Subgroups — #14907402

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077326	C₂	1	1	yes	maximal, characteristic
2	#13070444	C₂	1	2	yes	maximal, complemented
3	#13070441	C₂	1	2	yes	maximal, complemented
4	#13070439	C₂	1	2	yes	maximal, complemented
5	#13070438	C₂	1	2	yes	maximal, complemented
6	#13070416	C₂	1	2	yes	maximal, complemented
7	#13070230	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070228	C₂	1	2	yes	maximal, 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	#10622742	C₄	1	1	yes	characteristic
17	#10622741	C₄	1	2	yes	—
18	#10622741	C₄	1	2	yes	—
19	#10622731	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
21	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
22	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
23	C₂×#66876	C₂²	1	1	yes	characteristic
24	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×#66862	C₂²	1	2	yes	—
26	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
27	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
28	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
29	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
30	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
31	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
32	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
33	#10622140	C₂²	1	2	yes	—
34	#10622140	C₂²	1	2	yes	—
35	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
36	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
37	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
38	C₂×#4339	C₂×C₄	1	1	yes	characteristic
39	C₁₁×#131	—	4	1	no	—
40	C₁₁×#131	—	4	1	no	—
41	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	#67000	C₈	1	1	yes	characteristic
48	#66997	C₈	1	1	yes	characteristic
49	#66993	C₈	1	1	yes	characteristic
50	#66992	C₈	1	2	yes	—
51	#66992	C₈	1	2	yes	—
52	#66989	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
54	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×#4318	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
58	#66954	—	4	1	no	—
59	#66954	—	4	1	no	—
60	C₂×#4313	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₁₁	C₂³	1	2	yes	—
62	C₁₁×M₃₂	—	4	1	no	—
63	C₂×C₁₁×C₁₆	—	4	1	no	—
64	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
66	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
67	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
68	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
69	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
70	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
72	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
73	C₈×Dic₁₁	C₂³	1	2	yes	—
74	#66876	—	4	1	no	—
75	C₂×C₁₁⋊C₁₆	—	4	1	no	—
76	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
78	#66862	—	4	2	no	—
79	C₁₆×D₁₁	—	4	2	no	—
80	#33494	—	11	1	no	maximal, Sylow
81	C₁₁×#41	—	4	1	no	—
82	C₁₁×#41	—	4	1	no	—
83	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
84	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
85	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
86	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
91	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
92	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
93	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
94	#4339	—	4	1	no	—
95	#4339	—	4	1	no	—
96	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
98	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
99	C₁₁×M₁₆	—	4	1	no	—
100	C₁₁×M₁₆	—	4	1	no	—
101	C₁₁×M₁₆	—	4	1	no	—
102	C₂×C₈×C₁₁	—	2	1	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	—	2	1	no	—
105	C₂×C₈×C₁₁	—	2	1	no	—
106	C₂×C₈×C₁₁	—	2	1	no	—
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
112	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
