Subgroups — C₁₁×#22258 #14599451

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2961	C₂	1	2	yes	maximal
3	C₁₁×#1995	C₂	1	2	yes	maximal
4	C₁₁×#1922	C₂	1	8	yes	maximal
5	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₂²	1	2	yes	—
8	C₁₁×#500	C₄	1	2	yes	complemented
9	C₁₁×#499	C₄	1	4	yes	complemented
10	C₁₁×#498	C₄	1	2	yes	complemented
11	C₁₁×#446	—	2	8	no	—
12	C₁₁×#427	C₂²	1	4	yes	—
13	C₁₁×#424	C₂²	1	4	yes	—
14	C₁₁×#423	C₂²	1	2	yes	—
15	C₁₁×#405	C₂²	1	4	yes	—
16	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#376	C₂²	1	1	yes	characteristic
19	C₁₁×#341	C₂²	1	4	yes	—
20	C₁₁×#339	C₂²	1	8	yes	—
21	C₁₁×#336	C₂²	1	4	yes	—
22	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
24	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
25	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₁₁×#125	C₂×C₄	1	4	yes	—
27	C₁₁×C₂²⋊Q₈	—	2	4	no	—
28	C₄×Q₈×C₁₁	—	2	4	no	—
29	C₁₁×#117	C₂³	1	4	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₁₁×#107	C₂×C₄	1	8	yes	—
33	C₁₁×#106	C₂×C₄	1	8	yes	—
34	C₁₁×C₄⋊C₈	—	2	8	no	—
35	C₁₁×C₄⋊C₈	—	2	4	no	—
36	C₁₁×#97	—	2	4	no	—
37	C₁₁×#97	D₄	1	4	yes	—
38	C₄×C₈×C₁₁	—	2	4	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₁₁×#95	—	2	2	no	—
43	#22258	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×Q₈×C₁₁	—	2	4	no	—
45	C₂²×C₄×C₁₁	—	2	2	no	—
46	C₂²×C₄×C₁₁	#41	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
48	C₁₁×M₁₆	—	2	8	no	—
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
54	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
55	C₁₁×C₄⋊C₄	—	2	8	no	—
56	C₁₁×C₄⋊C₄	—	2	4	no	—
57	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
58	C₁₁×C₂²⋊C₄	—	2	4	no	—
59	C₄²×C₁₁	—	2	4	no	—
60	C₄²×C₁₁	—	2	4	no	—
61	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₄²×C₁₁	C₂×D₄	1	2	yes	—
64	#3160	C₂×C₁₁	1	1	yes	characteristic
65	#2961	C₂×C₁₁	1	2	yes	—
66	#1995	C₂×C₁₁	1	2	yes	—
67	#1922	C₂×C₁₁	1	8	yes	—
68	#1837	C₂×C₁₁	1	1	yes	characteristic
69	#1746	C₂×C₁₁	1	1	yes	characteristic
70	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
71	Q₈×C₁₁	—	8	4	no	—
72	C₂×C₄×C₁₁	—	2	8	no	—
73	C₂×C₄×C₁₁	—	4	2	no	—
74	C₂×C₄×C₁₁	—	4	4	no	—
75	C₂×C₄×C₁₁	—	4	2	no	—
76	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
78	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
81	C₈×C₁₁	—	2	2	no	—
82	C₈×C₁₁	—	2	2	no	—
83	C₈×C₁₁	—	2	4	no	—
84	C₈×C₁₁	—	4	4	no	—
85	#533	C₂²×C₁₁	1	2	yes	—
86	#500	C₄×C₁₁	1	2	yes	complemented
87	#499	C₄×C₁₁	1	4	yes	complemented
88	#498	C₄×C₁₁	1	2	yes	complemented
89	#446	—	2	8	no	—
90	#427	C₂²×C₁₁	1	4	yes	—
91	#424	C₂²×C₁₁	1	4	yes	—
92	#423	C₂²×C₁₁	1	2	yes	—
93	#405	C₂²×C₁₁	1	4	yes	—
94	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
95	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
96	#376	C₂²×C₁₁	1	1	yes	characteristic
97	#341	C₂²×C₁₁	1	4	yes	—
98	#339	C₂²×C₁₁	1	8	yes	—
99	#336	C₂²×C₁₁	1	4	yes	—
100	C₂²×C₁₁	—	2	2	no	—
101	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
102	C₂²×C₁₁	#541	1	2	yes	—
103	C₄×C₁₁	—	2	2	no	—
104	C₄×C₁₁	—	2	2	no	—
105	C₄×C₁₁	—	4	8	no	—
106	C₄×C₁₁	—	8	2	no	—
107	C₄×C₁₁	#519	1	2	yes	—
108	C₄×C₁₁	#536	1	2	yes	—
109	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
110	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
111	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
112	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
113	#125	C₂×C₄×C₁₁	1	4	yes	—
114	C₂²⋊Q₈	—	2	4	no	—
115	C₄×Q₈	—	2	4	no	—
116	#117	C₂³×C₁₁	1	4	yes	—
117	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
118	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
119	#107	C₂×C₄×C₁₁	1	8	yes	—
120	#106	C₂×C₄×C₁₁	1	8	yes	—
121	C₄⋊C₈	—	2	8	no	—
122	C₄⋊C₈	—	2	4	no	—
123	#97	—	2	4	no	—
124	#97	D₄×C₁₁	1	4	yes	—
125	C₄×C₈	—	2	4	no	—
126	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
127	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
128	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
129	#95	—	2	2	no	—
130	C₂×C₁₁	—	2	2	no	—
131	C₂×C₁₁	#2327	1	1	yes	characteristic
132	C₂×C₁₁	#2957	1	2	yes	—
133	C₂×Q₈	—	2	4	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	C₁₁×#41	1	2	yes	—
136	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
137	M₁₆	—	2	8	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
142	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
143	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
144	C₄⋊C₄	—	2	8	no	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
147	C₂²⋊C₄	—	2	4	no	—
148	C₄²	—	2	4	no	—
149	C₄²	—	2	4	no	—
150	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
151	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
152	C₄²	C₂×D₄×C₁₁	1	2	yes	—
153	C₁₁	#22258	1	1	yes	characteristic, direct product factor, Sylow
154	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
155	Q₈	—	8	4	no	—
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	4	2	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
161	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
162	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
165	C₈	—	2	2	no	—
166	C₈	—	2	2	no	—
167	C₈	—	2	4	no	—
168	C₈	—	4	4	no	—
169	C₂²	—	2	2	no	—
170	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
171	C₂²	C₁₁×#541	1	2	yes	—
172	C₄	—	2	2	no	—
173	C₄	—	2	2	no	—
174	C₄	—	4	8	no	—
175	C₄	—	8	2	no	—
176	C₄	C₁₁×#519	1	2	yes	—
177	C₄	C₁₁×#536	1	2	yes	—
178	C₂	—	2	2	no	—
179	C₂	C₁₁×#2327	1	1	yes	characteristic
180	C₂	C₁₁×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₂×#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₁×#500	C₄	semidirect
9. C₁₁×#499	C₄	semidirect
10. C₁₁×#498	C₄	semidirect
43. #22258	C₁₁	direct (N × H)
86. #500	C₄×C₁₁	semidirect
87. #499	C₄×C₁₁	semidirect
88. #498	C₄×C₁₁	semidirect
153. C₁₁	#22258	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3160	2
C₁₁×#2961	2
C₁₁×#1995	2
C₁₁×#1922	2
C₁₁×#1837	2
C₁₁×#1746	2
#22258	11

Subgroups — C11×#22258 #14599451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22258 #14599451