Subgroups — #14909889

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079195	C₂	1	1	yes	maximal, characteristic
2	#13079130	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070898	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070891	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070840	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070840	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070808	C₂	1	4	yes	maximal, complemented
8	#13070774	C₂	1	4	yes	maximal, complemented
9	C₁₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623008	—	2	1	no	—
11	#10623001	—	2	1	no	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622728	—	2	1	no	—
14	#10622728	C₂²	1	2	yes	—
15	#10622719	—	2	1	no	—
16	#10622719	C₂²	1	2	yes	—
17	#10622308	C₂²	1	1	yes	characteristic
18	#10622307	—	2	1	no	—
19	C₄×D₈₈	—	2	1	no	—
20	C₄×D₈₈	C₂²	1	2	yes	—
21	#10622296	—	2	1	no	—
22	#10622296	C₂²	1	2	yes	—
23	#10622295	C₂²	1	1	yes	characteristic
24	#10622295	C₂²	1	1	yes	characteristic
25	#10622295	C₂²	1	1	yes	characteristic
26	#10622293	—	2	1	no	—
27	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
28	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
29	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
31	#10622147	C₂²	1	4	yes	—
32	#10622147	C₂²	1	4	yes	—
33	#10622143	C₂²	1	4	yes	—
34	#10622142	C₂²	1	4	yes	—
35	C₂×#4339	—	4	1	no	—
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	#66983	—	2	2	no	—
40	#66983	—	4	1	no	—
41	#66979	—	2	2	no	—
42	#66977	—	4	1	no	—
43	#66977	—	4	1	no	—
44	C₂×D₈₈	—	2	1	no	—
45	C₂×D₈₈	C₂³	1	2	yes	—
46	#66928	—	4	1	no	—
47	#66927	—	2	1	no	—
48	C₄×D₄₄	—	2	2	no	—
49	C₄×D₄₄	—	4	1	no	—
50	#66923	—	2	2	no	—
51	#66922	—	2	1	no	—
52	#66922	—	2	1	no	—
53	#66922	—	2	1	no	—
54	C₄×Dic₂₂	—	4	1	no	—
55	C₄×Dic₂₂	—	4	1	no	—
56	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
57	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
58	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
59	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	#66885	—	2	2	no	—
63	#66885	—	2	2	no	—
64	#66882	—	2	1	no	—
65	#66882	—	2	1	no	—
66	#66882	—	2	1	no	—
67	#66882	C₂³	1	2	yes	—
68	#66882	C₂³	1	2	yes	—
69	#66882	C₂³	1	2	yes	—
70	#66881	—	2	2	no	—
71	#66881	—	2	2	no	—
72	#33794	—	11	1	no	maximal, Sylow
73	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₁	—	4	2	no	—
77	#4339	—	8	4	no	—
78	C₂×D₄₄	—	2	2	no	—
79	C₂×D₄₄	—	4	1	no	—
80	C₂×D₄₄	—	4	1	no	—
81	C₂×C₄×D₁₁	—	4	2	no	—
82	C₂×Dic₂₂	—	4	1	no	—
83	C₂×Dic₂₂	—	4	1	no	—
84	C₂×Dic₂₂	—	4	1	no	—
85	C₂×C₈×C₁₁	—	2	2	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₄²×C₁₁	D₈	1	1	yes	characteristic
92	C₄²×C₁₁	D₈	1	1	yes	characteristic
93	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
95	C₂²⋊Dic₁₁	—	4	2	no	—
96	(C₂×D₁₁)⋊C₄	—	4	2	no	—
97	(C₂×D₁₁)⋊C₄	—	4	2	no	—
98	C₄⋊Dic₁₁	—	2	2	no	—
99	C₄⋊Dic₁₁	—	2	2	no	—
100	C₄⋊Dic₁₁	—	2	2	no	—
101	C₄⋊Dic₁₁	—	4	1	no	—
102	C₄⋊Dic₁₁	—	4	1	no	—
103	C₄⋊Dic₁₁	—	4	1	no	—
104	Dic₁₁⋊C₄	—	4	2	no	—
105	Dic₁₁⋊C₄	—	4	2	no	—
106	C₄×Dic₁₁	—	4	2	no	—
107	D₈₈	—	2	4	no	—
108	D₈₈	—	4	2	no	—
109	C₁₁×C₁₆	—	2	2	no	—
110	C₁₁×C₁₆	—	2	2	no	—
