Subgroups — #14909284

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079149	C₂	1	2	yes	maximal
2	#13070901	C₂	1	2	yes	maximal, complemented
3	#13070899	C₂	1	2	yes	maximal, complemented
4	#13070897	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070895	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070894	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070403	C₂	1	2	yes	maximal
8	#13070399	C₂	1	1	yes	maximal, characteristic
9	D₁₁×#367	C₂	1	1	yes	maximal, characteristic
10	#13070211	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#2254	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623260	—	2	2	no	—
13	C₁₁×#500	C₂²	1	2	yes	—
14	#10622693	—	2	2	no	—
15	C₂×#66862	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
17	#10622494	—	2	2	no	—
18	#10622493	C₂²	1	2	yes	—
19	D₁₁×#107	C₂²	1	2	yes	—
20	#10622491	C₂²	1	2	yes	—
21	#10622489	—	2	2	no	—
22	#10622487	C₂²	1	2	yes	—
23	#10622302	C₂²	1	1	yes	characteristic
24	#10622296	C₂²	1	2	yes	—
25	C₁₁×#367	C₂²	1	1	yes	characteristic
26	C₁₁×#367	C₂²	1	1	yes	characteristic
27	C₁₁×#367	C₂²	1	2	yes	—
28	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
29	#10622143	C₂²	1	1	yes	characteristic
30	#10622143	C₂²	1	1	yes	characteristic
31	#10622142	C₂²	1	2	yes	—
32	#10622140	C₂²	1	1	yes	characteristic
33	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
34	#10622128	C₂²	1	2	yes	—
35	#10622128	C₂²	1	2	yes	—
36	#10622127	C₂²	1	2	yes	—
37	#10622127	C₂²	1	2	yes	—
38	#10622099	C₂²	1	1	yes	characteristic
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	#66999	—	4	2	no	—
41	#66997	—	4	2	no	—
42	C₂×#4313	D₄	1	1	yes	characteristic
43	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
44	#66949	—	4	2	no	—
45	#66945	—	2	2	no	—
46	C₄⋊C₄×D₁₁	—	2	2	no	—
47	#66943	—	2	2	no	—
48	#66942	—	4	2	no	—
49	#66941	—	2	2	no	—
50	#66925	D₄	1	1	yes	characteristic
51	#66923	—	2	2	no	—
52	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
54	C₁₁×#107	—	2	2	no	—
55	C₁₁×#107	C₂³	1	2	yes	—
56	C₁₁×#107	C₂³	1	2	yes	—
57	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	#66882	C₂³	1	2	yes	—
59	#66882	C₂³	1	2	yes	—
60	#66881	—	2	2	no	—
61	#66879	D₄	1	1	yes	characteristic
62	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
65	#66872	—	2	2	no	—
66	#66872	—	2	2	no	—
67	#66871	—	2	2	no	—
68	#66871	—	2	2	no	—
69	#66867	D₄	1	1	yes	characteristic
70	#66862	Q₈	1	4	yes	complemented
71	C₁₆×D₁₁	Q₈	1	4	yes	complemented
72	#33730	—	11	1	no	maximal, Sylow
73	C₂×Q₈×C₁₁	—	4	2	no	—
74	C₂×C₄×D₁₁	—	4	2	no	—
75	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×Dic₂₂	—	4	2	no	—
77	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₁₁×C₄⋊C₄	—	2	2	no	—
80	C₁₁×C₄⋊C₄	—	2	2	no	—
81	C₁₁×C₄⋊C₄	—	4	2	no	—
82	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
83	(C₂×D₁₁)⋊C₄	—	4	2	no	—
84	(C₂×D₁₁)⋊C₄	D₈	1	2	yes	—
85	C₄⋊Dic₁₁	—	2	2	no	—
86	C₄⋊Dic₁₁	—	2	2	no	—
87	C₄⋊Dic₁₁	—	4	2	no	—
88	Dic₁₁⋊C₄	—	4	2	no	—
89	Dic₁₁⋊C₄	—	4	2	no	—
90	Dic₁₁⋊C₄	—	4	2	no	—
91	Dic₁₁⋊C₄	—	4	2	no	—
92	Dic₁₁⋊C₄	—	4	2	no	—
93	Dic₁₁⋊C₄	D₈	1	2	yes	—
