Subgroups — C₁₁×#19203 #14596396

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3208	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1688	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1668	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1545	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₁×D₈	—	2	1	no	—
9	C₂²×C₁₁×D₈	—	2	1	no	—
10	C₁₁×#533	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#127	C₂²	1	2	yes	—
12	C₁₁×#493	—	2	1	no	—
13	C₁₁×#493	—	2	1	no	—
14	C₁₁×#493	C₂²	1	2	yes	—
15	C₁₁×#493	C₂²	1	2	yes	—
16	C₁₁×#492	—	2	2	no	—
17	C₁₁×#486	—	2	2	no	—
18	C₁₁×#460	C₂²	1	8	yes	complemented
19	C₁₁×#450	—	2	4	no	—
20	C₁₁×#446	—	2	1	no	—
21	C₁₁×#446	C₂²	1	2	yes	complemented
22	C₈×Q₈×C₁₁	—	2	1	no	—
23	C₈×Q₈×C₁₁	C₂²	1	2	yes	complemented
24	C₁₁×#431	C₂²	1	2	yes	—
25	C₁₁×#424	—	2	1	no	—
26	C₁₁×#423	C₂²	1	1	yes	characteristic
27	C₁₁×#405	—	2	1	no	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#335	C₂²	1	2	yes	complemented
30	C₁₁×#334	C₂²	1	2	yes	complemented
31	C₁₁×#331	C₂²	1	8	yes	complemented
32	C₂²×D₄×C₁₁	—	2	2	no	—
33	C₂²×D₄×C₁₁	—	2	2	no	—
34	C₂²×D₄×C₁₁	—	2	2	no	—
35	C₂×C₁₁×SD₁₆	—	2	8	no	—
36	C₂×C₁₁×D₈	—	2	2	no	—
37	C₂×C₁₁×D₈	—	2	2	no	—
38	C₂×C₁₁×D₈	—	2	2	no	—
39	C₂×C₁₁×D₈	—	2	2	no	—
40	C₂×C₁₁×D₈	—	4	4	no	—
41	C₂×C₁₁×D₈	—	4	4	no	—
42	C₂×C₁₁×M₁₆	—	2	1	no	—
43	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
46	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
47	C₁₁×#127	—	2	2	no	—
48	C₁₁×#127	—	2	2	no	—
49	C₁₁×#127	—	2	2	no	—
50	C₁₁×#127	C₂³	1	4	yes	—
51	C₁₁×#125	—	2	1	no	—
52	C₁₁×C₂²⋊Q₈	—	2	1	no	—
53	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
54	C₄×Q₈×C₁₁	—	2	1	no	—
55	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
56	C₁₁×#117	—	2	1	no	—
57	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×C₄⋊C₈	—	2	2	no	—
59	C₁₁×C₄⋊C₈	—	2	2	no	—
60	C₁₁×C₄⋊C₈	—	2	1	no	—
61	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
62	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
63	C₁₁×#102	—	2	8	no	—
64	C₁₁×C₂²⋊C₈	—	2	2	no	—
65	C₁₁×#97	—	2	2	no	—
66	C₄×C₈×C₁₁	—	2	2	no	—
67	C₄×C₈×C₁₁	—	2	2	no	—
68	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
69	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	#19203	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₁	—	4	2	no	—
74	C₂×Q₈×C₁₁	—	2	1	no	—
75	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
76	C₂×D₄×C₁₁	—	2	4	no	—
77	C₂×D₄×C₁₁	—	2	4	no	—
78	C₂×D₄×C₁₁	—	2	4	no	—
79	C₂×D₄×C₁₁	—	4	2	no	—
80	C₂×D₄×C₁₁	—	4	2	no	—
81	C₂×D₄×C₁₁	—	4	2	no	—
82	C₂×D₄×C₁₁	—	4	4	no	—
83	C₂×D₄×C₁₁	—	4	4	no	—
84	C₂×D₄×C₁₁	—	8	4	no	—
85	C₂×D₄×C₁₁	—	8	4	no	—
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
89	C₁₁×SD₁₆	—	8	8	no	—
90	C₁₁×D₈	—	4	4	no	—
91	C₁₁×D₈	—	4	4	no	—
92	C₁₁×D₈	—	4	4	no	—
93	C₁₁×D₈	—	4	4	no	—
94	C₁₁×M₁₆	—	4	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	4	no	—
98	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
99	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₁₁×C₄⋊C₄	—	2	1	no	—
104	C₁₁×C₄⋊C₄	—	2	1	no	—
105	C₁₁×C₄⋊C₄	—	2	1	no	—
106	C₁₁×C₄⋊C₄	—	2	2	no	—
107	C₁₁×C₄⋊C₄	—	2	2	no	—
108	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
109	C₁₁×C₂²⋊C₄	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₁	#41	1	1	yes	characteristic
114	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
115	#3208	C₂×C₁₁	1	2	yes	complemented
116	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
