Subgroups — #14911152

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13080985	C₂	1	2	yes	maximal
2	#13070895	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070825	C₂	1	2	yes	maximal, complemented
4	#13070814	C₂	1	2	yes	maximal, complemented
5	#13070781	C₂	1	2	yes	maximal, complemented
6	#13070707	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070707	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Dic₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070400	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622142	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
12	#10623072	—	2	2	no	—
13	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
16	#10622729	C₂²	1	2	yes	—
17	#10622729	C₂²	1	2	yes	—
18	#10622719	C₂²	1	2	yes	—
19	C₂×#66882	C₂²	1	2	yes	—
20	C₂×Dic₈₈	C₂²	1	1	yes	characteristic
21	#10622442	—	2	2	no	—
22	#10622336	—	2	2	no	—
23	#10622334	—	2	2	no	—
24	C₄×Dic₄₄	C₂²	1	2	yes	—
25	#10622296	C₂²	1	2	yes	—
26	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
30	#10622143	C₂²	1	2	yes	—
31	#10622143	C₂²	1	2	yes	—
32	#10622142	C₂²	1	1	yes	characteristic
33	#10622142	C₂²	1	1	yes	characteristic
34	#10622142	C₂²	1	1	yes	characteristic
35	#10622142	C₂²	1	2	yes	—
36	#10622141	C₂²	1	2	yes	—
37	#10622141	C₂²	1	2	yes	—
38	#10622141	C₂²	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
42	#66988	—	4	2	no	—
43	#66979	—	2	2	no	—
44	C₂×C₄⋊Dic₁₁	—	2	2	no	—
45	#66977	—	2	2	no	—
46	#66977	—	2	2	no	—
47	C₂×Dic₄₄	C₂³	1	2	yes	—
48	#66942	—	4	2	no	—
49	#66932	—	4	2	no	—
50	#66930	—	4	2	no	—
51	#66923	—	2	2	no	—
52	C₄×Dic₂₂	—	2	2	no	—
53	C₂×C₁₁×C₁₆	—	2	2	no	—
54	C₂×C₁₁×C₁₆	—	2	2	no	—
55	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
60	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
61	C₁₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
62	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	#66882	—	2	2	no	—
64	#66882	C₂³	1	2	yes	—
65	#66882	C₂³	1	2	yes	—
66	#66882	C₂³	1	2	yes	—
67	#66881	—	2	2	no	—
68	#66881	—	2	2	no	—
69	#66880	—	2	2	no	—
70	#66880	—	2	2	no	—
71	#66880	—	2	2	no	—
72	Dic₈₈	—	2	2	no	—
73	#33903	—	11	1	no	maximal, Sylow
74	C₂×D₄×C₁₁	D₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₁₁	—	4	2	no	—
78	C₂×Dic₂₂	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	1	no	—
80	C₂×C₈×C₁₁	—	2	1	no	—
81	C₂×C₈×C₁₁	—	2	1	no	—
82	C₂×C₈×C₁₁	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
87	C₁₁×C₄⋊C₄	D₈	1	1	yes	characteristic
88	C₁₁×C₂²⋊C₄	D₈	1	1	yes	characteristic
89	C₁₁×C₂²⋊C₄	D₈	1	1	yes	characteristic
90	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
91	C₂²⋊Dic₁₁	—	4	2	no	—
92	C₂²⋊Dic₁₁	—	4	2	no	—
93	C₂²⋊Dic₁₁	—	4	2	no	—
94	C₄⋊Dic₁₁	—	2	2	no	—
95	C₄⋊Dic₁₁	—	2	2	no	—
96	C₄⋊Dic₁₁	—	2	2	no	—
97	C₄⋊Dic₁₁	—	4	2	no	—
98	Dic₁₁⋊C₄	—	4	2	no	—
99	Dic₁₁⋊C₄	—	4	2	no	—
100	Dic₁₁⋊C₄	—	4	2	no	—
101	Dic₁₁⋊C₄	—	4	2	no	—
102	Dic₁₁⋊C₄	—	4	2	no	—
103	C₄×Dic₁₁	—	4	2	no	—
104	C₄×Dic₁₁	—	4	2	no	—
105	Dic₄₄	—	2	2	no	—
106	Dic₄₄	—	2	2	no	—
107	C₁₁×C₁₆	—	2	1	no	—
108	C₁₁×C₁₆	—	2	1	no	—
109	C₁₁×C₁₆	—	2	1	no	—
110	C₁₁×C₁₆	#41	1	2	yes	—
111	#3336	—	11	2	no	—
112	#2253	—	11	1	no	—
113	#2237	—	11	2	no	—
114	#2235	—	11	2	no	—
115	#2229	—	11	2	no	—
