Subgroups — C₁₁×#13202 #14590395

Order 2816.

614 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×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#357	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×D₈	—	2	1	no	—
6	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
7	C₂×C₁₁×#127	—	2	1	no	—
8	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₁₁×#493	—	2	2	no	—
10	C₁₁×#493	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×#357	—	2	8	no	—
16	C₄×C₁₁×C₁₆	—	2	2	no	—
17	C₂²×D₄×C₁₁	—	2	2	no	—
18	C₂²×D₄×C₁₁	—	4	2	no	—
19	C₂×C₁₁×D₈	—	2	4	no	—
20	C₂×C₁₁×D₈	—	2	4	no	—
21	C₂×C₁₁×D₈	—	2	2	no	—
22	C₂×C₁₁×D₈	—	2	4	no	—
23	C₂×C₁₁×D₈	—	4	2	no	—
24	C₂×C₁₁×D₈	—	4	2	no	—
25	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₁₁×#127	—	2	4	no	—
29	C₁₁×#127	—	4	2	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	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	complemented
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	#13202	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₁	—	4	2	no	—
42	C₂×D₄×C₁₁	—	2	4	no	—
43	C₂×D₄×C₁₁	—	4	8	no	—
44	C₂×D₄×C₁₁	—	4	2	no	—
45	C₂×D₄×C₁₁	—	4	2	no	—
46	C₂×D₄×C₁₁	—	4	2	no	—
47	C₂×D₄×C₁₁	—	4	2	no	—
48	C₂×D₄×C₁₁	—	4	2	no	—
49	C₂×D₄×C₁₁	—	8	4	no	—
50	C₂×D₄×C₁₁	—	8	4	no	—
51	C₂²×C₄×C₁₁	—	4	2	no	—
52	C₂²×C₄×C₁₁	D₈	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₁₁×D₈	—	2	8	no	—
55	C₁₁×D₈	—	4	8	no	—
56	C₁₁×D₈	—	4	4	no	—
57	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₁	D₈	1	2	yes	—
59	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₁	#41	1	2	yes	—
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₁₁×C₄⋊C₄	—	8	4	no	—
67	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₁	SD₁₆	1	2	yes	—
69	C₁₁×C₁₆	—	2	4	no	—
70	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
71	C₂×#357	C₂×C₁₁	1	4	yes	complemented
72	C₂×C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
73	#1845	C₂×C₁₁	1	1	yes	characteristic, complemented
74	C₂³×C₁₁	—	4	4	no	—
75	C₂³×C₁₁	—	8	2	no	—
76	C₂³×C₁₁	—	8	2	no	—
77	C₂³×C₁₁	—	8	4	no	—
78	C₂³×C₁₁	—	8	4	no	—
79	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
80	D₄×C₁₁	—	4	4	no	—
81	D₄×C₁₁	—	4	4	no	—
82	D₄×C₁₁	—	8	16	no	—
83	D₄×C₁₁	—	8	2	no	—
84	D₄×C₁₁	—	8	2	no	—
85	C₂×C₄×C₁₁	—	8	2	no	—
86	C₂×C₄×C₁₁	—	8	4	no	—
87	C₂×C₄×C₁₁	#102	1	4	yes	—
88	C₂×C₄×C₁₁	D₁₆	1	4	yes	—
89	C₂×C₄×C₁₁	SD₃₂	1	4	yes	—
90	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
96	C₈×C₁₁	#102	1	4	yes	—
97	C₈×C₁₁	C₄×D₄	1	2	yes	—
98	C₈×C₁₁	#121	1	2	yes	—
99	C₂²×D₈	—	2	1	no	—
100	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
101	C₂×#127	—	2	1	no	—
102	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
103	#493	—	2	2	no	—
104	#493	C₄×C₁₁	1	4	yes	complemented
105	C₂×#107	—	2	1	no	—
106	C₂×#107	C₂²×C₁₁	1	2	yes	—
107	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
108	#384	—	2	1	no	—
109	#357	—	2	8	no	—
110	C₄×C₁₆	—	2	2	no	—
111	C₂²×C₁₁	—	8	8	no	—
112	C₂²×C₁₁	—	8	4	no	—
113	C₂²×C₁₁	—	16	4	no	—
114	C₂²×C₁₁	—	16	2	no	—
115	C₂²×C₁₁	—	16	2	no	—
116	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
117	C₂²×C₁₁	#486	1	1	yes	characteristic
118	C₂²×C₁₁	#493	1	1	yes	characteristic
119	C₂²×C₁₁	C₂×D₁₆	1	2	yes	—
120	C₂²×C₁₁	C₂×SD₃₂	1	2	yes	—
121	C₄×C₁₁	—	16	2	no	—
122	C₄×C₁₁	#357	1	8	yes	complemented
123	C₄×C₁₁	#390	1	1	yes	characteristic
124	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
125	C₄×C₁₁	#486	1	1	yes	characteristic
126	C₄×C₁₁	#492	1	1	yes	characteristic
127	C₂²×D₄	—	2	2	no	—
128	C₂²×D₄	—	4	2	no	—
129	C₂×D₈	—	2	4	no	—
130	C₂×D₈	—	2	4	no	—
131	C₂×D₈	—	2	2	no	—
132	C₂×D₈	—	2	4	no	—
133	C₂×D₈	—	4	2	no	—
134	C₂×D₈	—	4	2	no	—
135	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
136	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
