Subgroups — C₁₁×#17826 #14595019

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2906	C₂	1	2	yes	maximal
3	C₁₁×#1570	C₂	1	6	yes	maximal, complemented
4	C₁₁×#1566	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₁×#334	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₁×#131	—	2	2	no	—
7	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
8	C₈×Q₈×C₁₁	C₄	1	1	yes	characteristic
9	C₈×Q₈×C₁₁	C₄	1	1	yes	characteristic
10	C₈×D₄×C₁₁	C₄	1	3	yes	—
11	C₈×D₄×C₁₁	C₄	1	3	yes	—
12	C₁₁×#431	C₂²	1	3	yes	—
13	C₁₁×#424	—	2	6	no	—
14	C₁₁×#423	C₂²	1	6	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	6	yes	—
16	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
17	C₁₁×#334	C₂²	1	1	yes	characteristic
18	C₁₁×#334	C₂²	1	3	yes	—
19	C₁₁×#334	C₂²	1	6	yes	—
20	C₁₁×#334	C₂²	1	6	yes	—
21	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
22	C₁₁×#131	—	4	8	no	—
23	C₂×C₁₁×M₁₆	—	2	6	no	—
24	C₂²×C₈×C₁₁	—	2	6	no	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
27	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Q₈×C₁₁	Q₈	1	1	yes	characteristic
29	C₄×D₄×C₁₁	C₂×C₄	1	3	yes	—
30	C₄×D₄×C₁₁	Q₈	1	3	yes	—
31	C₁₁×#117	D₄	1	3	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
33	C₁₁×C₄⋊C₈	—	2	6	no	—
34	C₁₁×C₄⋊C₈	—	2	6	no	—
35	C₁₁×C₄⋊C₈	C₂×C₄	1	3	yes	—
36	C₁₁×C₄⋊C₈	C₂×C₄	1	3	yes	—
37	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
38	C₁₁×C₄⋊C₈	C₂³	1	6	yes	—
39	C₁₁×C₂²⋊C₈	C₂×C₄	1	6	yes	—
40	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
42	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₁₁	C₂³	1	3	yes	—
44	#17826	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₁₁×#41	SD₁₆	1	8	yes	—
46	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
47	C₂×D₄×C₁₁	C₄⋊C₄	1	3	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
49	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
50	C₂²×C₄×C₁₁	C₂×Q₈	1	3	yes	—
51	C₁₁×M₁₆	—	4	12	no	—
52	C₂×C₈×C₁₁	—	2	6	no	—
53	C₂×C₈×C₁₁	—	2	2	no	—
54	C₂×C₈×C₁₁	—	2	6	no	—
55	C₂×C₈×C₁₁	—	4	3	no	—
56	C₂×C₈×C₁₁	—	4	12	no	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
59	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₁₁×C₄⋊C₄	C₄⋊C₄	1	3	yes	—
62	C₁₁×C₄⋊C₄	C₄⋊C₄	1	3	yes	—
63	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	6	yes	—
64	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
65	C₄²×C₁₁	C₂×D₄	1	3	yes	—
66	C₄²×C₁₁	C₂×Q₈	1	3	yes	—
67	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
68	C₈×#41	C₂×C₁₁	1	1	yes	characteristic
69	#2906	C₂×C₁₁	1	2	yes	—
70	#1570	C₂×C₁₁	1	6	yes	complemented
71	#1566	C₂×C₁₁	1	3	yes	complemented
72	C₂×#334	C₂×C₁₁	1	3	yes	complemented
73	C₂³×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
74	Q₈×C₁₁	#106	1	4	yes	—
75	D₄×C₁₁	#106	1	12	yes	—
76	C₂×C₄×C₁₁	—	2	3	no	—
77	C₂×C₄×C₁₁	—	2	3	no	—
78	C₂×C₄×C₁₁	—	4	3	no	—
79	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
80	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
82	C₂×C₄×C₁₁	C₂×SD₁₆	1	12	yes	—
83	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
86	C₈×C₁₁	—	2	3	no	—
87	C₈×C₁₁	—	2	1	no	—
88	C₈×C₁₁	—	2	3	no	—
89	C₈×C₁₁	—	4	2	no	—
90	C₈×C₁₁	—	4	6	no	—
91	C₈×C₁₁	#131	1	2	yes	complemented
92	C₂×#131	—	2	2	no	—
93	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
94	C₈×Q₈	C₄×C₁₁	1	1	yes	characteristic
95	C₈×Q₈	C₄×C₁₁	1	1	yes	characteristic
96	C₈×D₄	C₄×C₁₁	1	3	yes	—
97	C₈×D₄	C₄×C₁₁	1	3	yes	—
98	#431	C₂²×C₁₁	1	3	yes	—
99	#424	—	2	6	no	—
100	#423	C₂²×C₁₁	1	6	yes	—
101	C₂×C₄⋊C₈	C₂²×C₁₁	1	6	yes	—
102	C₂×C₄×C₈	C₂²×C₁₁	1	3	yes	—
103	#334	C₂²×C₁₁	1	1	yes	characteristic
104	#334	C₂²×C₁₁	1	3	yes	—
105	#334	C₂²×C₁₁	1	6	yes	—
106	#334	C₂²×C₁₁	1	6	yes	—
107	C₂²×C₁₁	—	2	3	no	—
108	C₂²×C₁₁	—	2	3	no	—
109	C₂²×C₁₁	C₂×#106	1	6	yes	—
110	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
111	C₄×C₁₁	—	2	3	no	—
112	C₄×C₁₁	—	2	1	no	—
113	C₄×C₁₁	—	2	3	no	—
114	C₄×C₁₁	C₂×#106	1	6	yes	—
