Subgroups — #14907417

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	#13070523	C₂	1	4	yes	maximal, complemented
3	#13070522	C₂	1	4	yes	maximal, complemented
4	#13070419	C₂	1	1	yes	maximal, characteristic
5	#13070416	C₂	1	2	yes	maximal
6	#13070412	C₂	1	2	yes	maximal
7	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×Dic₂₂	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁⋊C₈	C₄	1	1	yes	characteristic
11	C₂×Dic₁₁⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
15	C₈×Dic₂₂	C₄	1	2	yes	—
16	C₈×Dic₂₂	C₄	1	2	yes	—
17	C₈×Dic₂₂	C₂²	1	2	yes	—
18	C₈×Dic₂₂	C₂²	1	2	yes	—
19	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
20	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
21	C₁₁×#346	C₂²	1	2	yes	—
22	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
23	#10622140	C₂²	1	4	yes	—
24	Dic₁₁⋊C₁₆	C₂²	1	4	yes	—
25	Dic₁₁⋊C₁₆	C₂²	1	4	yes	—
26	C₁₆×Dic₁₁	C₂²	1	4	yes	—
27	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
28	#10622099	C₂²	1	2	yes	—
29	C₂²×Dic₂₂	C₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₁	C₈	1	1	yes	characteristic
34	C₂×Dic₁₁⋊C₄	C₈	1	1	yes	characteristic
35	C₂×Dic₁₁⋊C₄	C₈	1	1	yes	characteristic
36	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₄×Dic₂₂	C₈	1	2	yes	—
41	C₄×Dic₂₂	C₈	1	2	yes	—
42	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
43	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
44	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
45	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
50	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
51	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
52	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
53	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
54	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
55	C₈×Dic₁₁	C₂³	1	2	yes	—
56	C₈×Dic₁₁	C₂³	1	2	yes	—
57	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
58	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
59	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
60	#33497	—	11	1	no	maximal, Sylow
61	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
65	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
66	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
67	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
68	C₂×Dic₂₂	—	2	4	no	—
69	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
70	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
71	C₂×C₈×C₁₁	—	2	2	no	—
72	C₂×C₈×C₁₁	—	4	1	no	—
73	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
77	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
78	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
79	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
82	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
83	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
84	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
85	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
86	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
87	C₄×Dic₁₁	C₂×C₈	1	2	yes	—
88	C₄×Dic₁₁	C₂×C₈	1	2	yes	—
89	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
90	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
91	C₂×C₁₁⋊C₈	—	4	1	no	—
92	C₂×C₁₁⋊C₈	—	4	1	no	—
93	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
94	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
95	C₁₁×C₁₆	—	2	4	no	—
96	C₁₁⋊C₁₆	—	2	4	no	—
97	C₂×C₈×Q₈	—	11	1	no	—
98	#2183	—	11	4	no	—
99	#2183	—	11	4	no	—
100	#2163	—	11	1	no	—
101	#2163	—	11	2	no	—
102	#2163	D₁₁	1	1	yes	characteristic
103	#2162	—	11	2	no	—
104	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	—	2	1	no	—
107	C₂×C₄×C₁₁	—	2	1	no	—
108	C₂×C₄×C₁₁	—	4	1	no	—
109	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
115	C₂×Dic₁₁	—	2	2	no	—
116	C₂×Dic₁₁	—	4	1	no	—
117	C₂×Dic₁₁	—	4	1	no	—
118	C₂×Dic₁₁	M₃₂	1	4	yes	—
119	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
120	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
121	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
122	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
123	Dic₂₂	—	2	4	no	—
124	Dic₂₂	—	2	4	no	—
125	C₈×C₁₁	—	2	1	no	—
126	C₈×C₁₁	—	2	1	no	—
127	C₈×C₁₁	—	2	1	no	—
128	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
129	C₁₁⋊C₈	—	2	2	no	—
130	C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₄×Q₈	—	11	1	no	—
132	C₈×Q₈	—	11	2	no	—
133	C₈×Q₈	—	11	2	no	—
134	C₈×Q₈	—	11	2	no	—
135	C₈×Q₈	—	11	2	no	—
136	C₂×C₄⋊C₈	—	11	1	no	—
137	C₂×C₄⋊C₈	—	11	1	no	—
138	C₂×C₄⋊C₈	—	11	1	no	—
139	C₂×C₄×C₈	—	11	1	no	—
140	C₂×C₄×C₈	—	11	1	no	—
141	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
142	C₄⋊C₁₆	—	11	4	no	—
143	C₄⋊C₁₆	—	11	4	no	—
144	C₄⋊C₁₆	—	11	2	no	—