137	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
138	#127	—	2	4	no	—
139	#127	—	4	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	4	2	no	—
142	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	—	2	2	no	—
145	C₂×C₁₆	D₄×C₁₁	1	4	yes	complemented
146	#107	—	2	4	no	—
147	#107	—	4	2	no	—
148	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
149	C₄×C₈	D₄×C₁₁	1	2	yes	—
150	C₂×C₁₁	—	16	4	no	—
151	C₂×C₁₁	#1957	1	1	yes	characteristic
152	C₂×C₁₁	C₂×#357	1	2	yes	—
153	C₂×C₁₁	#2240	1	2	yes	—
154	C₂×C₁₁	#2246	1	1	yes	characteristic
155	C₂×C₁₁	#2248	1	1	yes	characteristic
156	C₂⁴	—	4	2	no	—
157	C₂×D₄	—	2	4	no	—
158	C₂×D₄	—	4	8	no	—
159	C₂×D₄	—	4	2	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	4	2	no	—
162	C₂×D₄	—	4	2	no	—
163	C₂×D₄	—	4	2	no	—
164	C₂×D₄	—	8	4	no	—
165	C₂×D₄	—	8	4	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	C₁₁×D₈	1	2	yes	—
168	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
169	D₈	—	2	8	no	—
170	D₈	—	4	8	no	—
171	D₈	—	4	4	no	—
172	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
173	C₂×C₈	C₁₁×D₈	1	2	yes	—
174	C₂×C₈	C₁₁×SD₁₆	1	2	yes	—
175	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
176	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
177	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
178	C₂×C₈	C₁₁×#41	1	2	yes	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	8	4	no	—
182	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
183	C₄²	C₁₁×SD₁₆	1	2	yes	—
184	C₁₆	—	2	4	no	—
185	C₁₁	#13202	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³	—	4	4	no	—
187	C₂³	—	8	2	no	—
188	C₂³	—	8	4	no	—
189	C₂³	—	8	4	no	—
190	C₂³	—	8	2	no	—
191	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
192	D₄	—	4	4	no	—
193	D₄	—	4	4	no	—
194	D₄	—	8	2	no	—
195	D₄	—	8	16	no	—
196	D₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	8	4	no	—
199	C₂×C₄	C₁₁×#102	1	4	yes	—
200	C₂×C₄	C₁₁×D₁₆	1	4	yes	—
201	C₂×C₄	C₁₁×SD₃₂	1	4	yes	—
202	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
204	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
205	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
206	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
207	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
208	C₈	C₁₁×#102	1	4	yes	—
209	C₈	C₄×D₄×C₁₁	1	2	yes	—
210	C₈	C₁₁×#121	1	2	yes	—
211	C₂²	—	8	8	no	—
212	C₂²	—	8	4	no	—
213	C₂²	—	16	4	no	—
214	C₂²	—	16	2	no	—
215	C₂²	—	16	2	no	—
216	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
217	C₂²	C₁₁×#486	1	1	yes	characteristic
218	C₂²	C₁₁×#493	1	1	yes	characteristic
219	C₂²	C₂×C₁₁×D₁₆	1	2	yes	—
220	C₂²	C₂×C₁₁×SD₃₂	1	2	yes	—
221	C₄	—	16	2	no	—
222	C₄	C₁₁×#357	1	8	yes	complemented
223	C₄	C₁₁×#390	1	1	yes	characteristic
224	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
225	C₄	C₁₁×#486	1	1	yes	characteristic
226	C₄	C₁₁×#492	1	1	yes	characteristic
227	C₂	—	16	4	no	—
228	C₂	C₁₁×#1957	1	1	yes	characteristic
229	C₂	C₂×C₁₁×#357	1	2	yes	—
230	C₂	C₁₁×#2240	1	2	yes	—
231	C₂	C₁₁×#2246	1	1	yes	characteristic
232	C₂	C₁₁×#2248	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#493	C₂
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
2. C₂×C₁₁×#357	C₂	semidirect
3. C₂×C₄×C₁₁×C₁₆	C₂	semidirect
4. C₁₁×#1845	C₂	semidirect
10. C₁₁×#493	C₄	semidirect
35. C₂×C₁₁×C₁₆	D₄	semidirect
40. #13202	C₁₁	direct (N × H)
71. C₂×#357	C₂×C₁₁	semidirect
72. C₂×C₄×C₁₆	C₂×C₁₁	semidirect
73. #1845	C₂×C₁₁	semidirect
104. #493	C₄×C₁₁	semidirect
122. C₄×C₁₁	#357	semidirect
145. C₂×C₁₆	D₄×C₁₁	semidirect
185. C₁₁	#13202	direct (N × H)
222. C₄	C₁₁×#357	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#493	2
C₂×C₁₁×#357	2
C₂×C₄×C₁₁×C₁₆	2
C₁₁×#1845	2
#13202	11

Subgroups — C11×#13202 #14590395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13202 #14590395