111	#3169	—	11	1	no	—
112	#3160	—	11	1	no	—
113	#2254	—	11	1	no	—
114	#2252	—	11	1	no	—
115	#2240	—	11	1	no	—
116	#2240	—	11	1	no	—
117	#2234	—	11	4	no	—
118	#2228	—	11	4	no	—
119	#2162	D₁₁	1	1	yes	characteristic, complemented
120	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
121	C₂²×D₁₁	—	4	2	no	—
122	C₂×C₄×C₁₁	—	2	1	no	—
123	C₂×C₄×C₁₁	—	2	1	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	C₂²⋊D₁₁	—	8	4	no	—
133	C₂×Dic₁₁	—	4	2	no	—
134	C₂×Dic₁₁	—	4	2	no	—
135	C₂×Dic₁₁	—	4	2	no	—
136	D₄₄	—	4	2	no	—
137	D₄₄	—	4	2	no	—
138	D₄₄	—	8	2	no	—
139	D₄₄	—	8	2	no	—
140	C₄×D₁₁	—	8	4	no	—
141	Dic₂₂	—	8	2	no	—
142	Dic₂₂	—	8	2	no	—
143	Dic₂₂	—	8	2	no	—
144	C₈×C₁₁	—	2	1	no	—
145	C₈×C₁₁	—	2	1	no	—
146	C₈×C₁₁	#137	1	2	yes	—
147	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
148	#533	—	22	1	no	—
149	#532	—	22	1	no	—
150	#500	—	11	1	no	—
151	#500	—	11	1	no	—
152	#500	—	11	1	no	—
153	#499	—	11	2	no	—
154	#499	—	22	1	no	—
155	#498	—	22	1	no	—
156	#493	—	11	1	no	—
157	#486	—	22	1	no	—
158	#466	—	11	2	no	—
159	#466	—	22	1	no	—
160	C₄×D₈	—	11	2	no	—
161	C₄×D₈	—	22	1	no	—
162	#427	—	11	2	no	—
163	#427	—	22	1	no	—
164	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
165	#367	—	11	4	no	—
166	#366	—	11	4	no	—
167	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
168	#357	—	11	4	no	—
169	#357	—	11	4	no	—
170	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
171	C₄×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	C₂²×D₈	1	1	yes	characteristic
177	C₂×D₁₁	—	8	2	no	—
178	C₂×D₁₁	—	8	2	no	—
179	C₂×D₁₁	—	8	2	no	—
180	C₄×C₁₁	—	2	1	no	—
181	C₄×C₁₁	—	2	1	no	—
182	C₄×C₁₁	—	2	1	no	—
183	C₄×C₁₁	#508	1	2	yes	—
184	C₄×C₁₁	#509	1	2	yes	—
185	C₄×C₁₁	#536	1	1	yes	characteristic
186	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
187	Dic₁₁	—	8	2	no	—
188	Dic₁₁	—	8	2	no	—
189	Dic₁₁	—	8	2	no	—
190	C₂×#41	—	44	1	no	—
191	C₂×D₈	—	11	2	no	—
192	C₂×D₈	—	22	1	no	—
193	C₂²×C₈	D₄₄	1	1	yes	characteristic
194	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
195	C₄⋊Q₈	—	22	1	no	—
196	C₄⋊Q₈	—	22	1	no	—
197	C₄⋊Q₈	—	22	1	no	—
198	#127	—	22	1	no	—
199	#125	—	22	2	no	—
200	#124	—	44	1	no	—
201	C₂²⋊Q₈	—	44	1	no	—
202	C₂²⋊Q₈	—	44	1	no	—
203	#121	—	22	2	no	—
204	#121	—	44	1	no	—
205	C₄×Q₈	—	44	1	no	—
206	C₄×Q₈	—	44	1	no	—
207	C₄×D₄	—	22	2	no	—
208	C₄×D₄	—	44	1	no	—
209	#117	—	22	2	no	—
210	C₂×C₄²	D₄₄	1	1	yes	characteristic
211	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
212	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
213	#107	—	11	2	no	—
214	#107	—	11	2	no	—
215	#107	—	11	2	no	—
216	#107	—	22	1	no	—
217	#107	—	22	1	no	—
218	#107	—	22	1	no	—
219	#106	—	22	2	no	—
220	#106	—	22	2	no	—
221	#102	—	22	2	no	—
222	#102	—	22	2	no	—
223	C₄×C₈	D₄₄	1	1	yes	characteristic
224	C₄×C₈	D₄₄	1	1	yes	characteristic
225	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
226	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
227	C₂×C₁₁	—	4	1	no	—
228	C₂×C₁₁	#3226	1	1	yes	characteristic
229	C₂×C₁₁	C₂×#508	1	1	yes	characteristic
230	C₂×C₁₁	C₂×#509	1	1	yes	characteristic
231	D₁₁	—	16	2	no	—
232	#41	—	88	4	no	—
233	C₂×Q₈	—	44	1	no	—
234	C₂×Q₈	—	44	1	no	—
