Subgroups — C₁₁×#20830 #14598023

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2920	C₂	1	2	yes	maximal
2	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1849	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1838	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1810	C₂	1	4	yes	maximal
6	C₁₁×#1778	C₂	1	4	yes	maximal, complemented
7	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#432	—	2	4	no	—
10	C₁₁×#431	—	2	4	no	—
11	C₂×C₁₁×#108	C₂²	1	8	yes	—
12	C₁₁×#423	C₂²	1	4	yes	—
13	C₁₁×#407	C₂²	1	4	yes	—
14	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
15	C₂×C₁₁×#97	C₄	1	8	yes	—
16	C₂×C₁₁×#97	C₂²	1	2	yes	—
17	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
19	C₁₁×#341	C₂²	1	8	yes	—
20	C₂³×C₄×C₁₁	Q₈	1	2	yes	—
21	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
23	C₂²×C₈×C₁₁	—	2	8	no	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₁₁	D₄	1	4	yes	—
29	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₁₁×#108	—	2	16	no	—
33	C₁₁×C₄⋊C₈	—	2	8	no	—
34	C₁₁×C₂²⋊C₈	—	2	8	no	—
35	C₁₁×#97	—	2	4	no	—
36	C₁₁×#97	C₂×C₄	1	4	yes	—
37	C₁₁×#97	C₂×C₄	1	8	yes	—
38	C₁₁×#97	C₂×C₄	1	4	yes	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	#20830	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	—	2	4	no	—
43	C₂²×C₄×C₁₁	—	4	4	no	—
44	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
46	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
50	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
52	C₁₁×M₁₆	—	2	16	no	—
53	C₂×C₈×C₁₁	—	2	16	no	—
54	C₂×C₈×C₁₁	—	2	8	no	—
55	C₂×C₈×C₁₁	—	2	4	no	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
58	C₂×C₈×C₁₁	#41	1	8	yes	—
59	C₄²×C₁₁	C₄⋊C₄	1	8	yes	—
60	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
61	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
62	C₄²×C₁₁	C₂×D₄	1	2	yes	—
63	C₄²×C₁₁	C₂×D₄	1	2	yes	—
64	#2920	C₂×C₁₁	1	2	yes	—
65	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic
66	#1849	C₂×C₁₁	1	2	yes	complemented
67	#1838	C₂×C₁₁	1	2	yes	complemented
68	#1810	C₂×C₁₁	1	4	yes	—
69	#1778	C₂×C₁₁	1	4	yes	complemented
70	C₂³×C₁₁	—	2	2	no	—
71	C₂³×C₁₁	—	2	4	no	—
72	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
73	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	8	no	—
76	C₂×C₄×C₁₁	—	2	4	no	—
77	C₂×C₄×C₁₁	—	2	4	no	—
78	C₂×C₄×C₁₁	—	4	4	no	—
79	C₂×C₄×C₁₁	—	4	2	no	—
80	C₂×C₄×C₁₁	—	4	2	no	—
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
82	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
83	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
84	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
87	C₈×C₁₁	—	2	4	no	—
88	C₈×C₁₁	—	4	8	no	—
89	C₈×C₁₁	#117	1	8	yes	—
90	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
91	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
92	#432	—	2	4	no	—
93	#431	—	2	4	no	—
94	C₂×#108	C₂²×C₁₁	1	8	yes	—
95	#423	C₂²×C₁₁	1	4	yes	—
96	#407	C₂²×C₁₁	1	4	yes	—
97	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
98	C₂×#97	C₄×C₁₁	1	8	yes	—
99	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
100	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
101	C₂×#97	C₂²×C₁₁	1	2	yes	—
102	#341	C₂²×C₁₁	1	8	yes	—
103	C₂²×C₁₁	—	2	8	no	—
104	C₂²×C₁₁	—	2	2	no	—
105	C₂²×C₁₁	—	2	2	no	—
106	C₂²×C₁₁	—	2	2	no	—
107	C₂²×C₁₁	#430	1	4	yes	—
108	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₁₁	#533	1	2	yes	—
110	C₄×C₁₁	—	2	4	no	—
111	C₄×C₁₁	—	2	4	no	—
112	C₄×C₁₁	—	2	2	no	—
113	C₄×C₁₁	C₂×#117	1	2	yes	—
114	C₄×C₁₁	#532	1	2	yes	—
115	C₂³×C₄	Q₈×C₁₁	1	2	yes	—
116	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
117	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
118	C₂²×C₈	—	2	8	no	—
119	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	—
120	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
121	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
122	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
123	C₂×C₄²	D₄×C₁₁	1	4	yes	—
124	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
125	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
126	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
127	#108	—	2	16	no	—
128	C₄⋊C₈	—	2	8	no	—
129	C₂²⋊C₈	—	2	8	no	—
130	#97	—	2	4	no	—
131	#97	C₂×C₄×C₁₁	1	4	yes	—
132	#97	C₂×C₄×C₁₁	1	8	yes	—
133	#97	C₂×C₄×C₁₁	1	4	yes	—
134	C₄×C₈	—	2	4	no	—
135	C₂×C₁₁	—	2	2	no	—
136	C₂×C₁₁	—	2	4	no	—
137	C₂×C₁₁	#2285	1	1	yes	characteristic
138	C₂×C₁₁	C₂×#430	1	2	yes	—
139	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	4	4	no	—
142	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
143	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
144	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
145	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
146	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
147	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
148	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
149	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
150	M₁₆	—	2	16	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	2	16	no	—
153	C₂×C₈	—	2	8	no	—
154	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
155	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
156	C₂×C₈	C₁₁×#41	1	8	yes	—
157	C₄²	C₁₁×C₄⋊C₄	1	8	yes	—
158	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
159	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
160	C₄²	C₂×D₄×C₁₁	1	2	yes	—
161	C₄²	C₂×D₄×C₁₁	1	2	yes	—
162	C₁₁	#20830	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	—	2	2	no	—
164	C₂³	—	2	4	no	—
165	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
166	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	8	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
175	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
176	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
177	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
178	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
179	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
180	C₈	—	2	4	no	—
181	C₈	—	4	8	no	—
182	C₈	C₁₁×#117	1	8	yes	—
183	C₂²	—	2	8	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	2	2	no	—
186	C₂²	—	2	2	no	—
187	C₂²	C₁₁×#430	1	4	yes	—
188	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
189	C₂²	C₁₁×#533	1	2	yes	—
190	C₄	—	2	4	no	—
191	C₄	—	2	4	no	—
192	C₄	—	2	2	no	—
193	C₄	C₂×C₁₁×#117	1	2	yes	—
194	C₄	C₁₁×#532	1	2	yes	—
195	C₂	—	2	2	no	—
196	C₂	—	2	4	no	—
197	C₂	C₁₁×#2285	1	1	yes	characteristic
198	C₂	C₂×C₁₁×#430	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	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1849	C₂	semidirect
4. C₁₁×#1838	C₂	semidirect
6. C₁₁×#1778	C₂	semidirect
40. #20830	C₁₁	direct (N × H)
66. #1849	C₂×C₁₁	semidirect
67. #1838	C₂×C₁₁	semidirect
69. #1778	C₂×C₁₁	semidirect
162. C₁₁	#20830	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×#2920	2
C₂²×C₁₁×#97	2
C₁₁×#1849	2
C₁₁×#1838	2
C₁₁×#1810	2
C₁₁×#1778	2
#20830	11

Subgroups — C11×#20830 #14598023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#20830 #14598023