117	#2960	C₂×C₁₁	1	1	yes	characteristic, complemented
118	#1688	C₂×C₁₁	1	4	yes	complemented
119	#1668	C₂×C₁₁	1	4	yes	complemented
120	#1564	C₂×C₁₁	1	1	yes	characteristic, complemented
121	#1545	C₂×C₁₁	1	2	yes	complemented
122	C₂³×C₁₁	—	4	4	no	—
123	C₂³×C₁₁	—	8	4	no	—
124	C₂³×C₁₁	—	8	4	no	—
125	C₂³×C₁₁	—	8	4	no	—
126	C₂³×C₁₁	#121	1	1	yes	characteristic
127	Q₈×C₁₁	—	2	4	no	—
128	Q₈×C₁₁	—	4	2	no	—
129	D₄×C₁₁	—	4	4	no	—
130	D₄×C₁₁	—	4	4	no	—
131	D₄×C₁₁	—	4	8	no	—
132	D₄×C₁₁	—	8	4	no	—
133	D₄×C₁₁	—	8	4	no	—
134	D₄×C₁₁	—	8	4	no	—
135	D₄×C₁₁	—	8	4	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	2	no	—
140	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
145	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
148	C₈×C₁₁	—	2	1	no	—
149	C₈×C₁₁	—	2	1	no	—
150	C₈×C₁₁	—	4	2	no	—
151	C₈×C₁₁	—	4	4	no	—
152	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
153	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
154	C₂²×D₈	—	2	1	no	—
155	C₂²×D₈	—	2	1	no	—
156	#533	C₂²×C₁₁	1	1	yes	characteristic
157	C₂×#127	C₂²×C₁₁	1	2	yes	—
158	#493	—	2	1	no	—
159	#493	—	2	1	no	—
160	#493	C₂²×C₁₁	1	2	yes	—
161	#493	C₂²×C₁₁	1	2	yes	—
162	#492	—	2	2	no	—
163	#486	—	2	2	no	—
164	#460	C₂²×C₁₁	1	8	yes	complemented
165	#450	—	2	4	no	—
166	#446	—	2	1	no	—
167	#446	C₂²×C₁₁	1	2	yes	complemented
168	C₈×Q₈	—	2	1	no	—
169	C₈×Q₈	C₂²×C₁₁	1	2	yes	complemented
170	#431	C₂²×C₁₁	1	2	yes	—
171	#424	—	2	1	no	—
172	#423	C₂²×C₁₁	1	1	yes	characteristic
173	#405	—	2	1	no	—
174	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
175	#335	C₂²×C₁₁	1	2	yes	complemented
176	#334	C₂²×C₁₁	1	2	yes	complemented
177	#331	C₂²×C₁₁	1	8	yes	complemented
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	8	4	no	—
181	C₂²×C₁₁	—	8	4	no	—
182	C₂²×C₁₁	—	8	4	no	—
183	C₂²×C₁₁	—	16	8	no	—
184	C₂²×C₁₁	#460	1	2	yes	—
185	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	4	2	no	—
189	C₄×C₁₁	—	4	2	no	—
190	C₄×C₁₁	#460	1	2	yes	—
191	C₄×C₁₁	#472	1	2	yes	—
192	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₁₁	#576	1	2	yes	—
195	C₂²×D₄	—	2	2	no	—
196	C₂²×D₄	—	2	2	no	—
197	C₂²×D₄	—	2	2	no	—
198	C₂×SD₁₆	—	2	8	no	—
199	C₂×D₈	—	2	2	no	—
200	C₂×D₈	—	2	2	no	—
201	C₂×D₈	—	2	2	no	—
202	C₂×D₈	—	2	2	no	—
203	C₂×D₈	—	4	4	no	—
204	C₂×D₈	—	4	4	no	—
205	C₂×M₁₆	—	2	1	no	—
206	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
207	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
208	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
209	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
210	#127	—	2	2	no	—
211	#127	—	2	2	no	—
212	#127	—	2	2	no	—
213	#127	C₂³×C₁₁	1	4	yes	—
214	#125	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
219	#117	—	2	1	no	—
220	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	1	no	—
224	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
225	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
226	#102	—	2	8	no	—
227	C₂²⋊C₈	—	2	2	no	—
228	#97	—	2	2	no	—
229	C₄×C₈	—	2	2	no	—
230	C₄×C₈	—	2	2	no	—
231	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
232	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
233	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
235	C₂×C₁₁	—	2	2	no	—
236	C₂×C₁₁	—	16	4	no	—
237	C₂×C₁₁	C₂×#460	1	1	yes	characteristic
238	C₂×C₁₁	#3058	1	1	yes	characteristic
239	C₂×C₁₁	C₂×#472	1	1	yes	characteristic
240	C₂⁴	—	4	2	no	—
241	C₂×Q₈	—	2	1	no	—
242	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	2	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	—	8	4	no	—
