Subgroups — C₁₁×#22269 #14599462

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×#127	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1957	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1879	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×D₈	C₂²	1	4	yes	—
8	C₂×C₁₁×#127	C₂²	1	2	yes	—
9	C₂×C₄×D₄×C₁₁	—	2	2	no	—
10	C₂×C₄×D₄×C₁₁	—	2	2	no	—
11	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
12	C₁₁×#493	C₄	1	8	yes	complemented
13	C₂×C₁₁×#102	C₂²	1	8	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#390	—	2	2	no	—
17	C₁₁×#390	—	2	2	no	—
18	C₁₁×#390	C₂²	1	4	yes	—
19	C₁₁×#384	C₂²	1	2	yes	—
20	C₄³×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#340	C₂²	1	4	yes	—
22	C₁₁×#336	C₂²	1	4	yes	—
23	C₂²×D₄×C₁₁	—	2	2	no	—
24	C₂²×D₄×C₁₁	—	2	2	no	—
25	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
26	C₂³×C₄×C₁₁	—	2	4	no	—
27	C₂×C₁₁×D₈	—	4	8	no	—
28	C₂×C₁₁×D₈	C₂×C₄	1	16	yes	complemented
29	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
31	C₁₁×#127	—	2	4	no	—
32	C₁₁×#127	C₂×C₄	1	8	yes	complemented
33	C₄×D₄×C₁₁	—	4	8	no	—
34	C₄×D₄×C₁₁	—	4	8	no	—
35	C₄×D₄×C₁₁	—	4	8	no	—
36	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
38	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
39	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
40	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
41	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
42	C₂×C₄²×C₁₁	D₄	1	2	yes	—
43	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#102	—	4	8	no	—
48	C₄×C₈×C₁₁	—	2	2	no	—
49	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
50	#22269	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁴×C₁₁	—	2	4	no	—
52	C₂×D₄×C₁₁	—	2	8	no	—
53	C₂×D₄×C₁₁	—	2	8	no	—
54	C₂×D₄×C₁₁	—	2	4	no	—
55	C₂×D₄×C₁₁	—	2	8	no	—
56	C₂×D₄×C₁₁	—	2	8	no	—
57	C₂×D₄×C₁₁	—	4	4	no	—
58	C₂×D₄×C₁₁	—	4	4	no	—
59	C₂×D₄×C₁₁	—	4	4	no	—
60	C₂×D₄×C₁₁	—	4	4	no	—
61	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
62	C₂²×C₄×C₁₁	—	2	4	no	—
63	C₂²×C₄×C₁₁	—	4	8	no	—
64	C₂²×C₄×C₁₁	—	4	8	no	—
65	C₂²×C₄×C₁₁	—	4	8	no	—
66	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
68	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
71	C₁₁×D₈	—	4	16	no	—
72	C₂×C₈×C₁₁	—	2	2	no	—
73	C₂×C₈×C₁₁	—	2	4	no	—
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
76	C₁₁×C₄⋊C₄	—	2	8	no	—
77	C₁₁×C₄⋊C₄	—	4	4	no	—
78	C₁₁×C₄⋊C₄	—	4	4	no	—
79	C₁₁×C₂²⋊C₄	—	4	8	no	—
80	C₁₁×C₂²⋊C₄	—	4	8	no	—
81	C₁₁×C₂²⋊C₄	—	4	8	no	—
82	C₄²×C₁₁	—	2	2	no	—
83	C₄²×C₁₁	—	2	4	no	—
84	C₄²×C₁₁	—	2	4	no	—
85	C₄²×C₁₁	D₈	1	4	yes	complemented
86	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
87	C₄²×C₁₁	#41	1	2	yes	—
88	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
89	C₄×#127	C₂×C₁₁	1	2	yes	complemented
90	#1957	C₂×C₁₁	1	2	yes	complemented
91	#1879	C₂×C₁₁	1	8	yes	complemented
92	#1834	C₂×C₁₁	1	1	yes	characteristic, complemented
93	#1744	C₂×C₁₁	1	1	yes	characteristic, complemented
94	C₂³×C₁₁	—	2	8	no	—
95	C₂³×C₁₁	—	4	4	no	—
96	C₂³×C₁₁	—	4	4	no	—
97	C₂³×C₁₁	—	4	4	no	—
98	C₂³×C₁₁	—	4	4	no	—
99	C₂³×C₁₁	—	4	4	no	—
100	C₂³×C₁₁	—	4	4	no	—
101	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
102	D₄×C₁₁	—	2	16	no	—
103	D₄×C₁₁	—	4	8	no	—
104	D₄×C₁₁	—	4	16	no	—
105	D₄×C₁₁	—	4	16	no	—
106	C₂×C₄×C₁₁	—	2	2	no	—
107	C₂×C₄×C₁₁	—	2	2	no	—
108	C₂×C₄×C₁₁	—	2	2	no	—
109	C₂×C₄×C₁₁	—	2	2	no	—
