Subgroups — C₁₁×#22257 #14599450

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3162	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2960	C₂	1	2	yes	maximal
3	C₁₁×#1995	C₂	1	2	yes	maximal
4	C₁₁×#1922	C₂	1	8	yes	maximal
5	C₁₁×#1838	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₂²	1	2	yes	—
8	C₁₁×#501	C₄	1	4	yes	complemented
9	C₁₁×#501	C₄	1	4	yes	complemented
10	C₁₁×#446	—	2	2	no	—
11	C₁₁×#446	—	2	2	no	—
12	C₈×Q₈×C₁₁	—	2	2	no	—
13	C₈×Q₈×C₁₁	—	2	2	no	—
14	C₁₁×#427	C₂²	1	4	yes	—
15	C₁₁×#424	C₂²	1	4	yes	—
16	C₁₁×#423	C₂²	1	2	yes	—
17	C₁₁×#405	C₂²	1	4	yes	—
18	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#376	C₂²	1	1	yes	characteristic
21	C₁₁×#341	C₂²	1	4	yes	—
22	C₁₁×#339	C₂²	1	8	yes	—
23	C₁₁×#336	C₂²	1	4	yes	—
24	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
28	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₁×#125	C₂×C₄	1	4	yes	—
30	C₁₁×C₂²⋊Q₈	—	2	2	no	—
31	C₁₁×C₂²⋊Q₈	—	2	2	no	—
32	C₄×Q₈×C₁₁	—	2	2	no	—
33	C₄×Q₈×C₁₁	—	2	2	no	—
34	C₁₁×#117	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₁₁×#107	C₂×C₄	1	8	yes	—
38	C₁₁×#106	C₂×C₄	1	4	yes	—
39	C₁₁×#106	C₂×C₄	1	4	yes	—
40	C₁₁×C₄⋊C₈	—	2	4	no	—
41	C₁₁×C₄⋊C₈	—	2	4	no	—
42	C₁₁×C₄⋊C₈	—	2	2	no	—
43	C₁₁×C₄⋊C₈	—	2	2	no	—
44	C₁₁×#97	—	2	4	no	—
45	C₁₁×#97	C₂×C₄	1	4	yes	—
46	C₄×C₈×C₁₁	—	2	4	no	—
47	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₁	D₄	1	2	yes	—
49	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
50	C₁₁×#95	—	2	2	no	—
51	#22257	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂×Q₈×C₁₁	—	2	2	no	—
53	C₂×Q₈×C₁₁	—	2	2	no	—
54	C₂²×C₄×C₁₁	—	2	2	no	—
55	C₂²×C₄×C₁₁	#41	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
57	C₁₁×M₁₆	—	2	8	no	—
58	C₂×C₈×C₁₁	—	2	4	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	—	2	4	no	—
61	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
62	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
64	C₁₁×C₄⋊C₄	—	2	4	no	—
65	C₁₁×C₄⋊C₄	—	2	4	no	—
66	C₁₁×C₄⋊C₄	—	2	2	no	—
67	C₁₁×C₄⋊C₄	—	2	2	no	—
68	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
69	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
70	C₁₁×C₂²⋊C₄	—	2	4	no	—
71	C₄²×C₁₁	—	2	4	no	—
72	C₄²×C₁₁	—	2	4	no	—
73	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
76	#3162	C₂×C₁₁	1	1	yes	characteristic
77	#2960	C₂×C₁₁	1	2	yes	—
78	#1995	C₂×C₁₁	1	2	yes	—
79	#1922	C₂×C₁₁	1	8	yes	—
80	#1838	C₂×C₁₁	1	1	yes	characteristic
81	#1746	C₂×C₁₁	1	1	yes	characteristic
82	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
83	Q₈×C₁₁	—	4	4	no	—
84	Q₈×C₁₁	—	4	4	no	—
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	4	2	no	—
88	C₂×C₄×C₁₁	—	4	4	no	—
89	C₂×C₄×C₁₁	—	4	2	no	—
90	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
95	C₈×C₁₁	—	2	4	no	—
96	C₈×C₁₁	—	2	2	no	—
97	C₈×C₁₁	—	2	2	no	—
98	C₈×C₁₁	—	4	4	no	—
99	#533	C₂²×C₁₁	1	2	yes	—
100	#501	C₄×C₁₁	1	4	yes	complemented
101	#501	C₄×C₁₁	1	4	yes	complemented
102	#446	—	2	2	no	—
103	#446	—	2	2	no	—
104	C₈×Q₈	—	2	2	no	—
105	C₈×Q₈	—	2	2	no	—
106	#427	C₂²×C₁₁	1	4	yes	—
107	#424	C₂²×C₁₁	1	4	yes	—
108	#423	C₂²×C₁₁	1	2	yes	—
109	#405	C₂²×C₁₁	1	4	yes	—
110	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
112	#376	C₂²×C₁₁	1	1	yes	characteristic
113	#341	C₂²×C₁₁	1	4	yes	—
114	#339	C₂²×C₁₁	1	8	yes	—
115	#336	C₂²×C₁₁	1	4	yes	—
116	C₂²×C₁₁	—	2	2	no	—
117	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
