Subgroups — #14737027

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079769	C₂	1	2	yes	maximal
2	C₂×#10622295	C₂	1	1	yes	maximal, characteristic
3	#13077550	C₂	1	1	yes	maximal, characteristic
4	#13068145	C₂	1	4	yes	maximal, complemented
5	#13068021	C₂	1	4	yes	maximal, complemented
6	#13067296	C₂	1	2	yes	maximal
7	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic
8	#10623001	C₂²	1	1	yes	characteristic
9	C₂×#66922	C₂²	1	2	yes	—
10	C₁₁×#431	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×#66882	—	2	1	no	—
13	C₂×#66882	—	2	1	no	—
14	#10622715	—	2	1	no	—
15	#10622714	—	2	1	no	—
16	#10622537	C₂²	1	1	yes	characteristic
17	#10622463	C₂²	1	8	yes	—
18	#10622335	—	2	4	no	—
19	#10622295	—	2	2	no	—
20	#10622295	—	2	1	no	—
21	#10622295	—	2	1	no	—
22	#10622295	C₂²	1	2	yes	—
23	#10622295	C₂²	1	2	yes	—
24	#10622294	—	2	2	no	—
25	#10622292	—	2	1	no	—
26	#10622292	C₂²	1	2	yes	—
27	C₈×Dic₂₂	—	2	1	no	—
28	C₈×Dic₂₂	C₂²	1	2	yes	—
29	C₁₁×#335	C₂²	1	2	yes	—
30	C₁₁×#334	C₂²	1	2	yes	—
31	#10622119	C₂²	1	8	yes	—
32	C₂²×Dic₂₂	—	2	2	no	—
33	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
36	#66979	—	2	1	no	—
37	C₂×C₄⋊Dic₁₁	—	2	2	no	—
38	C₂×C₄⋊Dic₁₁	—	2	2	no	—
39	#66977	—	2	1	no	—
40	#66977	D₄	1	2	yes	—
41	C₂×#4318	—	2	1	no	—
42	#66923	—	2	1	no	—
43	#66922	—	2	2	no	—
44	#66922	—	2	2	no	—
45	#66922	—	2	2	no	—
46	#66922	D₄	1	1	yes	characteristic
47	#66922	D₄	1	1	yes	characteristic
48	#66922	C₂³	1	4	yes	—
49	C₄×Dic₂₂	—	2	1	no	—
50	C₄×Dic₂₂	C₂³	1	2	yes	—
51	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
52	C₁₁×C₂²⋊C₈	—	2	2	no	—
53	C₄×C₈×C₁₁	—	2	2	no	—
54	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
55	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
56	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	#66882	—	2	2	no	—
59	#66882	—	2	2	no	—
60	#66882	—	2	2	no	—
61	#66882	—	2	2	no	—
62	#66882	—	2	8	no	—
63	#66880	—	2	8	no	—
64	#66879	—	2	2	no	—
65	Dic₁₁⋊C₈	—	2	2	no	—
66	Dic₁₁⋊C₈	—	2	2	no	—
67	C₈×Dic₁₁	—	2	2	no	—
68	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
70	#19209	—	11	1	no	maximal, Sylow
71	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
74	C₂²×Dic₁₁	—	4	2	no	—
75	C₂×Dic₂₂	—	2	1	no	—
76	C₂×Dic₂₂	—	2	4	no	—
77	C₂×Dic₂₂	—	4	2	no	—
78	C₂×Dic₂₂	—	8	4	no	—
79	C₂×Dic₂₂	C₂×D₄	1	2	yes	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
83	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₄²×C₁₁	#41	1	1	yes	characteristic
90	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₂²⋊Dic₁₁	—	2	2	no	—
92	C₄⋊Dic₁₁	—	2	1	no	—
93	C₄⋊Dic₁₁	—	2	1	no	—
94	C₄⋊Dic₁₁	—	2	1	no	—
95	C₄⋊Dic₁₁	—	2	4	no	—
96	C₄⋊Dic₁₁	—	2	4	no	—
97	C₄⋊Dic₁₁	—	4	2	no	—
98	C₄⋊Dic₁₁	—	4	2	no	—
99	C₄⋊Dic₁₁	C₂×D₄	1	2	yes	—
100	Dic₁₁⋊C₄	—	2	2	no	—
101	Dic₁₁⋊C₄	—	2	2	no	—
102	C₄×Dic₁₁	—	2	2	no	—
103	#4318	—	4	2	no	—
104	C₂×C₁₁⋊C₈	—	2	2	no	—
105	#3230	—	11	2	no	—
106	C₂×#500	—	11	1	no	—
107	#2960	—	11	1	no	—
108	#1696	—	11	4	no	—
109	#1676	—	11	4	no	—