94	C₄×Dic₁₁	—	4	2	no	—
95	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
96	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
97	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
98	#4313	Q₁₆	1	4	yes	—
99	C₈×D₁₁	C₂×Q₈	1	2	yes	—
100	C₈×D₁₁	C₂×Q₈	1	2	yes	—
101	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
102	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
103	C₁₁⋊C₁₆	C₂×Q₈	1	2	yes	—
104	C₁₁⋊C₁₆	C₂×Q₈	1	2	yes	—
105	#3164	—	11	2	no	—
106	#2255	—	11	2	no	—
107	#2255	—	11	2	no	—
108	#2254	—	11	1	no	—
109	#2254	D₁₁	1	1	yes	characteristic, complemented
110	#2253	—	11	1	no	—
111	#2253	—	11	1	no	—
112	#2159	—	11	2	no	—
113	#2158	—	11	1	no	—
114	C₂×#367	—	11	1	no	—
115	#2108	—	11	1	no	—
116	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
117	Q₈×C₁₁	—	16	2	no	—
118	C₂×C₄×C₁₁	—	4	2	no	—
119	C₂×C₄×C₁₁	—	4	2	no	—
120	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
121	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
122	C₂×Dic₁₁	—	4	2	no	—
123	C₂×Dic₁₁	—	4	2	no	—
124	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
125	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
126	C₄×D₁₁	—	16	2	no	—
127	C₄×D₁₁	C₄⋊Q₈	1	2	yes	—
128	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
129	Dic₂₂	—	16	2	no	—
130	C₈×C₁₁	C₂×Q₁₆	1	2	yes	—
131	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
132	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
133	C₁₁⋊C₈	C₄⋊Q₈	1	2	yes	—
134	C₁₁⋊C₈	C₂×Q₁₆	1	2	yes	—
135	#544	—	22	2	no	—
136	C₂×M₃₂	—	11	1	no	—
137	C₂²×C₁₆	—	11	1	no	—
138	#501	—	22	2	no	—
139	#501	—	22	2	no	—
140	#500	—	11	2	no	—
141	#500	C₂×D₁₁	1	2	yes	—
142	#499	—	11	2	no	—
143	#499	—	11	2	no	—
144	#428	—	22	2	no	—
145	#427	—	11	2	no	—
146	C₂×#107	—	11	2	no	—
147	#405	—	11	1	no	—
148	#367	—	11	1	no	—
149	#367	—	11	1	no	—
150	#367	—	11	2	no	—
151	#367	—	11	2	no	—
152	#367	C₂×D₁₁	1	1	yes	characteristic
153	#367	C₂×D₁₁	1	1	yes	characteristic
154	#367	C₂×D₁₁	1	2	yes	—
155	#366	—	11	2	no	—
156	#366	—	11	2	no	—
157	#366	—	11	2	no	—
158	#346	—	11	1	no	—
159	#346	—	11	1	no	—
160	C₄×C₁₆	—	11	1	no	—
161	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
162	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
163	C₂×D₁₁	—	2	2	no	—
164	C₂×D₁₁	#500	1	2	yes	—
165	C₄×C₁₁	—	2	2	no	—
166	C₄×C₁₁	—	8	2	no	—
167	C₄×C₁₁	—	8	2	no	—
168	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
169	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
170	Dic₁₁	—	2	2	no	—
171	Dic₁₁	—	8	2	no	—
172	Dic₁₁	—	8	2	no	—
173	Dic₁₁	#500	1	2	yes	—
174	C₂×M₁₆	—	11	1	no	—
175	C₂²×C₈	—	11	1	no	—
176	C₄⋊Q₈	—	2	2	no	—
177	C₄⋊Q₈	—	22	2	no	—
178	C₄⋊Q₈	—	44	2	no	—
179	#125	—	22	2	no	—
180	#125	—	22	2	no	—
181	#125	—	44	2	no	—
182	C₂²⋊Q₈	—	44	2	no	—
183	C₂²⋊Q₈	—	44	2	no	—
184	#117	—	11	1	no	—
185	#117	—	22	2	no	—
186	C₂×C₄⋊C₄	—	22	2	no	—
187	M₃₂	—	11	4	no	—
188	C₂×C₁₆	—	11	1	no	—
189	C₂×C₁₆	—	11	1	no	—
190	C₂×C₁₆	—	11	4	no	—
191	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
192	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
