Subgroups — C₁₁×#22276 #14599469

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 206 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	C₁₁×#2328	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1961	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1879	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×D₈	C₂²	1	4	yes	—
8	C₂×C₁₁×#127	C₂²	1	2	yes	—
9	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#493	C₄	1	8	yes	complemented
11	C₂×C₁₁×#102	C₂²	1	8	yes	—
12	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#390	C₂²	1	4	yes	—
15	C₁₁×#386	—	2	8	no	—
16	C₁₁×#382	C₂²	1	2	yes	—
17	C₁₁×#376	C₂²	1	1	yes	characteristic
18	C₁₁×#340	C₂²	1	4	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₂²×D₄×C₁₁	—	2	4	no	—
21	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
22	C₂³×C₄×C₁₁	—	2	4	no	—
23	C₂×C₁₁×D₈	—	4	8	no	—
24	C₂×C₁₁×D₈	C₂×C₄	1	16	yes	complemented
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₁₁×#127	—	2	4	no	—
28	C₁₁×#127	C₂×C₄	1	8	yes	complemented
29	C₄×D₄×C₁₁	—	4	8	no	—
30	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
31	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
32	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
33	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
35	C₁₁×#102	—	4	8	no	—
36	C₁₁×#97	—	2	2	no	—
37	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
38	C₁₁×#95	—	2	4	no	—
39	C₁₁×#95	D₄	1	4	yes	—
40	#22276	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₁	—	2	4	no	—
42	C₂×D₄×C₁₁	—	2	16	no	—
43	C₂×D₄×C₁₁	—	2	4	no	—
44	C₂×D₄×C₁₁	—	2	8	no	—
45	C₂×D₄×C₁₁	—	2	8	no	—
46	C₂×D₄×C₁₁	—	8	8	no	—
47	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
48	C₂²×C₄×C₁₁	—	2	4	no	—
49	C₂²×C₄×C₁₁	—	4	8	no	—
50	C₂²×C₄×C₁₁	—	8	8	no	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
52	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
54	C₁₁×D₈	—	4	16	no	—
55	C₂×C₈×C₁₁	—	2	2	no	—
56	C₂×C₈×C₁₁	—	2	4	no	—
57	C₂×C₈×C₁₁	—	2	4	no	—
58	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
59	C₁₁×C₄⋊C₄	—	2	8	no	—
60	C₁₁×C₂²⋊C₄	—	4	8	no	—
61	C₁₁×C₂²⋊C₄	—	8	8	no	—
62	C₄²×C₁₁	—	2	4	no	—
63	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
64	C₄²×C₁₁	#41	1	2	yes	—
65	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
66	#2328	C₂×C₁₁	1	2	yes	complemented
67	#1961	C₂×C₁₁	1	2	yes	complemented
68	#1879	C₂×C₁₁	1	8	yes	complemented
69	#1835	C₂×C₁₁	1	1	yes	characteristic, complemented
70	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
71	C₂³×C₁₁	—	2	8	no	—
72	C₂³×C₁₁	—	4	4	no	—
73	C₂³×C₁₁	—	4	4	no	—
74	C₂³×C₁₁	—	4	8	no	—
75	C₂³×C₁₁	—	4	8	no	—
76	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
77	D₄×C₁₁	—	2	16	no	—
78	D₄×C₁₁	—	4	8	no	—
79	D₄×C₁₁	—	8	16	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	4	no	—
82	C₂×C₄×C₁₁	—	2	8	no	—
83	C₂×C₄×C₁₁	—	4	4	no	—
84	C₂×C₄×C₁₁	—	4	8	no	—
85	C₂×C₄×C₁₁	—	8	16	no	—
86	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
87	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
89	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
90	C₈×C₁₁	—	2	4	no	—
91	C₈×C₁₁	—	4	2	no	—
92	C₂²×D₈	C₂²×C₁₁	1	4	yes	—
93	C₂×#127	C₂²×C₁₁	1	2	yes	—
94	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
95	#493	C₄×C₁₁	1	8	yes	complemented
96	C₂×#102	C₂²×C₁₁	1	8	yes	—
97	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
98	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
99	#390	C₂²×C₁₁	1	4	yes	—
100	#386	—	2	8	no	—
101	#382	C₂²×C₁₁	1	2	yes	—
102	#376	C₂²×C₁₁	1	1	yes	characteristic
103	#340	C₂²×C₁₁	1	4	yes	—
104	#336	C₂²×C₁₁	1	4	yes	—
105	C₂²×C₁₁	—	4	8	no	—
106	C₂²×C₁₁	—	4	16	no	—
107	C₂²×C₁₁	—	8	4	no	—
108	C₂²×C₁₁	—	8	4	no	—
109	C₂²×C₁₁	—	8	8	no	—
110	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
