Subgroups — C₁₁×#19205 #14596398

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3246	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1690	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1688	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1666	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#135	—	2	1	no	—
10	C₂×C₁₁×#135	—	2	1	no	—
11	C₁₁×#533	C₂²	1	1	yes	characteristic
12	C₁₁×#532	C₂²	1	2	yes	—
13	C₁₁×#495	—	2	1	no	—
14	C₁₁×#495	—	2	1	no	—
15	C₁₁×#494	C₂²	1	1	yes	characteristic
16	C₁₁×#493	C₂²	1	1	yes	characteristic
17	C₁₁×#492	C₂²	1	2	yes	—
18	C₁₁×#476	—	2	2	no	—
19	C₁₁×#475	C₂²	1	4	yes	—
20	C₁₁×#465	—	2	4	no	—
21	C₁₁×#461	—	2	2	no	—
22	C₁₁×#460	C₂²	1	4	yes	—
23	C₁₁×#446	—	2	1	no	—
24	C₁₁×#446	C₂²	1	2	yes	—
25	C₈×Q₈×C₁₁	—	2	1	no	—
26	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
27	C₁₁×#424	—	2	1	no	—
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₁×#405	—	2	1	no	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#334	C₂²	1	2	yes	—
33	C₁₁×#334	C₂²	1	2	yes	—
34	C₁₁×#332	C₂²	1	4	yes	—
35	C₁₁×#331	C₂²	1	4	yes	—
36	C₂×C₁₁×#41	—	2	2	no	—
37	C₁₁×#135	—	4	4	no	—
38	C₁₁×#135	—	4	4	no	—
39	C₂×C₁₁×Q₁₆	—	2	1	no	—
40	C₂×C₁₁×Q₁₆	—	2	1	no	—
41	C₂×C₁₁×SD₁₆	—	2	4	no	—
42	C₂×C₁₁×SD₁₆	—	2	2	no	—
43	C₂×C₁₁×SD₁₆	—	2	2	no	—
44	C₂×C₁₁×D₈	—	2	1	no	—
45	C₂×C₁₁×D₈	—	2	1	no	—
46	C₂×C₁₁×M₁₆	—	2	1	no	—
47	C₂²×C₈×C₁₁	—	2	2	no	—
48	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
52	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₁×#127	C₂³	1	2	yes	—
54	C₁₁×#125	—	2	1	no	—
55	C₁₁×#124	—	2	2	no	—
56	C₁₁×C₂²⋊Q₈	—	2	1	no	—
57	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
58	C₁₁×#121	—	2	2	no	—
59	C₁₁×#121	—	2	2	no	—
60	C₄×Q₈×C₁₁	—	2	1	no	—
61	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
62	C₄×D₄×C₁₁	—	2	2	no	—
63	C₄×D₄×C₁₁	—	2	2	no	—
64	C₁₁×#117	—	2	1	no	—
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₁₁×#106	—	2	4	no	—
67	C₁₁×C₄⋊C₈	—	2	2	no	—
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	—	2	2	no	—
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
73	C₁₁×#103	—	2	4	no	—
74	C₁₁×#102	—	2	4	no	—
75	C₁₁×#97	—	2	2	no	—
76	C₄×C₈×C₁₁	—	2	2	no	—
77	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	#19205	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₁₁×#41	—	4	4	no	—
83	C₁₁×#41	—	4	4	no	—
84	C₂×Q₈×C₁₁	—	2	1	no	—
85	C₂×Q₈×C₁₁	—	2	2	no	—
86	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₁₁	—	2	2	no	—
88	C₂×D₄×C₁₁	—	2	2	no	—
89	C₂×D₄×C₁₁	—	2	2	no	—
90	C₂×D₄×C₁₁	—	4	2	no	—
91	C₂²×C₄×C₁₁	—	4	2	no	—
92	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
95	C₁₁×Q₁₆	—	4	2	no	—
96	C₁₁×Q₁₆	—	4	2	no	—
97	C₁₁×SD₁₆	—	4	4	no	—
98	C₁₁×SD₁₆	—	4	4	no	—
99	C₁₁×SD₁₆	—	8	4	no	—
100	C₁₁×D₈	—	4	2	no	—
101	C₁₁×D₈	—	4	2	no	—
102	C₁₁×M₁₆	—	4	2	no	—
103	C₂×C₈×C₁₁	—	2	2	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	4	no	—
106	C₂×C₈×C₁₁	—	8	2	no	—
107	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
108	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₁₁×C₄⋊C₄	—	2	1	no	—
113	C₁₁×C₄⋊C₄	—	2	1	no	—
114	C₁₁×C₄⋊C₄	—	2	1	no	—
115	C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₁₁×C₄⋊C₄	—	2	2	no	—
117	C₁₁×C₄⋊C₄	—	2	2	no	—
118	C₁₁×C₄⋊C₄	—	2	2	no	—
119	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
120	C₁₁×C₂²⋊C₄	—	2	2	no	—
