Subgroups — #14909314

Order 2816.

514 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	#13079199	C₂	1	2	yes	maximal
2	#13070890	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	#13070708	C₂	1	1	yes	maximal, characteristic
6	#13070706	C₂	1	2	yes	maximal
7	#13070704	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₈₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#66893	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₁×Q₃₂	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×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₁₁	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×#366	C₂²	1	1	yes	characteristic
29	C₁₁×#358	C₂²	1	2	yes	—
30	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
31	#10622202	C₂²	1	2	yes	—
32	#10622142	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	#10622127	C₂²	1	2	yes	—
38	C₄×C₁₁⋊C₁₆	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	C₁₆×D₁₁	—	2	2	no	—
74	C₁₆×D₁₁	—	2	2	no	—
75	#33734	—	11	1	no	maximal, Sylow
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×C₄×D₁₁	D₈	1	1	yes	characteristic
78	C₂×C₄×D₁₁	D₈	1	1	yes	characteristic
79	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂×Dic₂₂	—	2	2	no	—
81	C₂×Dic₂₂	—	4	2	no	—
82	C₁₁×Q₁₆	—	2	2	no	—
83	C₁₁×Q₁₆	—	2	2	no	—
84	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
86	C₁₁×C₄⋊C₄	—	2	2	no	—
87	C₁₁×C₄⋊C₄	—	4	2	no	—
88	C₄²×C₁₁	—	4	2	no	—
89	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
90	#4326	—	4	4	no	—
91	(C₂×D₁₁)⋊C₄	—	4	2	no	—
92	(C₂×D₁₁)⋊C₄	—	4	2	no	—
93	C₄⋊Dic₁₁	—	2	2	no	—
94	C₄⋊Dic₁₁	—	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	Dic₁₁⋊C₄	—	4	2	no	—
100	C₄×Dic₁₁	—	4	2	no	—
101	C₄×Dic₁₁	D₈	1	1	yes	characteristic
102	C₄×Dic₁₁	D₈	1	1	yes	characteristic
103	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
106	Dic₄₄	—	2	2	no	—
107	Dic₄₄	—	2	2	no	—
108	C₈×D₁₁	—	2	1	no	—
109	C₈×D₁₁	—	2	1	no	—
110	C₈×D₁₁	—	2	2	no	—
111	C₁₁×C₁₆	—	2	1	no	—
112	C₁₁×C₁₆	#41	1	2	yes	—
113	C₁₁⋊C₁₆	—	2	1	no	—
114	C₁₁⋊C₁₆	#41	1	2	yes	—
115	#3170	—	11	2	no	—
116	#2252	—	11	1	no	—
117	#2247	—	11	1	no	—
118	#2241	—	11	2	no	—
119	#2216	—	11	1	no	—
120	#2216	—	11	1	no	—
121	#2216	—	11	2	no	—
122	C₄×Q₃₂	—	11	2	no	—
123	C₄×Q₃₂	—	11	1	no	—
124	C₄×Q₃₂	D₁₁	1	1	yes	characteristic, complemented
125	C₂×C₄×C₁₆	—	11	1	no	—
126	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
127	Q₈×C₁₁	—	4	2	no	—
128	Q₈×C₁₁	—	4	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	—	4	2	no	—
136	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
137	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
138	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
139	C₄×D₁₁	—	2	1	no	—
140	C₄×D₁₁	—	2	1	no	—
141	C₄×D₁₁	—	2	2	no	—
142	C₄×D₁₁	Q₃₂	1	4	yes	complemented
143	Dic₂₂	—	4	2	no	—
144	Dic₂₂	—	4	2	no	—
145	Dic₂₂	—	8	4	no	—
146	C₈×C₁₁	—	2	1	no	—
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	#135	1	2	yes	—
151	#533	—	22	2	no	—
152	C₂×Q₃₂	—	11	2	no	—
153	C₂×Q₃₂	—	11	1	no	—
154	C₂×Q₃₂	C₂×D₁₁	1	1	yes	characteristic
155	C₂²×C₁₆	—	11	1	no	—
156	C₂²×C₁₆	—	11	1	no	—
157	#500	—	11	2	no	—
158	#494	—	11	2	no	—
159	#487	—	22	2	no	—
160	#467	—	11	2	no	—
161	#467	—	11	2	no	—
162	#467	—	22	2	no	—
163	C₄×Q₁₆	—	11	2	no	—
164	C₄×Q₁₆	—	22	2	no	—
165	C₄×Q₁₆	C₂×D₁₁	1	2	yes	—
166	C₂×C₄×C₈	—	11	1	no	—
167	#366	—	11	1	no	—
168	#366	—	11	2	no	—
169	#366	C₂×D₁₁	1	1	yes	characteristic
170	#358	—	11	2	no	—
171	#358	—	11	2	no	—
172	#358	—	11	2	no	—
173	#358	C₂×D₁₁	1	2	yes	—
174	C₄×C₁₆	—	11	1	no	—
175	C₄×C₁₆	—	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	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	C₂×Q₃₂	1	2	yes	—
186	C₄×C₁₁	#532	1	1	yes	characteristic
187	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
188	Dic₁₁	—	2	1	no	—
189	Dic₁₁	—	8	2	no	—
190	Dic₁₁	—	8	2	no	—
191	Dic₁₁	C₂×Q₃₂	1	2	yes	—
