Subgroups — C₁₁×#21973 #14599166

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2283	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1939	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1850	C₂	1	4	yes	maximal
6	C₁₁×#1843	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1832	C₂	1	2	yes	maximal, complemented
8	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×#431	—	2	4	no	—
11	C₂×C₁₁×C₄⋊C₈	—	2	4	no	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	—
17	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#383	C₄	1	2	yes	—
20	C₁₁×#382	C₄	1	2	yes	—
21	C₁₁×#381	C₄	1	2	yes	—
22	C₁₁×#380	C₄	1	2	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
24	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₁₁×#376	C₂²	1	2	yes	—
26	C₁₁×#336	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	4	no	—
31	C₂²×C₈×C₁₁	—	4	4	no	—
32	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
35	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
36	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	4	yes	—
40	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
41	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
42	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×C₄⋊C₈	—	2	4	no	—
45	C₁₁×C₄⋊C₈	—	2	4	no	—
46	C₁₁×C₄⋊C₈	—	2	2	no	—
47	C₁₁×C₄⋊C₈	—	2	2	no	—
48	C₁₁×C₄⋊C₈	—	4	8	no	—
49	C₁₁×C₂²⋊C₈	—	2	4	no	—
50	C₄×C₈×C₁₁	—	2	4	no	—
51	C₁₁×#95	C₂×C₄	1	4	yes	—
52	C₁₁×#95	C₂×C₄	1	4	yes	—
53	C₁₁×#95	C₂×C₄	1	4	yes	—
54	C₁₁×#95	C₂×C₄	1	4	yes	—
55	#21973	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	—	2	4	no	—
58	C₂²×C₄×C₁₁	—	2	4	no	—
59	C₂²×C₄×C₁₁	—	2	2	no	—
60	C₂²×C₄×C₁₁	—	2	2	no	—
61	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
62	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
71	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
72	C₂×C₈×C₁₁	—	2	2	no	—
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	—	2	4	no	—
76	C₂×C₈×C₁₁	—	2	8	no	—
77	C₂×C₈×C₁₁	—	2	4	no	—
78	C₂×C₈×C₁₁	—	4	8	no	—
79	C₁₁×C₄⋊C₄	—	2	8	no	—
80	C₁₁×C₂²⋊C₄	—	2	8	no	—
81	C₄²×C₁₁	—	2	4	no	—
82	C₄²×C₁₁	—	2	4	no	—
83	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
84	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
85	C₄²×C₁₁	C₂×D₄	1	2	yes	—
86	C₄²×C₁₁	C₂×D₄	1	2	yes	—
87	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
88	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
89	C₂×#431	C₂×C₁₁	1	1	yes	characteristic
90	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
91	#2283	C₂×C₁₁	1	1	yes	characteristic
92	#1939	C₂×C₁₁	1	4	yes	complemented
93	#1850	C₂×C₁₁	1	4	yes	—
94	#1843	C₂×C₁₁	1	2	yes	complemented
95	#1832	C₂×C₁₁	1	2	yes	complemented
96	C₂³×C₁₁	—	2	2	no	—
97	C₂³×C₁₁	—	2	2	no	—
98	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
99	C₂³×C₁₁	#131	1	4	yes	—
100	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	2	no	—
104	C₂×C₄×C₁₁	—	2	2	no	—
105	C₂×C₄×C₁₁	—	2	8	no	—
106	C₂×C₄×C₁₁	—	2	2	no	—
107	C₂×C₄×C₁₁	—	2	2	no	—
108	C₂×C₄×C₁₁	—	2	4	no	—
109	C₂×C₄×C₁₁	—	2	8	no	—
110	C₂×C₄×C₁₁	—	2	8	no	—
111	C₂×C₄×C₁₁	—	2	8	no	—
112	C₂×C₄×C₁₁	—	2	8	no	—
113	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
117	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₁₁	#131	1	4	yes	—
119	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
121	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
122	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
123	C₈×C₁₁	—	4	2	no	—
124	C₈×C₁₁	—	4	4	no	—
125	C₈×C₁₁	—	4	2	no	—
126	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
127	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
128	#431	—	2	4	no	—
129	C₂×C₄⋊C₈	—	2	4	no	—
130	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
131	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
133	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
134	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	—
135	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
136	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
137	#383	C₄×C₁₁	1	2	yes	—
138	#382	C₄×C₁₁	1	2	yes	—
139	#381	C₄×C₁₁	1	2	yes	—
140	#380	C₄×C₁₁	1	2	yes	—
141	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
142	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
143	#376	C₂²×C₁₁	1	2	yes	—
144	#336	C₂²×C₁₁	1	8	yes	—
145	C₂²×C₁₁	—	2	2	no	—
146	C₂²×C₁₁	—	2	2	no	—
147	C₂²×C₁₁	—	2	8	no	—
148	C₂²×C₁₁	#424	1	4	yes	—
149	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₁₁	#520	1	2	yes	—
151	C₂²×C₁₁	C₂×#131	1	2	yes	—
152	C₂²×C₁₁	C₂×#131	1	2	yes	—
153	C₄×C₁₁	—	2	2	no	—
154	C₄×C₁₁	—	2	2	no	—
155	C₄×C₁₁	—	2	2	no	—
156	C₄×C₁₁	—	2	2	no	—
157	C₄×C₁₁	—	4	8	no	—
158	C₄×C₁₁	#424	1	4	yes	—
159	C₄×C₁₁	#535	1	1	yes	characteristic