235	C₂×Q₈	—	44	1	no	—
236	C₂×D₄	—	22	2	no	—
237	C₂×D₄	—	44	2	no	—
238	C₂×D₄	—	44	1	no	—
239	C₂×D₄	—	44	1	no	—
240	C₂²×C₄	—	44	2	no	—
241	C₂²×C₄	D₈₈	1	1	yes	characteristic
242	C₂²×C₄	D₈₈	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
244	D₈	—	22	4	no	—
245	D₈	—	44	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
249	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
250	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
251	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
252	C₄⋊C₄	—	22	2	no	—
253	C₄⋊C₄	—	22	2	no	—
254	C₄⋊C₄	—	22	2	no	—
255	C₄⋊C₄	—	44	1	no	—
256	C₄⋊C₄	—	44	2	no	—
257	C₄⋊C₄	—	44	2	no	—
258	C₄⋊C₄	—	44	1	no	—
259	C₄⋊C₄	—	44	1	no	—
260	C₂²⋊C₄	—	44	2	no	—
261	C₂²⋊C₄	—	44	2	no	—
262	C₂²⋊C₄	—	44	2	no	—
263	C₄²	—	44	2	no	—
264	C₄²	D₈₈	1	1	yes	characteristic
265	C₄²	D₈₈	1	1	yes	characteristic
266	C₄²	C₂×D₄₄	1	1	yes	characteristic
267	C₄²	C₂×D₄₄	1	1	yes	characteristic
268	C₁₆	—	2	2	no	—
269	C₁₆	—	2	2	no	—
270	C₁₁	#33794	1	1	yes	characteristic, complemented, Sylow
271	C₂³	—	44	2	no	—
272	C₂³	C₂×D₈₈	1	1	yes	characteristic
273	Q₈	—	88	2	no	—
274	Q₈	—	88	2	no	—
275	Q₈	—	88	2	no	—
276	D₄	—	44	2	no	—
277	D₄	—	44	2	no	—
278	D₄	—	88	4	no	—
279	D₄	—	88	2	no	—
280	D₄	—	88	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	44	2	no	—
286	C₂×C₄	—	44	2	no	—
287	C₂×C₄	—	44	2	no	—
288	C₂×C₄	—	88	4	no	—
289	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
290	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
291	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
292	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
293	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
294	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
295	C₈	—	2	1	no	—
296	C₈	—	2	1	no	—
297	C₈	#66962	1	2	yes	—
298	C₈	#67043	1	2	yes	—
299	C₂²	—	2	1	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	88	2	no	—
303	C₂²	—	88	2	no	—
304	C₂²	—	88	2	no	—
305	C₂²	C₂²×D₈₈	1	1	yes	characteristic
306	C₄	—	2	1	no	—
307	C₄	—	2	1	no	—
308	C₄	—	2	1	no	—
309	C₄	—	88	2	no	—
310	C₄	—	88	2	no	—
311	C₄	—	88	2	no	—
312	C₄	#10622517	1	2	yes	—
313	C₄	#10622521	1	2	yes	—
314	C₄	#10623057	1	1	yes	characteristic
315	C₄	C₂×#66962	1	1	yes	characteristic
316	C₂	—	4	1	no	—
317	C₂	—	176	2	no	—
318	C₂	#13079739	1	1	yes	characteristic
319	C₂	C₂×#10622517	1	1	yes	characteristic
320	C₂	C₂×#10622521	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2162	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	#13079195	C₂
hypercenter	#2162	D₁₁
hypocenter	C₁₁	#33794
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

Complements

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

N	H ≅ G/N	type
2. #13079130	C₂	semidirect
3. #13070898	C₂	semidirect
4. #13070891	C₂	semidirect
5. #13070840	C₂	semidirect
6. #13070840	C₂	semidirect
7. #13070808	C₂	semidirect
8. #13070774	C₂	semidirect
9. C₁₁×#2162	C₂	semidirect
119. #2162	D₁₁	semidirect
270. C₁₁	#33794	semidirect

Maximal subgroups

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

subgroup	index
#13079195	2
#13079130	2
#13070898	2
#13070891	2
#13070840	2
#13070808	2
#13070774	2
C₁₁×#2162	2
#33794	11