Subgroups — C₁₁×#22243 #14599436

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	2	yes	maximal
2	C₁₁×#2399	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1985	C₂	1	2	yes	maximal
4	C₁₁×#1917	C₂	1	8	yes	maximal
5	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
8	C₁₁×#446	—	2	8	no	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₁₁×#97	C₂²	1	4	yes	—
12	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#398	C₄	1	4	yes	—
15	C₁₁×#395	C₄	1	4	yes	—
16	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
17	C₁₁×#376	C₂²	1	1	yes	characteristic
18	C₁₁×#336	C₂²	1	8	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₁₁×#336	C₂²	1	4	yes	—
21	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
24	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
25	C₄×Q₈×C₁₁	—	2	4	no	—
26	C₄×Q₈×C₁₁	—	2	4	no	—
27	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
28	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
31	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×C₄⋊C₈	—	2	8	no	—
34	C₁₁×C₄⋊C₈	—	2	4	no	—
35	C₁₁×#97	—	2	8	no	—
36	C₁₁×#97	—	2	2	no	—
37	C₄×C₈×C₁₁	D₄	1	4	yes	—
38	C₁₁×#95	C₂×C₄	1	4	yes	—
39	C₁₁×#95	C₂×C₄	1	4	yes	—
40	C₁₁×#95	C₂×C₄	1	4	yes	—
41	#22243	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×Q₈×C₁₁	—	2	4	no	—
43	C₂×Q₈×C₁₁	—	4	4	no	—
44	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
46	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	—	2	2	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	—	2	8	no	—
53	C₂×C₈×C₁₁	—	2	4	no	—
54	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
55	C₁₁×C₄⋊C₄	—	2	4	no	—
56	C₁₁×C₄⋊C₄	—	2	8	no	—
57	C₁₁×C₄⋊C₄	—	4	8	no	—
58	C₄²×C₁₁	—	2	4	no	—
59	C₄²×C₁₁	—	2	4	no	—
60	C₄²×C₁₁	—	2	4	no	—
61	C₄²×C₁₁	C₂×D₄	1	2	yes	—
62	C₄²×C₁₁	#41	1	2	yes	—
63	C₂×#446	C₂×C₁₁	1	2	yes	—
64	#2399	C₂×C₁₁	1	1	yes	characteristic
65	#1985	C₂×C₁₁	1	2	yes	—
66	#1917	C₂×C₁₁	1	8	yes	—
67	#1832	C₂×C₁₁	1	1	yes	characteristic
68	#1746	C₂×C₁₁	1	1	yes	characteristic
69	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
70	Q₈×C₁₁	—	4	8	no	—
71	C₂×C₄×C₁₁	—	2	4	no	—
72	C₂×C₄×C₁₁	—	2	4	no	—
73	C₂×C₄×C₁₁	—	2	4	no	—
74	C₂×C₄×C₁₁	—	2	4	no	—
75	C₂×C₄×C₁₁	—	2	4	no	—
76	C₂×C₄×C₁₁	—	2	8	no	—
77	C₂×C₄×C₁₁	—	2	8	no	—
78	C₂×C₄×C₁₁	—	2	4	no	—
79	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
80	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
82	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
83	C₈×C₁₁	—	2	4	no	—
84	C₈×C₁₁	—	4	4	no	—
85	C₈×C₁₁	—	4	2	no	—
86	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
87	#446	—	2	8	no	—
88	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
89	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
90	C₂×#97	C₂²×C₁₁	1	4	yes	—
91	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
93	#398	C₄×C₁₁	1	4	yes	—
94	#395	C₄×C₁₁	1	4	yes	—
95	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
96	#376	C₂²×C₁₁	1	1	yes	characteristic
97	#336	C₂²×C₁₁	1	4	yes	—
98	#336	C₂²×C₁₁	1	8	yes	—
99	#336	C₂²×C₁₁	1	4	yes	—
100	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
101	C₂²×C₁₁	#519	1	2	yes	—
102	C₂²×C₁₁	#568	1	4	yes	—
103	C₄×C₁₁	—	2	4	no	—
104	C₄×C₁₁	—	4	4	no	—
105	C₄×C₁₁	—	4	4	no	—
106	C₄×C₁₁	—	4	4	no	—
107	C₄×C₁₁	#536	1	2	yes	—
108	C₄×C₁₁	#541	1	2	yes	—
109	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
110	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
111	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
112	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
113	C₄×Q₈	—	2	4	no	—
114	C₄×Q₈	—	2	4	no	—
115	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
116	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
117	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
118	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
119	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
120	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
121	C₄⋊C₈	—	2	8	no	—
122	C₄⋊C₈	—	2	4	no	—
123	#97	—	2	8	no	—
124	#97	—	2	2	no	—
125	C₄×C₈	D₄×C₁₁	1	4	yes	—
126	#95	C₂×C₄×C₁₁	1	4	yes	—
127	#95	C₂×C₄×C₁₁	1	4	yes	—
128	#95	C₂×C₄×C₁₁	1	4	yes	—
129	C₂×C₁₁	#2327	1	1	yes	characteristic
130	C₂×C₁₁	#2930	1	2	yes	—
131	C₂×C₁₁	#2987	1	4	yes	—
132	C₂×Q₈	—	2	4	no	—
133	C₂×Q₈	—	4	4	no	—
134	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
135	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
136	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
137	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
138	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	8	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	2	8	no	—
147	C₄⋊C₄	—	4	8	no	—
148	C₄²	—	2	4	no	—
149	C₄²	—	2	4	no	—
150	C₄²	—	2	4	no	—
151	C₄²	C₂×D₄×C₁₁	1	2	yes	—
152	C₄²	C₁₁×#41	1	2	yes	—
153	C₁₁	#22243	1	1	yes	characteristic, direct product factor, Sylow
154	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
155	Q₈	—	4	8	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	2	8	no	—
162	C₂×C₄	—	2	8	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
165	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
166	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
167	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	4	4	no	—
170	C₈	—	4	2	no	—
171	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
172	C₂²	C₁₁×#519	1	2	yes	—
173	C₂²	C₁₁×#568	1	4	yes	—
174	C₄	—	2	4	no	—
175	C₄	—	4	4	no	—
176	C₄	—	4	4	no	—
177	C₄	—	4	4	no	—
178	C₄	C₁₁×#536	1	2	yes	—
179	C₄	C₁₁×#541	1	2	yes	—
180	C₂	C₁₁×#2327	1	1	yes	characteristic
181	C₂	C₁₁×#2930	1	2	yes	—
182	C₂	C₁₁×#2987	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle, prime radical	C₂³×C₁₁	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
41. #22243	C₁₁	direct (N × H)
153. C₁₁	#22243	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×#446	2
C₁₁×#2399	2
C₁₁×#1985	2
C₁₁×#1917	2
C₁₁×#1832	2
C₁₁×#1746	2
#22243	11

Subgroups — C11×#22243 #14599436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22243 #14599436