Subgroups — #14640972

Order 2816.

246 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	#13070372	C₂	1	1	yes	maximal, characteristic
2	#13068773	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#431	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66881	—	2	1	no	—
7	C₂×#66881	C₄	1	2	yes	—
8	C₂×#66876	—	2	1	no	—
9	#10622548	—	2	1	no	—
10	C₁₁×#335	C₄	1	2	yes	complemented
11	C₁₁×#334	—	2	1	no	—
12	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
13	C₄⋊(C₁₁⋊C₁₆)	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₁	—	2	2	no	—
18	C₂×C₄⋊Dic₁₁	—	4	1	no	—
19	C₂×C₄⋊Dic₁₁	—	4	1	no	—
20	C₁₁×C₄⋊C₈	—	2	2	no	—
21	C₁₁×C₂²⋊C₈	—	4	1	no	—
22	C₄×C₈×C₁₁	—	4	1	no	—
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
27	#66881	—	4	1	no	—
28	#66881	—	4	1	no	—
29	#66881	—	4	2	no	—
30	#66876	—	4	1	no	—
31	#66876	—	4	1	no	—
32	C₂×C₁₁⋊C₁₆	—	2	2	no	—
33	#7278	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
37	C₂²×Dic₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	—	2	1	no	—
39	C₂×C₈×C₁₁	—	2	1	no	—
40	C₂×C₈×C₁₁	—	4	2	no	—
41	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
46	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
49	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
52	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
53	C₄⋊Dic₁₁	—	4	2	no	—
54	C₄⋊Dic₁₁	—	4	2	no	—
55	C₄⋊Dic₁₁	—	8	2	no	—
56	C₄⋊Dic₁₁	—	8	2	no	—
57	C₁₁⋊C₁₆	—	4	2	no	—
58	#2150	—	11	1	no	—
59	#1844	—	11	1	no	—
60	#1564	D₁₁	1	1	yes	characteristic
61	C₂³×C₁₁	#102	1	1	yes	characteristic
62	C₂×C₄×C₁₁	—	2	2	no	—
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
72	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
74	C₂×Dic₁₁	—	8	2	no	—
75	C₂×Dic₁₁	—	8	2	no	—
76	C₂×Dic₁₁	—	8	2	no	—
77	C₈×C₁₁	—	2	1	no	—
78	C₈×C₁₁	—	2	1	no	—
79	C₈×C₁₁	—	8	2	no	—
80	C₈×C₁₁	#102	1	1	yes	characteristic
81	C₈×C₁₁	#103	1	1	yes	characteristic
82	C₈×C₁₁	#106	1	1	yes	characteristic
83	C₈×C₁₁	#107	1	1	yes	characteristic
84	C₂×M₃₂	—	22	1	no	—
85	#431	—	2	1	no	—
86	C₂×#106	—	11	2	no	—
87	C₂×#106	—	22	1	no	—
88	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
89	#384	—	22	1	no	—
90	C₄⋊C₁₆	—	11	2	no	—
91	C₄⋊C₁₆	—	22	1	no	—
92	#335	Dic₁₁	1	2	yes	complemented
93	#334	—	2	1	no	—
94	C₂²×C₁₁	—	2	1	no	—
95	C₂²×C₁₁	—	2	1	no	—
96	C₂²×C₁₁	#331	1	1	yes	characteristic
97	C₂²×C₁₁	#332	1	1	yes	characteristic
98	C₂²×C₁₁	#340	1	1	yes	characteristic
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	#332	1	1	yes	characteristic
102	C₄×C₁₁	#333	1	1	yes	characteristic
103	C₄×C₁₁	#340	1	1	yes	characteristic
104	C₄×C₁₁	#343	1	1	yes	characteristic
105	C₄×C₁₁	#360	1	2	yes	—
106	C₄×C₁₁	#365	1	2	yes	—
107	Dic₁₁	—	16	2	no	—
108	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
109	C₂²×C₈	D₄₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄	—	22	2	no	—
111	C₂×C₄⋊C₄	—	44	1	no	—
112	C₂×C₄⋊C₄	—	44	1	no	—
113	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
114	M₃₂	—	44	1	no	—
115	M₃₂	—	44	1	no	—
116	C₂×C₁₆	—	22	2	no	—
117	#106	—	44	1	no	—
118	#106	—	44	1	no	—
119	#106	—	44	2	no	—
120	C₄⋊C₈	—	2	2	no	—
121	C₂²⋊C₈	—	4	1	no	—
122	C₄×C₈	—	4	1	no	—
123	C₄×C₈	Dic₂₂	1	1	yes	characteristic
124	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
125	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
