Subgroups — #14719360

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077572	C₂	1	2	yes	maximal
2	C₄×#66954	C₂	1	1	yes	maximal, characteristic
3	#13066898	C₂	1	2	yes	maximal, complemented
4	#13066897	C₂	1	2	yes	maximal, complemented
5	#13066895	C₂	1	4	yes	maximal, complemented
6	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈²×D₁₁	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66954	C₄	1	2	yes	—
10	C₄×#4339	C₂²	1	1	yes	characteristic
11	C₁₁×#431	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622714	C₄	1	2	yes	—
14	C₄×#4318	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
16	#10622447	C₄	1	4	yes	—
17	#10622443	C₄	1	4	yes	—
18	(C₂²⋊D₁₁)⋊C₈	C₄	1	8	yes	—
19	#10622302	C₄	1	4	yes	—
20	C₄×#4313	C₂²	1	2	yes	—
21	#10622298	C₂²	1	4	yes	—
22	C₄×C₈×D₁₁	C₂²	1	2	yes	—
23	C₄×C₈×D₁₁	C₂²	1	4	yes	—
24	C₁₁×#322	C₂²	1	2	yes	—
25	C₈²×C₁₁	C₂²	1	2	yes	—
26	#10622092	C₂²	1	4	yes	—
27	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×C₁₁⋊C₈	C₂²	1	4	yes	—
29	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
30	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×#4339	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₄×C₂²⋊D₁₁	C₂×C₄	1	4	yes	—
35	#66979	C₂×C₄	1	1	yes	characteristic
36	C₂×#4318	C₂×C₄	1	2	yes	—
37	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
38	#66954	C₈	1	16	yes	complemented
39	C₂×#4313	C₂×C₄	1	4	yes	—
40	C₂×C₈×D₁₁	C₂×C₄	1	8	yes	—
41	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
42	C₄×D₄₄	C₂×C₄	1	2	yes	—
43	#66925	C₂×C₄	1	2	yes	—
44	C₄²×D₁₁	C₂³	1	2	yes	—
45	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
46	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
47	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
48	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₁₁	C₂³	1	4	yes	—
50	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	(C₂×D₁₁)⋊C₈	C₂×C₄	1	8	yes	—
53	#66879	C₂×C₄	1	4	yes	—
54	Dic₁₁⋊C₈	C₂×C₄	1	8	yes	—
55	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
56	C₈×Dic₁₁	C₂×C₄	1	8	yes	—
57	#66867	C₂×C₄	1	2	yes	—
58	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
59	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
60	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
61	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
62	C₈×#131	—	11	1	no	maximal, Sylow
63	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₁	C₄²	1	2	yes	—
66	#4339	C₂×C₈	1	8	yes	—
67	C₂×D₄₄	C₄²	1	1	yes	characteristic
68	C₂×C₄×D₁₁	C₂²×C₄	1	4	yes	—
69	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
70	C₂×Dic₂₂	C₄²	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
72	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
73	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
74	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
75	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
76	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
78	C₂²⋊Dic₁₁	C₄²	1	2	yes	—
79	(C₂×D₁₁)⋊C₄	C₄²	1	4	yes	—
