Subgroups — #14644449

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66960	C₂	1	1	yes	maximal, characteristic
2	#13066999	C₂	1	1	yes	maximal, characteristic
3	#13066996	C₂	1	1	yes	maximal, characteristic
4	#13066900	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10622092	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#66960	C₄	1	2	yes	—
9	C₄×#4339	C₂²	1	1	yes	characteristic
10	C₁₁×#431	C₂²	1	1	yes	characteristic
11	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622735	C₄	1	2	yes	—
14	#10622538	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
17	#10622321	—	2	2	no	—
18	C₄×#4313	—	2	1	no	—
19	C₄×C₈×D₁₁	—	2	1	no	—
20	#10622122	C₄	1	2	yes	—
21	#10622121	C₄	1	2	yes	—
22	#10622097	C₄	1	2	yes	—
23	#10622094	C₄	1	2	yes	—
24	#10622092	—	2	2	no	—
25	#10622092	—	2	1	no	—
26	C₈×C₁₁⋊C₈	—	2	1	no	—
27	C₂×#4339	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₁	—	2	1	no	—
30	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
31	C₄×C₂²⋊D₁₁	—	2	1	no	—
32	C₄×C₂²⋊D₁₁	—	2	1	no	—
33	#66979	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₁₁⋊C₈	—	2	1	no	—
35	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
36	#66960	—	2	4	no	—
37	#66960	C₈	1	8	yes	complemented
38	C₂×#4313	—	2	2	no	—
39	C₂×C₈×D₁₁	—	2	2	no	—
40	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
41	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
42	#66925	—	2	1	no	—
43	C₄²×D₁₁	—	2	1	no	—
44	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
45	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
46	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
47	C₁₁×C₂²⋊C₈	—	2	1	no	—
48	C₁₁×#97	—	2	1	no	—
49	C₄×C₈×C₁₁	—	2	1	no	—
50	C₄×C₈×C₁₁	—	2	1	no	—
51	C₄×C₈×C₁₁	—	2	1	no	—
52	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
53	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
54	#66879	—	2	2	no	—
55	C₈×Dic₁₁	—	2	2	no	—
56	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
57	C₄×C₁₁⋊C₈	—	2	1	no	—
58	C₄×C₁₁⋊C₈	—	2	1	no	—
59	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
61	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
62	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
63	#8185	—	11	1	no	maximal, Sylow
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₁	—	2	1	no	—
68	#4339	—	2	2	no	—
69	#4339	C₂×C₈	1	4	yes	—
70	C₂×D₄₄	C₄²	1	1	yes	characteristic
71	C₂×C₄×D₁₁	—	2	1	no	—
72	C₂×C₄×D₁₁	—	2	1	no	—
73	C₂×C₄×D₁₁	—	2	1	no	—
74	C₂×Dic₂₂	C₄²	1	1	yes	characteristic
75	C₁₁×M₁₆	—	2	2	no	—
76	C₁₁×M₁₆	C₂×C₈	1	4	yes	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	4	2	no	—
81	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
82	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂²⋊Dic₁₁	—	2	1	no	—
86	(C₂×D₁₁)⋊C₄	—	2	1	no	—
87	(C₂×D₁₁)⋊C₄	—	2	1	no	—
88	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
89	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
90	Dic₁₁⋊C₄	—	2	1	no	—
91	Dic₁₁⋊C₄	—	2	1	no	—
92	C₄×Dic₁₁	—	2	1	no	—
93	C₄×Dic₁₁	—	2	1	no	—
94	C₄×Dic₁₁	—	2	1	no	—
95	C₂×C₁₁⋊C₈	—	2	2	no	—
96	C₂×C₁₁⋊C₈	—	2	2	no	—
97	C₂×C₁₁⋊C₈	—	4	2	no	—
98	C₂×C₁₁⋊C₈	C₂²⋊C₄	1	2	yes	—
