Subgroups — C₁₁×#17824 #14595017

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2989	C₂	1	2	yes	maximal
2	C₁₁×#2922	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1574	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1573	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1572	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1570	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1569	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
11	C₁₁×#446	—	2	2	no	—
12	C₁₁×#436	—	2	2	no	—
13	C₁₁×#435	—	2	2	no	—
14	C₁₁×#435	—	2	2	no	—
15	C₁₁×#433	C₄	1	4	yes	—
16	C₁₁×#432	C₂²	1	2	yes	—
17	C₁₁×#432	C₂²	1	2	yes	—
18	C₁₁×#431	C₂²	1	2	yes	—
19	C₁₁×#431	C₂²	1	2	yes	—
20	C₁₁×#431	C₂²	1	2	yes	—
21	C₁₁×#424	C₄	1	2	yes	—
22	C₁₁×#423	C₂²	1	2	yes	—
23	C₁₁×#423	C₂²	1	2	yes	—
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₁×#408	C₄	1	2	yes	—
26	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₁₁×#335	C₂²	1	2	yes	—
29	C₁₁×#335	C₂²	1	2	yes	—
30	C₁₁×#335	C₂²	1	2	yes	—
31	C₁₁×#334	C₂²	1	2	yes	—
32	C₁₁×#334	C₂²	1	1	yes	characteristic
33	C₁₁×#334	C₂²	1	1	yes	characteristic
34	C₁₁×#334	C₂²	1	1	yes	characteristic
35	C₁₁×#334	C₂²	1	1	yes	characteristic
36	C₁₁×#334	C₂²	1	2	yes	—
37	C₁₁×#334	C₂²	1	2	yes	—
38	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₁×M₁₆	—	2	2	no	—
40	C₂×C₁₁×M₁₆	—	2	2	no	—
41	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₁	—	2	2	no	—
43	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₁	Q₈	1	1	yes	characteristic
46	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
47	C₄×D₄×C₁₁	D₄	1	2	yes	—
48	C₄×D₄×C₁₁	Q₈	1	1	yes	characteristic
49	C₄×D₄×C₁₁	Q₈	1	2	yes	—
50	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#117	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
54	C₁₁×C₄⋊C₈	—	2	2	no	—
55	C₁₁×C₄⋊C₈	—	2	2	no	—
56	C₁₁×C₄⋊C₈	—	2	2	no	—
57	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
60	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
61	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
62	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
63	C₁₁×C₂²⋊C₈	—	2	2	no	—
64	C₁₁×C₂²⋊C₈	—	2	2	no	—
65	C₁₁×C₂²⋊C₈	—	2	2	no	—
66	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
68	C₁₁×#97	—	2	2	no	—
69	C₁₁×#97	—	2	2	no	—
70	C₁₁×#97	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₁	—	2	2	no	—
72	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂³	1	2	yes	—
76	#17824	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₁₁×#41	—	4	2	no	—
78	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂×D₄×C₁₁	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
87	C₁₁×M₁₆	—	4	2	no	—
88	C₁₁×M₁₆	—	8	2	no	—
89	C₁₁×M₁₆	—	8	2	no	—
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	4	2	no	—
95	C₂×C₈×C₁₁	—	8	2	no	—
96	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
99	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
100	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
101	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
102	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
103	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
104	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
105	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
106	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₁	C₂×D₄	1	2	yes	—
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
112	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
113	#2989	C₂×C₁₁	1	2	yes	—
114	#2922	C₂×C₁₁	1	1	yes	characteristic
115	#1574	C₂×C₁₁	1	2	yes	complemented
116	#1573	C₂×C₁₁	1	2	yes	complemented
117	#1572	C₂×C₁₁	1	2	yes	complemented
118	#1570	C₂×C₁₁	1	2	yes	complemented
119	#1569	C₂×C₁₁	1	2	yes	complemented
120	#1568	C₂×C₁₁	1	1	yes	characteristic, complemented
121	#1566	C₂×C₁₁	1	1	yes	characteristic, complemented
122	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
123	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
124	Q₈×C₁₁	—	4	1	no	—
125	D₄×C₁₁	—	4	1	no	—
126	D₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	4	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	4	1	no	—
133	C₂×C₄×C₁₁	—	4	2	no	—
134	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
143	C₈×C₁₁	—	2	2	no	—
144	C₈×C₁₁	—	2	2	no	—
145	C₈×C₁₁	—	2	4	no	—
146	C₈×C₁₁	—	4	2	no	—
147	C₈×C₁₁	—	4	2	no	—
148	C₈×C₁₁	—	4	2	no	—
149	C₈×C₁₁	—	4	2	no	—
150	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
151	#446	—	2	2	no	—
152	#436	—	2	2	no	—
153	#435	—	2	2	no	—
154	#435	—	2	2	no	—
155	#433	C₄×C₁₁	1	4	yes	—
156	#432	C₂²×C₁₁	1	2	yes	—
157	#432	C₂²×C₁₁	1	2	yes	—
158	#431	C₂²×C₁₁	1	2	yes	—
159	#431	C₂²×C₁₁	1	2	yes	—
160	#431	C₂²×C₁₁	1	2	yes	—
161	#424	C₄×C₁₁	1	2	yes	—
162	#423	C₂²×C₁₁	1	2	yes	—
163	#423	C₂²×C₁₁	1	2	yes	—
164	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
165	#408	C₄×C₁₁	1	2	yes	—
166	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
168	#335	C₂²×C₁₁	1	2	yes	—
169	#335	C₂²×C₁₁	1	2	yes	—
170	#335	C₂²×C₁₁	1	2	yes	—
171	#334	C₂²×C₁₁	1	2	yes	—
172	#334	C₂²×C₁₁	1	1	yes	characteristic
173	#334	C₂²×C₁₁	1	1	yes	characteristic
174	#334	C₂²×C₁₁	1	1	yes	characteristic
175	#334	C₂²×C₁₁	1	1	yes	characteristic
176	#334	C₂²×C₁₁	1	2	yes	—
177	#334	C₂²×C₁₁	1	2	yes	—
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	—	2	2	no	—
