Subgroups — C₁₁×#21978 #14599171

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1940	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1851	C₂	1	4	yes	maximal
6	C₁₁×#1842	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1831	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
9	C₂×C₁₁×#117	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#432	—	2	4	no	—
12	C₁₁×#423	—	2	4	no	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	—
18	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×#97	C₂²	1	2	yes	—
20	C₄×C₁₁×C₄⋊C₄	C₄	1	2	yes	—
21	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
22	C₄×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₁₁×#376	C₄	1	1	yes	characteristic
25	C₁₁×#376	C₄	1	1	yes	characteristic
26	C₄³×C₁₁	C₂²	1	2	yes	—
27	C₁₁×#336	C₂²	1	8	yes	—
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
31	C₂×C₁₁×M₁₆	—	2	4	no	—
32	C₂×C₁₁×M₁₆	—	4	4	no	—
33	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
35	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
36	C₁₁×#117	—	2	8	no	—
37	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
38	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₁	D₄	1	4	yes	—
45	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
46	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×C₄⋊C₈	—	2	4	no	—
50	C₁₁×C₄⋊C₈	—	2	4	no	—
51	C₁₁×C₄⋊C₈	—	2	2	no	—
52	C₁₁×C₄⋊C₈	—	2	2	no	—
53	C₁₁×C₄⋊C₈	—	4	8	no	—
54	C₁₁×C₂²⋊C₈	—	2	4	no	—
55	C₁₁×#97	—	2	4	no	—
56	C₁₁×#95	C₂×C₄	1	2	yes	—
57	C₁₁×#95	C₂×C₄	1	2	yes	—
58	C₁₁×#95	C₂×C₄	1	2	yes	—
59	C₁₁×#95	C₂×C₄	1	2	yes	—
60	#21978	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	—	2	4	no	—
63	C₂²×C₄×C₁₁	—	2	2	no	—
64	C₂²×C₄×C₁₁	—	2	2	no	—
65	C₂²×C₄×C₁₁	—	4	2	no	—
66	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
78	C₁₁×M₁₆	—	4	8	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	4	no	—
82	C₂×C₈×C₁₁	—	2	4	no	—
83	C₂×C₈×C₁₁	—	2	8	no	—
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₁₁×C₄⋊C₄	—	2	8	no	—
86	C₁₁×C₂²⋊C₄	—	2	8	no	—
87	C₄²×C₁₁	—	2	4	no	—
88	C₄²×C₁₁	—	2	4	no	—
89	C₄²×C₁₁	—	2	4	no	—
90	C₄²×C₁₁	—	4	4	no	—
91	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
92	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
93	C₄²×C₁₁	M₁₆	1	8	yes	complemented
94	C₄²×C₁₁	C₂×D₄	1	2	yes	—
95	C₄²×C₁₁	C₂×D₄	1	2	yes	—
96	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
97	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
98	C₂×#432	C₂×C₁₁	1	1	yes	characteristic
99	C₂×#423	C₂×C₁₁	1	1	yes	characteristic
100	C₄×#117	C₂×C₁₁	1	1	yes	characteristic
101	#1940	C₂×C₁₁	1	4	yes	complemented
102	#1851	C₂×C₁₁	1	4	yes	—
103	#1842	C₂×C₁₁	1	2	yes	complemented
104	#1831	C₂×C₁₁	1	2	yes	complemented
105	C₂³×C₁₁	—	2	2	no	—
106	C₂³×C₁₁	—	2	2	no	—
107	C₂³×C₁₁	—	2	2	no	—
108	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
109	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	—	2	4	no	—
111	C₂×C₄×C₁₁	—	2	2	no	—
112	C₂×C₄×C₁₁	—	2	2	no	—
113	C₂×C₄×C₁₁	—	2	2	no	—
114	C₂×C₄×C₁₁	—	2	4	no	—
115	C₂×C₄×C₁₁	—	2	2	no	—
116	C₂×C₄×C₁₁	—	2	2	no	—
117	C₂×C₄×C₁₁	—	2	2	no	—
118	C₂×C₄×C₁₁	—	2	4	no	—
119	C₂×C₄×C₁₁	—	2	8	no	—
120	C₂×C₄×C₁₁	—	2	4	no	—
121	C₂×C₄×C₁₁	—	2	4	no	—
122	C₂×C₄×C₁₁	—	2	4	no	—
123	C₂×C₄×C₁₁	—	4	4	no	—
124	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₁₁	C₂×M₁₆	1	8	yes	—
130	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
131	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
134	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
135	C₈×C₁₁	—	4	2	no	—
136	C₈×C₁₁	—	4	4	no	—
137	C₈×C₁₁	—	4	2	no	—
138	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
139	C₂×#117	C₄×C₁₁	1	2	yes	—
140	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
141	#432	—	2	4	no	—
142	#423	—	2	4	no	—
143	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
144	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
145	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
149	C₂×#97	C₂²×C₁₁	1	2	yes	—
150	C₄×C₄⋊C₄	C₄×C₁₁	1	2	yes	—
151	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
152	C₄×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
153	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
154	#376	C₄×C₁₁	1	1	yes	characteristic
155	#376	C₄×C₁₁	1	1	yes	characteristic
156	C₄³	C₂²×C₁₁	1	2	yes	—
157	#336	C₂²×C₁₁	1	8	yes	—
158	C₂²×C₁₁	—	2	2	no	—
159	C₂²×C₁₁	—	2	2	no	—
160	C₂²×C₁₁	—	2	2	no	—
161	C₂²×C₁₁	—	4	4	no	—
162	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×C₁₁	#520	1	2	yes	—
164	C₂²×C₁₁	C₂²×M₁₆	1	2	yes	—
165	C₂²×C₁₁	#568	1	2	yes	—
166	C₄×C₁₁	—	2	2	no	—
167	C₄×C₁₁	—	2	2	no	—
168	C₄×C₁₁	—	2	2	no	—
169	C₄×C₁₁	—	2	2	no	—
170	C₄×C₁₁	—	2	8	no	—
171	C₄×C₁₁	—	4	4	no	—
172	C₄×C₁₁	#423	1	4	yes	—
173	C₄×C₁₁	#535	1	1	yes	characteristic
174	C₄×C₁₁	#536	1	1	yes	characteristic
175	C₄×C₁₁	#544	1	2	yes	—
176	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
177	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
178	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
179	C₂×M₁₆	—	2	4	no	—
180	C₂×M₁₆	—	4	4	no	—
181	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
