Subgroups — #14906965

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10622753	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077326	C₂	1	1	yes	maximal, characteristic
4	#13070444	C₂	1	4	yes	maximal, complemented
5	#13070438	C₂	1	4	yes	maximal, complemented
6	#13070371	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10622140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
11	#10623363	C₄	1	1	yes	characteristic
12	C₂×#66954	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	#10622847	C₄	1	1	yes	characteristic
16	#10622753	—	2	4	no	—
17	#10622742	C₄	1	1	yes	characteristic
18	#10622741	C₄	1	4	yes	—
19	#10622731	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₁	C₂²	1	4	yes	—
21	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
22	C₂×#66876	C₂²	1	1	yes	characteristic
23	C₂×#66876	C₂²	1	2	yes	—
24	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
25	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
26	#10622520	—	2	4	no	—
27	C₂×#66862	C₂²	1	2	yes	—
28	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
29	C₁₁×C₂²⋊C₁₆	C₂²	1	4	yes	—
30	(C₂×D₁₁)⋊C₁₆	C₂²	1	4	yes	—
31	#10622140	C₂²	1	2	yes	—
32	#10622140	C₂²	1	2	yes	—
33	Dic₁₁⋊C₁₆	C₂²	1	4	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
35	C₂×#4339	C₂×C₄	1	1	yes	characteristic
36	C₁₁×#131	—	2	2	no	—
37	C₁₁×#131	—	2	2	no	—
38	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	#67000	C₈	1	1	yes	characteristic
43	#66997	C₈	1	1	yes	characteristic
44	#66993	C₈	1	1	yes	characteristic
45	#66992	C₈	1	4	yes	—
46	#66989	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₁	C₂×C₄	1	4	yes	—
48	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂×#4318	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
51	#66954	—	2	2	no	—
52	#66954	—	2	2	no	—
53	C₂×#4313	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₁₁	C₂³	1	2	yes	—
55	C₁₁×M₃₂	—	2	2	no	—
56	C₂×C₁₁×C₁₆	—	2	2	no	—
57	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
58	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
59	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
60	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
61	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
62	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
63	C₈×Dic₁₁	C₂³	1	2	yes	—
64	#66876	—	2	2	no	—
65	#66876	—	2	4	no	—
66	C₂×C₁₁⋊C₁₆	—	2	4	no	—
67	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	complemented
68	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
71	#66862	—	2	4	no	—
72	C₁₆×D₁₁	—	2	4	no	—
73	#33435	—	11	1	no	maximal, Sylow
74	C₁₁×#41	—	2	2	no	—
75	C₁₁×#41	—	2	2	no	—
76	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
77	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
78	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
82	C₂×C₂²⋊D₁₁	C₂×C₈	1	4	yes	—
83	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
84	#4339	—	2	2	no	—
85	#4339	—	2	2	no	—
86	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
88	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
89	C₁₁×M₁₆	—	2	4	no	—
90	C₁₁×M₁₆	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₁₁	#41	1	2	yes	—
97	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
98	C₂²⋊Dic₁₁	C₂×C₈	1	4	yes	—
99	(C₂×D₁₁)⋊C₄	C₂×C₈	1	4	yes	—
100	Dic₁₁⋊C₄	C₂×C₈	1	4	yes	—
101	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
102	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
103	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
104	#4318	—	2	2	no	—
105	C₂×C₁₁⋊C₈	—	2	2	no	—
