Subgroups — #14909387

Order 2816.

484 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	#13079276	C₂	1	1	yes	maximal, characteristic
2	#13079272	C₂	1	1	yes	maximal, characteristic
3	#13070892	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070868	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070862	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070723	C₂	1	2	yes	maximal
7	#13070706	C₂	1	2	yes	maximal
8	#13070484	C₂	1	2	yes	maximal, complemented
9	#13070472	C₂	1	2	yes	maximal, complemented
10	#13070214	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#2245	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623262	—	2	1	no	—
13	#10623228	—	2	1	no	—
14	C₁₁×#499	C₂²	1	1	yes	characteristic
15	C₁₁×#494	C₂²	1	1	yes	characteristic
16	#10622802	—	2	1	no	—
17	#10622801	C₂²	1	2	yes	—
18	#10622797	—	2	1	no	—
19	Q₁₆×Dic₁₁	C₂²	1	2	yes	—
20	C₂×#66893	C₂²	1	2	yes	—
21	C₂×#66893	C₂²	1	2	yes	—
22	#10622695	—	2	1	no	—
23	#10622682	—	2	1	no	—
24	C₂×#66862	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
26	#10622500	C₂²	1	2	yes	—
27	#10622486	C₂²	1	2	yes	—
28	#10622481	—	2	1	no	—
29	#10622466	—	2	1	no	—
30	#10622312	C₂²	1	1	yes	characteristic
31	#10622302	C₂²	1	1	yes	characteristic
32	#10622296	C₂²	1	1	yes	characteristic
33	C₁₁×#358	C₂²	1	2	yes	—
34	C₁₁×#358	C₂²	1	2	yes	—
35	C₁₁×#346	C₂²	1	1	yes	characteristic
36	#10622141	C₂²	1	2	yes	—
37	#10622141	C₂²	1	2	yes	—
38	#10622140	C₂²	1	1	yes	characteristic
39	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
40	#10622128	C₂²	1	2	yes	—
41	#10622127	C₂²	1	2	yes	—
42	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₁₁×Q₁₆	—	2	1	no	—
44	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
45	C₁₁×C₄⋊Q₈	—	2	1	no	—
46	C₁₁×#125	—	2	1	no	—
47	#66999	—	2	2	no	—
48	Q₈×Dic₁₁	—	2	2	no	—
49	C₂×Dic₄₄	—	2	1	no	—
50	C₂×Dic₄₄	C₂³	1	2	yes	—
51	C₂×#4313	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
53	#66951	—	4	2	no	—
54	#66951	—	4	2	no	—
55	#66950	—	2	2	no	—
56	#66943	—	4	2	no	—
57	#66942	—	4	2	no	—
58	#66940	—	2	2	no	—
59	#66925	D₄	1	1	yes	characteristic
60	#66923	—	2	1	no	—
61	#66922	—	2	1	no	—
62	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
64	C₁₁×#107	C₂³	1	2	yes	—
65	C₁₁×#106	—	2	1	no	—
66	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	#66899	—	2	2	no	—
68	#66899	—	2	2	no	—
69	#66893	—	2	4	no	—
70	#66893	—	2	4	no	—
71	#66882	C₂³	1	2	yes	—
72	#66881	—	2	1	no	—
73	#66879	D₄	1	1	yes	characteristic
74	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
75	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
77	#66874	—	2	2	no	—
78	#66874	—	2	2	no	—
79	#66867	D₄	1	1	yes	characteristic
80	#66862	—	2	2	no	—
81	C₁₆×D₁₁	—	2	2	no	—
82	#33741	—	11	1	no	maximal, Sylow
83	C₂×Q₈×C₁₁	—	2	2	no	—
84	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂×Dic₂₂	—	2	2	no	—
86	C₁₁×Q₁₆	—	2	2	no	—
87	C₁₁×Q₁₆	—	2	2	no	—
88	C₁₁×Q₁₆	—	4	2	no	—
89	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₁₁×C₄⋊C₄	—	2	2	no	—
92	C₁₁×C₄⋊C₄	—	4	2	no	—
93	C₁₁×C₄⋊C₄	—	4	2	no	—
94	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
95	(C₂×D₁₁)⋊C₄	—	4	2	no	—
96	(C₂×D₁₁)⋊C₄	—	4	2	no	—