80	C₄⋊Dic₁₁	C₄²	1	2	yes	—
81	Dic₁₁⋊C₄	C₄²	1	4	yes	—
82	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
83	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
84	#4318	C₂×C₈	1	8	yes	complemented
85	C₂×C₁₁⋊C₈	—	2	8	no	—
86	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
87	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
88	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
89	#4313	C₂×C₈	1	16	yes	complemented
90	C₈×D₁₁	—	2	16	no	—
91	C₈×D₁₁	C₂×C₈	1	16	yes	complemented
92	C₈×#41	—	11	2	no	—
93	C₄×#131	—	11	1	no	—
94	#1450	—	11	2	no	—
95	#1450	D₁₁	1	1	yes	characteristic, complemented
96	C₈×M₁₆	—	11	2	no	—
97	C₈×M₁₆	—	11	4	no	—
98	C₂×C₈²	—	11	1	no	—
99	C₂×C₈²	—	11	2	no	—
100	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
101	C₂²×D₁₁	C₂×C₄²	1	2	yes	—
102	C₂×C₄×C₁₁	—	2	4	no	—
103	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
106	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
108	C₂²⋊D₁₁	C₄×C₈	1	8	yes	—
109	C₂×Dic₁₁	C₂×C₄²	1	4	yes	—
110	C₂×Dic₁₁	C₂×C₄²	1	2	yes	—
111	D₄₄	C₄×C₈	1	4	yes	—
112	C₄×D₁₁	—	2	8	no	—
113	C₄×D₁₁	C₂²×C₈	1	8	yes	—
114	Dic₂₂	C₄×C₈	1	4	yes	—
115	C₈×C₁₁	—	2	8	no	—
116	C₈×C₁₁	C₂²×C₈	1	4	yes	—
117	C₈×C₁₁	C₂²×C₈	1	4	yes	—
118	C₁₁⋊C₈	—	2	4	no	—
119	C₁₁⋊C₈	C₂²×C₈	1	8	yes	—
120	C₁₁⋊C₈	#131	1	8	yes	complemented
121	C₂×#131	—	11	2	no	—
122	C₄×#41	—	11	1	no	—
123	C₈×Q₈	—	11	4	no	—
124	C₈×D₄	—	11	4	no	—
125	C₈×D₄	—	11	8	no	—
126	#431	—	11	4	no	—
127	#431	C₂×D₁₁	1	2	yes	—
128	#405	—	11	2	no	—
129	#405	—	11	4	no	—
130	C₄×M₁₆	—	11	1	no	—
131	C₄×M₁₆	—	11	2	no	—
132	C₂×C₄×C₈	—	11	2	no	—
133	C₂×C₄×C₈	—	11	4	no	—
134	C₂×C₄×C₈	—	11	2	no	—
135	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
136	#322	—	11	4	no	—
137	#322	C₂×D₁₁	1	2	yes	—
138	C₈²	—	11	4	no	—
139	C₈²	—	11	2	no	—
140	C₈²	—	11	1	no	—
141	C₈²	—	11	1	no	—
142	C₈²	C₂×D₁₁	1	2	yes	—
143	C₂²×C₁₁	—	2	2	no	—
144	C₂²×C₁₁	C₂×C₄×C₈	1	2	yes	—
145	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
146	C₂×D₁₁	—	2	4	no	—
147	C₂×D₁₁	C₂×C₄×C₈	1	4	yes	—
148	C₄×C₁₁	—	2	2	no	—
149	C₄×C₁₁	C₂×C₄×C₈	1	2	yes	—
150	C₄×C₁₁	C₂³×C₈	1	2	yes	—
151	C₄×C₁₁	C₂×#131	1	4	yes	—
152	Dic₁₁	—	2	4	no	—
153	Dic₁₁	C₂×C₄×C₈	1	4	yes	—
154	C₂×#41	—	11	1	no	—
155	#131	—	11	16	no	—
156	C₂×M₁₆	—	11	2	no	—
157	C₂×M₁₆	—	11	4	no	—
158	C₂²×C₈	—	11	4	no	—
159	C₂²×C₈	—	11	4	no	—
160	C₂²×C₈	—	11	8	no	—
161	C₂²×C₈	C₄×D₁₁	1	2	yes	—
162	C₄×Q₈	—	11	2	no	—
163	C₄×D₄	—	11	4	no	—
164	C₄×D₄	—	11	2	no	—
165	#117	—	11	1	no	—
166	#117	—	11	2	no	—
167	C₂×C₄²	—	11	2	no	—
168	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
169	C₄⋊C₈	—	11	8	no	—
170	C₄⋊C₈	C₄×D₁₁	1	4	yes	—
171	C₂²⋊C₈	—	11	8	no	—
172	C₂²⋊C₈	C₄×D₁₁	1	4	yes	—
173	#97	—	11	4	no	—
174	#97	—	11	2	no	—
175	C₄×C₈	—	11	4	no	—
176	C₄×C₈	—	11	8	no	—
177	C₄×C₈	—	11	4	no	—
178	C₄×C₈	—	11	2	no	—
179	C₄×C₈	—	11	2	no	—
180	C₄×C₈	—	11	2	no	—
181	C₄×C₈	C₄×D₁₁	1	2	yes	—
182	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
183	C₄×C₈	C₂²×D₁₁	1	4	yes	—
