Subgroups — #14909473

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079199	C₂	1	2	yes	maximal
2	#13070897	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070867	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070842	C₂	1	2	yes	maximal, complemented
5	#13070725	C₂	1	1	yes	maximal, characteristic
6	#13070723	C₂	1	2	yes	maximal
7	#13070721	C₂	1	1	yes	maximal, characteristic
8	#13070488	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070485	C₂	1	2	yes	maximal, complemented
10	#13070209	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#2176	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623109	—	2	2	no	—
13	C₂×C₁₁×Q₃₂	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	—
15	#10622801	C₂²	1	2	yes	—
16	#10622794	C₂²	1	2	yes	—
17	C₂×#66893	C₂²	1	2	yes	—
18	C₄×#4326	—	2	2	no	—
19	C₂×Dic₈₈	C₂²	1	1	yes	characteristic
20	C₂×#66862	C₂²	1	1	yes	characteristic
21	C₂×#66862	C₂²	1	1	yes	characteristic
22	#10622500	C₂²	1	2	yes	—
23	#10622487	C₂²	1	2	yes	—
24	#10622426	—	2	2	no	—
25	#10622405	—	2	2	no	—
26	C₄×Dic₄₄	C₂²	1	2	yes	—
27	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#367	C₂²	1	1	yes	characteristic
29	C₁₁×#358	C₂²	1	2	yes	—
30	C₁₁×#346	C₂²	1	1	yes	characteristic
31	#10622202	C₂²	1	2	yes	—
32	#10622143	C₂²	1	1	yes	characteristic
33	#10622141	C₂²	1	2	yes	—
34	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
35	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
36	#10622130	C₂²	1	2	yes	—
37	#10622128	C₂²	1	2	yes	—
38	#10622099	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₄×Q₈×C₁₁	—	2	2	no	—
41	#66999	—	2	2	no	—
42	#66997	—	2	2	no	—
43	C₂×#4326	—	2	2	no	—
44	C₂×Dic₄₄	C₂³	1	2	yes	—
45	C₂×C₈×D₁₁	D₄	1	1	yes	characteristic
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	#66950	—	2	2	no	—
48	#66949	—	4	2	no	—
49	#66942	—	4	2	no	—
50	#66941	—	2	2	no	—
51	#66925	—	4	2	no	—
52	C₄²×D₁₁	D₄	1	1	yes	characteristic
53	C₄×Dic₂₂	—	2	2	no	—
54	C₄×Dic₂₂	—	4	2	no	—
55	C₁₁×Q₃₂	—	2	2	no	—
56	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
58	C₁₁×#107	C₂³	1	2	yes	—
59	C₁₁×#103	—	2	2	no	—
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	#66899	—	2	2	no	—
62	#66893	—	2	4	no	—
63	#66882	C₂³	1	2	yes	—
64	#66880	—	2	2	no	—
65	C₈×Dic₁₁	D₄	1	1	yes	characteristic
66	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
67	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
69	#66874	—	2	2	no	—
70	#66871	—	2	2	no	—
71	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
72	Dic₈₈	—	2	2	no	—
73	#66862	—	2	2	no	—
74	#66862	—	2	2	no	—
75	#33749	—	11	1	no	maximal, Sylow
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×C₄×D₁₁	D₈	1	2	yes	—
78	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×Dic₂₂	—	2	2	no	—
80	C₂×Dic₂₂	—	4	2	no	—
81	C₁₁×Q₁₆	—	2	2	no	—
82	C₁₁×Q₁₆	—	2	2	no	—
83	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	4	2	no	—
87	C₄²×C₁₁	—	4	2	no	—
88	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
89	#4326	—	4	4	no	—
90	(C₂×D₁₁)⋊C₄	—	4	2	no	—
91	(C₂×D₁₁)⋊C₄	—	4	2	no	—
92	C₄⋊Dic₁₁	—	2	2	no	—
93	C₄⋊Dic₁₁	—	4	2	no	—
94	Dic₁₁⋊C₄	—	4	2	no	—
