Subgroups — C₁₁×#23162 #14600355

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2369	C₂	1	2	yes	maximal
3	C₁₁×#1987	C₂	1	2	yes	maximal
4	C₁₁×#1943	C₂	1	2	yes	maximal
5	C₁₁×#1918	C₂	1	4	yes	maximal
6	C₁₁×#1776	C₂	1	2	yes	maximal
7	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₁₁×#500	C₄	1	8	yes	complemented
11	C₂×C₁₁×#107	C₂²	1	2	yes	—
12	C₂×C₁₁×#107	C₂²	1	2	yes	—
13	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#97	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#391	—	2	4	no	—
19	C₁₁×#389	—	2	2	no	—
20	C₁₁×#389	C₂²	1	4	yes	—
21	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
22	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₁₁×#340	C₂²	1	2	yes	—
26	C₁₁×#340	C₂²	1	4	yes	—
27	C₁₁×#340	C₂²	1	4	yes	—
28	C₁₁×#336	C₂²	1	2	yes	—
29	C₂²×Q₈×C₁₁	—	2	2	no	—
30	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×C₄⋊Q₈	—	2	4	no	—
34	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
35	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
37	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
38	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
39	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
40	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
41	C₂×C₄²×C₁₁	—	2	2	no	—
42	C₂×C₄²×C₁₁	—	2	4	no	—
43	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
44	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
45	C₁₁×#107	C₂×C₄	1	8	yes	—
46	C₁₁×#107	C₂×C₄	1	8	yes	—
47	C₁₁×#106	—	2	2	no	—
48	C₁₁×#106	Q₈	1	4	yes	complemented
49	C₁₁×C₄⋊C₈	—	2	2	no	—
50	C₁₁×#97	—	2	4	no	—
51	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
52	C₁₁×#95	—	2	4	no	—
53	C₁₁×#95	—	2	4	no	—
54	C₁₁×#95	—	2	2	no	—
55	C₁₁×#95	D₄	1	2	yes	—
56	#23162	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×Q₈×C₁₁	—	2	8	no	—
58	C₂×Q₈×C₁₁	—	8	2	no	—
59	C₂×Q₈×C₁₁	—	8	2	no	—
60	C₂²×C₄×C₁₁	—	2	2	no	—
61	C₂²×C₄×C₁₁	—	2	4	no	—
62	C₂²×C₄×C₁₁	—	2	2	no	—
63	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	2	2	no	—
69	C₂×C₈×C₁₁	—	2	1	no	—
70	C₂×C₈×C₁₁	—	2	1	no	—
71	C₂×C₈×C₁₁	—	2	2	no	—
72	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
73	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
74	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
75	C₂×C₈×C₁₁	#41	1	2	yes	—
76	C₁₁×C₄⋊C₄	—	2	8	no	—
77	C₁₁×C₄⋊C₄	—	2	4	no	—
78	C₁₁×C₄⋊C₄	—	2	4	no	—
79	C₁₁×C₄⋊C₄	—	2	2	no	—
80	C₁₁×C₄⋊C₄	—	2	2	no	—
81	C₁₁×C₄⋊C₄	—	2	2	no	—
82	C₁₁×C₄⋊C₄	—	8	4	no	—
83	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
84	C₁₁×C₄⋊C₄	C₂×Q₈	1	4	yes	—
85	C₄²×C₁₁	—	2	2	no	—
86	C₄²×C₁₁	—	2	2	no	—
87	C₄²×C₁₁	—	4	4	no	—
88	C₄²×C₁₁	—	8	4	no	—
89	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
90	C₄²×C₁₁	#41	1	2	yes	—
91	C₂×#500	C₂×C₁₁	1	1	yes	characteristic
92	#2369	C₂×C₁₁	1	2	yes	—
93	#1987	C₂×C₁₁	1	2	yes	—
94	#1943	C₂×C₁₁	1	2	yes	—
95	#1918	C₂×C₁₁	1	4	yes	—
96	#1776	C₂×C₁₁	1	2	yes	—
97	C₄×#106	C₂×C₁₁	1	1	yes	characteristic
98	#1770	C₂×C₁₁	1	1	yes	characteristic
99	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	Q₈×C₁₁	—	8	8	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	8	no	—
103	C₂×C₄×C₁₁	—	2	4	no	—
104	C₂×C₄×C₁₁	—	2	4	no	—
105	C₂×C₄×C₁₁	—	2	4	no	—
106	C₂×C₄×C₁₁	—	2	4	no	—
107	C₂×C₄×C₁₁	—	4	2	no	—
108	C₂×C₄×C₁₁	—	4	2	no	—
109	C₂×C₄×C₁₁	—	4	4	no	—
110	C₂×C₄×C₁₁	—	4	4	no	—
111	C₂×C₄×C₁₁	—	4	2	no	—
112	C₂×C₄×C₁₁	—	4	2	no	—
113	C₂×C₄×C₁₁	—	4	2	no	—
114	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
115	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
116	C₂×C₄×C₁₁	#137	1	4	yes	—
117	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
121	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
122	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
123	C₈×C₁₁	—	2	2	no	—
124	C₈×C₁₁	—	4	2	no	—
125	C₈×C₁₁	C₄×Q₈	1	4	yes	—
126	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
127	#500	C₄×C₁₁	1	8	yes	complemented
128	C₂×#107	C₂²×C₁₁	1	2	yes	—
129	C₂×#107	C₂²×C₁₁	1	2	yes	—
130	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
131	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
132	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
133	C₂×#97	C₂²×C₁₁	1	2	yes	—
134	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
135	#391	—	2	4	no	—
136	#389	—	2	2	no	—
137	#389	C₂²×C₁₁	1	4	yes	—
138	C₄×C₄⋊C₄	—	2	2	no	—
139	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
140	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
141	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
142	#340	C₂²×C₁₁	1	2	yes	—
143	#340	C₂²×C₁₁	1	4	yes	—
144	#340	C₂²×C₁₁	1	4	yes	—
145	#336	C₂²×C₁₁	1	2	yes	—
