Subgroups — C₁₁×#23646 #14600839

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#2896	C₂	1	2	yes	maximal
3	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2079	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2078	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1742	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×#117	C₂²	1	2	yes	—
13	C₁₁×#427	—	2	2	no	—
14	C₁₁×#427	—	2	2	no	—
15	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
16	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
17	C₁₁×#419	—	2	2	no	—
18	C₁₁×#418	—	2	2	no	—
19	C₁₁×#417	C₂²	1	8	yes	—
20	C₁₁×#416	—	2	4	no	—
21	C₁₁×#408	—	2	2	no	—
22	C₁₁×#408	C₂²	1	2	yes	—
23	C₁₁×#408	C₂²	1	2	yes	—
24	C₂×C₁₁×C₂²⋊C₈	—	2	2	no	—
25	C₁₁×#343	C₂²	1	8	yes	complemented
26	C₁₁×#341	C₂²	1	2	yes	complemented
27	C₁₁×#341	C₂²	1	2	yes	complemented
28	C₂×C₁₁×#41	—	2	1	no	—
29	C₂×C₁₁×#41	—	2	1	no	—
30	C₂×C₁₁×#41	—	2	4	no	—
31	C₂×C₁₁×#41	—	2	4	no	—
32	C₂×C₁₁×#41	D₄	1	2	yes	—
33	C₂×C₁₁×#41	C₂³	1	2	yes	—
34	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₁	—	2	1	no	—
36	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₁	—	2	1	no	—
38	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	—	2	1	no	—
40	C₂×C₁₁×M₁₆	—	2	2	no	—
41	C₂×C₁₁×M₁₆	—	2	4	no	—
42	C₂×C₁₁×M₁₆	—	2	4	no	—
43	C₂×C₁₁×M₁₆	—	2	4	no	—
44	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
45	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	—	2	4	no	—
47	C₂²×C₈×C₁₁	—	2	1	no	—
48	C₂²×C₈×C₁₁	—	2	2	no	—
49	C₂²×C₈×C₁₁	D₄	1	2	yes	—
50	C₂²×C₈×C₁₁	D₄	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×#117	—	2	2	no	—
54	C₁₁×#117	—	2	2	no	—
55	C₁₁×#117	—	2	2	no	—
56	C₁₁×#117	—	2	2	no	—
57	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
58	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₄²×C₁₁	—	2	2	no	—
60	C₁₁×#107	—	2	4	no	—
61	C₁₁×#106	—	2	4	no	—
62	C₁₁×#103	—	2	8	no	—
63	C₁₁×#102	—	2	8	no	—
64	C₁₁×C₂²⋊C₈	—	2	4	no	—
65	C₁₁×C₂²⋊C₈	—	2	4	no	—
66	#23646	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₁	—	2	1	no	—
68	C₂⁴×C₁₁	#41	1	1	yes	characteristic
69	C₁₁×#41	—	2	8	no	—
70	C₁₁×#41	—	2	4	no	—
71	C₁₁×#41	—	2	4	no	—
72	C₁₁×#41	—	4	2	no	—
73	C₁₁×#41	—	4	2	no	—
74	C₁₁×#41	—	4	4	no	—
75	C₂×Q₈×C₁₁	—	2	1	no	—
76	C₂×Q₈×C₁₁	—	2	4	no	—
77	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×D₄×C₁₁	—	2	2	no	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	—	2	1	no	—
81	C₂×D₄×C₁₁	—	2	4	no	—
82	C₂×D₄×C₁₁	—	4	4	no	—
83	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₁	—	2	1	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	2	2	no	—
87	C₂²×C₄×C₁₁	—	2	4	no	—
88	C₂²×C₄×C₁₁	—	4	2	no	—
89	C₂²×C₄×C₁₁	—	4	2	no	—
90	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₁	#41	1	4	yes	—
96	C₂²×C₄×C₁₁	#41	1	4	yes	—
97	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
98	C₁₁×M₁₆	—	2	4	no	—
99	C₁₁×M₁₆	—	2	4	no	—
100	C₁₁×M₁₆	—	2	4	no	—
101	C₁₁×M₁₆	—	4	4	no	—
102	C₁₁×M₁₆	—	4	2	no	—
103	C₂×C₈×C₁₁	—	2	4	no	—
104	C₂×C₈×C₁₁	—	2	4	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	4	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	4	4	no	—
110	C₂×C₈×C₁₁	—	4	2	no	—
111	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
113	C₁₁×C₄⋊C₄	—	2	4	no	—
114	C₁₁×C₄⋊C₄	—	2	4	no	—