99	C₂×C₁₁⋊C₈	C₂²⋊C₄	1	2	yes	—
100	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
101	C₂×C₁₁⋊C₈	M₁₆	1	4	yes	—
102	#4313	—	2	8	no	—
103	C₈×D₁₁	—	2	8	no	—
104	C₄×#131	—	11	1	no	—
105	#1476	—	11	1	no	—
106	#1476	—	11	1	no	—
107	#1450	—	11	1	no	—
108	C₂×#322	—	11	1	no	—
109	#1278	—	11	1	no	—
110	#1278	D₁₁	1	1	yes	characteristic, complemented
111	C₂³×C₁₁	#117	1	1	yes	characteristic
112	C₂²×D₁₁	—	2	1	no	—
113	C₂×C₄×C₁₁	—	2	2	no	—
114	C₂×C₄×C₁₁	—	2	2	no	—
115	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
122	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
123	C₂²⋊D₁₁	—	2	4	no	—
124	C₂×Dic₁₁	—	2	1	no	—
125	C₂×Dic₁₁	—	2	1	no	—
126	C₂×Dic₁₁	—	2	1	no	—
127	D₄₄	—	2	1	no	—
128	D₄₄	C₄×C₈	1	2	yes	—
129	C₄×D₁₁	—	2	4	no	—
130	C₄×D₁₁	—	4	2	no	—
131	C₄×D₁₁	—	4	2	no	—
132	Dic₂₂	—	2	1	no	—
133	Dic₂₂	C₄×C₈	1	2	yes	—
134	C₈×C₁₁	—	2	4	no	—
135	C₈×C₁₁	—	4	2	no	—
136	C₈×C₁₁	—	4	2	no	—
137	C₁₁⋊C₈	—	4	2	no	—
138	C₁₁⋊C₈	—	4	2	no	—
139	C₁₁⋊C₈	C₂²⋊C₈	1	4	yes	—
140	C₁₁⋊C₈	C₂²⋊C₈	1	4	yes	—
141	C₂×#131	—	11	2	no	—
142	C₄×#41	—	11	1	no	—
143	#431	—	11	1	no	—
144	#431	C₂×D₁₁	1	1	yes	characteristic
145	#405	—	11	2	no	—
146	#405	—	22	2	no	—
147	C₄×M₁₆	—	22	1	no	—
148	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
149	C₂×C₄×C₈	—	11	1	no	—
150	C₂×C₄×C₈	—	11	1	no	—
151	C₂×C₄×C₈	—	22	1	no	—
152	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
153	Q₈⋊C₈	—	11	2	no	—
154	Q₈⋊C₈	—	11	2	no	—
155	D₄⋊C₈	—	11	2	no	—
156	D₄⋊C₈	—	11	2	no	—
157	#322	—	22	2	no	—
158	#322	—	22	1	no	—
159	C₈²	—	22	1	no	—
160	C₂²×C₁₁	—	2	1	no	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₁₁	#431	1	2	yes	—
164	C₂×D₁₁	—	2	2	no	—
165	C₂×D₁₁	—	4	1	no	—
166	C₂×D₁₁	—	4	1	no	—
167	C₄×C₁₁	—	2	1	no	—
168	C₄×C₁₁	—	2	1	no	—
169	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
170	C₄×C₁₁	C₄×M₁₆	1	1	yes	characteristic
171	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
172	C₄×C₁₁	#444	1	2	yes	—
173	C₄×C₁₁	#444	1	2	yes	—
174	Dic₁₁	—	2	2	no	—
175	Dic₁₁	—	4	1	no	—
176	Dic₁₁	—	4	1	no	—
177	C₂×#41	—	11	1	no	—
178	#131	—	11	8	no	—
179	#131	—	22	4	no	—
180	C₂×M₁₆	—	22	2	no	—
181	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	—	11	2	no	—
184	C₂²×C₈	—	22	2	no	—
185	C₂²×C₈	—	22	1	no	—
186	C₄×Q₈	—	11	1	no	—
187	C₄×Q₈	—	11	1	no	—
188	C₄×D₄	—	11	1	no	—
189	C₄×D₄	—	11	1	no	—
190	C₄×D₄	—	22	1	no	—
191	C₄×D₄	—	22	1	no	—
192	#117	—	11	1	no	—
193	#117	—	22	1	no	—
194	C₂×C₄²	—	22	1	no	—
195	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
196	C₄⋊C₈	—	11	2	no	—
197	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
198	C₂²⋊C₈	—	2	1	no	—
199	C₂²⋊C₈	—	22	1	no	—
200	#97	—	2	1	no	—
201	#97	—	22	2	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	11	2	no	—
206	C₄×C₈	—	11	2	no	—
207	C₄×C₈	—	11	1	no	—
208	C₄×C₈	—	11	1	no	—
209	C₄×C₈	—	22	2	no	—
210	C₄×C₈	—	22	1	no	—
211	C₄×C₈	—	22	1	no	—
212	C₄×C₈	C₄×D₁₁	1	2	yes	—
213	C₂×C₁₁	—	2	2	no	—
214	C₂×C₁₁	C₄×C₂²⋊C₈	1	1	yes	characteristic
215	C₂×C₁₁	#1765	1	1	yes	characteristic
216	C₂×C₁₁	#1765	1	1	yes	characteristic
217	D₁₁	—	4	2	no	—
218	#41	—	11	4	no	—
219	#41	—	22	2	no	—
220	C₂×Q₈	—	11	1	no	—
221	C₂×D₄	—	11	1	no	—
