Subgroups — #14653148

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068780	C₂	1	1	yes	maximal, characteristic
2	#13067180	C₂	1	4	yes	maximal
3	#13066899	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#533	C₂²	1	2	yes	—
6	C₁₁×#500	C₄	1	2	yes	complemented
7	C₁₁×#499	—	2	1	no	—
8	C₁₁×#499	—	2	1	no	—
9	C₁₁×#498	C₄	1	2	yes	complemented
10	C₁₁×#427	—	2	1	no	—
11	C₁₁×#427	—	2	1	no	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×#66882	—	2	1	no	—
14	C₂×#66881	—	2	1	no	—
15	#10622549	C₂²	1	2	yes	—
16	#10622538	C₂²	1	2	yes	—
17	#10622176	—	2	8	no	—
18	#10622093	—	2	1	no	—
19	C₈×C₁₁⋊C₈	—	2	1	no	—
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
22	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
23	C₁₁×#125	—	2	2	no	—
24	C₁₁×C₂²⋊Q₈	—	2	4	no	—
25	C₄×Q₈×C₁₁	—	2	4	no	—
26	C₁₁×#117	—	2	2	no	—
27	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₁	—	2	2	no	—
29	C₁₁×#107	—	2	2	no	—
30	C₁₁×#107	—	2	2	no	—
31	C₁₁×#106	—	2	2	no	—
32	C₁₁×#106	—	2	2	no	—
33	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₁₁⋊#95	—	2	4	no	—
38	C₂²⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
39	#66882	—	4	2	no	—
40	#66881	—	4	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	C₄×C₁₁⋊C₈	—	2	2	no	—
43	#9755	—	11	1	no	maximal, Sylow
44	C₂×Q₈×C₁₁	—	2	4	no	—
45	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×Dic₁₁	—	4	2	no	—
48	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
53	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
54	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
55	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
56	C₁₁×C₄⋊C₄	—	2	4	no	—
57	C₁₁×C₄⋊C₄	—	2	4	no	—
58	C₁₁×C₄⋊C₄	—	4	4	no	—
59	C₁₁×C₂²⋊C₄	—	4	2	no	—
60	C₄²×C₁₁	—	4	2	no	—
61	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₁	#41	1	2	yes	—
64	C₄⋊Dic₁₁	—	4	2	no	—
65	C₄⋊Dic₁₁	—	4	2	no	—
66	C₂×C₁₁⋊C₈	—	2	4	no	—
67	#3160	D₁₁	1	1	yes	characteristic
68	#1846	—	11	1	no	—
69	#1518	—	11	4	no	—
70	#1450	—	11	1	no	—
71	C₂³×C₁₁	#127	1	1	yes	characteristic
72	Q₈×C₁₁	—	8	4	no	—
73	C₂×C₄×C₁₁	—	4	2	no	—
74	C₂×C₄×C₁₁	—	4	4	no	—
75	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
77	C₂×C₄×C₁₁	#121	1	2	yes	—
78	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×Dic₁₁	—	8	4	no	—
84	C₂×Dic₁₁	—	8	2	no	—
85	C₈×C₁₁	#103	1	2	yes	—
86	C₈×C₁₁	#103	1	2	yes	—
87	C₈×C₁₁	#103	1	2	yes	—
88	C₈×C₁₁	#103	1	2	yes	—
89	C₁₁⋊C₈	—	4	4	no	—
90	#533	C₂×D₁₁	1	2	yes	—
91	#500	Dic₁₁	1	2	yes	complemented
92	#499	—	2	1	no	—
93	#499	—	2	1	no	—
94	#498	Dic₁₁	1	2	yes	complemented
95	#431	—	11	2	no	—
96	#427	—	2	1	no	—
97	#427	—	2	1	no	—
98	C₂×#107	—	22	1	no	—
99	C₂×#106	—	22	1	no	—
100	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
101	#382	—	11	2	no	—
102	#328	—	22	8	no	—
103	#322	—	22	1	no	—
104	C₈²	—	22	1	no	—
105	C₂²×C₁₁	—	2	2	no	—
106	C₂²×C₁₁	#390	1	1	yes	characteristic
107	C₂²×C₁₁	#492	1	1	yes	characteristic
108	C₂²×C₁₁	#494	1	1	yes	characteristic
109	C₄×C₁₁	—	2	2	no	—
110	C₄×C₁₁	—	2	2	no	—
111	C₄×C₁₁	—	8	4	no	—
112	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
113	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
114	C₄×C₁₁	#487	1	1	yes	characteristic
115	C₄×C₁₁	#487	1	1	yes	characteristic
116	Dic₁₁	—	16	2	no	—
117	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