115	C₁₁×C₂²⋊C₄	—	4	2	no	—
116	C₁₁×C₂²⋊C₄	—	4	2	no	—
117	C₄²×C₁₁	—	4	2	no	—
118	C₄²×C₁₁	—	4	2	no	—
119	C₂×#427	C₂×C₁₁	1	1	yes	characteristic, complemented
120	#2896	C₂×C₁₁	1	2	yes	—
121	C₂×#408	C₂×C₁₁	1	1	yes	characteristic
122	#2079	C₂×C₁₁	1	4	yes	complemented
123	#2078	C₂×C₁₁	1	4	yes	complemented
124	#1742	C₂×C₁₁	1	2	yes	complemented
125	C₂×#341	C₂×C₁₁	1	1	yes	characteristic, complemented
126	C₂³×C₁₁	—	2	2	no	—
127	C₂³×C₁₁	—	4	2	no	—
128	C₂³×C₁₁	—	4	4	no	—
129	C₂³×C₁₁	—	4	2	no	—
130	C₂³×C₁₁	#121	1	1	yes	characteristic
131	C₂³×C₁₁	#121	1	1	yes	characteristic
132	C₂³×C₁₁	#126	1	4	yes	—
133	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
134	Q₈×C₁₁	—	2	4	no	—
135	Q₈×C₁₁	—	4	2	no	—
136	D₄×C₁₁	—	2	4	no	—
137	D₄×C₁₁	—	4	4	no	—
138	D₄×C₁₁	—	4	4	no	—
139	D₄×C₁₁	—	4	2	no	—
140	C₂×C₄×C₁₁	—	2	2	no	—
141	C₂×C₄×C₁₁	—	4	2	no	—
142	C₂×C₄×C₁₁	—	4	2	no	—
143	C₂×C₄×C₁₁	—	4	2	no	—
144	C₂×C₄×C₁₁	—	4	4	no	—
145	C₂×C₄×C₁₁	—	4	4	no	—
146	C₂×C₄×C₁₁	—	8	4	no	—
147	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₁	#123	1	2	yes	—
150	C₂×C₄×C₁₁	#123	1	2	yes	—
151	C₂×C₄×C₁₁	#123	1	4	yes	—
152	C₂×C₄×C₁₁	#123	1	4	yes	—
153	C₂×C₄×C₁₁	#124	1	2	yes	—
154	C₂×C₄×C₁₁	#124	1	2	yes	—
155	C₂×C₄×C₁₁	#126	1	4	yes	—
156	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
160	C₈×C₁₁	—	2	2	no	—
161	C₈×C₁₁	—	2	2	no	—
162	C₈×C₁₁	—	4	4	no	—
163	C₈×C₁₁	—	4	2	no	—
164	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
165	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
167	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
168	C₂×#117	C₂²×C₁₁	1	2	yes	—
169	#427	—	2	2	no	—
170	#427	—	2	2	no	—
171	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
172	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
173	#419	—	2	2	no	—
174	#418	—	2	2	no	—
175	#417	C₂²×C₁₁	1	8	yes	—
176	#416	—	2	4	no	—
177	#408	—	2	2	no	—
178	#408	C₂²×C₁₁	1	2	yes	—
179	#408	C₂²×C₁₁	1	2	yes	—
180	C₂×C₂²⋊C₈	—	2	2	no	—
181	#343	C₂²×C₁₁	1	8	yes	complemented
182	#341	C₂²×C₁₁	1	2	yes	complemented
183	#341	C₂²×C₁₁	1	2	yes	complemented
184	C₂²×C₁₁	—	2	2	no	—
185	C₂²×C₁₁	—	2	2	no	—
186	C₂²×C₁₁	—	2	2	no	—
187	C₂²×C₁₁	—	4	4	no	—
188	C₂²×C₁₁	—	4	2	no	—
189	C₂²×C₁₁	—	4	4	no	—
190	C₂²×C₁₁	—	8	4	no	—
191	C₂²×C₁₁	#397	1	2	yes	—
192	C₂²×C₁₁	#397	1	2	yes	—
193	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
194	C₂²×C₁₁	C₂×#126	1	2	yes	—
195	C₄×C₁₁	—	4	2	no	—
196	C₄×C₁₁	—	8	4	no	—
197	C₄×C₁₁	#397	1	2	yes	—
198	C₄×C₁₁	#397	1	2	yes	—
199	C₄×C₁₁	C₂×#123	1	1	yes	characteristic
200	C₄×C₁₁	C₂×#123	1	2	yes	—
201	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
202	C₂×#41	—	2	1	no	—
203	C₂×#41	—	2	1	no	—
204	C₂×#41	—	2	4	no	—
205	C₂×#41	—	2	4	no	—
206	C₂×#41	D₄×C₁₁	1	2	yes	—
207	C₂×#41	C₂³×C₁₁	1	2	yes	—
208	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
213	C₂×M₁₆	—	2	1	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	—	2	4	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
219	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	D₄×C₁₁	1	2	yes	—
224	C₂²×C₈	D₄×C₁₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	—	2	2	no	—
231	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	#107	—	2	4	no	—
235	#106	—	2	4	no	—
236	#103	—	2	8	no	—
237	#102	—	2	8	no	—