192	Dic₁₁	#508	1	2	yes	—
193	C₂×Q₁₆	—	11	2	no	—
194	C₂×Q₁₆	—	22	2	no	—
195	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
196	C₂²×C₈	—	11	1	no	—
197	C₂²×C₈	—	11	1	no	—
198	C₄⋊Q₈	—	22	2	no	—
199	C₄⋊Q₈	—	22	2	no	—
200	#125	—	44	2	no	—
201	C₂²⋊Q₈	—	22	2	no	—
202	C₂²⋊Q₈	—	22	2	no	—
203	C₂²⋊Q₈	—	44	2	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	22	2	no	—
206	C₄×Q₈	—	44	2	no	—
207	#117	—	44	2	no	—
208	C₂×C₄²	—	11	1	no	—
209	Q₃₂	—	2	2	no	—
210	Q₃₂	—	22	4	no	—
211	Q₃₂	—	22	2	no	—
212	C₂×C₁₆	—	11	1	no	—
213	C₂×C₁₆	—	11	1	no	—
214	C₂×C₁₆	—	22	2	no	—
215	C₂×C₁₆	—	22	2	no	—
216	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
217	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
218	#107	—	11	2	no	—
219	#107	—	22	2	no	—
220	#107	C₂²×D₁₁	1	2	yes	—
221	#103	—	2	2	no	—
222	#103	—	22	2	no	—
223	#103	—	22	2	no	—
224	#103	—	22	2	no	—
225	C₄×C₈	—	11	1	no	—
226	C₄×C₈	—	11	1	no	—
227	C₄×C₈	—	11	1	no	—
228	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
229	C₂×C₁₁	#3169	1	1	yes	characteristic
230	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
231	C₂×C₁₁	C₂×#508	1	1	yes	characteristic
232	D₁₁	—	2	2	no	—
233	C₂×Q₈	—	2	2	no	—
234	C₂×Q₈	—	22	2	no	—
235	C₂×Q₈	—	44	2	no	—
236	C₂²×C₄	—	11	1	no	—
237	C₂²×C₄	—	11	1	no	—
238	C₂²×C₄	—	11	1	no	—
239	Q₁₆	—	2	2	no	—
240	Q₁₆	—	2	2	no	—
241	Q₁₆	—	22	2	no	—
242	Q₁₆	—	22	2	no	—
243	Q₁₆	—	44	4	no	—
244	C₂×C₈	—	11	1	no	—
245	C₂×C₈	—	11	1	no	—
246	C₂×C₈	—	22	2	no	—
247	C₂×C₈	—	22	1	no	—
248	C₂×C₈	—	22	1	no	—
249	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
250	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	4	2	no	—
253	C₄⋊C₄	—	22	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	C₄⋊C₄	—	44	2	no	—
259	C₄⋊C₄	—	44	2	no	—
260	C₂²⋊C₄	—	44	2	no	—
261	C₂²⋊C₄	—	44	2	no	—
262	C₄²	—	4	2	no	—
263	C₄²	—	11	1	no	—
264	C₄²	—	11	1	no	—
265	C₄²	—	11	1	no	—
266	C₄²	—	44	2	no	—
267	C₄²	D₄×D₁₁	1	1	yes	characteristic
268	C₁₆	—	2	1	no	—
269	C₁₆	—	11	2	no	—
270	C₁₆	—	22	1	no	—
271	C₁₆	#4339	1	2	yes	—
272	C₁₁	#33734	1	1	yes	characteristic, complemented, Sylow
273	C₂³	—	11	1	no	—
274	Q₈	—	4	2	no	—
275	Q₈	—	4	2	no	—
276	Q₈	—	44	2	no	—
277	Q₈	—	44	2	no	—
278	Q₈	—	88	4	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	11	1	no	—
282	C₂×C₄	—	11	1	no	—
283	C₂×C₄	—	11	4	no	—
284	C₂×C₄	—	11	1	no	—
285	C₂×C₄	—	22	2	no	—
286	C₂×C₄	—	22	1	no	—
287	C₂×C₄	—	22	1	no	—
288	C₂×C₄	—	44	2	no	—
289	C₂×C₄	—	44	2	no	—
290	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
291	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
292	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
293	C₈	—	2	1	no	—
294	C₈	—	11	2	no	—
295	C₈	—	22	1	no	—
296	C₈	C₂×#4339	1	1	yes	characteristic
297	C₈	#41×D₁₁	1	1	yes	characteristic
298	C₂²	—	11	2	no	—
299	C₂²	—	22	1	no	—
300	C₂²	—	22	1	no	—
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	—	11	2	no	—
307	C₄	—	22	1	no	—
308	C₄	—	88	2	no	—
309	C₄	—	88	2	no	—
310	C₄	D₁₁×Q₃₂	1	2	yes	—
311	C₄	#10623079	1	1	yes	characteristic
312	C₄	D₁₁×#135	1	1	yes	characteristic
313	C₂	—	22	2	no	—
314	C₂	#13079192	1	1	yes	characteristic
315	C₂	C₂×D₁₁×Q₃₂	1	1	yes	characteristic
316	C₂	D₁₁×#508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₄×C₁₁×Q₃₂	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	C₄×Q₃₂	D₁₁
hypocenter	C₁₁	#33734
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #13070890	C₂	semidirect
3. #13070867	C₂	semidirect
4. #13070842	C₂	semidirect
8. C₄×Dic₈₈	C₂	semidirect
9. C₄×#66893	C₂	semidirect
11. C₄×C₁₁×Q₃₂	C₂	semidirect
124. C₄×Q₃₂	D₁₁	semidirect
142. C₄×D₁₁	Q₃₂	semidirect
272. C₁₁	#33734	semidirect

Maximal subgroups

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

subgroup	index
#13079199	2
#13070890	2
#13070867	2
#13070842	2
#13070708	2
#13070706	2
#13070704	2
C₄×Dic₈₈	2
C₄×#66893	2
C₄×C₁₆×D₁₁	2
C₄×C₁₁×Q₃₂	2
#33734	11