97	(C₂×D₁₁)⋊C₄	D₈	1	2	yes	—
98	C₄⋊Dic₁₁	—	2	2	no	—
99	C₄⋊Dic₁₁	—	4	2	no	—
100	C₄⋊Dic₁₁	—	4	2	no	—
101	C₄⋊Dic₁₁	—	4	2	no	—
102	Dic₁₁⋊C₄	—	4	2	no	—
103	Dic₁₁⋊C₄	—	4	2	no	—
104	Dic₁₁⋊C₄	—	4	2	no	—
105	Dic₁₁⋊C₄	D₈	1	2	yes	—
106	C₄×Dic₁₁	—	4	2	no	—
107	C₄×Dic₁₁	—	4	2	no	—
108	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
111	Dic₄₄	—	2	2	no	—
112	Dic₄₄	—	2	2	no	—
113	Dic₄₄	—	4	2	no	—
114	#4313	—	2	2	no	—
115	C₈×D₁₁	—	2	1	no	—
116	C₈×D₁₁	—	2	1	no	—
117	C₁₁×C₁₆	—	2	1	no	—
118	C₁₁×C₁₆	—	2	1	no	—
119	C₁₁⋊C₁₆	#41	1	2	yes	—
120	C₁₁⋊C₁₆	#41	1	2	yes	—
121	#3177	—	11	1	no	—
122	#3177	—	11	1	no	—
123	#2253	—	11	1	no	—
124	#2247	—	11	1	no	—
125	#2245	—	11	1	no	—
126	#2245	D₁₁	1	1	yes	characteristic, complemented
127	#2219	—	11	2	no	—
128	#2216	—	11	2	no	—
129	#2176	—	11	2	no	—
130	C₄×Q₃₂	—	11	2	no	—
131	#2108	—	11	1	no	—
132	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₁₁	—	4	2	no	—
134	Q₈×C₁₁	—	4	2	no	—
135	C₂×C₄×C₁₁	—	4	2	no	—
136	C₂×C₄×C₁₁	—	4	2	no	—
137	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
138	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
139	C₂×Dic₁₁	—	4	2	no	—
140	C₂×Dic₁₁	—	4	2	no	—
141	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
142	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
143	C₄×D₁₁	—	2	1	no	—
144	C₄×D₁₁	—	2	1	no	—
145	Dic₂₂	—	4	2	no	—
146	Dic₂₂	—	4	2	no	—
147	C₈×C₁₁	#135	1	2	yes	—
148	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
149	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
150	C₁₁⋊C₈	—	2	1	no	—
151	C₁₁⋊C₈	—	2	1	no	—
152	#541	—	22	1	no	—
153	#541	—	22	1	no	—
154	C₂×Q₃₂	—	11	2	no	—
155	C₂×Q₃₂	—	11	2	no	—
156	C₂×M₃₂	—	11	1	no	—
157	C₂²×C₁₆	—	11	1	no	—
158	#499	—	11	1	no	—
159	#499	C₂×D₁₁	1	1	yes	characteristic
160	#494	—	11	1	no	—
161	#494	C₂×D₁₁	1	1	yes	characteristic
162	#491	—	22	1	no	—
163	#491	—	22	1	no	—
164	#470	—	22	1	no	—
165	#470	—	22	1	no	—
166	#467	—	11	2	no	—
167	#467	—	11	2	no	—
168	#441	—	22	1	no	—
169	#441	—	22	1	no	—
170	C₄×Q₁₆	—	11	2	no	—
171	C₄×Q₁₆	—	11	2	no	—
172	#405	—	11	1	no	—
173	#367	—	11	2	no	—
174	#366	—	11	2	no	—
175	#358	—	11	2	no	—
176	#358	—	11	2	no	—
177	#358	C₂×D₁₁	1	2	yes	—
178	#358	C₂×D₁₁	1	2	yes	—
179	#346	—	11	1	no	—
180	#346	C₂×D₁₁	1	1	yes	characteristic
181	C₄×C₁₆	—	11	1	no	—
182	C₄×C₁₆	—	11	1	no	—
183	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
184	C₂×D₁₁	—	2	2	no	—
185	C₂×D₁₁	—	2	1	no	—
186	C₄×C₁₁	—	2	2	no	—
187	C₄×C₁₁	—	8	2	no	—
188	C₄×C₁₁	—	8	2	no	—
189	C₄×C₁₁	#532	1	1	yes	characteristic
190	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
191	Dic₁₁	—	2	2	no	—
192	Dic₁₁	—	2	1	no	—
193	Dic₁₁	—	8	2	no	—
194	Dic₁₁	—	8	2	no	—
195	C₂×Q₁₆	—	2	1	no	—
196	C₂×Q₁₆	—	11	2	no	—
197	C₂×Q₁₆	—	22	1	no	—
198	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
199	C₂×M₁₆	—	11	1	no	—
200	C₂²×C₈	—	11	1	no	—
201	C₄⋊Q₈	—	2	1	no	—
202	C₄⋊Q₈	—	22	1	no	—
203	#126	—	44	2	no	—
204	#126	—	44	2	no	—
205	#125	—	2	1	no	—
206	#125	—	22	1	no	—
207	#125	—	44	2	no	—
208	#125	—	44	2	no	—
209	C₂²⋊Q₈	—	22	2	no	—
210	C₂²⋊Q₈	—	22	2	no	—
211	C₄×Q₈	—	22	2	no	—
212	C₄×Q₈	—	22	2	no	—
213	#117	—	11	1	no	—
214	Q₃₂	—	22	4	no	—
215	Q₃₂	—	22	4	no	—
216	M₃₂	—	22	2	no	—