238	C₂²⋊C₈	—	2	4	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	C₂×C₁₁	—	2	2	no	—
241	C₂×C₁₁	—	2	2	no	—
242	C₂×C₁₁	—	2	2	no	—
243	C₂×C₁₁	—	8	2	no	—
244	C₂×C₁₁	C₂×#397	1	1	yes	characteristic
245	C₂×C₁₁	#3067	1	2	yes	—
246	C₂⁴	—	2	1	no	—
247	C₂⁴	C₁₁×#41	1	1	yes	characteristic
248	#41	—	2	8	no	—
249	#41	—	2	4	no	—
250	#41	—	2	4	no	—
251	#41	—	4	2	no	—
252	#41	—	4	2	no	—
253	#41	—	4	4	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	4	no	—
262	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
274	C₂²×C₄	C₁₁×#41	1	4	yes	—
275	C₂²×C₄	C₁₁×#41	1	4	yes	—
276	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
277	M₁₆	—	2	4	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	—	2	4	no	—
280	M₁₆	—	4	4	no	—
281	M₁₆	—	4	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₁₁	#23646	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	—	2	2	no	—
300	C₂³	—	4	2	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	2	no	—
303	C₂³	C₁₁×#121	1	1	yes	characteristic
304	C₂³	C₁₁×#121	1	1	yes	characteristic
305	C₂³	C₁₁×#126	1	4	yes	—
306	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
307	Q₈	—	2	4	no	—
308	Q₈	—	4	2	no	—
309	D₄	—	2	4	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	8	4	no	—
320	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
321	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
322	C₂×C₄	C₁₁×#123	1	2	yes	—
323	C₂×C₄	C₁₁×#123	1	2	yes	—
324	C₂×C₄	C₁₁×#123	1	4	yes	—
325	C₂×C₄	C₁₁×#123	1	4	yes	—
326	C₂×C₄	C₁₁×#124	1	2	yes	—
327	C₂×C₄	C₁₁×#124	1	2	yes	—
328	C₂×C₄	C₁₁×#126	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
332	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
333	C₈	—	2	2	no	—
334	C₈	—	2	2	no	—
335	C₈	—	4	4	no	—
336	C₈	—	4	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	8	4	no	—
344	C₂²	C₁₁×#397	1	2	yes	—
345	C₂²	C₁₁×#397	1	2	yes	—
346	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
347	C₂²	C₂×C₁₁×#126	1	2	yes	—
348	C₄	—	4	2	no	—
349	C₄	—	8	4	no	—
350	C₄	C₁₁×#397	1	2	yes	—
351	C₄	C₁₁×#397	1	2	yes	—
352	C₄	C₂×C₁₁×#123	1	1	yes	characteristic
353	C₄	C₂×C₁₁×#123	1	2	yes	—
354	C₄	C₂×C₁₁×#124	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	2	2	no	—
358	C₂	—	8	2	no	—
359	C₂	C₂×C₁₁×#397	1	1	yes	characteristic
360	C₂	C₁₁×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#121
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#427	C₂	semidirect
4. C₁₁×#2079	C₂	semidirect
5. C₁₁×#2078	C₂	semidirect
6. C₁₁×#1742	C₂	semidirect
7. C₂×C₁₁×#341	C₂	semidirect
15. C₂×C₁₁×#107	C₂²	semidirect
16. C₂×C₁₁×#106	C₂²	semidirect
25. C₁₁×#343	C₂²	semidirect
26. C₁₁×#341	C₂²	semidirect
27. C₁₁×#341	C₂²	semidirect
66. #23646	C₁₁	direct (N × H)
119. C₂×#427	C₂×C₁₁	semidirect
122. #2079	C₂×C₁₁	semidirect
123. #2078	C₂×C₁₁	semidirect
124. #1742	C₂×C₁₁	semidirect
125. C₂×#341	C₂×C₁₁	semidirect
171. C₂×#107	C₂²×C₁₁	semidirect
172. C₂×#106	C₂²×C₁₁	semidirect
181. #343	C₂²×C₁₁	semidirect
182. #341	C₂²×C₁₁	semidirect
183. #341	C₂²×C₁₁	semidirect
298. C₁₁	#23646	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#427	2
C₁₁×#2896	2
C₂×C₁₁×#408	2
C₁₁×#2079	2
C₁₁×#2078	2
C₁₁×#1742	2
C₂×C₁₁×#341	2
#23646	11

Subgroups — C11×#23646 #14600839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23646 #14600839