Subgroups — #14909371

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079258	C₂	1	2	yes	maximal, complemented
2	#13070877	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070855	C₂	1	2	yes	maximal, complemented
4	#13070730	C₂	1	2	yes	maximal, complemented
5	#13070708	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070703	C₂	1	1	yes	maximal, characteristic
7	#13070479	C₂	1	2	yes	maximal, complemented
8	#13070474	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070462	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2252	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623264	—	2	2	no	—
13	C₁₁×#500	C₂²	1	2	yes	—
14	#10622702	—	2	2	no	—
15	C₂×Dic₈₈	C₂²	1	1	yes	characteristic
16	C₂×#66864	C₂²	1	2	yes	—
17	C₂×D₁₇₆	C₂²	1	1	yes	characteristic
18	C₂×#66862	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
20	#10622502	—	2	2	no	—
21	#10622500	C₂²	1	2	yes	—
22	#10622499	—	2	2	no	—
23	#10622496	C₂²	1	2	yes	—
24	#10622486	C₂²	1	2	yes	—
25	#10622485	C₂²	1	2	yes	—
26	#10622309	C₂²	1	2	yes	—
27	#10622302	C₂²	1	1	yes	characteristic
28	C₁₁×#366	C₂²	1	1	yes	characteristic
29	C₁₁×#366	C₂²	1	1	yes	characteristic
30	C₁₁×#366	C₂²	1	2	yes	—
31	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
32	#10622140	C₂²	1	1	yes	characteristic
33	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
34	#10622130	C₂²	1	2	yes	—
35	#10622130	C₂²	1	2	yes	—
36	#10622129	C₂²	1	2	yes	—
37	#10622129	C₂²	1	2	yes	—
38	#10622099	C₂²	1	1	yes	characteristic
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	#67000	—	4	2	no	—
41	#66999	—	4	2	no	—
42	C₂×Dic₄₄	C₂³	1	2	yes	—
43	C₂×D₈₈	C₂³	1	2	yes	—
44	C₂×#4314	—	2	2	no	—
45	C₂×#4313	D₄	1	1	yes	characteristic
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	#66951	—	4	2	no	—
48	#66950	—	2	2	no	—
49	#66948	—	2	2	no	—
50	#66947	—	4	2	no	—
51	#66946	—	2	2	no	—
52	#66940	—	2	2	no	—
53	#66928	—	2	2	no	—
54	#66925	D₄	1	1	yes	characteristic
55	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
57	C₁₁×#107	—	2	2	no	—
58	C₁₁×#107	C₂³	1	2	yes	—
59	C₁₁×#107	C₂³	1	2	yes	—
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
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	#66874	—	2	2	no	—
66	#66874	—	2	2	no	—
67	#66873	—	2	2	no	—
68	#66873	—	2	2	no	—
69	#66867	D₄	1	1	yes	characteristic
70	Dic₈₈	—	2	2	no	—
71	#66864	—	2	4	no	—
72	D₁₇₆	—	2	2	no	—
73	#66862	—	2	2	no	—
74	C₁₆×D₁₁	—	2	2	no	—
75	#33739	—	11	1	no	maximal, Sylow
76	C₂×Q₈×C₁₁	—	4	2	no	—
77	C₂×D₄₄	—	2	2	no	—
78	C₂×D₄₄	—	4	2	no	—
79	C₂×C₄×D₁₁	—	4	2	no	—
80	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂×Dic₂₂	—	2	2	no	—
82	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
84	C₁₁×C₄⋊C₄	—	2	2	no	—
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	4	2	no	—
87	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
88	(C₂×D₁₁)⋊C₄	—	4	2	no	—
89	(C₂×D₁₁)⋊C₄	—	4	2	no	—
90	(C₂×D₁₁)⋊C₄	—	4	2	no	—
91	(C₂×D₁₁)⋊C₄	—	4	2	no	—
92	(C₂×D₁₁)⋊C₄	—	4	2	no	—
93	(C₂×D₁₁)⋊C₄	D₈	1	1	yes	characteristic
94	(C₂×D₁₁)⋊C₄	D₈	1	1	yes	characteristic
95	C₄⋊Dic₁₁	—	4	2	no	—
96	Dic₁₁⋊C₄	—	4	2	no	—
97	Dic₁₁⋊C₄	D₈	1	1	yes	characteristic
98	Dic₁₁⋊C₄	D₈	1	1	yes	characteristic
99	C₄×Dic₁₁	—	4	2	no	—
100	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