145	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
146	C₂²⋊C₁₆	—	11	2	no	—
147	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
148	#346	—	11	4	no	—
149	#346	—	11	2	no	—
150	#346	C₂×D₁₁	1	2	yes	—
151	C₄×C₁₆	—	11	4	no	—
152	C₂²×C₁₁	—	2	1	no	—
153	C₂²×C₁₁	—	2	1	no	—
154	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
155	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
156	C₄×C₁₁	—	2	1	no	—
157	C₄×C₁₁	—	2	1	no	—
158	C₄×C₁₁	—	2	1	no	—
159	C₄×C₁₁	—	2	1	no	—
160	C₄×C₁₁	—	2	1	no	—
161	C₄×C₁₁	#519	1	1	yes	characteristic
162	C₄×C₁₁	#568	1	1	yes	characteristic
163	Dic₁₁	—	2	2	no	—
164	Dic₁₁	—	2	2	no	—
165	Dic₁₁	—	2	2	no	—
166	Dic₁₁	C₂×M₃₂	1	4	yes	—
167	C₂²×Q₈	—	11	1	no	—
168	C₂²×C₈	—	11	1	no	—
169	C₂²×C₈	—	11	1	no	—
170	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
171	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
172	C₄×Q₈	—	11	2	no	—
173	C₄×Q₈	—	11	2	no	—
174	C₄×Q₈	—	11	2	no	—
175	C₄×Q₈	—	11	2	no	—
176	C₂×C₄⋊C₄	—	11	1	no	—
177	C₂×C₄⋊C₄	—	11	1	no	—
178	C₂×C₄⋊C₄	—	11	1	no	—
179	C₂×C₄²	—	11	1	no	—
180	C₂×C₄²	—	11	1	no	—
181	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
182	C₂×C₁₆	—	11	4	no	—
183	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
184	C₄⋊C₈	—	11	2	no	—
185	C₄⋊C₈	—	11	2	no	—
186	C₄⋊C₈	—	11	2	no	—
187	C₄⋊C₈	—	11	2	no	—
188	C₄⋊C₈	—	11	2	no	—
189	C₄⋊C₈	—	11	2	no	—
190	C₄×C₈	—	11	2	no	—
191	C₄×C₈	—	11	2	no	—
192	C₄×C₈	—	11	2	no	—
193	C₄×C₈	—	11	2	no	—
194	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
195	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
196	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
197	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
198	C₂×C₁₁	—	2	2	no	—
199	C₂×C₁₁	#2982	1	1	yes	characteristic
200	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
201	C₂×C₁₁	#3407	1	1	yes	characteristic
202	C₂×Q₈	—	11	2	no	—
203	C₂×Q₈	—	11	2	no	—
204	C₂×Q₈	—	22	4	no	—
205	C₂²×C₄	—	11	1	no	—
206	C₂²×C₄	—	11	1	no	—
207	C₂²×C₄	—	11	1	no	—
208	C₂²×C₄	—	11	1	no	—
209	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
210	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
211	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	4	1	no	—
214	C₂×C₈	—	11	2	no	—
215	C₂×C₈	—	11	2	no	—
216	C₂×C₈	—	44	1	no	—
217	C₂×C₈	—	44	1	no	—
218	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
219	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
220	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
221	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
222	C₄⋊C₄	—	11	2	no	—
223	C₄⋊C₄	—	11	2	no	—
224	C₄⋊C₄	—	11	2	no	—
225	C₄⋊C₄	—	11	2	no	—
226	C₄⋊C₄	—	11	2	no	—
227	C₄⋊C₄	—	11	2	no	—
228	C₄²	—	11	2	no	—
229	C₄²	—	11	2	no	—
230	C₄²	—	11	2	no	—
231	C₄²	—	11	2	no	—
232	C₄²	C₈×D₁₁	1	1	yes	characteristic
233	C₄²	C₈×D₁₁	1	1	yes	characteristic
234	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
235	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
236	C₁₆	—	2	4	no	—
237	C₁₆	—	22	4	no	—
238	C₁₁	#33497	1	1	yes	characteristic, complemented, Sylow
239	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
240	Q₈	—	22	4	no	—
241	Q₈	—	22	4	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	11	2	no	—
247	C₂×C₄	—	11	4	no	—
248	C₂×C₄	—	11	2	no	—
249	C₂×C₄	—	11	2	no	—
250	C₂×C₄	—	11	2	no	—
251	C₂×C₄	—	22	2	no	—
252	C₂×C₄	—	44	1	no	—
253	C₂×C₄	—	44	1	no	—
254	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
255	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
256	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
257	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
258	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
259	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
260	C₈	—	2	1	no	—
261	C₈	—	2	1	no	—
262	C₈	—	2	1	no	—
263	C₈	—	22	2	no	—
264	C₈	—	22	2	no	—
265	C₈	#67043	1	2	yes	—
266	C₂²	—	2	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	D₁₁×M₃₂	1	2	yes	—
269	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
270	C₄	—	2	1	no	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	2	1	no	—
275	C₄	—	11	4	no	—
276	C₄	—	22	2	no	—
277	C₄	—	22	2	no	—
278	C₄	—	22	2	no	—
279	C₄	#10623047	1	1	yes	characteristic
280	C₄	#10623276	1	1	yes	characteristic
281	C₂	—	2	2	no	—
282	C₂	#13077696	1	1	yes	characteristic
283	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
284	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2163	C₂
prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2163	D₁₁
hypocenter	C₁₁	#33497
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #13070523	C₂	semidirect
3. #13070522	C₂	semidirect
238. C₁₁	#33497	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₂₂	2
#13070523	2
#13070522	2
#13070419	2
#13070416	2
#13070412	2
C₁₁×#2163	2
#33497	11