113	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
114	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
115	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
116	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
117	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
118	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
119	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
120	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
121	#4318	—	4	1	no	—
122	C₂×C₁₁⋊C₈	—	4	1	no	—
123	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
125	#4313	—	4	2	no	—
126	C₈×D₁₁	—	2	2	no	—
127	C₈×D₁₁	—	2	2	no	—
128	C₁₁×C₁₆	—	2	2	no	—
129	C₁₁×C₁₆	—	2	2	no	—
130	C₁₁⋊C₁₆	—	2	2	no	—
131	C₁₁⋊C₁₆	—	2	2	no	—
132	#2931	—	11	1	no	—
133	#2168	—	11	2	no	—
134	#2168	—	11	2	no	—
135	#2168	—	11	2	no	—
136	#2168	—	11	2	no	—
137	#2163	—	11	2	no	—
138	#2113	—	11	2	no	—
139	#2113	—	11	1	no	—
140	#2113	D₁₁	1	1	yes	characteristic, complemented
141	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
142	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
143	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
144	C₂²×D₁₁	C₂²×C₈	1	2	yes	—
145	Q₈×C₁₁	—	4	1	no	—
146	D₄×C₁₁	—	4	1	no	—
147	D₄×C₁₁	—	4	1	no	—
148	D₄×C₁₁	—	4	1	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	1	no	—
155	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
159	C₂²⋊D₁₁	—	4	2	no	—
160	C₂²⋊D₁₁	—	4	2	no	—
161	C₂²⋊D₁₁	—	4	2	no	—
162	C₂×Dic₁₁	—	4	2	no	—
163	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
164	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
165	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
166	D₄₄	—	4	1	no	—
167	C₄×D₁₁	—	2	2	no	—
168	C₄×D₁₁	—	2	2	no	—
169	Dic₂₂	—	4	1	no	—
170	C₈×C₁₁	—	2	1	no	—
171	C₈×C₁₁	—	2	1	no	—
172	C₈×C₁₁	—	2	1	no	—
173	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₁₁⋊C₈	—	2	2	no	—
176	C₁₁⋊C₈	—	2	2	no	—
177	C₂×#131	—	11	1	no	—
178	C₂×#131	C₂×D₁₁	1	1	yes	characteristic
179	#532	—	11	1	no	—
180	C₂×M₃₂	—	11	1	no	—
181	C₂×M₃₂	—	11	2	no	—
182	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
183	C₂²×C₁₆	—	11	1	no	—
184	C₂²×C₁₆	—	11	2	no	—
185	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
186	#436	—	11	2	no	—
187	#436	—	11	2	no	—
188	C₈×D₄	—	11	2	no	—
189	C₈×D₄	—	11	2	no	—
190	#423	—	11	1	no	—
191	#408	—	11	1	no	—
192	#408	—	11	1	no	—
193	C₂×C₄×C₈	—	11	1	no	—
194	C₄⋊C₁₆	—	11	2	no	—
195	C₄⋊C₁₆	—	11	2	no	—
196	C₂²⋊C₁₆	—	11	2	no	—
197	C₂²⋊C₁₆	—	11	2	no	—
198	C₂²⋊C₁₆	—	11	2	no	—
199	C₂²⋊C₁₆	—	11	2	no	—
200	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
201	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
202	#346	—	11	2	no	—
203	#346	—	11	2	no	—
204	C₂²×C₁₁	—	2	2	no	—
205	C₂²×C₁₁	—	2	2	no	—
206	C₂²×C₁₁	—	2	2	no	—
207	C₂²×C₁₁	—	2	1	no	—
208	C₂²×C₁₁	—	2	1	no	—
209	C₂²×C₁₁	—	2	1	no	—
210	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
211	C₂×D₁₁	—	2	2	no	—
212	C₂×D₁₁	—	2	2	no	—
213	C₂×D₁₁	—	2	2	no	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	#518	1	1	yes	characteristic
218	C₄×C₁₁	#568	1	1	yes	characteristic
219	Dic₁₁	—	2	2	no	—
220	Dic₁₁	—	2	2	no	—
221	Dic₁₁	—	2	2	no	—
222	C₂×#41	—	11	1	no	—
223	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
224	#131	—	4	1	no	—
225	#131	—	4	1	no	—
226	#131	—	44	1	no	—
227	#131	—	44	1	no	—
228	C₂×M₁₆	—	11	1	no	—
229	C₂×M₁₆	—	11	2	no	—
230	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
231	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
232	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
233	C₂²×C₈	—	11	1	no	—
234	C₂²×C₈	—	11	2	no	—
235	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
236	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
237	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
238	C₄⋊Q₈	—	11	1	no	—