121	C₁₁×C₂²⋊C₄	—	4	2	no	—
122	C₁₁×C₂²⋊C₄	—	4	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₁	#41	1	1	yes	characteristic
127	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
128	#3246	C₂×C₁₁	1	2	yes	complemented
129	#3147	C₂×C₁₁	1	1	yes	characteristic
130	#2960	C₂×C₁₁	1	1	yes	characteristic, complemented
131	#1690	C₂×C₁₁	1	2	yes	complemented
132	#1688	C₂×C₁₁	1	2	yes	complemented
133	#1666	C₂×C₁₁	1	4	yes	complemented
134	C₂×#334	C₂×C₁₁	1	1	yes	characteristic, complemented
135	#1547	C₂×C₁₁	1	2	yes	complemented
136	C₂³×C₁₁	—	4	2	no	—
137	C₂³×C₁₁	#121	1	1	yes	characteristic
138	Q₈×C₁₁	—	2	4	no	—
139	Q₈×C₁₁	—	4	2	no	—
140	Q₈×C₁₁	—	4	2	no	—
141	Q₈×C₁₁	—	4	2	no	—
142	D₄×C₁₁	—	4	2	no	—
143	D₄×C₁₁	—	4	2	no	—
144	D₄×C₁₁	—	4	2	no	—
145	D₄×C₁₁	—	4	2	no	—
146	D₄×C₁₁	—	8	2	no	—
147	D₄×C₁₁	—	8	4	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	4	1	no	—
152	C₂×C₄×C₁₁	—	4	2	no	—
153	C₂×C₄×C₁₁	—	8	4	no	—
154	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₁	—	2	1	no	—
163	C₈×C₁₁	—	2	1	no	—
164	C₈×C₁₁	—	4	2	no	—
165	C₈×C₁₁	—	4	4	no	—
166	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
167	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
168	C₂×#135	—	2	1	no	—
169	C₂×#135	—	2	1	no	—
170	#533	C₂²×C₁₁	1	1	yes	characteristic
171	#532	C₂²×C₁₁	1	2	yes	—
172	#495	—	2	1	no	—
173	#495	—	2	1	no	—
174	#494	C₂²×C₁₁	1	1	yes	characteristic
175	#493	C₂²×C₁₁	1	1	yes	characteristic
176	#492	C₂²×C₁₁	1	2	yes	—
177	#476	—	2	2	no	—
178	#475	C₂²×C₁₁	1	4	yes	—
179	#465	—	2	4	no	—
180	#461	—	2	2	no	—
181	#460	C₂²×C₁₁	1	4	yes	—
182	#446	—	2	1	no	—
183	#446	C₂²×C₁₁	1	2	yes	—
184	C₈×Q₈	—	2	1	no	—
185	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
186	#424	—	2	1	no	—
187	#423	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
189	#405	—	2	1	no	—
190	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
191	#334	C₂²×C₁₁	1	2	yes	—
192	#334	C₂²×C₁₁	1	2	yes	—
193	#332	C₂²×C₁₁	1	4	yes	—
194	#331	C₂²×C₁₁	1	4	yes	—
195	C₂²×C₁₁	—	2	1	no	—
196	C₂²×C₁₁	—	2	1	no	—
197	C₂²×C₁₁	—	8	2	no	—
198	C₂²×C₁₁	—	8	2	no	—
199	C₂²×C₁₁	—	8	2	no	—
200	C₂²×C₁₁	#460	1	2	yes	—
201	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
202	C₄×C₁₁	—	2	1	no	—
203	C₄×C₁₁	—	2	1	no	—
204	C₄×C₁₁	—	2	1	no	—
205	C₄×C₁₁	—	4	2	no	—
206	C₄×C₁₁	—	4	2	no	—
207	C₄×C₁₁	—	8	2	no	—
208	C₄×C₁₁	#460	1	2	yes	—
209	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
210	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₄×C₁₁	#577	1	2	yes	—
212	C₂×#41	—	2	2	no	—
213	#135	—	4	4	no	—
214	#135	—	4	4	no	—
215	C₂×Q₁₆	—	2	1	no	—
216	C₂×Q₁₆	—	2	1	no	—
217	C₂×SD₁₆	—	2	4	no	—
218	C₂×SD₁₆	—	2	2	no	—
219	C₂×SD₁₆	—	2	2	no	—
220	C₂×D₈	—	2	1	no	—
221	C₂×D₈	—	2	1	no	—
222	C₂×M₁₆	—	2	1	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
225	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
226	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
227	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
228	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
229	#127	C₂³×C₁₁	1	2	yes	—
230	#125	—	2	1	no	—
231	#124	—	2	2	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
234	#121	—	2	2	no	—
235	#121	—	2	2	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	#117	—	2	1	no	—
241	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