110	C₂×C₄×C₁₁	—	2	2	no	—
111	C₂×C₄×C₁₁	—	4	4	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	4	4	no	—
114	C₂×C₄×C₁₁	—	8	16	no	—
115	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
116	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
117	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
118	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
119	C₂×C₄×C₁₁	#135	1	2	yes	—
120	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
121	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
123	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
124	C₈×C₁₁	—	2	4	no	—
125	C₈×C₁₁	—	4	2	no	—
126	C₂²×D₈	C₂²×C₁₁	1	4	yes	—
127	C₂×#127	C₂²×C₁₁	1	2	yes	—
128	C₂×C₄×D₄	—	2	2	no	—
129	C₂×C₄×D₄	—	2	2	no	—
130	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
131	#493	C₄×C₁₁	1	8	yes	complemented
132	C₂×#102	C₂²×C₁₁	1	8	yes	—
133	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
135	#390	—	2	2	no	—
136	#390	—	2	2	no	—
137	#390	C₂²×C₁₁	1	4	yes	—
138	#384	C₂²×C₁₁	1	2	yes	—
139	C₄³	C₂²×C₁₁	1	1	yes	characteristic
140	#340	C₂²×C₁₁	1	4	yes	—
141	#336	C₂²×C₁₁	1	4	yes	—
142	C₂²×C₁₁	—	4	8	no	—
143	C₂²×C₁₁	—	4	8	no	—
144	C₂²×C₁₁	—	4	8	no	—
145	C₂²×C₁₁	—	8	4	no	—
146	C₂²×C₁₁	—	8	4	no	—
147	C₂²×C₁₁	—	8	4	no	—
148	C₂²×C₁₁	—	8	4	no	—
149	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
150	C₂²×C₁₁	#535	1	2	yes	—
151	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
152	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
153	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
154	C₄×C₁₁	—	2	4	no	—
155	C₄×C₁₁	—	4	2	no	—
156	C₄×C₁₁	—	8	4	no	—
157	C₄×C₁₁	C₄×D₈	1	4	yes	—
158	C₄×C₁₁	#442	1	4	yes	—
159	C₄×C₁₁	#518	1	2	yes	—
160	C₄×C₁₁	#540	1	2	yes	—
161	C₂²×D₄	—	2	2	no	—
162	C₂²×D₄	—	2	2	no	—
163	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
164	C₂³×C₄	—	2	4	no	—
165	C₂×D₈	—	4	8	no	—
166	C₂×D₈	C₂×C₄×C₁₁	1	16	yes	complemented
167	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
168	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
169	#127	—	2	4	no	—
170	#127	C₂×C₄×C₁₁	1	8	yes	complemented
171	C₄×D₄	—	4	8	no	—
172	C₄×D₄	—	4	8	no	—
173	C₄×D₄	—	4	8	no	—
174	C₂×C₄⋊C₄	—	2	2	no	—
175	C₂×C₄⋊C₄	—	2	2	no	—
176	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
177	C₂×C₂²⋊C₄	—	2	4	no	—
178	C₂×C₂²⋊C₄	—	2	4	no	—
179	C₂×C₂²⋊C₄	—	2	4	no	—
180	C₂×C₄²	D₄×C₁₁	1	2	yes	—
181	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
182	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
183	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
184	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
185	#102	—	4	8	no	—
186	C₄×C₈	—	2	2	no	—
187	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
188	C₂×C₁₁	—	8	8	no	—
189	C₂×C₁₁	#2328	1	1	yes	characteristic
190	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
191	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
192	C₂×C₁₁	#3205	1	2	yes	—
193	C₂×C₁₁	#3207	1	2	yes	—
194	C₂⁴	—	2	4	no	—
195	C₂×D₄	—	2	8	no	—
196	C₂×D₄	—	2	8	no	—
197	C₂×D₄	—	2	4	no	—
198	C₂×D₄	—	2	8	no	—
199	C₂×D₄	—	2	8	no	—
200	C₂×D₄	—	4	4	no	—
201	C₂×D₄	—	4	4	no	—
202	C₂×D₄	—	4	4	no	—
203	C₂×D₄	—	4	4	no	—
204	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	4	8	no	—
207	C₂²×C₄	—	4	8	no	—
208	C₂²×C₄	—	4	8	no	—
209	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
210	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