217	C₂×C₁₆	—	11	1	no	—
218	C₂×C₁₆	—	11	1	no	—
219	C₂×C₁₆	—	22	2	no	—
220	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
221	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
222	#107	—	11	2	no	—
223	#107	C₂²×D₁₁	1	2	yes	—
224	#106	—	2	1	no	—
225	#106	—	22	1	no	—
226	#103	—	22	2	no	—
227	#103	—	22	2	no	—
228	#103	—	22	2	no	—
229	#103	—	22	2	no	—
230	#97	—	11	1	no	—
231	#97	—	11	1	no	—
232	C₄×C₈	—	11	1	no	—
233	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
234	C₂×C₁₁	#3169	1	1	yes	characteristic
235	C₂×C₁₁	#3417	1	2	yes	—
236	D₁₁	—	4	1	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	22	2	no	—
239	C₂²×C₄	—	11	1	no	—
240	Q₁₆	—	2	2	no	—
241	Q₁₆	—	2	2	no	—
242	Q₁₆	—	4	2	no	—
243	Q₁₆	—	22	2	no	—
244	Q₁₆	—	22	2	no	—
245	Q₁₆	—	44	2	no	—
246	M₁₆	—	22	2	no	—
247	C₂×C₈	—	11	1	no	—
248	C₂×C₈	—	11	1	no	—
249	C₂×C₈	—	22	1	no	—
250	C₂×C₈	—	22	1	no	—
251	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
252	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	4	2	no	—
255	C₄⋊C₄	—	4	2	no	—
256	C₄⋊C₄	—	11	2	no	—
257	C₄⋊C₄	—	22	2	no	—
258	C₄⋊C₄	—	44	2	no	—
259	C₄⋊C₄	—	44	2	no	—
260	C₄⋊C₄	—	44	2	no	—
261	C₄⋊C₄	—	44	2	no	—
262	C₄⋊C₄	—	44	2	no	—
263	C₄⋊C₄	—	44	2	no	—
264	C₂²⋊C₄	—	11	2	no	—
265	C₂²⋊C₄	—	44	2	no	—
266	C₂²⋊C₄	—	44	2	no	—
267	C₄²	—	11	1	no	—
268	C₄²	—	44	2	no	—
269	C₄²	—	44	2	no	—
270	C₄²	D₄×D₁₁	1	1	yes	characteristic
271	C₁₆	—	2	1	no	—
272	C₁₆	—	2	1	no	—
273	C₁₆	—	11	2	no	—
274	C₁₆	—	11	2	no	—
275	C₁₁	#33741	1	1	yes	characteristic, complemented, Sylow
276	C₂³	—	11	1	no	—
277	Q₈	—	4	2	no	—
278	Q₈	—	4	2	no	—
279	Q₈	—	44	2	no	—
280	Q₈	—	44	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	—	11	2	no	—
284	C₂×C₄	—	11	1	no	—
285	C₂×C₄	—	22	1	no	—
286	C₂×C₄	—	22	1	no	—
287	C₂×C₄	—	44	2	no	—
288	C₂×C₄	—	44	2	no	—
289	C₂×C₄	D₈×D₁₁	1	2	yes	—
290	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
291	C₈	—	22	1	no	—
292	C₈	—	22	1	no	—
293	C₈	#66969	1	2	yes	—
294	C₈	#41×D₁₁	1	1	yes	characteristic
295	C₈	#41×D₁₁	1	1	yes	characteristic
296	C₂²	—	22	1	no	—
297	C₂²	—	22	2	no	—
298	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
299	C₄	—	2	2	no	—
300	C₄	—	8	2	no	—
301	C₄	—	8	2	no	—
302	C₄	—	22	1	no	—
303	C₄	—	22	2	no	—
304	C₄	—	88	2	no	—
305	C₄	—	88	2	no	—
306	C₄	#10623199	1	1	yes	characteristic
307	C₄	C₂×#66969	1	1	yes	characteristic
308	C₂	—	44	1	no	—
309	C₂	#13079194	1	1	yes	characteristic
310	C₂	#13081768	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2245	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	#2245	D₁₁
hypocenter	C₁₁	#33741
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2245

Complements

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

N	H ≅ G/N	type
3. #13070892	C₂	semidirect
4. #13070868	C₂	semidirect
5. #13070862	C₂	semidirect
8. #13070484	C₂	semidirect
9. #13070472	C₂	semidirect
11. C₁₁×#2245	C₂	semidirect
126. #2245	D₁₁	semidirect
275. C₁₁	#33741	semidirect

Maximal subgroups

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

subgroup	index
#13079276	2
#13079272	2
#13070892	2
#13070868	2
#13070862	2
#13070723	2
#13070706	2
#13070484	2
#13070472	2
#13070214	2
C₁₁×#2245	2
#33741	11