242	#106	—	2	4	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
248	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
249	#103	—	2	4	no	—
250	#102	—	2	4	no	—
251	#97	—	2	2	no	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
254	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
256	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
257	C₂×C₁₁	—	2	2	no	—
258	C₂×C₁₁	—	16	2	no	—
259	C₂×C₁₁	C₂×#460	1	1	yes	characteristic
260	C₂×C₁₁	#3060	1	1	yes	characteristic
261	C₂×C₁₁	#3067	1	1	yes	characteristic
262	#41	—	4	4	no	—
263	#41	—	4	4	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
275	Q₁₆	—	4	2	no	—
276	Q₁₆	—	4	2	no	—
277	SD₁₆	—	4	4	no	—
278	SD₁₆	—	4	4	no	—
279	SD₁₆	—	8	4	no	—
280	D₈	—	4	2	no	—
281	D₈	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	8	2	no	—
287	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
288	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
289	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
290	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
300	C₂²⋊C₄	—	2	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
306	C₄²	C₁₁×#41	1	1	yes	characteristic
307	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
308	C₁₁	#19205	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³	—	4	2	no	—
310	C₂³	C₁₁×#121	1	1	yes	characteristic
311	Q₈	—	2	4	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	D₄	—	8	2	no	—
320	D₄	—	8	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	8	4	no	—
327	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
328	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
329	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
330	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
331	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
334	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	4	2	no	—
338	C₈	—	4	4	no	—
339	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
340	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	8	2	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	C₁₁×#460	1	2	yes	—
347	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	2	no	—
354	C₄	C₁₁×#460	1	2	yes	—
355	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
356	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₄	C₁₁×#577	1	2	yes	—
358	C₂	—	2	2	no	—
359	C₂	—	16	2	no	—
360	C₂	C₂×C₁₁×#460	1	1	yes	characteristic
361	C₂	C₁₁×#3060	1	1	yes	characteristic
362	C₂	C₁₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₁₁×#3147	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3246	C₂	semidirect
3. C₁₁×#2960	C₂	semidirect
4. C₁₁×#1690	C₂	semidirect
5. C₁₁×#1688	C₂	semidirect
6. C₁₁×#1666	C₂	semidirect
7. C₂×C₁₁×#334	C₂	semidirect
8. C₁₁×#1547	C₂	semidirect
81. #19205	C₁₁	direct (N × H)
107. C₂×C₈×C₁₁	SD₁₆	semidirect
128. #3246	C₂×C₁₁	semidirect
130. #2960	C₂×C₁₁	semidirect
131. #1690	C₂×C₁₁	semidirect
132. #1688	C₂×C₁₁	semidirect
133. #1666	C₂×C₁₁	semidirect
134. C₂×#334	C₂×C₁₁	semidirect
135. #1547	C₂×C₁₁	semidirect
287. C₂×C₈	C₁₁×SD₁₆	semidirect
308. C₁₁	#19205	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3246	2
C₁₁×#3147	2
C₁₁×#2960	2
C₁₁×#1690	2
C₁₁×#1688	2
C₁₁×#1666	2
C₂×C₁₁×#334	2
C₁₁×#1547	2
#19205	11

Subgroups — C11×#19205 #14596398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19205 #14596398