95	Dic₁₁⋊C₄	—	4	2	no	—
96	Dic₁₁⋊C₄	—	4	2	no	—
97	Dic₁₁⋊C₄	—	4	2	no	—
98	Dic₁₁⋊C₄	—	4	2	no	—
99	C₄×Dic₁₁	—	4	2	no	—
100	C₄×Dic₁₁	D₈	1	2	yes	—
101	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
103	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
104	Dic₄₄	—	2	2	no	—
105	Dic₄₄	—	2	2	no	—
106	C₈×D₁₁	—	2	1	no	—
107	C₈×D₁₁	—	2	1	no	—
108	C₈×D₁₁	—	2	2	no	—
109	C₁₁×C₁₆	—	2	1	no	—
110	C₁₁×C₁₆	#41	1	2	yes	—
111	C₁₁⋊C₁₆	—	2	1	no	—
112	C₁₁⋊C₁₆	#41	1	2	yes	—
113	#3170	—	11	2	no	—
114	#2254	—	11	1	no	—
115	#2247	—	11	1	no	—
116	#2241	—	11	2	no	—
117	#2219	—	11	1	no	—
118	#2219	—	11	1	no	—
119	#2219	—	11	2	no	—
120	#2176	—	11	2	no	—
121	#2176	—	11	1	no	—
122	#2176	D₁₁	1	1	yes	characteristic, complemented
123	C₄×M₃₂	—	11	1	no	—
124	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
125	Q₈×C₁₁	—	4	2	no	—
126	Q₈×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	—	4	2	no	—
128	C₂×C₄×C₁₁	—	4	2	no	—
129	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
130	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×Dic₁₁	—	4	2	no	—
132	C₂×Dic₁₁	—	4	2	no	—
133	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
134	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
135	C₄×D₁₁	—	2	1	no	—
136	C₄×D₁₁	—	2	1	no	—
137	C₄×D₁₁	—	2	4	no	—
138	Dic₂₂	—	4	2	no	—
139	Dic₂₂	—	4	2	no	—
140	Dic₂₂	—	8	4	no	—
141	C₈×C₁₁	—	2	1	no	—
142	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
143	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
144	C₁₁⋊C₈	—	2	1	no	—
145	C₁₁⋊C₈	#135	1	2	yes	—
146	#533	—	22	2	no	—
147	C₂×Q₃₂	—	11	2	no	—
148	C₂×Q₃₂	—	11	1	no	—
149	C₂×Q₃₂	C₂×D₁₁	1	1	yes	characteristic
150	C₂×M₃₂	—	11	1	no	—
151	C₂×M₃₂	—	11	1	no	—
152	#500	—	11	2	no	—
153	#494	—	11	2	no	—
154	#487	—	22	2	no	—
155	#467	—	11	2	no	—
156	#467	—	11	2	no	—
157	#467	—	22	2	no	—
158	C₄×Q₁₆	—	11	2	no	—
159	C₄×Q₁₆	—	22	2	no	—
160	C₄×Q₁₆	C₂×D₁₁	1	2	yes	—
161	C₂×C₄×C₈	—	11	1	no	—
162	#367	—	11	1	no	—
163	#367	—	11	2	no	—
164	#367	C₂×D₁₁	1	1	yes	characteristic
165	#358	—	11	2	no	—
166	#358	—	11	2	no	—
167	#358	—	11	2	no	—
168	#358	C₂×D₁₁	1	2	yes	—
169	#346	—	11	1	no	—
170	#346	C₂×D₁₁	1	1	yes	characteristic
171	C₄×C₁₆	—	11	1	no	—
172	C₄×C₁₆	—	11	1	no	—
173	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
174	C₂×D₁₁	—	2	2	no	—
175	C₂×D₁₁	—	2	1	no	—
176	C₄×C₁₁	—	2	2	no	—
177	C₄×C₁₁	—	8	2	no	—
178	C₄×C₁₁	—	8	2	no	—
179	C₄×C₁₁	#532	1	1	yes	characteristic
180	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
181	Dic₁₁	—	2	1	no	—
182	Dic₁₁	—	8	2	no	—
183	Dic₁₁	—	8	2	no	—
184	Dic₁₁	#510	1	4	yes	—
185	C₂×Q₁₆	—	11	2	no	—
186	C₂×Q₁₆	—	22	2	no	—
187	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
188	C₂²×C₈	—	11	1	no	—
189	C₂²×C₈	—	11	1	no	—
190	C₄⋊Q₈	—	22	2	no	—
191	C₄⋊Q₈	—	22	2	no	—
192	#125	—	44	2	no	—
193	C₂²⋊Q₈	—	22	2	no	—
194	C₂²⋊Q₈	—	22	2	no	—
195	C₂²⋊Q₈	—	44	2	no	—
196	C₄×Q₈	—	2	2	no	—
197	C₄×Q₈	—	22	2	no	—
198	C₄×Q₈	—	44	2	no	—
199	#117	—	44	2	no	—
200	C₂×C₄²	—	11	1	no	—
201	Q₃₂	—	2	2	no	—
202	Q₃₂	—	22	4	no	—
203	Q₃₂	—	22	2	no	—
204	M₃₂	—	22	2	no	—
205	M₃₂	—	22	2	no	—
206	C₂×C₁₆	—	11	1	no	—
207	C₂×C₁₆	—	11	1	no	—