116	#2216	—	11	1	no	—
117	#2216	—	11	1	no	—
118	C₄×Q₃₂	—	11	1	no	—
119	D₄×C₁₆	D₁₁	1	1	yes	characteristic
120	#2158	—	11	1	no	—
121	C₂×#366	—	11	1	no	—
122	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
123	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
124	D₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	1	no	—
126	C₂×C₄×C₁₁	—	2	1	no	—
127	C₂×C₄×C₁₁	—	2	1	no	—
128	C₂×C₄×C₁₁	—	2	1	no	—
129	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×Dic₁₁	—	4	2	no	—
135	C₂×Dic₁₁	—	4	2	no	—
136	C₂×Dic₁₁	—	4	2	no	—
137	C₂×Dic₁₁	—	4	2	no	—
138	C₂×Dic₁₁	—	8	4	no	—
139	Dic₂₂	—	4	2	no	—
140	Dic₂₂	—	4	2	no	—
141	C₈×C₁₁	—	2	1	no	—
142	C₈×C₁₁	—	2	1	no	—
143	C₈×C₁₁	—	2	1	no	—
144	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
145	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
146	#552	—	22	2	no	—
147	C₂×Q₃₂	—	11	1	no	—
148	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
149	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
150	#499	—	11	2	no	—
151	#485	—	22	2	no	—
152	#483	—	22	2	no	—
153	#479	—	22	2	no	—
154	#467	—	11	2	no	—
155	#467	—	11	2	no	—
156	C₄×Q₁₆	—	11	2	no	—
157	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
158	#427	—	11	2	no	—
159	C₂×#107	—	11	2	no	—
160	#367	—	11	2	no	—
161	#367	—	11	2	no	—
162	#366	—	11	1	no	—
163	#366	—	11	1	no	—
164	#366	—	11	2	no	—
165	#366	—	11	1	no	—
166	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
167	#358	—	11	2	no	—
168	#358	—	11	2	no	—
169	#358	—	11	2	no	—
170	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
171	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
172	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
173	C₂²×C₁₁	—	2	1	no	—
174	C₂²×C₁₁	—	2	1	no	—
175	C₂²×C₁₁	—	2	1	no	—
176	C₂²×C₁₁	—	2	1	no	—
177	C₂²×C₁₁	—	2	1	no	—
178	C₂²×C₁₁	#508	1	2	yes	—
179	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
180	C₄×C₁₁	—	2	1	no	—
181	C₄×C₁₁	—	2	1	no	—
182	C₄×C₁₁	—	2	1	no	—
183	C₄×C₁₁	—	2	1	no	—
184	C₄×C₁₁	#547	1	1	yes	characteristic
185	C₄×C₁₁	#578	1	1	yes	characteristic
186	Dic₁₁	—	8	2	no	—
187	Dic₁₁	—	8	2	no	—
188	Dic₁₁	—	8	2	no	—
189	Dic₁₁	—	8	2	no	—
190	C₂×Q₁₆	—	11	2	no	—
191	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
192	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
193	#126	—	44	2	no	—
194	#125	—	22	2	no	—
195	#125	—	44	2	no	—
196	#123	—	44	2	no	—
197	C₂²⋊Q₈	—	22	2	no	—
198	C₂²⋊Q₈	—	22	2	no	—
199	C₄×Q₈	—	22	2	no	—
200	C₄×D₄	D₄₄	1	1	yes	characteristic
201	#117	—	22	2	no	—
202	#117	—	44	2	no	—
203	C₂×C₄⋊C₄	—	22	2	no	—
204	Q₃₂	—	22	2	no	—
205	C₂×C₁₆	—	2	2	no	—
206	C₂×C₁₆	—	2	2	no	—
207	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
208	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
209	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
210	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
211	#107	—	11	2	no	—
212	#107	—	11	2	no	—
213	#107	—	11	2	no	—
214	#107	—	22	2	no	—
215	#106	—	22	2	no	—
216	#106	—	22	2	no	—
217	C₄⋊C₈	D₄₄	1	1	yes	characteristic
218	#103	—	22	2	no	—
219	#103	—	22	2	no	—
220	#103	—	22	2	no	—
221	C₂²⋊C₈	D₄₄	1	1	yes	characteristic
222	C₂²⋊C₈	D₄₄	1	1	yes	characteristic
223	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
