Subgroups — C₁₁×#22254 #14599447

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 226 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×#2331	C₂	1	2	yes	maximal
3	C₁₁×#1993	C₂	1	2	yes	maximal
4	C₁₁×#1921	C₂	1	4	yes	maximal
5	C₁₁×#1918	C₂	1	4	yes	maximal
6	C₁₁×#1835	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₁₁×#500	C₄	1	8	yes	complemented
10	C₂×C₁₁×#107	C₂²	1	2	yes	—
11	C₂×C₁₁×#107	C₂²	1	2	yes	—
12	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#391	—	2	4	no	—
15	C₁₁×#389	C₂²	1	4	yes	—
16	C₁₁×#387	—	2	4	no	—
17	C₁₁×#382	C₂²	1	2	yes	—
18	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
19	C₁₁×#376	C₂²	1	1	yes	characteristic
20	C₁₁×#340	C₂²	1	2	yes	—
21	C₁₁×#340	C₂²	1	8	yes	—
22	C₁₁×#340	C₂²	1	2	yes	—
23	C₁₁×#336	C₂²	1	2	yes	—
24	C₁₁×#336	C₂²	1	2	yes	—
25	C₂²×Q₈×C₁₁	—	2	2	no	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×C₄⋊Q₈	—	2	4	no	—
30	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
31	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
33	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
34	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₁	—	2	4	no	—
36	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
38	C₁₁×#107	C₂×C₄	1	8	yes	—
39	C₁₁×#107	C₂×C₄	1	8	yes	—
40	C₁₁×#97	—	2	2	no	—
41	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
42	C₁₁×#95	—	2	4	no	—
43	C₁₁×#95	—	2	2	no	—
44	C₁₁×#95	—	2	2	no	—
45	C₁₁×#95	—	2	4	no	—
46	C₁₁×#95	D₄	1	2	yes	—
47	C₁₁×#95	D₄	1	2	yes	—
48	#22254	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×Q₈×C₁₁	—	2	8	no	—
50	C₂×Q₈×C₁₁	—	8	4	no	—
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	—	2	4	no	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	—	2	2	no	—
61	C₂×C₈×C₁₁	—	2	2	no	—
62	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
63	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
64	C₁₁×C₄⋊C₄	—	2	8	no	—
65	C₁₁×C₄⋊C₄	—	2	4	no	—
66	C₁₁×C₄⋊C₄	—	2	4	no	—
67	C₁₁×C₄⋊C₄	—	2	4	no	—
68	C₁₁×C₄⋊C₄	—	8	4	no	—
69	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
70	C₄²×C₁₁	—	2	2	no	—
71	C₄²×C₁₁	—	2	2	no	—
72	C₄²×C₁₁	—	8	4	no	—
73	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
74	C₄²×C₁₁	#41	1	2	yes	—
75	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
76	#2331	C₂×C₁₁	1	2	yes	—
77	#1993	C₂×C₁₁	1	2	yes	—
78	#1921	C₂×C₁₁	1	4	yes	—
79	#1918	C₂×C₁₁	1	4	yes	—
80	#1835	C₂×C₁₁	1	1	yes	characteristic
81	#1746	C₂×C₁₁	1	1	yes	characteristic
82	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
83	Q₈×C₁₁	—	8	8	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	8	no	—
87	C₂×C₄×C₁₁	—	2	4	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	4	no	—
90	C₂×C₄×C₁₁	—	4	4	no	—
91	C₂×C₄×C₁₁	—	4	4	no	—
92	C₂×C₄×C₁₁	—	4	4	no	—
93	C₂×C₄×C₁₁	—	4	4	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
99	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
100	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
101	C₈×C₁₁	—	2	2	no	—
102	C₈×C₁₁	—	2	2	no	—
103	C₈×C₁₁	—	4	2	no	—
104	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
105	#500	C₄×C₁₁	1	8	yes	complemented
106	C₂×#107	C₂²×C₁₁	1	2	yes	—
107	C₂×#107	C₂²×C₁₁	1	2	yes	—
108	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
109	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	#391	—	2	4	no	—
111	#389	C₂²×C₁₁	1	4	yes	—
112	#387	—	2	4	no	—
113	#382	C₂²×C₁₁	1	2	yes	—
114	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
115	#376	C₂²×C₁₁	1	1	yes	characteristic
116	#340	C₂²×C₁₁	1	2	yes	—
