Subgroups — #14911173

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13081006	C₂	1	2	yes	maximal
2	#13070890	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070820	C₂	1	2	yes	maximal, complemented
4	#13070818	C₂	1	2	yes	maximal, complemented
5	#13070767	C₂	1	2	yes	maximal, complemented
6	#13070708	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070707	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic
10	D₁₁×#366	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#366	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623042	—	2	2	no	—
13	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#107	C₂²	1	2	yes	—
15	#10622729	C₂²	1	2	yes	—
16	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
17	#10622583	—	2	2	no	—
18	C₂×Dic₈₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
20	#10622500	C₂²	1	2	yes	—
21	#10622497	—	2	2	no	—
22	D₁₁×#107	C₂²	1	2	yes	—
23	#10622488	—	2	2	no	—
24	#10622487	C₂²	1	2	yes	—
25	#10622486	C₂²	1	2	yes	—
26	C₁₁×#366	C₂²	1	1	yes	characteristic
27	C₁₁×#366	C₂²	1	1	yes	characteristic
28	C₁₁×#366	C₂²	1	2	yes	—
29	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
30	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
31	#10622142	C₂²	1	1	yes	characteristic
32	#10622141	C₂²	1	2	yes	—
33	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
35	#10622130	C₂²	1	2	yes	—
36	#10622130	C₂²	1	2	yes	—
37	#10622127	C₂²	1	2	yes	—
38	#10622127	C₂²	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
41	C₄×C₂²⋊D₁₁	—	4	2	no	—
42	C₄×C₂²⋊D₁₁	D₄	1	1	yes	characteristic
43	#66977	—	2	2	no	—
44	#66977	—	4	2	no	—
45	C₂×Dic₄₄	C₂³	1	2	yes	—
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	#66950	—	2	2	no	—
48	#66949	—	4	2	no	—
49	C₄⋊C₄×D₁₁	—	2	2	no	—
50	#66942	—	4	2	no	—
51	#66941	—	2	2	no	—
52	#66940	—	2	2	no	—
53	C₂×C₁₁×C₁₆	—	2	2	no	—
54	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
56	C₁₁×#107	—	2	2	no	—
57	C₁₁×#107	C₂³	1	2	yes	—
58	C₁₁×#107	C₂³	1	2	yes	—
59	C₂²⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
60	(C₂×D₁₁)⋊C₈	D₄	1	1	yes	characteristic
61	#66882	C₂³	1	2	yes	—
62	#66880	—	2	2	no	—
63	Dic₁₁⋊C₈	D₄	1	1	yes	characteristic
64	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
67	#66874	—	2	2	no	—
68	#66874	—	2	2	no	—
69	#66871	—	2	2	no	—
70	#66871	—	2	2	no	—
71	Dic₈₈	—	2	2	no	—
72	C₁₆×D₁₁	—	2	2	no	—
73	#33905	—	11	1	no	maximal, Sylow
74	C₂²×C₄×C₁₁	—	4	2	no	—
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₁	D₈	1	1	yes	characteristic
77	C₂×C₄×D₁₁	—	4	2	no	—
78	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×Dic₂₂	—	2	2	no	—
80	C₂×Dic₂₂	—	4	2	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	C₂⁴	1	1	yes	characteristic
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₁₁×C₄⋊C₄	—	4	2	no	—
88	C₂²⋊Dic₁₁	—	4	2	no	—
89	C₂²⋊Dic₁₁	D₈	1	1	yes	characteristic
90	(C₂×D₁₁)⋊C₄	—	4	2	no	—
91	(C₂×D₁₁)⋊C₄	D₈	1	1	yes	characteristic
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	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	C₈×D₁₁	—	2	1	no	—
106	C₈×D₁₁	—	2	1	no	—
107	C₁₁×C₁₆	—	2	1	no	—
108	C₁₁×C₁₆	#41	1	2	yes	—
109	C₁₁⋊C₁₆	—	2	1	no	—
110	C₁₁⋊C₁₆	—	2	1	no	—