208	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
209	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
210	#107	—	11	2	no	—
211	#107	—	22	2	no	—
212	#107	C₂²×D₁₁	1	2	yes	—
213	#103	—	2	2	no	—
214	#103	—	22	2	no	—
215	#103	—	22	2	no	—
216	#103	—	22	2	no	—
217	C₄×C₈	—	11	1	no	—
218	C₄×C₈	—	11	1	no	—
219	C₄×C₈	—	11	1	no	—
220	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
221	C₂×C₁₁	#3169	1	1	yes	characteristic
222	C₂×C₁₁	C₂×#510	1	2	yes	—
223	D₁₁	—	4	1	no	—
224	C₂×Q₈	—	2	2	no	—
225	C₂×Q₈	—	22	2	no	—
226	C₂×Q₈	—	44	2	no	—
227	C₂²×C₄	—	11	2	no	—
228	C₂²×C₄	—	11	1	no	—
229	Q₁₆	—	2	2	no	—
230	Q₁₆	—	2	2	no	—
231	Q₁₆	—	22	2	no	—
232	Q₁₆	—	22	2	no	—
233	Q₁₆	—	44	4	no	—
234	C₂×C₈	—	11	1	no	—
235	C₂×C₈	—	11	1	no	—
236	C₂×C₈	—	22	2	no	—
237	C₂×C₈	—	22	1	no	—
238	C₂×C₈	—	22	1	no	—
239	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
240	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
241	C₄⋊C₄	—	2	2	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₄⋊C₄	—	22	2	no	—
244	C₄⋊C₄	—	44	2	no	—
245	C₄⋊C₄	—	44	2	no	—
246	C₄⋊C₄	—	44	2	no	—
247	C₄⋊C₄	—	44	2	no	—
248	C₄⋊C₄	—	44	2	no	—
249	C₄⋊C₄	—	44	2	no	—
250	C₂²⋊C₄	—	44	2	no	—
251	C₂²⋊C₄	—	44	2	no	—
252	C₄²	—	4	2	no	—
253	C₄²	—	11	2	no	—
254	C₄²	—	11	1	no	—
255	C₄²	—	44	2	no	—
256	C₄²	D₄×D₁₁	1	1	yes	characteristic
257	C₁₆	—	2	1	no	—
258	C₁₆	—	11	2	no	—
259	C₁₆	—	22	1	no	—
260	C₁₆	#4339	1	2	yes	—
261	C₁₁	#33749	1	1	yes	characteristic, complemented, Sylow
262	C₂³	—	11	1	no	—
263	Q₈	—	4	2	no	—
264	Q₈	—	4	2	no	—
265	Q₈	—	44	2	no	—
266	Q₈	—	44	2	no	—
267	Q₈	—	88	4	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	—	11	2	no	—
271	C₂×C₄	—	11	1	no	—
272	C₂×C₄	—	22	4	no	—
273	C₂×C₄	—	22	1	no	—
274	C₂×C₄	—	22	1	no	—
275	C₂×C₄	—	44	2	no	—
276	C₂×C₄	—	44	2	no	—
277	C₂×C₄	D₈×D₁₁	1	2	yes	—
278	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
279	C₈	—	2	1	no	—
280	C₈	—	11	2	no	—
281	C₈	—	22	1	no	—
282	C₈	C₂×#4339	1	1	yes	characteristic
283	C₈	#41×D₁₁	1	1	yes	characteristic
284	C₂²	—	22	2	no	—
285	C₂²	—	22	1	no	—
286	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
287	C₄	—	2	2	no	—
288	C₄	—	8	2	no	—
289	C₄	—	8	2	no	—
290	C₄	—	11	4	no	—
291	C₄	—	22	1	no	—
292	C₄	—	88	2	no	—
293	C₄	—	88	2	no	—
294	C₄	#10623079	1	1	yes	characteristic
295	C₄	D₁₁×#135	1	1	yes	characteristic
296	C₂	—	44	1	no	—
297	C₂	#13079192	1	1	yes	characteristic
298	C₂	D₁₁×#510	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2176	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	#2176	D₁₁
hypocenter	C₁₁	#33749
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2176

Complements

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

N	H ≅ G/N	type
2. #13070897	C₂	semidirect
3. #13070867	C₂	semidirect
4. #13070842	C₂	semidirect
8. #13070488	C₂	semidirect
9. #13070485	C₂	semidirect
11. C₁₁×#2176	C₂	semidirect
122. #2176	D₁₁	semidirect
261. C₁₁	#33749	semidirect

Maximal subgroups

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

subgroup	index
#13079199	2
#13070897	2
#13070867	2
#13070842	2
#13070725	2
#13070723	2
#13070721	2
#13070488	2
#13070485	2
#13070209	2
C₁₁×#2176	2
#33749	11