Subgroups — #14665260

Order 2816.

314 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#13067375	C₂	1	1	yes	maximal, characteristic
3	#13066674	C₂	1	2	yes	maximal, complemented
4	#13066665	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#533	—	2	1	no	—
7	C₁₁×#500	C₂²	1	1	yes	characteristic
8	C₁₁×#494	C₂²	1	1	yes	characteristic
9	C₁₁×#487	—	2	1	no	—
10	C₁₁×#467	—	2	1	no	—
11	C₁₁×#467	C₄	1	2	yes	—
12	C₄×C₁₁×Q₁₆	—	2	1	no	—
13	C₄×C₁₁×Q₁₆	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
16	#10622537	—	2	1	no	—
17	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
18	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
19	#10622096	—	2	1	no	—
20	#10622096	C₂²	1	2	yes	—
21	C₂×C₁₁×Q₁₆	—	2	1	no	—
22	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₁₁×C₄⋊Q₈	—	2	1	no	—
26	C₁₁×C₄⋊Q₈	—	2	1	no	—
27	C₁₁×#125	—	4	1	no	—
28	C₁₁×C₂²⋊Q₈	—	2	2	no	—
29	C₁₁×C₂²⋊Q₈	—	4	1	no	—
30	C₄×Q₈×C₁₁	—	2	2	no	—
31	C₄×Q₈×C₁₁	—	4	1	no	—
32	C₁₁×#117	—	4	1	no	—
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×#4318	—	4	1	no	—
35	C₁₁×#107	—	2	1	no	—
36	C₁₁×#107	C₂×C₄	1	2	yes	—
37	C₁₁×#103	—	2	2	no	—
38	C₁₁×#103	—	2	2	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	4	2	no	—
45	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
47	#11983	—	11	1	no	maximal, Sylow
48	C₂×Q₈×C₁₁	—	2	2	no	—
49	C₂×Q₈×C₁₁	—	4	1	no	—
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
53	C₁₁×Q₁₆	—	4	1	no	—
54	C₁₁×Q₁₆	—	4	1	no	—
55	C₁₁×Q₁₆	—	4	2	no	—
56	C₂×C₈×C₁₁	—	2	1	no	—
57	C₂×C₈×C₁₁	—	2	1	no	—
58	C₂×C₈×C₁₁	—	4	1	no	—
59	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₁₁×C₄⋊C₄	—	4	1	no	—
67	C₁₁×C₄⋊C₄	—	4	1	no	—
68	C₁₁×C₄⋊C₄	—	4	1	no	—
69	C₁₁×C₂²⋊C₄	—	4	2	no	—
70	C₄²×C₁₁	—	4	2	no	—
71	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₁	D₈	1	1	yes	characteristic
73	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	#4318	—	8	2	no	—
76	C₂×C₁₁⋊C₈	—	4	2	no	—
77	C₁₁⋊C₁₆	—	4	2	no	—
78	#3170	D₁₁	1	1	yes	characteristic
79	C₂×C₄⋊C₁₆	—	11	1	no	—
80	#1567	—	11	1	no	—
81	#1365	—	11	2	no	—
82	#1362	—	11	2	no	—
83	C₂³×C₁₁	#102	1	1	yes	characteristic
84	Q₈×C₁₁	—	4	2	no	—
85	Q₈×C₁₁	—	4	2	no	—
86	Q₈×C₁₁	—	8	2	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	4	1	no	—
90	C₂×C₄×C₁₁	—	4	2	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
93	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
94	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
95	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
96	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
100	C₈×C₁₁	—	2	1	no	—
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	—	2	1	no	—
103	C₈×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₈×C₁₁	#137	1	1	yes	characteristic
105	C₁₁⋊C₈	—	8	2	no	—
106	#533	—	2	1	no	—
107	C₂²×C₁₆	—	22	1	no	—
108	#500	C₂×D₁₁	1	1	yes	characteristic
109	#494	C₂×D₁₁	1	1	yes	characteristic
110	#487	—	2	1	no	—
111	#467	—	2	1	no	—
112	#467	Dic₁₁	1	2	yes	—
113	C₄×Q₁₆	—	2	1	no	—
114	C₄×Q₁₆	Dic₁₁	1	2	yes	—
115	#423	—	22	1	no	—
116	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
117	C₄⋊C₁₆	—	11	2	no	—
118	C₄⋊C₁₆	—	22	1	no	—
119	#335	—	11	2	no	—
120	#335	—	22	1	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	1	no	—
123	C₂²×C₁₁	#358	1	2	yes	—
124	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	8	2	no	—
129	C₄×C₁₁	—	8	2	no	—
130	C₄×C₁₁	#358	1	2	yes	—
131	C₄×C₁₁	#413	1	1	yes	characteristic
132	C₄×C₁₁	#417	1	1	yes	characteristic
133	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