102	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
103	Dic₄₄	—	2	2	no	—
104	Dic₄₄	—	2	2	no	—
105	D₈₈	—	2	2	no	—
106	D₈₈	—	2	2	no	—
107	#4314	—	4	4	no	—
108	#4313	—	2	2	no	—
109	C₈×D₁₁	—	2	1	no	—
110	C₈×D₁₁	—	2	1	no	—
111	C₁₁×C₁₆	#41	1	2	yes	—
112	C₁₁×C₁₆	#41	1	2	yes	—
113	C₁₁⋊C₁₆	—	2	1	no	—
114	C₁₁⋊C₁₆	—	2	1	no	—
115	#3175	—	11	2	no	—
116	#2252	D₁₁	1	1	yes	characteristic, complemented
117	#2249	—	11	1	no	—
118	#2243	—	11	2	no	—
119	#2220	—	11	2	no	—
120	#2216	—	11	1	no	—
121	#2215	—	11	1	no	—
122	#2175	—	11	2	no	—
123	C₄×Q₃₂	—	11	1	no	—
124	C₄×D₁₆	—	11	1	no	—
125	#2108	—	11	1	no	—
126	C₂²×D₁₁	—	4	2	no	—
127	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
128	Q₈×C₁₁	—	16	2	no	—
129	C₂×C₄×C₁₁	—	4	2	no	—
130	C₂×C₄×C₁₁	—	4	2	no	—
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	C₂×D₈	1	1	yes	characteristic
136	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
137	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
138	D₄₄	—	4	2	no	—
139	D₄₄	—	4	2	no	—
140	D₄₄	—	16	2	no	—
141	C₄×D₁₁	—	2	1	no	—
142	C₄×D₁₁	—	2	1	no	—
143	C₄×D₁₁	—	16	2	no	—
144	Dic₂₂	—	4	2	no	—
145	Dic₂₂	—	4	2	no	—
146	C₈×C₁₁	#135	1	2	yes	—
147	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
148	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
149	C₁₁⋊C₈	—	2	1	no	—
150	C₁₁⋊C₈	—	2	1	no	—
151	#542	—	22	2	no	—
152	C₂×Q₃₂	—	11	1	no	—
153	C₂×SD₃₂	—	11	2	no	—
154	C₂×D₁₆	—	11	1	no	—
155	C₂×M₃₂	—	11	1	no	—
156	C₂²×C₁₆	—	11	1	no	—
157	#500	C₂×D₁₁	1	2	yes	—
158	#495	—	11	2	no	—
159	#489	—	22	2	no	—
160	#468	—	22	2	no	—
161	#467	—	11	2	no	—
162	#466	—	11	2	no	—
163	#440	—	22	2	no	—
164	C₄×Q₁₆	—	11	2	no	—
165	C₄×D₈	—	11	2	no	—
166	#405	—	11	1	no	—
167	#366	C₂×D₁₁	1	1	yes	characteristic
168	#366	C₂×D₁₁	1	1	yes	characteristic
169	#366	C₂×D₁₁	1	2	yes	—
170	#358	—	11	2	no	—
171	#358	—	11	2	no	—
172	#357	—	11	2	no	—
173	#357	—	11	2	no	—
174	#346	—	11	1	no	—
175	#346	—	11	1	no	—
176	C₄×C₁₆	—	11	1	no	—
177	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
178	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
179	C₂×D₁₁	—	2	1	no	—
180	C₂×D₁₁	—	2	1	no	—
181	C₂×D₁₁	—	2	1	no	—
182	C₂×D₁₁	—	8	2	no	—
183	C₂×D₁₁	—	8	2	no	—
184	C₂×D₁₁	—	8	2	no	—
185	C₄×C₁₁	—	2	1	no	—
186	C₄×C₁₁	—	2	1	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	1	no	—
192	Dic₁₁	—	2	1	no	—
193	Dic₁₁	—	2	1	no	—
194	Dic₁₁	—	8	2	no	—
195	C₂×Q₁₆	—	11	2	no	—
196	C₂×SD₁₆	—	22	2	no	—
197	C₂×D₈	—	11	2	no	—
198	C₂×M₁₆	—	11	1	no	—
199	C₂²×C₈	—	11	1	no	—
200	C₄⋊Q₈	—	2	2	no	—
201	#126	—	44	2	no	—
202	#124	—	22	2	no	—
203	#124	—	44	2	no	—
204	#123	—	44	2	no	—
205	C₂²⋊Q₈	—	22	2	no	—
206	C₂²⋊Q₈	—	44	2	no	—
207	#121	—	22	2	no	—
208	C₄×Q₈	—	22	2	no	—
209	C₄×D₄	—	22	2	no	—
210	#117	—	11	1	no	—
211	Q₃₂	—	22	2	no	—
212	SD₃₂	—	22	4	no	—
213	D₁₆	—	22	2	no	—
214	M₃₂	—	22	2	no	—
215	C₂×C₁₆	—	11	1	no	—
216	C₂×C₁₆	—	11	1	no	—
217	C₂×C₁₆	—	22	2	no	—
218	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
219	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
220	#107	—	2	2	no	—
221	#107	C₂²×D₁₁	1	2	yes	—
222	#107	C₂²×D₁₁	1	2	yes	—
223	#103	—	22	2	no	—
224	#103	—	22	2	no	—
225	#102	—	22	2	no	—
226	#102	—	22	2	no	—
227	#97	—	11	1	no	—
228	#97	—	11	1	no	—
229	C₄×C₈	—	11	1	no	—
230	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
