Subgroups — #14722997

Order 2816.

702 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	#13077184	C₂	1	2	yes	maximal
2	#13067387	C₂	1	6	yes	maximal, complemented
3	#13067372	C₂	1	3	yes	maximal, complemented
4	C₂×#10622095	C₂	1	3	yes	maximal, complemented
5	C₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
6	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
7	C₂×#67001	—	2	2	no	—
8	C₈×Q₈×C₁₁	C₄	1	1	yes	characteristic
9	C₈×Q₈×C₁₁	C₄	1	1	yes	characteristic
10	C₈×D₄×C₁₁	C₄	1	3	yes	—
11	C₈×D₄×C₁₁	C₄	1	3	yes	—
12	C₁₁×#431	C₂²	1	3	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
14	#10622612	—	2	6	no	—
15	#10622537	C₂²	1	6	yes	—
16	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	6	yes	—
17	#10622095	C₂²	1	1	yes	characteristic
18	#10622095	C₂²	1	3	yes	—
19	#10622095	C₂²	1	6	yes	—
20	#10622095	C₂²	1	6	yes	—
21	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
24	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Q₈×C₁₁	Q₈	1	1	yes	characteristic
26	C₄×D₄×C₁₁	C₂×C₄	1	3	yes	—
27	C₄×D₄×C₁₁	Q₈	1	3	yes	—
28	C₁₁×#117	D₄	1	3	yes	—
29	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
30	#67001	—	4	8	no	—
31	C₂×#4318	—	2	6	no	—
32	C₂²×C₁₁⋊C₈	—	2	6	no	—
33	C₁₁×C₄⋊C₈	C₂×C₄	1	3	yes	—
34	C₁₁×C₄⋊C₈	C₂×C₄	1	3	yes	—
35	C₁₁×C₂²⋊C₈	C₂×C₄	1	6	yes	—
36	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
37	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
38	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	C₄×C₈×C₁₁	C₂³	1	3	yes	—
40	C₄⋊(C₁₁⋊C₈)	—	2	6	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	6	no	—
42	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
43	C₄⋊(C₁₁⋊C₈)	C₂³	1	6	yes	—
44	#17826	—	11	1	no	maximal, Sylow
45	C₁₁×#41	SD₁₆	1	8	yes	—
46	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
47	C₂×D₄×C₁₁	C₄⋊C₄	1	3	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
49	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
50	C₂²×C₄×C₁₁	C₂×Q₈	1	3	yes	—
51	C₂×C₈×C₁₁	—	2	6	no	—
52	C₂×C₈×C₁₁	—	4	3	no	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
55	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₁₁×C₄⋊C₄	C₄⋊C₄	1	3	yes	—
58	C₁₁×C₄⋊C₄	C₄⋊C₄	1	3	yes	—
59	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	6	yes	—
60	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
61	C₄²×C₁₁	C₂×D₄	1	3	yes	—
62	C₄²×C₁₁	C₂×Q₈	1	3	yes	—
63	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
64	#4318	—	4	12	no	—
65	C₂×C₁₁⋊C₈	—	2	2	no	—
66	C₂×C₁₁⋊C₈	—	2	6	no	—
67	C₂×C₁₁⋊C₈	—	4	12	no	—
68	C₈×#41	D₁₁	1	1	yes	characteristic
69	#2906	—	11	2	no	—
70	#1570	—	11	6	no	—
71	#1566	—	11	3	no	—
72	C₂×#334	—	11	3	no	—
73	C₂³×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
74	Q₈×C₁₁	#106	1	4	yes	—
75	D₄×C₁₁	#106	1	12	yes	—
76	C₂×C₄×C₁₁	—	2	3	no	—
77	C₂×C₄×C₁₁	—	2	3	no	—
78	C₂×C₄×C₁₁	—	4	3	no	—
79	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
80	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
82	C₂×C₄×C₁₁	C₂×SD₁₆	1	12	yes	—
83	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
86	C₈×C₁₁	—	2	3	no	—
87	C₈×C₁₁	—	2	1	no	—
88	C₈×C₁₁	—	2	3	no	—
89	C₈×C₁₁	#131	1	2	yes	complemented
90	C₁₁⋊C₈	—	4	2	no	—
91	C₁₁⋊C₈	—	4	6	no	—
92	C₂×#131	—	22	2	no	—
93	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
94	C₈×Q₈	Dic₁₁	1	1	yes	characteristic
95	C₈×Q₈	Dic₁₁	1	1	yes	characteristic
96	C₈×D₄	Dic₁₁	1	3	yes	—
97	C₈×D₄	Dic₁₁	1	3	yes	—
98	#431	C₂×D₁₁	1	3	yes	—
99	#424	—	22	6	no	—
100	#423	—	11	6	no	—
101	C₂×C₄⋊C₈	—	11	6	no	—
102	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
103	#334	—	11	1	no	—
104	#334	—	11	3	no	—
105	#334	—	11	6	no	—
106	#334	—	11	6	no	—
107	C₂²×C₁₁	—	2	3	no	—
108	C₂²×C₁₁	—	2	3	no	—