211	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
212	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
213	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
214	D₈	—	4	16	no	—
215	C₂×C₈	—	2	4	no	—
216	C₂×C₈	—	2	2	no	—
217	C₂×C₈	—	2	4	no	—
218	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
219	C₄⋊C₄	—	2	8	no	—
220	C₄⋊C₄	—	4	4	no	—
221	C₄⋊C₄	—	4	4	no	—
222	C₂²⋊C₄	—	4	8	no	—
223	C₂²⋊C₄	—	4	8	no	—
224	C₂²⋊C₄	—	4	8	no	—
225	C₄²	—	2	2	no	—
226	C₄²	—	2	4	no	—
227	C₄²	—	2	4	no	—
228	C₄²	C₁₁×D₈	1	4	yes	complemented
229	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
230	C₄²	C₁₁×#41	1	2	yes	—
231	C₁₁	#22269	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³	—	2	8	no	—
233	C₂³	—	4	4	no	—
234	C₂³	—	4	4	no	—
235	C₂³	—	4	4	no	—
236	C₂³	—	4	4	no	—
237	C₂³	—	4	4	no	—
238	C₂³	—	4	4	no	—
239	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
240	D₄	—	2	16	no	—
241	D₄	—	4	8	no	—
242	D₄	—	4	16	no	—
243	D₄	—	4	16	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	4	4	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	8	16	no	—
253	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
254	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
255	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
256	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
257	C₂×C₄	C₁₁×#135	1	2	yes	—
258	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
259	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
260	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
261	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
262	C₈	—	2	4	no	—
263	C₈	—	4	2	no	—
264	C₂²	—	4	8	no	—
265	C₂²	—	4	8	no	—
266	C₂²	—	4	8	no	—
267	C₂²	—	8	4	no	—
268	C₂²	—	8	4	no	—
269	C₂²	—	8	4	no	—
270	C₂²	—	8	4	no	—
271	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
272	C₂²	C₁₁×#535	1	2	yes	—
273	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
274	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
275	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
276	C₄	—	2	4	no	—
277	C₄	—	4	2	no	—
278	C₄	—	8	4	no	—
279	C₄	C₄×C₁₁×D₈	1	4	yes	—
280	C₄	C₁₁×#442	1	4	yes	—
281	C₄	C₁₁×#518	1	2	yes	—
282	C₄	C₁₁×#540	1	2	yes	—
283	C₂	—	8	8	no	—
284	C₂	C₁₁×#2328	1	1	yes	characteristic
285	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
286	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
287	C₂	C₁₁×#3205	1	2	yes	—
288	C₂	C₁₁×#3207	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₁×#127	C₂	semidirect
3. C₁₁×#1957	C₂	semidirect
4. C₁₁×#1879	C₂	semidirect
5. C₁₁×#1834	C₂	semidirect
6. C₁₁×#1744	C₂	semidirect
12. C₁₁×#493	C₄	semidirect
28. C₂×C₁₁×D₈	C₂×C₄	semidirect
32. C₁₁×#127	C₂×C₄	semidirect
49. C₄×C₈×C₁₁	C₂×C₄	semidirect
50. #22269	C₁₁	direct (N × H)
85. C₄²×C₁₁	D₈	semidirect
89. C₄×#127	C₂×C₁₁	semidirect
90. #1957	C₂×C₁₁	semidirect
91. #1879	C₂×C₁₁	semidirect
92. #1834	C₂×C₁₁	semidirect
93. #1744	C₂×C₁₁	semidirect
131. #493	C₄×C₁₁	semidirect
166. C₂×D₈	C₂×C₄×C₁₁	semidirect
170. #127	C₂×C₄×C₁₁	semidirect
187. C₄×C₈	C₂×C₄×C₁₁	semidirect
228. C₄²	C₁₁×D₈	semidirect
231. C₁₁	#22269	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×#493	2
C₄×C₁₁×#127	2
C₁₁×#1957	2
C₁₁×#1879	2
C₁₁×#1834	2
C₁₁×#1744	2
#22269	11

Subgroups — C11×#22269 #14599462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22269 #14599462