—
104	#358	—	2	8	no	—
105	C₄×C₁₆	—	2	2	no	—
106	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
107	C₂²×C₁₁	#486	1	1	yes	characteristic
108	C₂²×C₁₁	#493	1	1	yes	characteristic
109	C₂²×C₁₁	C₂×SD₃₂	1	2	yes	—
110	C₂²×C₁₁	C₂×Q₃₂	1	2	yes	—
111	C₄×C₁₁	—	8	4	no	—
112	C₄×C₁₁	—	16	2	no	—
113	C₄×C₁₁	#358	1	8	yes	complemented
114	C₄×C₁₁	#390	1	1	yes	characteristic
115	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
116	C₄×C₁₁	#486	1	1	yes	characteristic
117	C₄×C₁₁	#492	1	1	yes	characteristic
118	C₂²×Q₈	—	2	2	no	—
119	C₂×Q₁₆	—	2	4	no	—
120	C₂×Q₁₆	—	2	4	no	—
121	C₂×Q₁₆	—	2	2	no	—
122	C₂×Q₁₆	—	2	4	no	—
123	C₂×Q₁₆	—	4	2	no	—
124	C₂×Q₁₆	—	4	2	no	—
125	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
126	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
127	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
128	C₄⋊Q₈	—	2	4	no	—
129	C₄⋊Q₈	—	4	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	4	2	no	—
132	C₂×C₄⋊C₄	—	4	2	no	—
133	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
134	C₂×C₁₆	—	2	2	no	—
135	C₂×C₁₆	—	2	2	no	—
136	C₂×C₁₆	D₄×C₁₁	1	4	yes	—
137	#107	—	2	4	no	—
138	#107	—	4	2	no	—
139	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
140	C₄×C₈	D₄×C₁₁	1	2	yes	—
141	C₂×C₁₁	#1957	1	1	yes	characteristic
142	C₂×C₁₁	C₂×#358	1	2	yes	—
143	C₂×C₁₁	#2241	1	2	yes	—
144	C₂×C₁₁	#2247	1	1	yes	characteristic
145	C₂×C₁₁	#2248	1	1	yes	characteristic
146	C₂×Q₈	—	2	4	no	—
147	C₂×Q₈	—	4	2	no	—
148	C₂×Q₈	—	4	2	no	—
149	C₂×Q₈	—	4	2	no	—
150	C₂×Q₈	—	4	2	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	C₁₁×D₈	1	2	yes	—
155	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
156	Q₁₆	—	2	8	no	—
157	Q₁₆	—	4	8	no	—
158	Q₁₆	—	4	4	no	—
159	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
160	C₂×C₈	C₁₁×D₈	1	2	yes	—
161	C₂×C₈	C₁₁×SD₁₆	1	2	yes	—
162	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
164	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
165	C₂×C₈	C₁₁×#41	1	2	yes	—
166	C₄⋊C₄	—	4	8	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	8	4	no	—
170	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
171	C₄²	C₁₁×SD₁₆	1	2	yes	—
172	C₁₆	—	2	4	no	—
173	C₁₁	#13203	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
175	Q₈	—	4	4	no	—
176	Q₈	—	4	4	no	—
177	Q₈	—	8	2	no	—
178	Q₈	—	8	2	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	8	4	no	—
184	C₂×C₄	C₁₁×#102	1	4	yes	—
185	C₂×C₄	C₁₁×SD₃₂	1	4	yes	—
186	C₂×C₄	C₁₁×Q₃₂	1	4	yes	—
187	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
189	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
190	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
191	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
192	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
193	C₈	C₁₁×#102	1	4	yes	—
194	C₈	C₄×D₄×C₁₁	1	2	yes	—
195	C₈	C₁₁×#121	1	2	yes	—
196	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
197	C₂²	C₁₁×#486	1	1	yes	characteristic
198	C₂²	C₁₁×#493	1	1	yes	characteristic
199	C₂²	C₂×C₁₁×SD₃₂	1	2	yes	—
200	C₂²	C₂×C₁₁×Q₃₂	1	2	yes	—
201	C₄	—	8	4	no	—
202	C₄	—	16	2	no	—
203	C₄	C₁₁×#358	1	8	yes	complemented
204	C₄	C₁₁×#390	1	1	yes	characteristic
205	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
206	C₄	C₁₁×#486	1	1	yes	characteristic
207	C₄	C₁₁×#492	1	1	yes	characteristic
208	C₂	C₁₁×#1957	1	1	yes	characteristic
209	C₂	C₂×C₁₁×#358	1	2	yes	—
210	C₂	C₁₁×#2241	1	2	yes	—
211	C₂	C₁₁×#2247	1	1	yes	characteristic
212	C₂	C₁₁×#2248	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₁×#494	C₄	semidirect
40. #13203	C₁₁	direct (N × H)
99. #494	C₄×C₁₁	semidirect
113. C₄×C₁₁	#358	semidirect
173. C₁₁	#13203	direct (N × H)
203. C₄	C₁₁×#358	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#494	2
C₂×C₁₁×#358	2
C₂×C₄×C₁₁×C₁₆	2
C₁₁×#1845	2
#13203	11

Subgroups — C11×#13203 #14590396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13203 #14590396