119	C₄⋊Q₈	C₂×Dic₁₁	1	4	yes	—
120	#125	—	2	2	no	—
121	C₂²⋊Q₈	—	2	4	no	—
122	C₄×Q₈	—	2	4	no	—
123	#117	—	2	2	no	—
124	C₂×C₄⋊C₄	—	22	2	no	—
125	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
126	#107	—	2	2	no	—
127	#107	—	2	2	no	—
128	#107	—	44	2	no	—
129	#106	—	2	2	no	—
130	#106	—	2	2	no	—
131	#106	—	44	2	no	—
132	C₄⋊C₈	—	22	2	no	—
133	C₂²⋊C₈	—	11	4	no	—
134	C₄×C₈	—	22	2	no	—
135	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
136	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
137	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
138	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
139	#95	—	22	4	no	—
140	C₂×C₁₁	—	2	1	no	—
141	C₂×C₁₁	—	2	1	no	—
142	C₂×C₁₁	#1956	1	1	yes	characteristic
143	C₂×C₁₁	#1976	1	2	yes	—
144	C₂×Q₈	—	2	4	no	—
145	C₂²×C₄	—	44	2	no	—
146	C₂²×C₄	D₄×D₁₁	1	2	yes	—
147	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
148	C₂×C₈	—	22	4	no	—
149	C₂×C₈	#4325	1	2	yes	—
150	C₂×C₈	#4325	1	2	yes	—
151	C₂×C₈	#4326	1	2	yes	—
152	C₂×C₈	#4326	1	2	yes	—
153	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
154	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
155	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
156	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
157	C₄⋊C₄	—	2	4	no	—
158	C₄⋊C₄	—	2	4	no	—
159	C₄⋊C₄	—	4	4	no	—
160	C₄⋊C₄	—	44	2	no	—
161	C₄⋊C₄	—	44	2	no	—
162	C₂²⋊C₄	—	4	2	no	—
163	C₄²	—	4	2	no	—
164	C₄²	#4341	1	2	yes	—
165	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
166	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
167	C₁₁	#9755	1	1	yes	characteristic, complemented, Sylow
168	C₂³	#66993	1	1	yes	characteristic
169	Q₈	—	8	4	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	88	4	no	—
173	C₂×C₄	—	88	2	no	—
174	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
175	C₂×C₄	#66989	1	1	yes	characteristic
176	C₂×C₄	#66991	1	2	yes	—
177	C₂×C₄	C₂×#4325	1	1	yes	characteristic
178	C₂×C₄	C₂×#4325	1	1	yes	characteristic
179	C₂×C₄	C₂×#4326	1	1	yes	characteristic
180	C₂×C₄	C₂×#4326	1	1	yes	characteristic
181	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
182	C₈	—	44	4	no	—
183	C₈	#66899	1	2	yes	—
184	C₈	#66899	1	2	yes	—
185	C₈	#66899	1	2	yes	—
186	C₈	#66899	1	2	yes	—
187	C₂²	—	2	2	no	—
188	C₂²	#10622698	1	1	yes	characteristic
189	C₂²	#10622705	1	1	yes	characteristic
190	C₂²	#10622834	1	1	yes	characteristic
191	C₄	—	2	2	no	—
192	C₄	—	2	2	no	—
193	C₄	—	8	4	no	—
194	C₄	—	176	2	no	—
195	C₄	#10622694	1	1	yes	characteristic
196	C₄	#10622694	1	1	yes	characteristic
197	C₄	C₂×#66899	1	1	yes	characteristic
198	C₄	C₂×#66899	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	#13069419	1	1	yes	characteristic
202	C₂	#13069515	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622834
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#3160	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#127
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#3160	D₁₁
hypocenter	C₁₁	#9755
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
6. C₁₁×#500	C₄	semidirect
9. C₁₁×#498	C₄	semidirect
91. #500	Dic₁₁	semidirect
94. #498	Dic₁₁	semidirect
167. C₁₁	#9755	semidirect

Maximal subgroups

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

subgroup	index
#13068780	2
#13067180	2
#13066899	2
C₁₁×#3160	2
#9755	11