106	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
107	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
108	#4313	—	2	4	no	—
109	C₈×D₁₁	—	2	2	no	—
110	C₈×D₁₁	—	2	2	no	—
111	C₁₁×C₁₆	—	2	2	no	—
112	C₁₁×C₁₆	—	2	2	no	—
113	C₁₁⋊C₁₆	—	2	2	no	—
114	C₁₁⋊C₁₆	C₂×D₄	1	2	yes	—
115	C₁₁⋊C₁₆	C₂×D₄	1	2	yes	—
116	C₂×#504	—	11	1	no	—
117	C₂×#504	—	11	1	no	—
118	#2931	—	11	1	no	—
119	#2168	—	11	4	no	—
120	#2168	—	11	4	no	—
121	#2150	—	11	1	no	—
122	#2113	—	11	1	no	—
123	#2113	D₁₁	1	1	yes	characteristic, complemented
124	C₂×#346	—	11	1	no	—
125	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
126	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
127	C₂²×D₁₁	C₂²×C₈	1	2	yes	—
128	Q₈×C₁₁	—	2	2	no	—
129	D₄×C₁₁	—	2	4	no	—
130	D₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₁₁	#131	1	2	yes	—
137	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
138	C₂²⋊D₁₁	—	2	4	no	—
139	C₂²⋊D₁₁	—	4	4	no	—
140	C₂×Dic₁₁	—	4	2	no	—
141	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
142	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
143	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
144	D₄₄	—	2	2	no	—
145	C₄×D₁₁	—	2	2	no	—
146	C₄×D₁₁	—	2	2	no	—
147	Dic₂₂	—	2	2	no	—
148	C₈×C₁₁	—	2	2	no	—
149	C₈×C₁₁	C₄×D₄	1	2	yes	—
150	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
152	C₁₁⋊C₈	—	2	2	no	—
153	C₁₁⋊C₈	—	2	2	no	—
154	C₂×#131	—	11	1	no	—
155	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
156	#532	—	11	1	no	—
157	#504	—	22	4	no	—
158	#504	—	22	4	no	—
159	C₂×M₃₂	—	11	1	no	—
160	C₂×M₃₂	—	11	2	no	—
161	C₂×M₃₂	—	11	2	no	—
162	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
163	C₂²×C₁₆	—	11	1	no	—
164	C₂²×C₁₆	—	11	2	no	—
165	C₂²×C₁₆	—	11	2	no	—
166	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
167	#436	—	11	4	no	—
168	C₈×D₄	—	11	4	no	—
169	#423	—	11	1	no	—
170	#408	—	11	1	no	—
171	#408	—	11	1	no	—
172	C₂×C₄×C₈	—	11	1	no	—
173	C₄⋊C₁₆	—	11	4	no	—
174	C₂²⋊C₁₆	—	11	4	no	—
175	C₂²⋊C₁₆	C₂×D₁₁	1	4	yes	—
176	#346	—	11	2	no	—
177	#346	—	11	2	no	—
178	C₂²×C₁₁	—	2	2	no	—
179	C₂²×C₁₁	—	2	4	no	—
180	C₂²×C₁₁	—	2	2	no	—
181	C₂²×C₁₁	C₈×D₄	1	2	yes	—
182	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
183	C₂×D₁₁	—	2	4	no	—
184	C₂×D₁₁	—	2	2	no	—
185	C₄×C₁₁	—	2	2	no	—
186	C₄×C₁₁	C₈×D₄	1	2	yes	—
187	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
188	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
189	Dic₁₁	—	2	2	no	—
190	Dic₁₁	—	2	2	no	—
191	Dic₁₁	—	2	2	no	—
192	C₂×#41	—	11	1	no	—
193	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
194	#131	—	2	2	no	—
195	#131	—	2	2	no	—
196	#131	—	22	2	no	—
197	#131	—	22	2	no	—
198	C₂×M₁₆	—	11	1	no	—
199	C₂×M₁₆	—	11	2	no	—
200	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
201	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
202	C₂²×C₈	—	11	1	no	—
203	C₂²×C₈	—	11	2	no	—
204	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
205	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
206	C₄⋊Q₈	—	11	1	no	—
207	#127	—	11	1	no	—
208	#124	—	11	1	no	—
209	#124	—	11	1	no	—
210	#121	—	11	4	no	—
211	C₄×D₄	—	11	4	no	—
212	C₂×C₄²	—	11	1	no	—
213	M₃₂	—	2	2	no	—
214	M₃₂	—	22	4	no	—
215	M₃₂	—	22	4	no	—
216	M₃₂	—	22	2	no	—
217	C₂×C₁₆	—	2	2	no	—
218	C₂×C₁₆	—	11	4	no	—
219	C₂×C₁₆	—	11	1	no	—
220	C₂×C₁₆	—	11	1	no	—
221	C₂×C₁₆	—	11	2	no	—
222	C₂×C₁₆	—	22	4	no	—
223	C₂×C₁₆	—	22	4	no	—
224	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
225	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
226	C₄⋊C₈	—	11	4	no	—
227	C₂²⋊C₈	—	11	4	no	—
228	C₂²⋊C₈	—	11	4	no	—
229	C₄×C₈	—	11	2	no	—
