Subgroups — #14643137

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068361	C₂	1	1	yes	maximal, characteristic
2	#13068361	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622092	C₂	1	1	yes	maximal, characteristic
5	C₂×#10622092	C₂	1	1	yes	maximal, characteristic
6	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₁	C₄	1	4	yes	—
12	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₁₁×#322	C₄	1	4	yes	complemented
17	#10622188	C₄	1	4	yes	—
18	#10622188	C₄	1	4	yes	—
19	#10622093	C₄	1	4	yes	complemented
20	#10622092	C₄	1	4	yes	complemented
21	#10622092	C₄	1	4	yes	complemented
22	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
28	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
29	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
31	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
38	C₈×Dic₁₁	—	2	8	no	—
39	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
40	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
41	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
42	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
43	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
44	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
45	#7843	—	11	1	no	maximal, Sylow
46	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
49	C₂²×Dic₁₁	C₄²	1	4	yes	—
50	C₂×C₈×C₁₁	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	—	2	4	no	—
53	C₂×C₈×C₁₁	C₄²	1	4	yes	—
54	C₂×C₈×C₁₁	C₄²	1	4	yes	—
55	C₂×C₈×C₁₁	C₄²	1	4	yes	—
56	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₄×Dic₁₁	—	2	4	no	—
61	C₄×Dic₁₁	—	2	4	no	—
62	C₄×Dic₁₁	M₁₆	1	8	yes	—
63	C₂×C₁₁⋊C₈	—	2	4	no	—
64	C₂×C₁₁⋊C₈	—	2	4	no	—
65	C₂×C₁₁⋊C₈	—	2	4	no	—
66	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
67	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
68	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
69	#1744	—	11	1	no	—
70	#1744	—	11	1	no	—
71	C₄²×C₈	—	11	1	no	—
72	C₂×#322	—	11	1	no	—
73	C₂×#322	—	11	1	no	—
74	C₂×#322	—	11	1	no	—
75	C₂×#322	D₁₁	1	1	yes	characteristic
76	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
84	C₂×C₄×C₁₁	#131	1	4	yes	—
85	C₂×C₄×C₁₁	#131	1	4	yes	—
86	C₂×Dic₁₁	—	2	4	no	—
87	C₂×Dic₁₁	—	2	4	no	—
88	C₂×Dic₁₁	#97	1	8	yes	—
89	C₈×C₁₁	—	2	4	no	—
90	C₈×C₁₁	—	2	4	no	—
91	C₈×C₁₁	—	2	4	no	—
92	C₁₁⋊C₈	—	2	4	no	—
93	C₁₁⋊C₈	—	2	4	no	—
94	C₁₁⋊C₈	—	2	4	no	—
95	C₂×C₄×C₈	—	11	1	no	—
96	C₂×C₄×C₈	—	11	1	no	—
97	C₂×C₄×C₈	—	11	1	no	—
98	C₂×C₄×C₈	—	11	4	no	—
99	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
102	C₄³	—	11	1	no	—
103	#336	—	11	4	no	—
104	#336	—	11	4	no	—
105	#322	—	11	4	no	—
106	#322	—	11	4	no	—
107	#322	—	11	4	no	—
108	#322	Dic₁₁	1	4	yes	complemented
109	C₂²×C₁₁	C₄³	1	1	yes	characteristic
110	C₂²×C₁₁	C₂×#97	1	2	yes	—
111	C₂²×C₁₁	#405	1	2	yes	—
112	C₂²×C₁₁	#405	1	2	yes	—
113	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
114	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
115	C₄×C₁₁	#405	1	2	yes	—
116	C₄×C₁₁	#405	1	2	yes	—
117	C₄×C₁₁	#405	1	2	yes	—
118	C₄×C₁₁	#405	1	2	yes	—
119	Dic₁₁	—	2	8	no	—
120	C₂²×C₈	—	11	2	no	—
121	C₂²×C₈	—	11	2	no	—
122	C₂²×C₈	—	11	2	no	—
123	C₂²×C₈	C₄×D₁₁	1	2	yes	—