117	#340	C₂²×C₁₁	1	2	yes	—
118	#340	C₂²×C₁₁	1	8	yes	—
119	#336	C₂²×C₁₁	1	2	yes	—
120	#336	C₂²×C₁₁	1	2	yes	—
121	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
122	C₂²×C₁₁	#536	1	2	yes	—
123	C₂²×C₁₁	#576	1	2	yes	—
124	C₂²×C₁₁	#578	1	2	yes	—
125	C₄×C₁₁	—	2	2	no	—
126	C₄×C₁₁	—	2	2	no	—
127	C₄×C₁₁	—	4	8	no	—
128	C₄×C₁₁	—	4	4	no	—
129	C₄×C₁₁	—	8	4	no	—
130	C₄×C₁₁	#519	1	1	yes	characteristic
131	C₄×C₁₁	#519	1	1	yes	characteristic
132	C₄×C₁₁	#541	1	2	yes	—
133	C₂²×Q₈	—	2	2	no	—
134	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
135	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
136	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
137	C₄⋊Q₈	—	2	4	no	—
138	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	4	no	—
141	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
142	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
143	C₂×C₄²	—	2	4	no	—
144	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
145	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
146	#107	C₂×C₄×C₁₁	1	8	yes	—
147	#107	C₂×C₄×C₁₁	1	8	yes	—
148	#97	—	2	2	no	—
149	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
150	#95	—	2	4	no	—
151	#95	—	2	2	no	—
152	#95	—	2	2	no	—
153	#95	—	2	4	no	—
154	#95	D₄×C₁₁	1	2	yes	—
155	#95	D₄×C₁₁	1	2	yes	—
156	C₂×C₁₁	#2327	1	1	yes	characteristic
157	C₂×C₁₁	#2948	1	1	yes	characteristic
158	C₂×C₁₁	#2950	1	1	yes	characteristic
159	C₂×C₁₁	#3243	1	4	yes	—
160	C₂×Q₈	—	2	8	no	—
161	C₂×Q₈	—	8	4	no	—
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
165	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
167	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
174	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
175	C₄⋊C₄	—	2	8	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	8	4	no	—
180	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	8	4	no	—
184	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
185	C₄²	C₁₁×#41	1	2	yes	—
186	C₁₁	#22254	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
188	Q₈	—	8	8	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	8	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	4	4	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
201	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
202	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
203	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
204	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
205	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
206	C₈	—	2	2	no	—
207	C₈	—	2	2	no	—
208	C₈	—	4	2	no	—
209	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
210	C₂²	C₁₁×#536	1	2	yes	—
211	C₂²	C₁₁×#576	1	2	yes	—
212	C₂²	C₁₁×#578	1	2	yes	—
213	C₄	—	2	2	no	—
214	C₄	—	2	2	no	—
215	C₄	—	4	8	no	—
216	C₄	—	4	4	no	—
217	C₄	—	8	4	no	—
218	C₄	C₁₁×#519	1	1	yes	characteristic
219	C₄	C₁₁×#519	1	1	yes	characteristic
220	C₄	C₁₁×#541	1	2	yes	—
221	C₂	C₁₁×#2327	1	1	yes	characteristic
222	C₂	C₁₁×#2948	1	1	yes	characteristic
223	C₂	C₁₁×#2950	1	1	yes	characteristic
224	C₂	C₁₁×#3243	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₁₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₁×#500	C₄	semidirect
48. #22254	C₁₁	direct (N × H)
105. #500	C₄×C₁₁	semidirect
186. C₁₁	#22254	direct (N × H)

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×#2331	2
C₁₁×#1993	2
C₁₁×#1921	2
C₁₁×#1918	2
C₁₁×#1835	2
C₁₁×#1746	2
#22254	11

Subgroups — C11×#22254 #14599447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22254 #14599447