252	C₂×D₄	—	8	4	no	—
253	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
255	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
256	SD₁₆	—	8	8	no	—
257	D₈	—	4	4	no	—
258	D₈	—	4	4	no	—
259	D₈	—	4	4	no	—
260	D₈	—	4	4	no	—
261	M₁₆	—	4	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
266	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
267	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
268	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
269	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₄⋊C₄	—	2	1	no	—
271	C₄⋊C₄	—	2	1	no	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
276	C₂²⋊C₄	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
279	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
280	C₄²	C₁₁×#41	1	1	yes	characteristic
281	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
282	C₁₁	#19203	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	4	4	no	—
284	C₂³	—	8	4	no	—
285	C₂³	—	8	4	no	—
286	C₂³	—	8	4	no	—
287	C₂³	C₁₁×#121	1	1	yes	characteristic
288	Q₈	—	2	4	no	—
289	Q₈	—	4	2	no	—
290	D₄	—	4	4	no	—
291	D₄	—	4	4	no	—
292	D₄	—	4	8	no	—
293	D₄	—	8	4	no	—
294	D₄	—	8	4	no	—
295	D₄	—	8	4	no	—
296	D₄	—	8	4	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
302	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
303	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
304	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
305	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
306	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
308	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	4	2	no	—
312	C₈	—	4	4	no	—
313	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
314	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	8	4	no	—
318	C₂²	—	8	4	no	—
319	C₂²	—	8	4	no	—
320	C₂²	—	16	8	no	—
321	C₂²	C₁₁×#460	1	2	yes	—
322	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	2	no	—
327	C₄	C₁₁×#460	1	2	yes	—
328	C₄	C₁₁×#472	1	2	yes	—
329	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
330	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
331	C₄	C₁₁×#576	1	2	yes	—
332	C₂	—	2	2	no	—
333	C₂	—	16	4	no	—
334	C₂	C₂×C₁₁×#460	1	1	yes	characteristic
335	C₂	C₁₁×#3058	1	1	yes	characteristic
336	C₂	C₂×C₁₁×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	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×#3208	C₂	semidirect
3. C₁₁×#2960	C₂	semidirect
4. C₁₁×#1688	C₂	semidirect
5. C₁₁×#1668	C₂	semidirect
6. C₁₁×#1564	C₂	semidirect
7. C₁₁×#1545	C₂	semidirect
18. C₁₁×#460	C₂²	semidirect
21. C₁₁×#446	C₂²	semidirect
23. C₈×Q₈×C₁₁	C₂²	semidirect
29. C₁₁×#335	C₂²	semidirect
30. C₁₁×#334	C₂²	semidirect
31. C₁₁×#331	C₂²	semidirect
72. #19203	C₁₁	direct (N × H)
98. C₂×C₈×C₁₁	SD₁₆	semidirect
115. #3208	C₂×C₁₁	semidirect
117. #2960	C₂×C₁₁	semidirect
118. #1688	C₂×C₁₁	semidirect
119. #1668	C₂×C₁₁	semidirect
120. #1564	C₂×C₁₁	semidirect
121. #1545	C₂×C₁₁	semidirect
164. #460	C₂²×C₁₁	semidirect
167. #446	C₂²×C₁₁	semidirect
169. C₈×Q₈	C₂²×C₁₁	semidirect
175. #335	C₂²×C₁₁	semidirect
176. #334	C₂²×C₁₁	semidirect
177. #331	C₂²×C₁₁	semidirect
265. C₂×C₈	C₁₁×SD₁₆	semidirect
282. C₁₁	#19203	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×#3208	2
C₂×C₁₁×#493	2
C₁₁×#2960	2
C₁₁×#1688	2
C₁₁×#1668	2
C₁₁×#1564	2
C₁₁×#1545	2
#19203	11

Subgroups — C11×#19203 #14596396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#19203 #14596396