193	#107	—	2	2	no	—
194	#107	—	11	2	no	—
195	#107	—	11	2	no	—
196	#107	—	22	2	no	—
197	#107	—	22	2	no	—
198	#107	C₂²×D₁₁	1	2	yes	—
199	#107	C₂²×D₁₁	1	2	yes	—
200	#106	—	22	2	no	—
201	#106	—	22	2	no	—
202	#106	—	22	2	no	—
203	#97	—	11	1	no	—
204	#97	—	11	1	no	—
205	C₄×C₈	—	11	1	no	—
206	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
207	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
208	C₂×C₁₁	#3416	1	2	yes	—
209	D₁₁	—	2	2	no	—
210	C₂×Q₈	—	4	2	no	—
211	C₂×Q₈	—	44	2	no	—
212	C₂²×C₄	—	11	1	no	—
213	C₂²×C₄	—	44	2	no	—
214	M₁₆	—	11	4	no	—
215	C₂×C₈	—	11	1	no	—
216	C₂×C₈	—	11	1	no	—
217	C₂×C₈	—	11	2	no	—
218	C₂×C₈	—	11	2	no	—
219	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
220	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
221	C₄⋊C₄	—	2	2	no	—
222	C₄⋊C₄	—	2	2	no	—
223	C₄⋊C₄	—	4	2	no	—
224	C₄⋊C₄	—	11	2	no	—
225	C₄⋊C₄	—	22	2	no	—
226	C₄⋊C₄	—	22	2	no	—
227	C₄⋊C₄	—	44	2	no	—
228	C₄⋊C₄	—	44	2	no	—
229	C₄⋊C₄	—	44	2	no	—
230	C₄⋊C₄	—	44	2	no	—
231	C₄⋊C₄	—	44	2	no	—
232	C₄⋊C₄	—	44	2	no	—
233	C₂²⋊C₄	—	11	2	no	—
234	C₂²⋊C₄	—	44	2	no	—
235	C₄²	—	11	1	no	—
236	C₄²	—	44	2	no	—
237	C₄²	D₄×D₁₁	1	1	yes	characteristic
238	C₁₆	—	11	2	no	—
239	C₁₆	—	11	2	no	—
240	C₁₆	Q₈×D₁₁	1	2	yes	—
241	C₁₆	Q₈×D₁₁	1	2	yes	—
242	C₁₁	#33730	1	1	yes	characteristic, complemented, Sylow
243	C₂³	—	11	1	no	—
244	Q₈	—	16	2	no	—
245	Q₈	—	176	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	11	1	no	—
249	C₂×C₄	—	11	2	no	—
250	C₂×C₄	—	11	2	no	—
251	C₂×C₄	—	11	2	no	—
252	C₂×C₄	—	44	2	no	—
253	C₂×C₄	—	44	2	no	—
254	C₂×C₄	—	176	2	no	—
255	C₂×C₄	D₈×D₁₁	1	2	yes	—
256	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
257	C₈	—	11	2	no	—
258	C₈	—	11	2	no	—
259	C₈	Q₁₆×D₁₁	1	2	yes	—
260	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
261	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
262	C₂²	—	11	2	no	—
263	C₂²	—	22	2	no	—
264	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
265	C₄	—	2	2	no	—
266	C₄	—	8	2	no	—
267	C₄	—	8	2	no	—
268	C₄	—	11	2	no	—
269	C₄	—	22	2	no	—
270	C₄	—	88	2	no	—
271	C₄	—	88	2	no	—
272	C₄	D₁₁×C₄⋊Q₈	1	1	yes	characteristic
273	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
274	C₂	—	22	2	no	—
275	C₂	D₁₁×#500	1	1	yes	characteristic
276	C₂	#13081758	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2254	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	#2254	D₁₁
hypocenter	C₁₁	#33730
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2254

Complements

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

N	H ≅ G/N	type
2. #13070901	C₂	semidirect
3. #13070899	C₂	semidirect
4. #13070897	C₂	semidirect
5. #13070895	C₂	semidirect
6. #13070894	C₂	semidirect
11. C₁₁×#2254	C₂	semidirect
70. #66862	Q₈	semidirect
71. C₁₆×D₁₁	Q₈	semidirect
109. #2254	D₁₁	semidirect
242. C₁₁	#33730	semidirect

Maximal subgroups

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

subgroup	index
#13079149	2
#13070901	2
#13070899	2
#13070897	2
#13070895	2
#13070894	2
#13070403	2
#13070399	2
D₁₁×#367	2
#13070211	2
C₁₁×#2254	2
#33730	11