111	#3338	—	11	2	no	—
112	#2252	—	11	1	no	—
113	#2236	—	11	2	no	—
114	#2236	—	11	2	no	—
115	#2227	—	11	2	no	—
116	#2216	—	11	1	no	—
117	#2216	—	11	1	no	—
118	C₄×Q₃₂	—	11	1	no	—
119	D₄×C₁₆	—	11	1	no	—
120	C₂×#366	—	11	1	no	—
121	C₂×#366	D₁₁	1	1	yes	characteristic, complemented
122	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
123	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
124	C₂×C₄×C₁₁	—	2	1	no	—
125	C₂×C₄×C₁₁	—	2	1	no	—
126	C₂×C₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	—	4	2	no	—
128	C₂×C₄×C₁₁	—	16	2	no	—
129	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂²⋊D₁₁	Q₃₂	1	4	yes	complemented
132	C₂×Dic₁₁	—	4	2	no	—
133	C₂×Dic₁₁	—	4	2	no	—
134	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
135	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
136	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
137	C₄×D₁₁	—	2	1	no	—
138	C₄×D₁₁	—	2	1	no	—
139	C₄×D₁₁	—	16	2	no	—
140	Dic₂₂	—	4	2	no	—
141	Dic₂₂	—	4	2	no	—
142	Dic₂₂	—	16	2	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	C₁₁⋊C₈	—	2	1	no	—
147	C₁₁⋊C₈	—	2	1	no	—
148	#554	—	22	2	no	—
149	C₂×Q₃₂	—	11	1	no	—
150	C₂²×C₁₆	—	11	1	no	—
151	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
152	#500	—	11	2	no	—
153	#484	—	22	2	no	—
154	#484	—	22	2	no	—
155	#477	—	22	2	no	—
156	#467	—	11	2	no	—
157	#467	—	11	2	no	—
158	C₄×Q₁₆	—	11	2	no	—
159	C₈×D₄	—	11	1	no	—
160	C₂×#107	—	11	2	no	—
161	C₂×#107	C₂×D₁₁	1	2	yes	—
162	#366	—	11	1	no	—
163	#366	—	11	2	no	—
164	#366	—	11	2	no	—
165	#366	C₂×D₁₁	1	1	yes	characteristic
166	#366	C₂×D₁₁	1	1	yes	characteristic
167	#366	C₂×D₁₁	1	2	yes	—
168	C₄⋊C₁₆	—	11	1	no	—
169	#358	—	11	2	no	—
170	#358	—	11	2	no	—
171	#358	—	11	2	no	—
172	C₂²⋊C₁₆	—	11	1	no	—
173	C₂²⋊C₁₆	—	11	1	no	—
174	C₄×C₁₆	—	11	1	no	—
175	C₂²×C₁₁	—	2	1	no	—
176	C₂²×C₁₁	—	2	1	no	—
177	C₂²×C₁₁	C₂×Q₃₂	1	2	yes	—
178	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
179	C₂×D₁₁	—	2	1	no	—
180	C₂×D₁₁	—	2	1	no	—
181	C₂×D₁₁	C₂×Q₃₂	1	2	yes	—
182	C₄×C₁₁	—	2	1	no	—
183	C₄×C₁₁	—	8	2	no	—
184	C₄×C₁₁	—	8	2	no	—
185	C₄×C₁₁	#547	1	1	yes	characteristic
186	C₄×C₁₁	#578	1	1	yes	characteristic
187	Dic₁₁	—	2	1	no	—
188	Dic₁₁	—	2	1	no	—
189	Dic₁₁	—	8	2	no	—
190	Dic₁₁	—	8	2	no	—
191	Dic₁₁	C₂×Q₃₂	1	2	yes	—
192	C₂×Q₁₆	—	11	2	no	—
193	C₂²×C₈	—	11	1	no	—
194	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
195	C₄⋊Q₈	—	22	2	no	—
196	#125	—	44	2	no	—
197	C₂²⋊Q₈	—	22	2	no	—
198	C₂²⋊Q₈	—	22	2	no	—
199	C₂²⋊Q₈	—	44	2	no	—
200	C₂²⋊Q₈	—	44	2	no	—
201	C₄×Q₈	—	22	2	no	—
202	C₄×D₄	—	11	1	no	—
203	C₄×D₄	—	44	2	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	22	2	no	—
206	Q₃₂	—	22	2	no	—
207	C₂×C₁₆	—	2	2	no	—
208	C₂×C₁₆	—	11	1	no	—
209	C₂×C₁₆	—	11	1	no	—
210	C₂×C₁₆	—	22	2	no	—
211	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
212	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
213	#107	—	2	2	no	—
214	#107	—	11	2	no	—
215	#107	—	22	2	no	—
216	#107	—	22	2	no	—
217	#107	C₂²×D₁₁	1	2	yes	—
218	#107	C₂²×D₁₁	1	2	yes	—
219	C₄⋊C₈	—	11	1	no	—
220	#103	—	22	2	no	—
221	#103	—	22	2	no	—
222	#103	—	22	2	no	—
223	C₂²⋊C₈	—	11	1	no	—
224	C₂²⋊C₈	—	11	1	no	—
225	C₄×C₈	—	11	1	no	—
