Subgroups — C₁₁×#21959 #14599152

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2285	C₂	1	2	yes	maximal
3	C₁₁×#1948	C₂	1	8	yes	maximal, complemented
4	C₁₁×#1807	C₂	1	4	yes	maximal
5	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
6	C₂×C₁₁×#117	—	2	2	no	—
7	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#106	C₂²	1	8	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₄	1	8	yes	complemented
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
11	C₁₁×#384	C₂²	1	4	yes	—
12	C₁₁×#382	—	2	2	no	—
13	C₁₁×#380	—	2	2	no	—
14	C₁₁×#380	C₂²	1	4	yes	—
15	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
16	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
17	C₁₁×#340	C₂²	1	8	yes	—
18	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	—	4	4	no	—
22	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
24	C₁₁×#117	—	4	8	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
28	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
29	C₂×C₄²×C₁₁	—	2	4	no	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₁	D₄	1	2	yes	—
32	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
34	C₁₁×#106	—	4	8	no	—
35	C₁₁×C₄⋊C₈	C₂×C₄	1	16	yes	—
36	C₁₁×#95	—	2	4	no	—
37	C₁₁×#95	—	2	4	no	—
38	#21959	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	—	2	2	no	—
41	C₂²×C₄×C₁₁	—	2	2	no	—
42	C₂²×C₄×C₁₁	—	2	8	no	—
43	C₂²×C₄×C₁₁	—	4	2	no	—
44	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
46	C₂²×C₄×C₁₁	SD₁₆	1	8	yes	—
47	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
50	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
52	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
53	C₂×C₈×C₁₁	—	2	8	no	—
54	C₂×C₈×C₁₁	—	4	8	no	—
55	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
56	C₁₁×C₄⋊C₄	—	2	8	no	—
57	C₁₁×C₄⋊C₄	—	2	8	no	—
58	C₁₁×C₄⋊C₄	—	4	8	no	—
59	C₁₁×C₄⋊C₄	—	4	8	no	—
60	C₁₁×C₂²⋊C₄	—	4	8	no	—
61	C₄²×C₁₁	—	4	8	no	—
62	C₄²×C₁₁	C₄⋊C₄	1	8	yes	—
63	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
64	C₄²×C₁₁	C₂×Q₈	1	4	yes	—
65	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
66	#2285	C₂×C₁₁	1	2	yes	—
67	#1948	C₂×C₁₁	1	8	yes	complemented
68	#1807	C₂×C₁₁	1	4	yes	—
69	C₂³×C₁₁	—	2	2	no	—
70	C₂³×C₁₁	—	2	2	no	—
71	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
72	C₂³×C₁₁	C₂×SD₁₆	1	4	yes	—
73	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	4	no	—
76	C₂×C₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	2	4	no	—
79	C₂×C₄×C₁₁	—	4	4	no	—
80	C₂×C₄×C₁₁	—	4	8	no	—
81	C₂×C₄×C₁₁	—	4	8	no	—
82	C₂×C₄×C₁₁	—	4	8	no	—
83	C₂×C₄×C₁₁	#106	1	16	yes	complemented
84	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
85	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
86	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
87	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
88	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
89	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
92	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
93	C₈×C₁₁	—	2	8	no	—
94	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
95	C₂×#117	—	2	2	no	—
96	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
97	C₂×#106	C₂²×C₁₁	1	8	yes	—
98	C₂×C₄⋊C₈	C₄×C₁₁	1	8	yes	complemented
99	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
100	#384	C₂²×C₁₁	1	4	yes	—
101	#382	—	2	2	no	—
102	#380	—	2	2	no	—
103	#380	C₂²×C₁₁	1	4	yes	—
104	C₄×C₄⋊C₄	—	2	2	no	—
105	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
106	#340	C₂²×C₁₁	1	8	yes	—
107	C₂²×C₁₁	—	2	2	no	—
108	C₂²×C₁₁	—	2	2	no	—
109	C₂²×C₁₁	—	2	8	no	—
110	C₂²×C₁₁	C₂×#106	1	4	yes	—
111	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₁₁	#537	1	2	yes	—
113	C₂²×C₁₁	C₂²×SD₁₆	1	2	yes	—
114	C₂²×C₁₁	#575	1	2	yes	—
115	C₄×C₁₁	—	2	2	no	—
116	C₄×C₁₁	—	2	4	no	—
117	C₄×C₁₁	—	8	8	no	—
118	C₄×C₁₁	C₂×#106	1	8	yes	—
119	C₄×C₁₁	#518	1	1	yes	characteristic
120	C₄×C₁₁	#519	1	1	yes	characteristic
121	C₄×C₁₁	#544	1	2	yes	—
