Subgroups — C₁₁×#22253 #14599446

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#498	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2331	C₂	1	2	yes	maximal
3	C₁₁×#1993	C₂	1	2	yes	maximal
4	C₁₁×#1920	C₂	1	4	yes	maximal
5	C₁₁×#1919	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×#498	C₄	1	8	yes	complemented
10	C₂×C₁₁×#106	C₂²	1	4	yes	—
11	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#391	—	2	4	no	—
14	C₁₁×#389	C₂²	1	4	yes	—
15	C₁₁×#387	—	2	4	no	—
16	C₁₁×#382	C₂²	1	2	yes	—
17	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
18	C₁₁×#376	C₂²	1	1	yes	characteristic
19	C₁₁×#340	C₂²	1	4	yes	—
20	C₁₁×#340	C₂²	1	4	yes	—
21	C₁₁×#340	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	2	yes	—
23	C₁₁×#336	C₂²	1	2	yes	—
24	C₂²×Q₈×C₁₁	—	2	2	no	—
25	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
28	C₁₁×C₄⋊Q₈	—	2	4	no	—
29	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
30	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
32	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
34	C₂×C₄²×C₁₁	—	2	4	no	—
35	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₁₁×#106	C₂×C₄	1	16	yes	—
38	C₁₁×#97	—	2	2	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
40	C₁₁×#95	—	2	4	no	—
41	C₁₁×#95	—	2	2	no	—
42	C₁₁×#95	—	2	2	no	—
43	C₁₁×#95	—	2	4	no	—
44	C₁₁×#95	D₄	1	4	yes	—
45	#22253	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×Q₈×C₁₁	—	2	8	no	—
47	C₂×Q₈×C₁₁	—	8	4	no	—
48	C₂²×C₄×C₁₁	—	2	4	no	—
49	C₂²×C₄×C₁₁	—	2	4	no	—
50	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
53	C₂×C₈×C₁₁	—	2	1	no	—
54	C₂×C₈×C₁₁	—	2	1	no	—
55	C₂×C₈×C₁₁	—	2	2	no	—
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
60	C₁₁×C₄⋊C₄	—	2	8	no	—
61	C₁₁×C₄⋊C₄	—	2	4	no	—
62	C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	2	4	no	—
64	C₁₁×C₄⋊C₄	—	8	4	no	—
65	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
66	C₄²×C₁₁	—	2	2	no	—
67	C₄²×C₁₁	—	2	2	no	—
68	C₄²×C₁₁	—	8	4	no	—
69	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
70	C₄²×C₁₁	#41	1	2	yes	—
71	C₂×#498	C₂×C₁₁	1	1	yes	characteristic
72	#2331	C₂×C₁₁	1	2	yes	—
73	#1993	C₂×C₁₁	1	2	yes	—
74	#1920	C₂×C₁₁	1	4	yes	—
75	#1919	C₂×C₁₁	1	4	yes	—
76	#1835	C₂×C₁₁	1	1	yes	characteristic
77	#1746	C₂×C₁₁	1	1	yes	characteristic
78	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
79	Q₈×C₁₁	—	8	8	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	2	8	no	—
82	C₂×C₄×C₁₁	—	2	4	no	—
83	C₂×C₄×C₁₁	—	2	4	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	4	4	no	—
86	C₂×C₄×C₁₁	—	4	4	no	—
87	C₂×C₄×C₁₁	—	4	4	no	—
88	C₂×C₄×C₁₁	—	4	4	no	—
89	C₂×C₄×C₁₁	—	4	4	no	—
90	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
91	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
93	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
94	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
95	C₈×C₁₁	—	2	4	no	—
96	C₈×C₁₁	—	4	1	no	—
97	C₈×C₁₁	—	4	1	no	—
98	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
99	#498	C₄×C₁₁	1	8	yes	complemented
100	C₂×#106	C₂²×C₁₁	1	4	yes	—
101	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
102	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
103	#391	—	2	4	no	—
104	#389	C₂²×C₁₁	1	4	yes	—
105	#387	—	2	4	no	—
106	#382	C₂²×C₁₁	1	2	yes	—