118	C₂²×C₁₁	#541	1	2	yes	—
119	C₄×C₁₁	—	2	2	no	—
120	C₄×C₁₁	—	2	2	no	—
121	C₄×C₁₁	—	4	4	no	—
122	C₄×C₁₁	—	4	4	no	—
123	C₄×C₁₁	—	8	2	no	—
124	C₄×C₁₁	#519	1	2	yes	—
125	C₄×C₁₁	#536	1	2	yes	—
126	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
127	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
128	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
129	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
130	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
131	#125	C₂×C₄×C₁₁	1	4	yes	—
132	C₂²⋊Q₈	—	2	2	no	—
133	C₂²⋊Q₈	—	2	2	no	—
134	C₄×Q₈	—	2	2	no	—
135	C₄×Q₈	—	2	2	no	—
136	#117	C₂³×C₁₁	1	4	yes	—
137	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
138	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
139	#107	C₂×C₄×C₁₁	1	8	yes	—
140	#106	C₂×C₄×C₁₁	1	4	yes	—
141	#106	C₂×C₄×C₁₁	1	4	yes	—
142	C₄⋊C₈	—	2	4	no	—
143	C₄⋊C₈	—	2	4	no	—
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	2	2	no	—
146	#97	—	2	4	no	—
147	#97	C₂×C₄×C₁₁	1	4	yes	—
148	C₄×C₈	—	2	4	no	—
149	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
150	C₄×C₈	D₄×C₁₁	1	2	yes	—
151	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
152	#95	—	2	2	no	—
153	C₂×C₁₁	—	2	2	no	—
154	C₂×C₁₁	#2327	1	1	yes	characteristic
155	C₂×C₁₁	#2955	1	2	yes	—
156	C₂×Q₈	—	2	2	no	—
157	C₂×Q₈	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	C₁₁×#41	1	2	yes	—
160	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
161	M₁₆	—	2	8	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	—	2	4	no	—
165	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
166	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
167	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
168	C₄⋊C₄	—	2	4	no	—
169	C₄⋊C₄	—	2	4	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
173	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
174	C₂²⋊C₄	—	2	4	no	—
175	C₄²	—	2	4	no	—
176	C₄²	—	2	4	no	—
177	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
178	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
179	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
180	C₁₁	#22257	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
182	Q₈	—	4	4	no	—
183	Q₈	—	4	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
190	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
191	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
192	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
193	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
194	C₈	—	2	4	no	—
195	C₈	—	2	2	no	—
196	C₈	—	2	2	no	—
197	C₈	—	4	4	no	—
198	C₂²	—	2	2	no	—
199	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
200	C₂²	C₁₁×#541	1	2	yes	—
201	C₄	—	2	2	no	—
202	C₄	—	2	2	no	—
203	C₄	—	4	4	no	—
204	C₄	—	4	4	no	—
205	C₄	—	8	2	no	—
206	C₄	C₁₁×#519	1	2	yes	—
207	C₄	C₁₁×#536	1	2	yes	—
208	C₂	—	2	2	no	—
209	C₂	C₁₁×#2327	1	1	yes	characteristic
210	C₂	C₁₁×#2955	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×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₁×#501	C₄	semidirect
9. C₁₁×#501	C₄	semidirect
51. #22257	C₁₁	direct (N × H)
100. #501	C₄×C₁₁	semidirect
101. #501	C₄×C₁₁	semidirect
180. C₁₁	#22257	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×#3162	2
C₁₁×#2960	2
C₁₁×#1995	2
C₁₁×#1922	2
C₁₁×#1838	2
C₁₁×#1746	2
#22257	11

Subgroups — C11×#22257 #14599450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22257 #14599450