Subgroups — C₁₁×#22248 #14599441

Order 2816.

790 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×#500	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₁₁×#1990	C₂	1	2	yes	maximal
4	C₁₁×#1921	C₂	1	8	yes	maximal
5	C₁₁×#1834	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₄×Q₈×C₁₁	—	2	2	no	—
9	C₁₁×#500	C₄	1	8	yes	complemented
10	C₂×C₁₁×#107	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#391	—	2	2	no	—
14	C₁₁×#389	—	2	2	no	—
15	C₁₁×#389	C₂²	1	4	yes	—
16	C₁₁×#384	C₂²	1	2	yes	—
17	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
18	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
19	C₄³×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#340	C₂²	1	8	yes	—
21	C₁₁×#340	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₁	—	2	2	no	—
24	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₁₁×C₄⋊Q₈	—	2	4	no	—
27	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
28	C₄×Q₈×C₁₁	—	4	8	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
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	D₄	1	2	yes	—
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×#107	C₂×C₄	1	16	yes	—
42	C₄×C₈×C₁₁	—	2	2	no	—
43	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
44	C₁₁×#95	—	2	4	no	—
45	C₁₁×#95	—	2	4	no	—
46	#22248	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₁	—	2	8	no	—
48	C₂×Q₈×C₁₁	—	4	4	no	—
49	C₂×Q₈×C₁₁	—	4	4	no	—
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	2	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	4	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
61	C₁₁×C₄⋊C₄	—	2	8	no	—
62	C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	2	8	no	—
64	C₁₁×C₄⋊C₄	—	4	8	no	—
65	C₁₁×C₄⋊C₄	—	4	4	no	—
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
68	C₄²×C₁₁	—	2	2	no	—
69	C₄²×C₁₁	—	2	4	no	—
70	C₄²×C₁₁	—	2	4	no	—
71	C₄²×C₁₁	—	4	8	no	—
72	C₄²×C₁₁	Q₁₆	1	4	yes	—
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	C₄×C₄⋊Q₈	C₂×C₁₁	1	2	yes	—
77	#1990	C₂×C₁₁	1	2	yes	—
78	#1921	C₂×C₁₁	1	8	yes	—
79	#1834	C₂×C₁₁	1	1	yes	characteristic
80	#1744	C₂×C₁₁	1	1	yes	characteristic
81	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
82	Q₈×C₁₁	—	4	16	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	8	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	4	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	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₁₁	C₂×Q₁₆	1	4	yes	—
97	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
98	C₂×C₄×C₁₁	#135	1	2	yes	—
99	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
100	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
102	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
103	C₈×C₁₁	—	2	4	no	—
104	C₈×C₁₁	—	4	2	no	—
105	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
106	C₂×C₄×Q₈	—	2	2	no	—
107	#500	C₄×C₁₁	1	8	yes	complemented
108	C₂×#107	C₂²×C₁₁	1	4	yes	—
109	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
111	#391	—	2	2	no	—
112	#389	—	2	2	no	—
113	#389	C₂²×C₁₁	1	4	yes	—
114	#384	C₂²×C₁₁	1	2	yes	—
115	C₄×C₄⋊C₄	—	2	2	no	—
116	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
117	C₄³	C₂²×C₁₁	1	1	yes	characteristic
118	#340	C₂²×C₁₁	1	4	yes	—
119	#340	C₂²×C₁₁	1	8	yes	—
120	#336	C₂²×C₁₁	1	4	yes	—
121	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
122	C₂²×C₁₁	#536	1	2	yes	—
123	C₂²×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
124	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
125	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
126	C₄×C₁₁	—	2	4	no	—
127	C₄×C₁₁	—	4	8	no	—
128	C₄×C₁₁	—	4	2	no	—
129	C₄×C₁₁	—	8	4	no	—
130	C₄×C₁₁	C₄×Q₁₆	1	4	yes	—
131	C₄×C₁₁	#442	1	4	yes	—
132	C₄×C₁₁	#519	1	2	yes	—
133	C₄×C₁₁	#541	1	2	yes	—
134	C₂²×Q₈	—	2	2	no	—
135	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
136	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
137	C₄⋊Q₈	—	2	4	no	—
138	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
139	C₄×Q₈	—	4	8	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	4	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
145	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
146	C₂×C₄²	—	2	4	no	—
147	C₂×C₄²	D₄×C₁₁	1	2	yes	—
148	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
149	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
150	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
151	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
152	#107	C₂×C₄×C₁₁	1	16	yes	—
153	C₄×C₈	—	2	2	no	—
154	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
155	#95	—	2	4	no	—
156	#95	—	2	4	no	—
157	C₂×C₁₁	#2327	1	1	yes	characteristic
158	C₂×C₁₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
159	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
160	C₂×C₁₁	#3228	1	2	yes	—
161	C₂×C₁₁	#3230	1	2	yes	—
162	C₂×Q₈	—	2	8	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂²×C₄	—	2	4	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
168	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
169	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
171	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
176	C₄⋊C₄	—	2	8	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	2	8	no	—
179	C₄⋊C₄	—	4	8	no	—
180	C₄⋊C₄	—	4	4	no	—
181	C₄⋊C₄	—	4	4	no	—
182	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	4	8	no	—
187	C₄²	C₁₁×Q₁₆	1	4	yes	—
188	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
189	C₄²	C₁₁×#41	1	2	yes	—
190	C₁₁	#22248	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
192	Q₈	—	4	16	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	4	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
205	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
206	C₂×C₄	C₂×C₁₁×Q₁₆	1	4	yes	—
207	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
208	C₂×C₄	C₁₁×#135	1	2	yes	—
209	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
210	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
211	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
212	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
213	C₈	—	2	4	no	—
214	C₈	—	4	2	no	—
215	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
216	C₂²	C₁₁×#536	1	2	yes	—
217	C₂²	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
218	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
219	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
220	C₄	—	2	4	no	—
221	C₄	—	4	8	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	4	no	—
224	C₄	C₄×C₁₁×Q₁₆	1	4	yes	—
225	C₄	C₁₁×#442	1	4	yes	—
226	C₄	C₁₁×#519	1	2	yes	—
227	C₄	C₁₁×#541	1	2	yes	—
228	C₂	C₁₁×#2327	1	1	yes	characteristic
229	C₂	C₂×C₄×C₁₁×Q₁₆	1	1	yes	characteristic
230	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
231	C₂	C₁₁×#3228	1	2	yes	—
232	C₂	C₁₁×#3230	1	2	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 ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₁×#500	C₄	semidirect
46. #22248	C₁₁	direct (N × H)
107. #500	C₄×C₁₁	semidirect
190. C₁₁	#22248	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
C₄×C₁₁×C₄⋊Q₈	2
C₁₁×#1990	2
C₁₁×#1921	2
C₁₁×#1834	2
C₁₁×#1744	2
#22248	11

Subgroups — C11×#22248 #14599441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22248 #14599441