122	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
123	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
124	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
125	C₂²×C₈	—	4	4	no	—
126	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	—
127	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
128	#117	—	4	8	no	—
129	C₂×C₄⋊C₄	—	2	4	no	—
130	C₂×C₄⋊C₄	—	2	4	no	—
131	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
132	C₂×C₂²⋊C₄	—	2	4	no	—
133	C₂×C₄²	—	2	4	no	—
134	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
135	C₂×C₄²	D₄×C₁₁	1	2	yes	—
136	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
137	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
138	#106	—	4	8	no	—
139	C₄⋊C₈	C₂×C₄×C₁₁	1	16	yes	—
140	#95	—	2	4	no	—
141	#95	—	2	4	no	—
142	C₂×C₁₁	—	2	4	no	—
143	C₂×C₁₁	#2316	1	1	yes	characteristic
144	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
145	C₂×C₁₁	#2911	1	1	yes	characteristic
146	C₂×C₁₁	#3246	1	4	yes	—
147	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	8	no	—
151	C₂²×C₄	—	4	2	no	—
152	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
153	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
154	C₂²×C₄	C₁₁×SD₁₆	1	8	yes	—
155	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
156	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
157	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
158	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
159	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
160	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
161	C₂×C₈	—	2	8	no	—
162	C₂×C₈	—	4	8	no	—
163	C₂×C₈	C₂²×C₄×C₁₁	1	8	yes	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄⋊C₄	—	2	8	no	—
166	C₄⋊C₄	—	4	8	no	—
167	C₄⋊C₄	—	4	8	no	—
168	C₂²⋊C₄	—	4	8	no	—
169	C₄²	—	4	8	no	—
170	C₄²	C₁₁×C₄⋊C₄	1	8	yes	—
171	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
172	C₄²	C₂×Q₈×C₁₁	1	4	yes	—
173	C₁₁	#21959	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	—	2	2	no	—
175	C₂³	—	2	2	no	—
176	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
177	C₂³	C₂×C₁₁×SD₁₆	1	4	yes	—
178	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	8	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	—	4	8	no	—
188	C₂×C₄	C₁₁×#106	1	16	yes	complemented
189	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
190	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
191	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
192	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
193	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
194	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
195	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
196	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
198	C₈	—	2	8	no	—
199	C₂²	—	2	2	no	—
200	C₂²	—	2	8	no	—
201	C₂²	—	2	2	no	—
202	C₂²	C₂×C₁₁×#106	1	4	yes	—
203	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
204	C₂²	C₁₁×#537	1	2	yes	—
205	C₂²	C₂²×C₁₁×SD₁₆	1	2	yes	—
206	C₂²	C₁₁×#575	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	2	no	—
209	C₄	—	8	8	no	—
210	C₄	C₂×C₁₁×#106	1	8	yes	—
211	C₄	C₁₁×#518	1	1	yes	characteristic
212	C₄	C₁₁×#519	1	1	yes	characteristic
213	C₄	C₁₁×#544	1	2	yes	—
214	C₂	—	2	4	no	—
215	C₂	C₁₁×#2316	1	1	yes	characteristic
216	C₂	C₂²×C₁₁×#106	1	1	yes	characteristic
217	C₂	C₁₁×#2911	1	1	yes	characteristic
218	C₂	C₁₁×#3246	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	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1948	C₂	semidirect
9. C₂×C₁₁×C₄⋊C₈	C₄	semidirect
38. #21959	C₁₁	direct (N × H)
67. #1948	C₂×C₁₁	semidirect
83. C₂×C₄×C₁₁	#106	semidirect
98. C₂×C₄⋊C₈	C₄×C₁₁	semidirect
173. C₁₁	#21959	direct (N × H)
188. C₂×C₄	C₁₁×#106	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×C₄⋊C₈	2
C₁₁×#2285	2
C₁₁×#1948	2
C₁₁×#1807	2
#21959	11

Subgroups — C11×#21959 #14599152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21959 #14599152