180	C₂²×C₁₁	—	2	2	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	—	2	2	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₁₁	—	2	1	no	—
186	C₄×C₁₁	—	2	2	no	—
187	C₄×C₁₁	—	2	2	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	2	1	no	—
190	C₄×C₁₁	—	2	1	no	—
191	C₄×C₁₁	—	2	2	no	—
192	C₄×C₁₁	#568	1	2	yes	—
193	C₄×C₁₁	#577	1	2	yes	—
194	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
200	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
201	C₄×Q₈	Q₈×C₁₁	1	1	yes	characteristic
202	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
203	C₄×D₄	D₄×C₁₁	1	2	yes	—
204	C₄×D₄	Q₈×C₁₁	1	1	yes	characteristic
205	C₄×D₄	Q₈×C₁₁	1	2	yes	—
206	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
207	#117	C₂×C₄×C₁₁	1	2	yes	—
208	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
209	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
210	C₄⋊C₈	—	2	2	no	—
211	C₄⋊C₈	—	2	2	no	—
212	C₄⋊C₈	—	2	2	no	—
213	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
214	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
215	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
216	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
217	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
218	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
219	C₂²⋊C₈	—	2	2	no	—
220	C₂²⋊C₈	—	2	2	no	—
221	C₂²⋊C₈	—	2	2	no	—
222	C₂²⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
223	C₂²⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
224	#97	—	2	2	no	—
225	#97	—	2	2	no	—
226	#97	C₂×C₄×C₁₁	1	2	yes	—
227	C₄×C₈	—	2	2	no	—
228	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
229	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
230	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
231	C₄×C₈	C₂³×C₁₁	1	2	yes	—
232	C₂×C₁₁	—	4	1	no	—
233	C₂×C₁₁	—	4	2	no	—
234	C₂×C₁₁	#2905	1	1	yes	characteristic
235	C₂×C₁₁	#2912	1	1	yes	characteristic
236	C₂×C₁₁	#2916	1	1	yes	characteristic
237	#41	—	4	2	no	—
238	C₂×Q₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
239	C₂×D₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
240	C₂×D₄	C₁₁×C₄⋊C₄	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
244	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
245	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
246	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
247	M₁₆	—	4	2	no	—
248	M₁₆	—	8	2	no	—
249	M₁₆	—	8	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	8	2	no	—
256	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
257	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
259	C₄⋊C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
260	C₄⋊C₄	C₁₁×C₄⋊C₄	1	2	yes	—
261	C₄⋊C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
262	C₄⋊C₄	C₁₁×C₄⋊C₄	1	2	yes	—
263	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	2	yes	—
264	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	2	yes	—
265	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	2	yes	—
266	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
267	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
268	C₄²	C₂×D₄×C₁₁	1	2	yes	—
269	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₄²	C₂×Q₈×C₁₁	1	1	yes	characteristic
271	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
272	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
273	C₁₁	#17824	1	1	yes	characteristic, direct product factor, Sylow
274	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
275	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
276	Q₈	—	4	1	no	—
277	D₄	—	4	1	no	—
278	D₄	—	4	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
288	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
289	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
290	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
291	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
293	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
294	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
295	C₈	—	2	2	no	—
296	C₈	—	2	2	no	—
297	C₈	—	2	4	no	—
298	C₈	—	4	2	no	—
299	C₈	—	4	2	no	—
300	C₈	—	4	2	no	—
301	C₈	—	4	2	no	—
302	C₂²	—	2	1	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	1	no	—
308	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
309	C₄	—	2	1	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	2	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	2	no	—
316	C₄	C₁₁×#568	1	2	yes	—
317	C₄	C₁₁×#577	1	2	yes	—
318	C₂	—	4	1	no	—
319	C₂	—	4	2	no	—
320	C₂	C₁₁×#2905	1	1	yes	characteristic
321	C₂	C₁₁×#2912	1	1	yes	characteristic
322	C₂	C₁₁×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1574	C₂	semidirect
4. C₁₁×#1573	C₂	semidirect
5. C₁₁×#1572	C₂	semidirect
6. C₁₁×#1570	C₂	semidirect
7. C₁₁×#1569	C₂	semidirect
8. C₁₁×#1568	C₂	semidirect
9. C₁₁×#1566	C₂	semidirect
76. #17824	C₁₁	direct (N × H)
115. #1574	C₂×C₁₁	semidirect
116. #1573	C₂×C₁₁	semidirect
117. #1572	C₂×C₁₁	semidirect
118. #1570	C₂×C₁₁	semidirect
119. #1569	C₂×C₁₁	semidirect
120. #1568	C₂×C₁₁	semidirect
121. #1566	C₂×C₁₁	semidirect
273. C₁₁	#17824	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×#2989	2
C₁₁×#2922	2
C₁₁×#1574	2
C₁₁×#1573	2
C₁₁×#1572	2
C₁₁×#1570	2
C₁₁×#1569	2
C₁₁×#1568	2
C₁₁×#1566	2
#17824	11

Subgroups — C11×#17824 #14595017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17824 #14595017