224	C₂×C₁₁	—	2	2	no	—
225	C₂×C₁₁	—	4	1	no	—
226	C₂×C₁₁	#3334	1	1	yes	characteristic
227	C₂×C₁₁	C₂×#508	1	1	yes	characteristic
228	C₂×C₁₁	#3417	1	1	yes	characteristic
229	C₂×Q₈	—	22	2	no	—
230	C₂×D₄	D₈₈	1	1	yes	characteristic
231	C₂²×C₄	—	44	2	no	—
232	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
234	Q₁₆	—	22	2	no	—
235	Q₁₆	—	22	2	no	—
236	C₂×C₈	—	2	1	no	—
237	C₂×C₈	—	2	1	no	—
238	C₂×C₈	—	2	1	no	—
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
241	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
242	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
243	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
244	C₄⋊C₄	—	22	2	no	—
245	C₄⋊C₄	—	22	2	no	—
246	C₄⋊C₄	—	22	2	no	—
247	C₄⋊C₄	—	44	2	no	—
248	C₄⋊C₄	—	44	2	no	—
249	C₄⋊C₄	—	44	2	no	—
250	C₄⋊C₄	—	44	2	no	—
251	C₄⋊C₄	—	44	2	no	—
252	C₄⋊C₄	—	44	2	no	—
253	C₄⋊C₄	D₈₈	1	1	yes	characteristic
254	C₂²⋊C₄	—	44	2	no	—
255	C₂²⋊C₄	—	44	2	no	—
256	C₂²⋊C₄	—	44	2	no	—
257	C₂²⋊C₄	D₈₈	1	1	yes	characteristic
258	C₂²⋊C₄	D₈₈	1	1	yes	characteristic
259	C₄²	—	44	2	no	—
260	C₄²	—	44	2	no	—
261	C₄²	C₂×D₄₄	1	1	yes	characteristic
262	C₁₆	—	2	1	no	—
263	C₁₆	—	2	1	no	—
264	C₁₆	—	2	1	no	—
265	C₁₆	#4341	1	2	yes	—
266	C₁₁	#33903	1	1	yes	characteristic, complemented, Sylow
267	C₂³	C₂×D₈₈	1	1	yes	characteristic
268	C₂³	C₂×D₈₈	1	1	yes	characteristic
269	Q₈	—	44	2	no	—
270	Q₈	—	44	2	no	—
271	D₄	—	2	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	44	2	no	—
277	C₂×C₄	—	44	2	no	—
278	C₂×C₄	—	44	2	no	—
279	C₂×C₄	—	44	2	no	—
280	C₂×C₄	—	88	4	no	—
281	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
282	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
283	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
284	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
285	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
286	C₈	—	2	1	no	—
287	C₈	—	2	1	no	—
288	C₈	—	2	1	no	—
289	C₈	C₂×#4341	1	1	yes	characteristic
290	C₈	#67043	1	1	yes	characteristic
291	C₂²	—	2	1	no	—
292	C₂²	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	#10622517	1	2	yes	—
297	C₂²	C₂²×D₈₈	1	1	yes	characteristic
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	88	2	no	—
303	C₄	—	88	2	no	—
304	C₄	—	88	2	no	—
305	C₄	—	88	2	no	—
306	C₄	#10623086	1	1	yes	characteristic
307	C₄	#10623284	1	1	yes	characteristic
308	C₂	—	2	2	no	—
309	C₂	—	4	1	no	—
310	C₂	#13080964	1	1	yes	characteristic
311	C₂	C₂×#10622517	1	1	yes	characteristic
312	C₂	#13081769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	D₄×C₁₁×C₁₆	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂×D₄×C₁₁	D₈
hypercenter	D₄×C₁₆	D₁₁
hypocenter	C₁₁	#33903
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13070895	C₂	semidirect
3. #13070825	C₂	semidirect
4. #13070814	C₂	semidirect
5. #13070781	C₂	semidirect
6. #13070707	C₂	semidirect
7. #13070707	C₂	semidirect
8. C₄×Dic₈₈	C₂	semidirect
9. #13070400	C₂	semidirect
10. C₂×#10622142	C₂	semidirect
266. C₁₁	#33903	semidirect

Maximal subgroups

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

subgroup	index
#13080985	2
#13070895	2
#13070825	2
#13070814	2
#13070781	2
#13070707	2
C₄×Dic₈₈	2
#13070400	2
C₂×#10622142	2
D₄×C₁₁×C₁₆	2
#33903	11