126	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
127	C₂×C₁₁	—	2	1	no	—
128	C₂×C₁₁	—	2	1	no	—
129	C₂×C₁₁	#1296	1	1	yes	characteristic
130	C₂×C₁₁	#1383	1	1	yes	characteristic
131	C₂×C₁₁	#1386	1	1	yes	characteristic
132	C₂²×C₄	—	44	2	no	—
133	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
134	C₂²×C₄	#4323	1	1	yes	characteristic
135	C₂²×C₄	#4325	1	1	yes	characteristic
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	4	2	no	—
139	C₂×C₈	#4314	1	1	yes	characteristic
140	C₂×C₈	#4314	1	1	yes	characteristic
141	C₂×C₈	D₈₈	1	1	yes	characteristic
142	C₂×C₈	Dic₄₄	1	1	yes	characteristic
143	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
144	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
145	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
146	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
147	C₄⋊C₄	—	44	2	no	—
148	C₄⋊C₄	—	44	2	no	—
149	C₄⋊C₄	—	88	2	no	—
150	C₄⋊C₄	—	88	2	no	—
151	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
152	C₄²	#4324	1	1	yes	characteristic
153	C₄²	#4326	1	1	yes	characteristic
154	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
155	C₁₆	—	44	2	no	—
156	C₁₁	#7278	1	1	yes	characteristic, complemented, Sylow
157	C₂³	#66873	1	1	yes	characteristic
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	88	2	no	—
161	C₂×C₄	—	88	2	no	—
162	C₂×C₄	—	88	2	no	—
163	C₂×C₄	#66871	1	1	yes	characteristic
164	C₂×C₄	#66872	1	1	yes	characteristic
165	C₂×C₄	#66874	1	1	yes	characteristic
166	C₂×C₄	#66880	1	1	yes	characteristic
167	C₂×C₄	#66885	1	1	yes	characteristic
168	C₂×C₄	#66887	1	1	yes	characteristic
169	C₂×C₄	#66888	1	1	yes	characteristic
170	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
171	C₂×C₄	#66896	1	1	yes	characteristic
172	C₂×C₄	#66899	1	1	yes	characteristic
173	C₈	—	2	1	no	—
174	C₈	—	2	1	no	—
175	C₈	—	8	2	no	—
176	C₈	#66880	1	1	yes	characteristic
177	C₈	#66881	1	1	yes	characteristic
178	C₈	#66882	1	1	yes	characteristic
179	C₈	#66885	1	1	yes	characteristic
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	#10622120	1	1	yes	characteristic
183	C₂²	#10622123	1	1	yes	characteristic
184	C₂²	#10622167	1	1	yes	characteristic
185	C₄	—	2	1	no	—
186	C₄	—	2	1	no	—
187	C₄	—	176	2	no	—
188	C₄	#10622119	1	1	yes	characteristic
189	C₄	#10622124	1	1	yes	characteristic
190	C₄	#10622132	1	2	yes	—
191	C₄	#10622189	1	1	yes	characteristic
192	C₄	#10622192	1	1	yes	characteristic
193	C₄	#10622204	1	2	yes	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	#13066500	1	1	yes	characteristic
197	C₂	#13066716	1	1	yes	characteristic
198	C₂	#13066721	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622167
commutator	C₂×C₈×C₁₁	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#1564	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂³×C₁₁	#102
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	#1564	D₁₁
hypocenter	C₁₁	#7278
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1564

Complements

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

N	H ≅ G/N	type
10. C₁₁×#335	C₄	semidirect
13. C₄⋊(C₁₁⋊C₁₆)	C₄	semidirect
92. #335	Dic₁₁	semidirect
156. C₁₁	#7278	semidirect

Maximal subgroups

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

subgroup	index
#13070372	2
#13068773	2
C₁₁×#1564	2
#7278	11