231	C₂×C₁₁	#3169	1	1	yes	characteristic
232	C₂×C₁₁	#3415	1	1	yes	characteristic
233	C₂×C₁₁	#3417	1	1	yes	characteristic
234	D₁₁	—	4	1	no	—
235	D₁₁	—	16	2	no	—
236	C₂×Q₈	—	4	2	no	—
237	C₂×Q₈	—	22	2	no	—
238	C₂×D₄	—	22	2	no	—
239	C₂×D₄	—	44	2	no	—
240	C₂²×C₄	—	11	1	no	—
241	C₂²×C₄	—	44	2	no	—
242	Q₁₆	—	22	2	no	—
243	Q₁₆	—	22	2	no	—
244	SD₁₆	—	44	4	no	—
245	D₈	—	22	2	no	—
246	D₈	—	22	2	no	—
247	M₁₆	—	22	2	no	—
248	C₂×C₈	—	11	1	no	—
249	C₂×C₈	—	11	1	no	—
250	C₂×C₈	—	22	1	no	—
251	C₂×C₈	—	22	1	no	—
252	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
253	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	11	1	no	—
258	C₄⋊C₄	—	11	1	no	—
259	C₄⋊C₄	—	44	2	no	—
260	C₄⋊C₄	—	44	2	no	—
261	C₂²⋊C₄	—	11	1	no	—
262	C₂²⋊C₄	—	11	1	no	—
263	C₂²⋊C₄	—	44	2	no	—
264	C₂²⋊C₄	—	44	2	no	—
265	C₂²⋊C₄	—	44	2	no	—
266	C₂²⋊C₄	—	44	2	no	—
267	C₂²⋊C₄	—	44	2	no	—
268	C₄²	—	11	1	no	—
269	C₄²	—	44	2	no	—
270	C₄²	D₄×D₁₁	1	1	yes	characteristic
271	C₁₆	—	22	1	no	—
272	C₁₆	—	22	1	no	—
273	C₁₆	#4343	1	2	yes	—
274	C₁₆	#4343	1	2	yes	—
275	C₁₁	#33739	1	1	yes	characteristic, complemented, Sylow
276	C₂³	—	11	1	no	—
277	C₂³	—	44	2	no	—
278	Q₈	—	16	2	no	—
279	Q₈	—	44	2	no	—
280	Q₈	—	44	2	no	—
281	D₄	—	44	2	no	—
282	D₄	—	44	2	no	—
283	D₄	—	176	2	no	—
284	C₂×C₄	—	4	2	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	11	1	no	—
287	C₂×C₄	—	11	1	no	—
288	C₂×C₄	—	11	1	no	—
289	C₂×C₄	—	22	1	no	—
290	C₂×C₄	—	22	1	no	—
291	C₂×C₄	—	44	2	no	—
292	C₂×C₄	—	176	2	no	—
293	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
294	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
295	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
296	C₈	—	22	1	no	—
297	C₈	—	22	1	no	—
298	C₈	#66972	1	2	yes	—
299	C₈	C₂×#4343	1	1	yes	characteristic
300	C₈	C₂×#4343	1	1	yes	characteristic
301	C₂²	—	22	1	no	—
302	C₂²	—	22	1	no	—
303	C₂²	—	22	1	no	—
304	C₂²	—	88	2	no	—
305	C₂²	—	88	2	no	—
306	C₂²	—	88	2	no	—
307	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
308	C₄	—	2	1	no	—
309	C₄	—	2	1	no	—
310	C₄	—	8	2	no	—
311	C₄	—	8	2	no	—
312	C₄	—	22	1	no	—
313	C₄	—	22	1	no	—
314	C₄	—	22	1	no	—
315	C₄	—	88	2	no	—
316	C₄	#10623256	1	1	yes	characteristic
317	C₄	C₂×#66972	1	1	yes	characteristic
318	C₂	—	44	1	no	—
319	C₂	—	176	2	no	—
320	C₂	#13079196	1	1	yes	characteristic
321	C₂	#13081753	1	1	yes	characteristic
322	C₂	#13081765	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2252	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	#13070703	C₂
hypercenter	#2252	D₁₁
hypocenter	C₁₁	#33739
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

Complements

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

N	H ≅ G/N	type
1. #13079258	C₂	semidirect
2. #13070877	C₂	semidirect
3. #13070855	C₂	semidirect
4. #13070730	C₂	semidirect
5. #13070708	C₂	semidirect
7. #13070479	C₂	semidirect
8. #13070474	C₂	semidirect
9. #13070462	C₂	semidirect
10. #13070211	C₂	semidirect
11. C₁₁×#2252	C₂	semidirect
116. #2252	D₁₁	semidirect
275. C₁₁	#33739	semidirect

Maximal subgroups

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

subgroup	index
#13079258	2
#13070877	2
#13070855	2
#13070730	2
#13070708	2
#13070703	2
#13070479	2
#13070474	2
#13070462	2
#13070211	2
C₁₁×#2252	2
#33739	11