230	C₄×C₈	—	11	2	no	—
231	C₂×C₁₁	—	2	2	no	—
232	C₂×C₁₁	—	4	2	no	—
233	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
234	C₂×C₁₁	#3407	1	2	yes	—
235	D₁₁	—	4	2	no	—
236	#41	—	2	2	no	—
237	#41	—	2	2	no	—
238	#41	—	22	2	no	—
239	#41	—	22	2	no	—
240	C₂×Q₈	—	11	1	no	—
241	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
242	C₂×D₄	—	11	2	no	—
243	C₂×D₄	—	11	4	no	—
244	C₂×D₄	—	11	1	no	—
245	C₂×D₄	C₈×D₁₁	1	2	yes	—
246	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
247	C₂²×C₄	—	11	2	no	—
248	C₂²×C₄	—	11	2	no	—
249	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
250	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
251	M₁₆	—	2	2	no	—
252	M₁₆	—	2	4	no	—
253	M₁₆	—	22	2	no	—
254	M₁₆	—	22	4	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	11	2	no	—
258	C₂×C₈	—	11	2	no	—
259	C₂×C₈	—	22	2	no	—
260	C₂×C₈	—	22	2	no	—
261	C₂×C₈	—	22	2	no	—
262	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
263	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
264	C₂×C₈	D₄×D₁₁	1	2	yes	—
265	C₂×C₈	#4341	1	2	yes	—
266	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
267	C₄⋊C₄	—	11	4	no	—
268	C₂²⋊C₄	—	11	4	no	—
269	C₂²⋊C₄	—	11	4	no	—
270	C₄²	—	11	1	no	—
271	C₄²	—	11	1	no	—
272	C₄²	—	11	2	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	2	no	—
275	C₁₆	—	11	2	no	—
276	C₁₆	—	11	2	no	—
277	C₁₆	—	22	2	no	—
278	C₁₁	#33435	1	1	yes	characteristic, complemented, Sylow
279	C₂³	—	11	2	no	—
280	C₂³	C₂×C₈×D₁₁	1	2	yes	—
281	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
282	Q₈	—	2	2	no	—
283	Q₈	—	22	2	no	—
284	D₄	—	2	4	no	—
285	D₄	—	2	2	no	—
286	D₄	—	22	4	no	—
287	D₄	—	22	2	no	—
288	D₄	—	44	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	11	2	no	—
292	C₂×C₄	—	11	2	no	—
293	C₂×C₄	—	11	2	no	—
294	C₂×C₄	—	22	2	no	—
295	C₂×C₄	—	22	2	no	—
296	C₂×C₄	—	44	2	no	—
297	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
298	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
299	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
300	C₂×C₄	#66960	1	2	yes	—
301	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
302	C₈	—	2	2	no	—
303	C₈	—	22	2	no	—
304	C₈	—	22	2	no	—
305	C₈	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
306	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
307	C₈	C₂×#4341	1	1	yes	characteristic
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	4	no	—
311	C₂²	—	22	2	no	—
312	C₂²	—	22	4	no	—
313	C₂²	(C₂²⋊D₁₁)⋊C₈	1	2	yes	—
314	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
315	C₄	—	2	2	no	—
316	C₄	—	22	2	no	—
317	C₄	—	22	2	no	—
318	C₄	—	22	2	no	—
319	C₄	(C₂²⋊D₁₁)⋊C₈	1	2	yes	—
320	C₄	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
321	C₄	C₂×#66960	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	4	2	no	—
324	C₂	—	44	2	no	—
325	C₂	C₂×(C₂²⋊D₁₁)⋊C₈	1	1	yes	characteristic
326	C₂	#13081717	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2113	C₂
prime radical	#10623363	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2113	D₁₁
hypocenter	C₁₁	#33435
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
1. C₂×#10622520	C₂	semidirect
2. C₂×#10622753	C₂	semidirect
4. #13070444	C₂	semidirect
5. #13070438	C₂	semidirect
6. #13070371	C₂	semidirect
7. #13070229	C₂	semidirect
8. C₂×#10622140	C₂	semidirect
9. C₁₁×#2113	C₂	semidirect
67. C₂×C₁₁⋊C₁₆	D₄	semidirect
123. #2113	D₁₁	semidirect
278. C₁₁	#33435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622520	2
C₂×#10622753	2
#13077326	2
#13070444	2
#13070438	2
#13070371	2
#13070229	2
C₂×#10622140	2
C₁₁×#2113	2
#33435	11