115	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
116	C₄×C₁₁	#568	1	1	yes	characteristic
117	C₄×C₁₁	C₂²×SD₁₆	1	2	yes	—
118	C₂×#41	D₄×C₁₁	1	1	yes	characteristic
119	#131	—	4	8	no	—
120	C₂×M₁₆	—	2	6	no	—
121	C₂²×C₈	—	2	6	no	—
122	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
123	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
124	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
125	C₄×Q₈	Q₈×C₁₁	1	1	yes	characteristic
126	C₄×D₄	C₂×C₄×C₁₁	1	3	yes	—
127	C₄×D₄	Q₈×C₁₁	1	3	yes	—
128	#117	D₄×C₁₁	1	3	yes	—
129	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
130	C₄⋊C₈	—	2	6	no	—
131	C₄⋊C₈	—	2	6	no	—
132	C₄⋊C₈	C₂×C₄×C₁₁	1	3	yes	—
133	C₄⋊C₈	C₂×C₄×C₁₁	1	3	yes	—
134	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
135	C₄⋊C₈	C₂³×C₁₁	1	6	yes	—
136	C₂²⋊C₈	C₂×C₄×C₁₁	1	6	yes	—
137	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
138	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
139	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
140	C₄×C₈	C₂³×C₁₁	1	3	yes	—
141	C₂×C₁₁	—	2	6	no	—
142	C₂×C₁₁	#2906	1	1	yes	characteristic
143	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
144	C₂×C₁₁	#2916	1	1	yes	characteristic
145	#41	C₁₁×SD₁₆	1	8	yes	—
146	C₂×Q₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
147	C₂×D₄	C₁₁×C₄⋊C₄	1	3	yes	—
148	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
149	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
150	C₂²×C₄	C₂×Q₈×C₁₁	1	3	yes	—
151	M₁₆	—	4	12	no	—
152	C₂×C₈	—	2	6	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	6	no	—
155	C₂×C₈	—	4	3	no	—
156	C₂×C₈	—	4	12	no	—
157	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
158	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
159	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
160	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
161	C₄⋊C₄	C₁₁×C₄⋊C₄	1	3	yes	—
162	C₄⋊C₄	C₁₁×C₄⋊C₄	1	3	yes	—
163	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	6	yes	—
164	C₄²	C₂²×C₄×C₁₁	1	3	yes	—
165	C₄²	C₂×D₄×C₁₁	1	3	yes	—
166	C₄²	C₂×Q₈×C₁₁	1	3	yes	—
167	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
168	C₁₁	#17826	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
170	Q₈	C₁₁×#106	1	4	yes	—
171	D₄	C₁₁×#106	1	12	yes	—
172	C₂×C₄	—	2	3	no	—
173	C₂×C₄	—	2	3	no	—
174	C₂×C₄	—	4	3	no	—
175	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
176	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
177	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	3	yes	—
178	C₂×C₄	C₂×C₁₁×SD₁₆	1	12	yes	—
179	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
180	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
181	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
182	C₈	—	2	3	no	—
183	C₈	—	2	1	no	—
184	C₈	—	2	3	no	—
185	C₈	—	4	2	no	—
186	C₈	—	4	6	no	—
187	C₈	C₁₁×#131	1	2	yes	complemented
188	C₂²	—	2	3	no	—
189	C₂²	—	2	3	no	—
190	C₂²	C₂×C₁₁×#106	1	6	yes	—
191	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
192	C₄	—	2	3	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	3	no	—
195	C₄	C₂×C₁₁×#106	1	6	yes	—
196	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
197	C₄	C₁₁×#568	1	1	yes	characteristic
198	C₄	C₂²×C₁₁×SD₁₆	1	2	yes	—
199	C₂	—	2	6	no	—
200	C₂	C₁₁×#2906	1	1	yes	characteristic
201	C₂	C₂²×C₁₁×#106	1	1	yes	characteristic
202	C₂	C₁₁×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1570	C₂	semidirect
4. C₁₁×#1566	C₂	semidirect
5. C₂×C₁₁×#334	C₂	semidirect
44. #17826	C₁₁	direct (N × H)
70. #1570	C₂×C₁₁	semidirect
71. #1566	C₂×C₁₁	semidirect
72. C₂×#334	C₂×C₁₁	semidirect
91. C₈×C₁₁	#131	semidirect
168. C₁₁	#17826	direct (N × H)
187. C₈	C₁₁×#131	semidirect

Maximal subgroups

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

subgroup	index
C₈×C₁₁×#41	2
C₁₁×#2906	2
C₁₁×#1570	2
C₁₁×#1566	2
C₂×C₁₁×#334	2
#17826	11

Subgroups — C11×#17826 #14595019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17826 #14595019