184	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
185	C₂×C₁₁	—	2	2	no	—
186	C₂×C₁₁	C₂²×C₄×C₈	1	1	yes	characteristic
187	C₂×C₁₁	C₄×#131	1	2	yes	—
188	D₁₁	—	2	4	no	—
189	#41	—	11	8	no	—
190	C₂×Q₈	—	11	1	no	—
191	C₂×D₄	—	11	2	no	—
192	C₂×D₄	—	11	1	no	—
193	C₂²×C₄	—	11	2	no	—
194	C₂²×C₄	—	11	4	no	—
195	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
196	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
197	M₁₆	—	11	8	no	—
198	M₁₆	—	11	16	no	—
199	C₂×C₈	—	11	4	no	—
200	C₂×C₈	—	11	4	no	—
201	C₂×C₈	—	11	16	no	—
202	C₂×C₈	—	11	4	no	—
203	C₂×C₈	—	22	16	no	—
204	C₂×C₈	—	22	8	no	—
205	C₂×C₈	C₈×D₁₁	1	8	yes	complemented
206	C₂×C₈	C₂×C₄×D₁₁	1	8	yes	—
207	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
208	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
209	C₄⋊C₄	—	11	4	no	—
210	C₄⋊C₄	—	11	2	no	—
211	C₂²⋊C₄	—	11	2	no	—
212	C₂²⋊C₄	—	11	4	no	—
213	C₄²	—	11	2	no	—
214	C₄²	—	11	4	no	—
215	C₄²	C₂×C₄×D₁₁	1	2	yes	—
216	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
217	C₄²	C₂³×D₁₁	1	1	yes	characteristic
218	C₁₁	C₈×#131	1	1	yes	characteristic, complemented, Sylow
219	C₂³	—	11	2	no	—
220	C₂³	C₄²×D₁₁	1	1	yes	characteristic
221	Q₈	—	11	4	no	—
222	D₄	—	11	8	no	—
223	D₄	—	11	4	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	11	2	no	—
226	C₂×C₄	—	11	8	no	—
227	C₂×C₄	—	11	4	no	—
228	C₂×C₄	—	22	8	no	—
229	C₂×C₄	C₄²×D₁₁	1	2	yes	—
230	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
231	C₂×C₄	C₂×C₈×D₁₁	1	4	yes	—
232	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
233	C₂×C₄	C₂²×C₄×D₁₁	1	2	yes	—
234	C₈	—	2	8	no	—
235	C₈	—	11	8	no	—
236	C₈	—	11	8	no	—
237	C₈	—	22	4	no	—
238	C₈	C₂×C₈×D₁₁	1	4	yes	—
239	C₈	C₂×C₈×D₁₁	1	4	yes	—
240	C₂²	—	2	2	no	—
241	C₂²	—	11	4	no	—
242	C₂²	—	22	4	no	—
243	C₂²	C₄×C₈×D₁₁	1	2	yes	—
244	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	11	4	no	—
247	C₄	—	22	4	no	—
248	C₄	C₄×C₈×D₁₁	1	2	yes	—
249	C₄	C₂²×C₈×D₁₁	1	2	yes	—
250	C₄	D₁₁×#131	1	4	yes	—
251	C₂	—	2	2	no	—
252	C₂	—	22	4	no	—
253	C₂	C₂×C₄×C₈×D₁₁	1	1	yes	characteristic
254	C₂	#13077038	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1450	C₂
socle	C₂²×C₁₁	C₂²×C₄²
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1450	D₁₁
hypocenter	C₁₁	C₈×#131
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₈ ◁ #1450

Complements

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

N	H ≅ G/N	type
3. #13066898	C₂	semidirect
4. #13066897	C₂	semidirect
5. #13066895	C₂	semidirect
6. C₂×C₈×C₁₁⋊C₈	C₂	semidirect
7. C₈²×D₁₁	C₂	semidirect
8. C₁₁×#1450	C₂	semidirect
38. #66954	C₈	semidirect
71. C₂×C₈×C₁₁	C₂×C₈	semidirect
84. #4318	C₂×C₈	semidirect
89. #4313	C₂×C₈	semidirect
91. C₈×D₁₁	C₂×C₈	semidirect
95. #1450	D₁₁	semidirect
120. C₁₁⋊C₈	#131	semidirect
205. C₂×C₈	C₈×D₁₁	semidirect
218. C₁₁	C₈×#131	semidirect

Maximal subgroups

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

subgroup	index
#13077572	2
C₄×#66954	2
#13066898	2
#13066897	2
#13066895	2
C₂×C₈×C₁₁⋊C₈	2
C₈²×D₁₁	2
C₁₁×#1450	2
C₈×#131	11