226	C₂×C₁₁	—	2	2	no	—
227	C₂×C₁₁	#3334	1	1	yes	characteristic
228	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
229	C₂×C₁₁	#3415	1	1	yes	characteristic
230	D₁₁	—	2	2	no	—
231	C₂×Q₈	—	22	2	no	—
232	C₂×Q₈	—	44	2	no	—
233	C₂×D₄	—	11	1	no	—
234	C₂²×C₄	—	4	2	no	—
235	C₂²×C₄	—	11	1	no	—
236	C₂²×C₄	—	44	2	no	—
237	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
238	Q₁₆	—	22	2	no	—
239	Q₁₆	—	22	2	no	—
240	C₂×C₈	—	2	1	no	—
241	C₂×C₈	—	2	1	no	—
242	C₂×C₈	—	11	1	no	—
243	C₂×C₈	—	11	1	no	—
244	C₂×C₈	—	22	1	no	—
245	C₂×C₈	—	22	1	no	—
246	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
247	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	4	2	no	—
251	C₄⋊C₄	—	11	1	no	—
252	C₄⋊C₄	—	22	2	no	—
253	C₄⋊C₄	—	44	2	no	—
254	C₄⋊C₄	—	44	2	no	—
255	C₄⋊C₄	—	44	2	no	—
256	C₄⋊C₄	—	44	2	no	—
257	C₄⋊C₄	—	44	2	no	—
258	C₂²⋊C₄	—	11	1	no	—
259	C₂²⋊C₄	—	11	1	no	—
260	C₂²⋊C₄	—	44	2	no	—
261	C₂²⋊C₄	—	44	2	no	—
262	C₄²	—	11	1	no	—
263	C₄²	—	44	2	no	—
264	C₁₆	—	2	1	no	—
265	C₁₆	—	22	1	no	—
266	C₁₆	—	22	1	no	—
267	C₁₆	#4339	1	2	yes	—
268	C₁₁	#33905	1	1	yes	characteristic, complemented, Sylow
269	C₂³	—	11	1	no	—
270	C₂³	D₈×D₁₁	1	1	yes	characteristic
271	Q₈	—	44	2	no	—
272	Q₈	—	44	2	no	—
273	Q₈	—	176	2	no	—
274	D₄	—	11	4	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	4	2	no	—
278	C₂×C₄	—	4	2	no	—
279	C₂×C₄	—	11	1	no	—
280	C₂×C₄	—	11	1	no	—
281	C₂×C₄	—	11	1	no	—
282	C₂×C₄	—	16	2	no	—
283	C₂×C₄	—	22	1	no	—
284	C₂×C₄	—	22	1	no	—
285	C₂×C₄	—	44	2	no	—
286	C₂×C₄	—	44	2	no	—
287	C₂×C₄	—	176	2	no	—
288	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
289	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
290	C₈	—	2	1	no	—
291	C₈	—	22	1	no	—
292	C₈	—	22	1	no	—
293	C₈	C₂×#4339	1	1	yes	characteristic
294	C₈	#67040	1	1	yes	characteristic
295	C₂²	—	2	1	no	—
296	C₂²	—	2	1	no	—
297	C₂²	—	11	2	no	—
298	C₂²	—	22	1	no	—
299	C₂²	—	22	1	no	—
300	C₂²	D₁₁×Q₃₂	1	2	yes	—
301	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
302	C₄	—	2	1	no	—
303	C₄	—	8	2	no	—
304	C₄	—	8	2	no	—
305	C₄	—	11	2	no	—
306	C₄	—	22	1	no	—
307	C₄	—	22	1	no	—
308	C₄	—	88	2	no	—
309	C₄	—	88	2	no	—
310	C₄	#10623038	1	1	yes	characteristic
311	C₄	#10623297	1	1	yes	characteristic
312	C₂	—	2	2	no	—
313	C₂	—	22	2	no	—
314	C₂	#13080961	1	1	yes	characteristic
315	C₂	C₂×D₁₁×Q₃₂	1	1	yes	characteristic
316	C₂	#13081753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#366	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂×C₂²⋊D₁₁	D₈
hypercenter	C₂×#366	D₁₁
hypocenter	C₁₁	#33905
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
2. #13070890	C₂	semidirect
3. #13070820	C₂	semidirect
4. #13070818	C₂	semidirect
5. #13070767	C₂	semidirect
6. #13070708	C₂	semidirect
7. #13070707	C₂	semidirect
8. #13070474	C₂	semidirect
10. D₁₁×#366	C₂	semidirect
11. C₂×C₁₁×#366	C₂	semidirect
121. C₂×#366	D₁₁	semidirect
131. C₂²⋊D₁₁	Q₃₂	semidirect
268. C₁₁	#33905	semidirect

Maximal subgroups

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

subgroup	index
#13081006	2
#13070890	2
#13070820	2
#13070818	2
#13070767	2
#13070708	2
#13070707	2
#13070474	2
C₁₆×C₂²⋊D₁₁	2
D₁₁×#366	2
C₂×C₁₁×#366	2
#33905	11