160	C₄×C₁₁	#536	1	1	yes	characteristic
161	C₄×C₁₁	#544	1	2	yes	—
162	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
163	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
164	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
165	C₂²×C₈	—	2	4	no	—
166	C₂²×C₈	—	4	4	no	—
167	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
168	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
169	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
170	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
171	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
172	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
173	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
174	C₂×C₄²	D₄×C₁₁	1	4	yes	—
175	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
176	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
177	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
178	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
179	C₄⋊C₈	—	2	4	no	—
180	C₄⋊C₈	—	2	4	no	—
181	C₄⋊C₈	—	2	2	no	—
182	C₄⋊C₈	—	2	2	no	—
183	C₄⋊C₈	—	4	8	no	—
184	C₂²⋊C₈	—	2	4	no	—
185	C₄×C₈	—	2	4	no	—
186	#95	C₂×C₄×C₁₁	1	4	yes	—
187	#95	C₂×C₄×C₁₁	1	4	yes	—
188	#95	C₂×C₄×C₁₁	1	4	yes	—
189	#95	C₂×C₄×C₁₁	1	4	yes	—
190	C₂×C₁₁	—	2	4	no	—
191	C₂×C₁₁	#2317	1	1	yes	characteristic
192	C₂×C₁₁	C₂×#424	1	1	yes	characteristic
193	C₂×C₁₁	C₂×#424	1	1	yes	characteristic
194	C₂×C₁₁	#2994	1	4	yes	—
195	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
196	C₂²×C₄	—	2	4	no	—
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
201	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
202	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
203	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
204	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
205	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
206	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
207	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
209	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
210	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	4	no	—
215	C₂×C₈	—	2	8	no	—
216	C₂×C₈	—	2	4	no	—
217	C₂×C₈	—	4	8	no	—
218	C₄⋊C₄	—	2	8	no	—
219	C₂²⋊C₄	—	2	8	no	—
220	C₄²	—	2	4	no	—
221	C₄²	—	2	4	no	—
222	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
223	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
224	C₄²	C₂×D₄×C₁₁	1	2	yes	—
225	C₄²	C₂×D₄×C₁₁	1	2	yes	—
226	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
227	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
228	C₁₁	#21973	1	1	yes	characteristic, direct product factor, Sylow
229	C₂³	—	2	2	no	—
230	C₂³	—	2	2	no	—
231	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
232	C₂³	C₁₁×#131	1	4	yes	—
233	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	8	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	4	no	—
242	C₂×C₄	—	2	8	no	—
243	C₂×C₄	—	2	8	no	—
244	C₂×C₄	—	2	8	no	—
245	C₂×C₄	—	2	8	no	—
246	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
247	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
248	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
249	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
250	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
251	C₂×C₄	C₁₁×#131	1	4	yes	—
252	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
253	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
254	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
255	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
256	C₈	—	4	4	no	—
257	C₈	—	4	2	no	—
258	C₈	—	4	2	no	—
259	C₂²	—	2	2	no	—
260	C₂²	—	2	8	no	—
261	C₂²	—	2	2	no	—
262	C₂²	C₁₁×#424	1	4	yes	—
263	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
264	C₂²	C₁₁×#520	1	2	yes	—
265	C₂²	C₂×C₁₁×#131	1	2	yes	—
266	C₂²	C₂×C₁₁×#131	1	2	yes	—
267	C₄	—	2	2	no	—
268	C₄	—	2	2	no	—
269	C₄	—	2	2	no	—
270	C₄	—	2	2	no	—
271	C₄	—	4	8	no	—
272	C₄	C₁₁×#424	1	4	yes	—
273	C₄	C₁₁×#535	1	1	yes	characteristic
274	C₄	C₁₁×#536	1	1	yes	characteristic
275	C₄	C₁₁×#544	1	2	yes	—
276	C₂	—	2	4	no	—
277	C₂	C₁₁×#2317	1	1	yes	characteristic
278	C₂	C₂×C₁₁×#424	1	1	yes	characteristic
279	C₂	C₂×C₁₁×#424	1	1	yes	characteristic
280	C₂	C₁₁×#2994	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×#1939	C₂	semidirect
6. C₁₁×#1843	C₂	semidirect
7. C₁₁×#1832	C₂	semidirect
55. #21973	C₁₁	direct (N × H)
92. #1939	C₂×C₁₁	semidirect
94. #1843	C₂×C₁₁	semidirect
95. #1832	C₂×C₁₁	semidirect
228. C₁₁	#21973	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×#431	2
C₂²×C₁₁×C₄⋊C₈	2
C₁₁×#2283	2
C₁₁×#1939	2
C₁₁×#1850	2
C₁₁×#1843	2
C₁₁×#1832	2
#21973	11

Subgroups — C11×#21973 #14599166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21973 #14599166