146	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
147	C₂²×C₁₁	#547	1	1	yes	characteristic
148	C₂²×C₁₁	D₄×Q₈	1	1	yes	characteristic
149	C₂²×C₁₁	C₂×#137	1	2	yes	—
150	C₂²×C₁₁	#576	1	2	yes	—
151	C₄×C₁₁	—	2	2	no	—
152	C₄×C₁₁	—	4	4	no	—
153	C₄×C₁₁	—	4	4	no	—
154	C₄×C₁₁	—	4	8	no	—
155	C₄×C₁₁	—	8	2	no	—
156	C₄×C₁₁	#441	1	4	yes	—
157	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
158	C₄×C₁₁	#519	1	1	yes	characteristic
159	C₄×C₁₁	#556	1	1	yes	characteristic
160	C₄×C₁₁	#557	1	1	yes	characteristic
161	C₂²×Q₈	—	2	2	no	—
162	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
163	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
164	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
165	C₄⋊Q₈	—	2	4	no	—
166	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	4	no	—
169	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
170	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
171	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
172	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
173	C₂×C₄²	—	2	2	no	—
174	C₂×C₄²	—	2	4	no	—
175	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
176	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
177	#107	C₂×C₄×C₁₁	1	8	yes	—
178	#107	C₂×C₄×C₁₁	1	8	yes	—
179	#106	—	2	2	no	—
180	#106	Q₈×C₁₁	1	4	yes	complemented
181	C₄⋊C₈	—	2	2	no	—
182	#97	—	2	4	no	—
183	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
184	#95	—	2	4	no	—
185	#95	—	2	4	no	—
186	#95	—	2	2	no	—
187	#95	D₄×C₁₁	1	2	yes	—
188	C₂×C₁₁	#2365	1	1	yes	characteristic
189	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
190	C₂×C₁₁	#2948	1	1	yes	characteristic
191	C₂×C₁₁	#3357	1	2	yes	—
192	C₂×C₁₁	#3385	1	2	yes	—
193	C₂×Q₈	—	2	8	no	—
194	C₂×Q₈	—	8	2	no	—
195	C₂×Q₈	—	8	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
200	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
201	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
202	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
209	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
210	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
211	C₂×C₈	C₁₁×#41	1	2	yes	—
212	C₄⋊C₄	—	2	8	no	—
213	C₄⋊C₄	—	2	4	no	—
214	C₄⋊C₄	—	2	4	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	2	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	8	4	no	—
219	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
220	C₄⋊C₄	C₂×Q₈×C₁₁	1	4	yes	—
221	C₄²	—	2	2	no	—
222	C₄²	—	2	2	no	—
223	C₄²	—	4	4	no	—
224	C₄²	—	8	4	no	—
225	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
226	C₄²	C₁₁×#41	1	2	yes	—
227	C₁₁	#23162	1	1	yes	characteristic, direct product factor, Sylow
228	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
229	Q₈	—	8	8	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	8	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	—	4	4	no	—
240	C₂×C₄	—	4	2	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	2	no	—
243	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
244	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
245	C₂×C₄	C₁₁×#137	1	4	yes	—
246	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
248	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
249	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
250	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
251	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
252	C₈	—	2	2	no	—
253	C₈	—	4	2	no	—
254	C₈	C₄×Q₈×C₁₁	1	4	yes	—
255	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
256	C₂²	C₁₁×#547	1	1	yes	characteristic
257	C₂²	D₄×Q₈×C₁₁	1	1	yes	characteristic
258	C₂²	C₂×C₁₁×#137	1	2	yes	—
259	C₂²	C₁₁×#576	1	2	yes	—
260	C₄	—	2	2	no	—
261	C₄	—	4	8	no	—
262	C₄	—	4	4	no	—
263	C₄	—	4	4	no	—
264	C₄	—	8	2	no	—
265	C₄	C₁₁×#441	1	4	yes	—
266	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
267	C₄	C₁₁×#519	1	1	yes	characteristic
268	C₄	C₁₁×#556	1	1	yes	characteristic
269	C₄	C₁₁×#557	1	1	yes	characteristic
270	C₂	C₁₁×#2365	1	1	yes	characteristic
271	C₂	C₂×C₁₁×#441	1	1	yes	characteristic
272	C₂	C₁₁×#2948	1	1	yes	characteristic
273	C₂	C₁₁×#3357	1	2	yes	—
274	C₂	C₁₁×#3385	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
10. C₁₁×#500	C₄	semidirect
48. C₁₁×#106	Q₈	semidirect
56. #23162	C₁₁	direct (N × H)
127. #500	C₄×C₁₁	semidirect
180. #106	Q₈×C₁₁	semidirect
227. C₁₁	#23162	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×#500	2
C₁₁×#2369	2
C₁₁×#1987	2
C₁₁×#1943	2
C₁₁×#1918	2
C₁₁×#1776	2
C₄×C₁₁×#106	2
C₁₁×#1770	2
#23162	11

Subgroups — C11×#23162 #14600355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23162 #14600355