107	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
108	#376	C₂²×C₁₁	1	1	yes	characteristic
109	#340	C₂²×C₁₁	1	4	yes	—
110	#340	C₂²×C₁₁	1	4	yes	—
111	#340	C₂²×C₁₁	1	4	yes	—
112	#336	C₂²×C₁₁	1	2	yes	—
113	#336	C₂²×C₁₁	1	2	yes	—
114	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
115	C₂²×C₁₁	#536	1	2	yes	—
116	C₂²×C₁₁	#577	1	4	yes	—
117	C₄×C₁₁	—	2	4	no	—
118	C₄×C₁₁	—	4	8	no	—
119	C₄×C₁₁	—	4	4	no	—
120	C₄×C₁₁	—	8	4	no	—
121	C₄×C₁₁	#519	1	2	yes	—
122	C₄×C₁₁	#541	1	1	yes	characteristic
123	C₄×C₁₁	#541	1	1	yes	characteristic
124	C₂²×Q₈	—	2	2	no	—
125	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
126	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
127	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
128	C₄⋊Q₈	—	2	4	no	—
129	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	4	no	—
132	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
133	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
134	C₂×C₄²	—	2	4	no	—
135	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
136	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
137	#106	C₂×C₄×C₁₁	1	16	yes	—
138	#97	—	2	2	no	—
139	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
140	#95	—	2	4	no	—
141	#95	—	2	2	no	—
142	#95	—	2	2	no	—
143	#95	—	2	4	no	—
144	#95	D₄×C₁₁	1	4	yes	—
145	C₂×C₁₁	#2327	1	1	yes	characteristic
146	C₂×C₁₁	#2949	1	2	yes	—
147	C₂×C₁₁	#3244	1	4	yes	—
148	C₂×Q₈	—	2	8	no	—
149	C₂×Q₈	—	8	4	no	—
150	C₂²×C₄	—	2	4	no	—
151	C₂²×C₄	—	2	4	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	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
162	C₄⋊C₄	—	2	8	no	—
163	C₄⋊C₄	—	2	4	no	—
164	C₄⋊C₄	—	2	4	no	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	8	4	no	—
167	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
168	C₄²	—	2	2	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	8	4	no	—
171	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
172	C₄²	C₁₁×#41	1	2	yes	—
173	C₁₁	#22253	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
175	Q₈	—	8	8	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	8	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	4	4	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
187	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
188	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
189	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
190	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
191	C₈	—	2	4	no	—
192	C₈	—	4	1	no	—
193	C₈	—	4	1	no	—
194	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
195	C₂²	C₁₁×#536	1	2	yes	—
196	C₂²	C₁₁×#577	1	4	yes	—
197	C₄	—	2	4	no	—
198	C₄	—	4	8	no	—
199	C₄	—	4	4	no	—
200	C₄	—	8	4	no	—
201	C₄	C₁₁×#519	1	2	yes	—
202	C₄	C₁₁×#541	1	1	yes	characteristic
203	C₄	C₁₁×#541	1	1	yes	characteristic
204	C₂	C₁₁×#2327	1	1	yes	characteristic
205	C₂	C₁₁×#2949	1	2	yes	—
206	C₂	C₁₁×#3244	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×#498	C₄	semidirect
45. #22253	C₁₁	direct (N × H)
99. #498	C₄×C₁₁	semidirect
173. C₁₁	#22253	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×#498	2
C₁₁×#2331	2
C₁₁×#1993	2
C₁₁×#1920	2
C₁₁×#1919	2
C₁₁×#1835	2
C₁₁×#1746	2
#22253	11

Subgroups — C11×#22253 #14599446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22253 #14599446