182	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
183	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
184	#117	—	2	8	no	—
185	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
186	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
187	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
188	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
189	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
190	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
191	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
192	C₂×C₄²	D₄×C₁₁	1	4	yes	—
193	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
194	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
195	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
196	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
197	C₄⋊C₈	—	2	4	no	—
198	C₄⋊C₈	—	2	4	no	—
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	2	2	no	—
201	C₄⋊C₈	—	4	8	no	—
202	C₂²⋊C₈	—	2	4	no	—
203	#97	—	2	4	no	—
204	#95	C₂×C₄×C₁₁	1	2	yes	—
205	#95	C₂×C₄×C₁₁	1	2	yes	—
206	#95	C₂×C₄×C₁₁	1	2	yes	—
207	#95	C₂×C₄×C₁₁	1	2	yes	—
208	C₂×C₁₁	—	4	2	no	—
209	C₂×C₁₁	#2317	1	1	yes	characteristic
210	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
211	C₂×C₁₁	#2905	1	1	yes	characteristic
212	C₂×C₁₁	#2989	1	4	yes	—
213	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	2	no	—
216	C₂²×C₄	—	2	2	no	—
217	C₂²×C₄	—	4	2	no	—
218	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
219	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
220	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
221	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
222	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
223	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
224	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
225	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
226	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
227	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
228	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
229	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
230	M₁₆	—	4	8	no	—
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	2	4	no	—
234	C₂×C₈	—	2	4	no	—
235	C₂×C₈	—	2	8	no	—
236	C₂×C₈	—	2	4	no	—
237	C₄⋊C₄	—	2	8	no	—
238	C₂²⋊C₄	—	2	8	no	—
239	C₄²	—	2	4	no	—
240	C₄²	—	2	4	no	—
241	C₄²	—	2	4	no	—
242	C₄²	—	4	4	no	—
243	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
244	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
245	C₄²	C₁₁×M₁₆	1	8	yes	complemented
246	C₄²	C₂×D₄×C₁₁	1	2	yes	—
247	C₄²	C₂×D₄×C₁₁	1	2	yes	—
248	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
249	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
250	C₁₁	#21978	1	1	yes	characteristic, direct product factor, Sylow
251	C₂³	—	2	2	no	—
252	C₂³	—	2	2	no	—
253	C₂³	—	2	2	no	—
254	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
255	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	4	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	2	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	2	8	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	4	4	no	—
270	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
271	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
272	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
273	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
274	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
275	C₂×C₄	C₂×C₁₁×M₁₆	1	8	yes	—
276	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
277	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
278	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
279	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
280	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
281	C₈	—	4	4	no	—
282	C₈	—	4	2	no	—
283	C₈	—	4	2	no	—
284	C₂²	—	2	2	no	—
285	C₂²	—	2	2	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	4	4	no	—
288	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
289	C₂²	C₁₁×#520	1	2	yes	—
290	C₂²	C₂²×C₁₁×M₁₆	1	2	yes	—
291	C₂²	C₁₁×#568	1	2	yes	—
292	C₄	—	2	2	no	—
293	C₄	—	2	2	no	—
294	C₄	—	2	2	no	—
295	C₄	—	2	8	no	—
296	C₄	—	2	2	no	—
297	C₄	—	4	4	no	—
298	C₄	C₁₁×#423	1	4	yes	—
299	C₄	C₁₁×#535	1	1	yes	characteristic
300	C₄	C₁₁×#536	1	1	yes	characteristic
301	C₄	C₁₁×#544	1	2	yes	—
302	C₂	—	4	2	no	—
303	C₂	C₁₁×#2317	1	1	yes	characteristic
304	C₂	C₂×C₁₁×#423	1	1	yes	characteristic
305	C₂	C₁₁×#2905	1	1	yes	characteristic
306	C₂	C₁₁×#2989	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1940	C₂	semidirect
6. C₁₁×#1842	C₂	semidirect
7. C₁₁×#1831	C₂	semidirect
60. #21978	C₁₁	direct (N × H)
93. C₄²×C₁₁	M₁₆	semidirect
101. #1940	C₂×C₁₁	semidirect
103. #1842	C₂×C₁₁	semidirect
104. #1831	C₂×C₁₁	semidirect
245. C₄²	C₁₁×M₁₆	semidirect
250. C₁₁	#21978	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×#432	2
C₂×C₁₁×#423	2
C₄×C₁₁×#117	2
C₁₁×#1940	2
C₁₁×#1851	2
C₁₁×#1842	2
C₁₁×#1831	2
#21978	11

Subgroups — C11×#21978 #14599171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21978 #14599171