109	C₂²×C₁₁	C₂×#106	1	6	yes	—
110	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
111	C₄×C₁₁	—	2	3	no	—
112	C₄×C₁₁	—	2	1	no	—
113	C₄×C₁₁	—	2	3	no	—
114	C₄×C₁₁	C₂×#106	1	6	yes	—
115	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
116	C₄×C₁₁	#568	1	1	yes	characteristic
117	C₄×C₁₁	C₂²×SD₁₆	1	2	yes	—
118	C₂×#41	D₄₄	1	1	yes	characteristic
119	#131	—	44	8	no	—
120	C₂×M₁₆	—	22	6	no	—
121	C₂²×C₈	—	22	6	no	—
122	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
123	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
124	C₄×Q₈	Dic₂₂	1	1	yes	characteristic
125	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
126	C₄×D₄	Dic₂₂	1	3	yes	—
127	C₄×D₄	C₂×Dic₁₁	1	3	yes	—
128	#117	D₄₄	1	3	yes	—
129	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
130	C₄⋊C₈	—	11	2	no	—
131	C₄⋊C₈	—	11	6	no	—
132	C₄⋊C₈	—	22	6	no	—
133	C₄⋊C₈	—	22	6	no	—
134	C₄⋊C₈	C₂×Dic₁₁	1	3	yes	—
135	C₄⋊C₈	C₂×Dic₁₁	1	3	yes	—
136	C₂²⋊C₈	C₂×Dic₁₁	1	6	yes	—
137	C₄×C₈	C₂×Dic₁₁	1	3	yes	—
138	C₄×C₈	C₂×Dic₁₁	1	3	yes	—
139	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
140	C₄×C₈	C₂²×D₁₁	1	3	yes	—
141	C₂×C₁₁	—	2	6	no	—
142	C₂×C₁₁	#2906	1	1	yes	characteristic
143	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
144	C₂×C₁₁	#2916	1	1	yes	characteristic
145	#41	#4314	1	8	yes	—
146	C₂×Q₈	C₄⋊Dic₁₁	1	1	yes	characteristic
147	C₂×D₄	C₄⋊Dic₁₁	1	3	yes	—
148	C₂²×C₄	C₂×Dic₂₂	1	3	yes	—
149	C₂²×C₄	C₂×D₄₄	1	3	yes	—
150	C₂²×C₄	C₂²×Dic₁₁	1	3	yes	—
151	M₁₆	—	44	12	no	—
152	C₂×C₈	—	2	6	no	—
153	C₂×C₈	—	4	3	no	—
154	C₂×C₈	—	22	2	no	—
155	C₂×C₈	—	22	6	no	—
156	C₂×C₈	—	44	12	no	—
157	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
158	C₂×C₈	C₂²×Dic₁₁	1	3	yes	—
159	C₂×C₈	C₂²×Dic₁₁	1	3	yes	—
160	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
161	C₄⋊C₄	C₄⋊Dic₁₁	1	3	yes	—
162	C₄⋊C₄	C₄⋊Dic₁₁	1	3	yes	—
163	C₂²⋊C₄	C₄⋊Dic₁₁	1	6	yes	—
164	C₄²	C₂×Dic₂₂	1	3	yes	—
165	C₄²	C₂×D₄₄	1	3	yes	—
166	C₄²	C₂²×Dic₁₁	1	3	yes	—
167	C₄²	C₂³×D₁₁	1	1	yes	characteristic
168	C₁₁	#17826	1	1	yes	characteristic, complemented, Sylow
169	C₂³	C₂×C₄⋊Dic₁₁	1	3	yes	—
170	Q₈	#66881	1	4	yes	—
171	D₄	#66881	1	12	yes	—
172	C₂×C₄	—	2	3	no	—
173	C₂×C₄	—	2	3	no	—
174	C₂×C₄	—	4	3	no	—
175	C₂×C₄	C₂×#4314	1	12	yes	—
176	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
177	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
178	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
179	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
180	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
181	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
182	C₈	—	2	3	no	—
183	C₈	—	2	1	no	—
184	C₈	—	2	3	no	—
185	C₈	—	44	2	no	—
186	C₈	—	44	6	no	—
187	C₈	#67001	1	2	yes	complemented
188	C₂²	—	2	3	no	—
189	C₂²	—	2	3	no	—
190	C₂²	C₂×#66881	1	6	yes	—
191	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
192	C₄	—	2	3	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	3	no	—
195	C₄	C₂×#66881	1	6	yes	—
196	C₄	C₂²×#4314	1	2	yes	—
197	C₄	C₂×#67001	1	1	yes	characteristic
198	C₄	#10623350	1	1	yes	characteristic
199	C₂	—	2	6	no	—
200	C₂	#13077184	1	1	yes	characteristic
201	C₂	C₂²×#66881	1	1	yes	characteristic
202	C₂	#13077227	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₈×C₁₁×#41	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×#41	D₁₁
hypocenter	C₁₁	#17826
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #13067387	C₂	semidirect
3. #13067372	C₂	semidirect
4. C₂×#10622095	C₂	semidirect
89. C₈×C₁₁	#131	semidirect
168. C₁₁	#17826	semidirect
187. C₈	#67001	semidirect

Maximal subgroups

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

subgroup	index
#13077184	2
#13067387	2
#13067372	2
C₂×#10622095	2
C₈×C₁₁×#41	2
#17826	11