124	C₂²×C₈	C₄×D₁₁	1	2	yes	—
125	C₂²×C₈	C₄×D₁₁	1	2	yes	—
126	C₂×C₄²	—	11	2	no	—
127	C₂×C₄²	—	11	2	no	—
128	C₂×C₄²	—	11	2	no	—
129	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
130	C₄×C₈	—	11	2	no	—
131	C₄×C₈	—	11	2	no	—
132	C₄×C₈	—	11	2	no	—
133	C₄×C₈	—	11	2	no	—
134	C₄×C₈	—	11	2	no	—
135	C₄×C₈	—	11	2	no	—
136	C₄×C₈	—	22	8	no	—
137	C₄×C₈	C₄×D₁₁	1	2	yes	—
138	C₄×C₈	C₄×D₁₁	1	2	yes	—
139	C₄×C₈	C₄×D₁₁	1	2	yes	—
140	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
141	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
142	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
143	C₂×C₁₁	#1452	1	4	yes	—
144	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
145	C₂×C₁₁	#1726	1	1	yes	characteristic
146	C₂×C₁₁	#1726	1	1	yes	characteristic
147	C₂²×C₄	—	11	4	no	—
148	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
149	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	11	4	no	—
155	C₂×C₈	—	11	4	no	—
156	C₂×C₈	—	11	4	no	—
157	C₂×C₈	—	22	4	no	—
158	C₂×C₈	—	22	4	no	—
159	C₂×C₈	—	22	4	no	—
160	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
161	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
162	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
163	C₄²	—	11	8	no	—
164	C₄²	—	22	4	no	—
165	C₄²	—	22	4	no	—
166	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
167	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
168	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
169	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
170	C₁₁	#7843	1	1	yes	characteristic, complemented, Sylow
171	C₂³	C₄²×D₁₁	1	1	yes	characteristic
172	C₂×C₄	—	11	8	no	—
173	C₂×C₄	—	22	4	no	—
174	C₂×C₄	—	22	4	no	—
175	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
176	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
177	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
178	C₂×C₄	#66954	1	4	yes	—
179	C₂×C₄	M₁₆×D₁₁	1	4	yes	—
180	C₂×C₄	#66960	1	4	yes	—
181	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
182	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
184	C₈	—	2	4	no	—
185	C₈	—	2	4	no	—
186	C₈	—	2	4	no	—
187	C₈	—	22	4	no	—
188	C₈	—	22	4	no	—
189	C₈	—	22	4	no	—
190	C₂²	#10622302	1	2	yes	—
191	C₂²	D₁₁×#97	1	2	yes	—
192	C₂²	#10622321	1	2	yes	—
193	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
194	C₄	—	22	8	no	—
195	C₄	#10622302	1	2	yes	—
196	C₄	#10622320	1	2	yes	—
197	C₄	#10622321	1	2	yes	—
198	C₄	#10622714	1	2	yes	—
199	C₄	M₁₆×Dic₁₁	1	2	yes	—
200	C₄	#10622735	1	2	yes	—
201	C₂	#13066907	1	4	yes	—
202	C₂	#97×Dic₁₁	1	1	yes	characteristic
203	C₂	#13068302	1	1	yes	characteristic
204	C₂	#13068304	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₂×C₁₁×#322	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#322	D₁₁
hypocenter	C₁₁	#7843
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
16. C₁₁×#322	C₄	semidirect
19. #10622093	C₄	semidirect
20. #10622092	C₄	semidirect
21. #10622092	C₄	semidirect
108. #322	Dic₁₁	semidirect
170. C₁₁	#7843	semidirect

Maximal subgroups

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

subgroup	index
#13068361	2
C₄×C₈×Dic₁₁	2
C₂×#10622092	2
C₂×#10622093	2
C₂×C₁₁×#322	2
#7843	11