239	#127	—	11	1	no	—
240	#124	—	11	1	no	—
241	#124	—	11	1	no	—
242	#121	—	11	2	no	—
243	#121	—	11	2	no	—
244	C₄×D₄	—	11	2	no	—
245	C₄×D₄	—	11	2	no	—
246	C₂×C₄²	—	11	1	no	—
247	M₃₂	—	4	1	no	—
248	M₃₂	—	44	2	no	—
249	M₃₂	—	44	1	no	—
250	C₂×C₁₆	—	4	1	no	—
251	C₂×C₁₆	—	11	2	no	—
252	C₂×C₁₆	—	11	2	no	—
253	C₂×C₁₆	—	44	2	no	—
254	C₂×C₁₆	—	44	1	no	—
255	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
256	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
257	C₄⋊C₈	—	11	2	no	—
258	C₄⋊C₈	—	11	2	no	—
259	C₂²⋊C₈	—	11	2	no	—
260	C₂²⋊C₈	—	11	2	no	—
261	C₂²⋊C₈	—	11	2	no	—
262	C₂²⋊C₈	—	11	2	no	—
263	C₄×C₈	—	11	2	no	—
264	C₄×C₈	—	11	2	no	—
265	C₂×C₁₁	—	4	1	no	—
266	C₂×C₁₁	—	4	1	no	—
267	C₂×C₁₁	—	4	1	no	—
268	C₂×C₁₁	#2972	1	1	yes	characteristic
269	C₂×C₁₁	#3407	1	2	yes	—
270	D₁₁	—	4	2	no	—
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	#41	—	44	1	no	—
274	#41	—	44	1	no	—
275	C₂×Q₈	—	11	1	no	—
276	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
277	C₂×D₄	—	11	2	no	—
278	C₂×D₄	—	11	2	no	—
279	C₂×D₄	—	11	2	no	—
280	C₂×D₄	—	11	1	no	—
281	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
282	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
283	C₂×D₄	C₈×D₁₁	1	1	yes	characteristic
284	C₂²×C₄	—	11	2	no	—
285	C₂²×C₄	—	11	2	no	—
286	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
289	M₁₆	—	4	1	no	—
290	M₁₆	—	4	1	no	—
291	M₁₆	—	4	1	no	—
292	M₁₆	—	44	2	no	—
293	M₁₆	—	44	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	11	2	no	—
301	C₂×C₈	—	11	2	no	—
302	C₂×C₈	—	22	2	no	—
303	C₂×C₈	—	22	2	no	—
304	C₂×C₈	—	44	1	no	—
305	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
308	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
309	C₄⋊C₄	—	11	2	no	—
310	C₄⋊C₄	—	11	2	no	—
311	C₂²⋊C₄	—	11	2	no	—
312	C₂²⋊C₄	—	11	2	no	—
313	C₂²⋊C₄	—	11	2	no	—
314	C₂²⋊C₄	—	11	2	no	—
315	C₄²	—	11	1	no	—
316	C₄²	—	11	1	no	—
317	C₄²	—	11	2	no	—
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	22	2	no	—
321	C₁₆	—	22	2	no	—
322	C₁₁	#33494	1	1	yes	characteristic, complemented, Sylow
323	C₂³	—	11	2	no	—
324	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
325	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
326	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
327	Q₈	—	4	1	no	—
328	Q₈	—	44	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	44	1	no	—
333	D₄	—	44	2	no	—
334	D₄	—	44	2	no	—
335	D₄	—	44	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	11	2	no	—
343	C₂×C₄	—	11	2	no	—
344	C₂×C₄	—	11	2	no	—
345	C₂×C₄	—	22	2	no	—
346	C₂×C₄	—	22	2	no	—
347	C₂×C₄	—	44	2	no	—
348	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	22	2	no	—
356	C₈	—	22	2	no	—
357	C₈	#67037	1	1	yes	characteristic
358	C₈	#67037	1	1	yes	characteristic
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	22	2	no	—
366	C₂²	—	22	2	no	—
367	C₂²	—	22	2	no	—
368	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	22	2	no	—
373	C₄	—	22	2	no	—
374	C₄	—	22	2	no	—
375	C₄	#10623017	1	1	yes	characteristic
376	C₄	#10623276	1	1	yes	characteristic
377	C₂	—	4	1	no	—
378	C₂	—	4	1	no	—
379	C₂	—	4	1	no	—
380	C₂	—	44	2	no	—
381	C₂	#13077638	1	1	yes	characteristic
382	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	#33494
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
2. #13070444	C₂	semidirect
3. #13070441	C₂	semidirect
4. #13070439	C₂	semidirect
5. #13070438	C₂	semidirect
6. #13070416	C₂	semidirect
7. #13070230	C₂	semidirect
8. #13070228	C₂	semidirect
9. C₁₁×#2113	C₂	semidirect
140. #2113	D₁₁	semidirect
322. C₁₁	#33494	semidirect

Maximal subgroups

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

subgroup	index
#13077326	2
#13070444	2
#13070441	2
#13070439	2
#13070438	2
#13070416	2
#13070230	2
#13070228	2
C₁₁×#2113	2
#33494	11