222	C₂×D₄	—	22	1	no	—
223	C₂²×C₄	—	22	1	no	—
224	C₂²×C₄	—	22	1	no	—
225	C₂²×C₄	—	22	1	no	—
226	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
227	C₂²×C₄	#4341	1	1	yes	characteristic
228	C₂²×C₄	#4343	1	1	yes	characteristic
229	M₁₆	—	2	2	no	—
230	M₁₆	—	22	8	no	—
231	M₁₆	C₈×D₁₁	1	4	yes	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	—	11	2	no	—
237	C₂×C₈	—	11	2	no	—
238	C₂×C₈	—	11	4	no	—
239	C₂×C₈	—	11	4	no	—
240	C₂×C₈	—	22	8	no	—
241	C₂×C₈	—	22	2	no	—
242	C₂×C₈	—	22	2	no	—
243	C₂×C₈	—	44	2	no	—
244	C₄⋊C₄	—	11	1	no	—
245	C₄⋊C₄	—	11	1	no	—
246	C₄⋊C₄	—	22	1	no	—
247	C₄⋊C₄	—	22	1	no	—
248	C₂²⋊C₄	—	22	1	no	—
249	C₂²⋊C₄	—	22	1	no	—
250	C₂²⋊C₄	—	22	1	no	—
251	C₄²	—	22	1	no	—
252	C₄²	—	22	1	no	—
253	C₄²	—	22	1	no	—
254	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
255	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
256	C₄²	D₄×D₁₁	1	1	yes	characteristic
257	C₄²	D₄×D₁₁	1	1	yes	characteristic
258	C₁₁	#8185	1	1	yes	characteristic, complemented, Sylow
259	C₂³	—	22	1	no	—
260	C₂³	#66945	1	1	yes	characteristic
261	Q₈	—	11	2	no	—
262	Q₈	—	22	1	no	—
263	D₄	—	11	2	no	—
264	D₄	—	22	4	no	—
265	D₄	—	22	1	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	22	1	no	—
269	C₂×C₄	—	22	4	no	—
270	C₂×C₄	—	22	1	no	—
271	C₂×C₄	—	22	1	no	—
272	C₂×C₄	—	44	2	no	—
273	C₂×C₄	—	44	2	no	—
274	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
275	C₂×C₄	C₂²⋊C₄×D₁₁	1	1	yes	characteristic
276	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
277	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
278	C₂×C₄	#66946	1	1	yes	characteristic
279	C₂×C₄	#66946	1	1	yes	characteristic
280	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
281	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
282	C₈	—	2	4	no	—
283	C₈	—	4	2	no	—
284	C₈	—	4	2	no	—
285	C₈	—	11	4	no	—
286	C₈	—	11	4	no	—
287	C₈	—	44	2	no	—
288	C₈	—	44	2	no	—
289	C₂²	—	2	1	no	—
290	C₂²	—	2	1	no	—
291	C₂²	—	22	2	no	—
292	C₂²	—	44	1	no	—
293	C₂²	—	44	1	no	—
294	C₂²	#10622279	1	1	yes	characteristic
295	C₂²	#10622446	1	2	yes	—
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	22	2	no	—
299	C₄	—	44	1	no	—
300	C₄	—	44	1	no	—
301	C₄	C₄×C₈×D₁₁	1	1	yes	characteristic
302	C₄	#10622320	1	1	yes	characteristic
303	C₄	D₁₁×C₂²⋊C₈	1	2	yes	—
304	C₄	#10622436	1	2	yes	—
305	C₄	#10622507	1	2	yes	—
306	C₂	—	2	2	no	—
307	C₂	—	44	2	no	—
308	C₂	#13068373	1	1	yes	characteristic
309	C₂	#13068457	1	1	yes	characteristic
310	C₂	#13068459	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1278	C₂
socle	C₂²×C₁₁	C₄×C₂²⋊C₄
prime radical	C₂×#4339	C₂×C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1278	D₁₁
hypocenter	C₁₁	#8185
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1278

Complements

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

N	H ≅ G/N	type
4. #13066900	C₂	semidirect
5. C₂×#10622092	C₂	semidirect
6. #13066454	C₂	semidirect
7. C₁₁×#1278	C₂	semidirect
37. #66960	C₈	semidirect
110. #1278	D₁₁	semidirect
258. C₁₁	#8185	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66960	2
#13066999	2
#13066996	2
#13066900	2
C₂×#10622092	2
#13066454	2
C₁₁×#1278	2
#8185	11