110	#1564	D₁₁	1	1	yes	characteristic
111	#1548	—	11	2	no	—
112	C₂³×C₁₁	#121	1	1	yes	characteristic
113	C₂×C₄×C₁₁	—	2	2	no	—
114	C₂×C₄×C₁₁	—	2	2	no	—
115	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
117	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
119	C₂×C₄×C₁₁	#137	1	2	yes	—
120	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
123	C₂×Dic₁₁	—	2	2	no	—
124	C₂×Dic₁₁	—	2	2	no	—
125	C₂×Dic₁₁	—	4	4	no	—
126	C₂×Dic₁₁	—	8	4	no	—
127	Dic₂₂	—	2	4	no	—
128	Dic₂₂	—	4	2	no	—
129	Dic₂₂	—	8	4	no	—
130	Dic₂₂	—	8	4	no	—
131	C₈×C₁₁	—	2	1	no	—
132	C₈×C₁₁	—	2	1	no	—
133	C₈×C₁₁	—	4	4	no	—
134	C₈×C₁₁	C₂×Q₁₆	1	2	yes	—
135	C₈×C₁₁	C₂×Q₁₆	1	2	yes	—
136	C₁₁⋊C₈	—	4	2	no	—
137	#533	—	11	1	no	—
138	C₂×C₄⋊Q₈	—	11	2	no	—
139	#500	—	11	2	no	—
140	#500	—	11	2	no	—
141	#500	—	22	2	no	—
142	#500	—	22	1	no	—
143	#500	—	22	1	no	—
144	#487	—	22	2	no	—
145	#484	—	22	4	no	—
146	#477	—	11	8	no	—
147	#446	—	11	2	no	—
148	#446	—	22	1	no	—
149	C₈×Q₈	—	11	2	no	—
150	C₈×Q₈	—	22	1	no	—
151	#431	C₂×D₁₁	1	2	yes	—
152	C₂×#107	—	22	1	no	—
153	C₂×#107	—	22	1	no	—
154	#424	—	22	1	no	—
155	#423	—	11	1	no	—
156	#405	—	22	1	no	—
157	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
158	#335	C₂×D₁₁	1	2	yes	—
159	#334	C₂×D₁₁	1	2	yes	—
160	#333	—	11	8	no	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	—	2	1	no	—
163	C₂²×C₁₁	#462	1	2	yes	—
164	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
165	C₄×C₁₁	—	2	1	no	—
166	C₄×C₁₁	—	2	1	no	—
167	C₄×C₁₁	#462	1	2	yes	—
168	C₄×C₁₁	#472	1	2	yes	—
169	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
170	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
171	C₄×C₁₁	#578	1	2	yes	—
172	Dic₁₁	—	4	2	no	—
173	Dic₁₁	—	4	2	no	—
174	Dic₁₁	—	8	4	no	—
175	C₂²×Q₈	—	22	2	no	—
176	C₂×M₁₆	—	22	1	no	—
177	C₂²×C₈	D₄₄	1	1	yes	characteristic
178	C₂²×C₈	D₄₄	1	1	yes	characteristic
179	C₄⋊Q₈	—	11	1	no	—
180	C₄⋊Q₈	—	11	1	no	—
181	C₄⋊Q₈	—	11	4	no	—
182	C₄⋊Q₈	—	22	2	no	—
183	C₄⋊Q₈	—	22	2	no	—
184	C₄⋊Q₈	—	22	2	no	—
185	#125	—	22	1	no	—
186	C₂²⋊Q₈	—	11	2	no	—
187	C₂²⋊Q₈	—	22	1	no	—
188	C₄×Q₈	—	11	2	no	—
189	C₄×Q₈	—	22	1	no	—
190	#117	—	22	1	no	—
191	C₂×C₄⋊C₄	—	22	2	no	—
192	C₂×C₄⋊C₄	—	22	2	no	—
193	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
194	#107	—	22	8	no	—
195	#107	—	22	2	no	—
196	#107	—	22	2	no	—
197	#107	—	22	2	no	—
198	#107	—	22	2	no	—
199	C₄⋊C₈	—	11	2	no	—
200	C₄⋊C₈	—	22	2	no	—
201	C₄⋊C₈	—	22	2	no	—
202	C₄⋊C₈	—	22	1	no	—
203	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
204	#103	—	22	8	no	—
205	C₂²⋊C₈	—	2	2	no	—
206	#97	—	22	2	no	—
207	C₄×C₈	—	2	2	no	—
208	C₄×C₈	—	22	2	no	—
209	C₄×C₈	D₄₄	1	1	yes	characteristic
210	C₄×C₈	D₄₄	1	1	yes	characteristic
211	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
212	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
213	C₂×C₁₁	—	2	2	no	—
214	C₂×C₁₁	C₂×#462	1	1	yes	characteristic
215	C₂×C₁₁	#3059	1	1	yes	characteristic
216	C₂×C₁₁	C₂×#472	1	1	yes	characteristic