134	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
135	C₂×Q₁₆	—	2	1	no	—
136	C₂×Q₁₆	C₂×Dic₁₁	1	2	yes	—
137	C₂×M₁₆	—	44	1	no	—
138	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
139	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
140	C₄⋊Q₈	—	2	1	no	—
141	C₄⋊Q₈	—	2	1	no	—
142	#125	—	4	1	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	4	1	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	4	1	no	—
147	#117	—	4	1	no	—
148	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
149	C₂×C₁₆	—	22	2	no	—
150	C₂×C₁₆	—	44	2	no	—
151	#107	—	2	1	no	—
152	#107	C₂×Dic₁₁	1	2	yes	—
153	C₄⋊C₈	—	22	2	no	—
154	C₄⋊C₈	—	44	1	no	—
155	#103	—	2	2	no	—
156	#103	—	2	2	no	—
157	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
158	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
160	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
161	C₂×C₁₁	—	2	2	no	—
162	C₂×C₁₁	#1547	1	1	yes	characteristic
163	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
164	C₂×C₁₁	#2148	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	4	1	no	—
167	C₂²×C₄	#4323	1	1	yes	characteristic
168	C₂²×C₄	#4324	1	1	yes	characteristic
169	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
170	Q₁₆	—	4	2	no	—
171	Q₁₆	—	4	1	no	—
172	Q₁₆	—	4	1	no	—
173	M₁₆	—	88	2	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	44	2	no	—
178	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
179	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
180	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	1	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₂²⋊C₄	—	4	2	no	—
189	C₄²	—	4	2	no	—
190	C₄²	#4323	1	1	yes	characteristic
191	C₄²	#4324	1	1	yes	characteristic
192	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
194	C₁₆	—	44	2	no	—
195	C₁₁	#11983	1	1	yes	characteristic, complemented, Sylow
196	C₂³	#66896	1	1	yes	characteristic
197	Q₈	—	4	2	no	—
198	Q₈	—	4	2	no	—
199	Q₈	—	8	2	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	#66892	1	2	yes	—
206	C₂×C₄	#66893	1	2	yes	—
207	C₂×C₄	#66896	1	1	yes	characteristic
208	C₂×C₄	#66896	1	1	yes	characteristic
209	C₂×C₄	#66896	1	1	yes	characteristic
210	C₂×C₄	C₂×#4323	1	1	yes	characteristic
211	C₂×C₄	C₂×#4324	1	1	yes	characteristic
212	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	—	2	1	no	—
216	C₈	—	88	2	no	—
217	C₈	#67002	1	1	yes	characteristic
218	C₈	#67004	1	1	yes	characteristic
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#10622202	1	2	yes	—
222	C₂²	C₂×#66896	1	1	yes	characteristic
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	8	2	no	—
227	C₄	—	8	2	no	—
228	C₄	#10622202	1	2	yes	—
229	C₄	C₂×#66892	1	1	yes	characteristic
230	C₄	C₂×#66893	1	1	yes	characteristic
231	C₄	#10622845	1	1	yes	characteristic
232	C₄	#10622850	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#13067293	1	1	yes	characteristic
235	C₂	C₂×#10622202	1	1	yes	characteristic
236	C₂	#13070365	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#66896
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#3170	C₂
socle	C₂²×C₁₁	C₂×#102
prime radical	C₂³×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	#3170	D₁₁
hypocenter	C₁₁	#11983
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3170

Complements

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

N	H ≅ G/N	type
3. #13066674	C₂	semidirect
4. #13066665	C₂	semidirect
195. C₁₁	#11983	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₁₁⋊C₁₆)	2
#13067375	2
#13066674	2
#13066665	2
C₁₁×#3170	2
#11983	11