111	C₂²×C₁₁	#535	1	2	yes	—
112	C₂²×C₁₁	#576	1	4	yes	—
113	C₄×C₁₁	—	2	4	no	—
114	C₄×C₁₁	—	4	4	no	—
115	C₄×C₁₁	—	8	4	no	—
116	C₄×C₁₁	#518	1	2	yes	—
117	C₄×C₁₁	#540	1	2	yes	—
118	C₂²×D₄	—	2	4	no	—
119	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
120	C₂³×C₄	—	2	4	no	—
121	C₂×D₈	—	4	8	no	—
122	C₂×D₈	C₂×C₄×C₁₁	1	16	yes	complemented
123	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
124	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
125	#127	—	2	4	no	—
126	#127	C₂×C₄×C₁₁	1	8	yes	complemented
127	C₄×D₄	—	4	8	no	—
128	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
129	C₂×C₂²⋊C₄	—	2	4	no	—
130	C₂×C₂²⋊C₄	—	2	8	no	—
131	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
132	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
133	#102	—	4	8	no	—
134	#97	—	2	2	no	—
135	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
136	#95	—	2	4	no	—
137	#95	D₄×C₁₁	1	4	yes	—
138	C₂×C₁₁	—	8	8	no	—
139	C₂×C₁₁	#2328	1	1	yes	characteristic
140	C₂×C₁₁	#2948	1	2	yes	—
141	C₂×C₁₁	#3220	1	4	yes	—
142	C₂⁴	—	2	4	no	—
143	C₂×D₄	—	2	16	no	—
144	C₂×D₄	—	2	4	no	—
145	C₂×D₄	—	2	8	no	—
146	C₂×D₄	—	2	8	no	—
147	C₂×D₄	—	8	8	no	—
148	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
149	C₂²×C₄	—	2	4	no	—
150	C₂²×C₄	—	4	8	no	—
151	C₂²×C₄	—	8	8	no	—
152	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
153	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
154	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
155	D₈	—	4	16	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
160	C₄⋊C₄	—	2	8	no	—
161	C₂²⋊C₄	—	4	8	no	—
162	C₂²⋊C₄	—	8	8	no	—
163	C₄²	—	2	4	no	—
164	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
165	C₄²	C₁₁×#41	1	2	yes	—
166	C₁₁	#22276	1	1	yes	characteristic, direct product factor, Sylow
167	C₂³	—	2	8	no	—
168	C₂³	—	4	4	no	—
169	C₂³	—	4	4	no	—
170	C₂³	—	4	8	no	—
171	C₂³	—	4	8	no	—
172	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
173	D₄	—	2	16	no	—
174	D₄	—	4	8	no	—
175	D₄	—	8	16	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	8	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	8	no	—
181	C₂×C₄	—	8	16	no	—
182	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
183	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
184	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
185	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
186	C₈	—	2	4	no	—
187	C₈	—	4	2	no	—
188	C₂²	—	4	16	no	—
189	C₂²	—	4	8	no	—
190	C₂²	—	8	4	no	—
191	C₂²	—	8	4	no	—
192	C₂²	—	8	8	no	—
193	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
194	C₂²	C₁₁×#535	1	2	yes	—
195	C₂²	C₁₁×#576	1	4	yes	—
196	C₄	—	2	4	no	—
197	C₄	—	4	4	no	—
198	C₄	—	8	4	no	—
199	C₄	C₁₁×#518	1	2	yes	—
200	C₄	C₁₁×#540	1	2	yes	—
201	C₂	—	8	8	no	—
202	C₂	C₁₁×#2328	1	1	yes	characteristic
203	C₂	C₁₁×#2948	1	2	yes	—
204	C₂	C₁₁×#3220	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
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
2. C₁₁×#2328	C₂	semidirect
3. C₁₁×#1961	C₂	semidirect
4. C₁₁×#1879	C₂	semidirect
5. C₁₁×#1835	C₂	semidirect
6. C₁₁×#1746	C₂	semidirect
10. C₁₁×#493	C₄	semidirect
24. C₂×C₁₁×D₈	C₂×C₄	semidirect
28. C₁₁×#127	C₂×C₄	semidirect
37. C₄×C₈×C₁₁	C₂×C₄	semidirect
40. #22276	C₁₁	direct (N × H)
66. #2328	C₂×C₁₁	semidirect
67. #1961	C₂×C₁₁	semidirect
68. #1879	C₂×C₁₁	semidirect
69. #1835	C₂×C₁₁	semidirect
70. #1746	C₂×C₁₁	semidirect
95. #493	C₄×C₁₁	semidirect
122. C₂×D₈	C₂×C₄×C₁₁	semidirect
126. #127	C₂×C₄×C₁₁	semidirect
135. C₄×C₈	C₂×C₄×C₁₁	semidirect
166. C₁₁	#22276	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×#493	2
C₁₁×#2328	2
C₁₁×#1961	2
C₁₁×#1879	2
C₁₁×#1835	2
C₁₁×#1746	2
#22276	11

Subgroups — C11×#22276 #14599469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22276 #14599469