217	C₂×Q₈	—	11	2	no	—
218	C₂×Q₈	—	22	1	no	—
219	C₂×Q₈	—	22	4	no	—
220	C₂×Q₈	—	44	2	no	—
221	C₂×Q₈	—	88	4	no	—
222	C₂²×C₄	—	44	2	no	—
223	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
224	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
225	C₂²×C₄	#4343	1	1	yes	characteristic
226	M₁₆	—	44	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	22	2	no	—
230	C₂×C₈	Dic₄₄	1	4	yes	—
231	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
232	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
233	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
234	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
235	C₄⋊C₄	—	11	2	no	—
236	C₄⋊C₄	—	22	1	no	—
237	C₄⋊C₄	—	22	1	no	—
238	C₄⋊C₄	—	22	2	no	—
239	C₄⋊C₄	—	22	1	no	—
240	C₄⋊C₄	—	22	2	no	—
241	C₄⋊C₄	—	22	4	no	—
242	C₄⋊C₄	—	22	4	no	—
243	C₄⋊C₄	—	44	2	no	—
244	C₄⋊C₄	—	44	2	no	—
245	C₂²⋊C₄	—	22	2	no	—
246	C₄²	—	22	2	no	—
247	C₄²	C₂×D₄₄	1	1	yes	characteristic
248	C₄²	D₄×D₁₁	1	1	yes	characteristic
249	C₄²	#4343	1	1	yes	characteristic
250	C₄²	C₂³×D₁₁	1	1	yes	characteristic
251	C₁₁	#19209	1	1	yes	characteristic, complemented, Sylow
252	C₂³	#66948	1	1	yes	characteristic
253	Q₈	—	22	4	no	—
254	Q₈	—	44	2	no	—
255	Q₈	—	88	4	no	—
256	Q₈	—	88	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	22	2	no	—
260	C₂×C₄	—	22	2	no	—
261	C₂×C₄	—	44	4	no	—
262	C₂×C₄	—	88	4	no	—
263	C₂×C₄	#66948	1	1	yes	characteristic
264	C₂×C₄	#66948	1	1	yes	characteristic
265	C₂×C₄	#66948	1	1	yes	characteristic
266	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
267	C₂×C₄	#66962	1	2	yes	—
268	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
269	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
270	C₂×C₄	C₂×#4343	1	1	yes	characteristic
271	C₈	—	2	1	no	—
272	C₈	—	2	1	no	—
273	C₈	—	4	4	no	—
274	C₈	—	44	2	no	—
275	C₈	C₂×Dic₄₄	1	2	yes	—
276	C₈	C₂×Dic₄₄	1	2	yes	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	#10622462	1	2	yes	—
280	C₂²	C₂×#66948	1	1	yes	characteristic
281	C₄	—	2	1	no	—
282	C₄	—	2	1	no	—
283	C₄	—	44	2	no	—
284	C₄	—	44	2	no	—
285	C₄	—	88	4	no	—
286	C₄	#10622462	1	2	yes	—
287	C₄	#10622510	1	2	yes	—
288	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
289	C₄	C₂×#66962	1	1	yes	characteristic
290	C₄	#10623302	1	2	yes	—
291	C₂	—	2	2	no	—
292	C₂	C₂×#10622462	1	1	yes	characteristic
293	C₂	#13078272	1	1	yes	characteristic
294	C₂	C₂×#10622510	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#66948
commutator, cosocle	C₄²×C₁₁	C₂⁴
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1564	C₂
socle	C₂²×C₁₁	C₂×#121
prime radical	C₂³×C₁₁	#121
hypercenter	#1564	D₁₁
hypocenter	C₁₁	#19209
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #13068145	C₂	semidirect
5. #13068021	C₂	semidirect
251. C₁₁	#19209	semidirect

Maximal subgroups

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

subgroup	index
#13079769	2
C₂×#10622295	2
#13077550	2
#13068145	2
#13068021	2
#13067296	2
C₁₁×#1564	2
#19209	11