Subgroups — C₁₁×#2663 #13065501

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#123	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#397	C₂	1	2	yes	maximal, complemented
6	C₁₁×#395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#394	C₂	1	2	yes	maximal
8	C₁₁×#393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#389	C₂	1	2	yes	maximal, complemented
10	C₁₁×#388	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#123	—	2	4	no	—
16	C₁₁×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
31	C₁₁×#95	C₂²	1	1	yes	characteristic
32	C₁₁×#95	C₂²	1	1	yes	characteristic
33	C₁₁×#95	C₂²	1	2	yes	—
34	C₁₁×#95	C₂²	1	2	yes	—
35	C₁₁×#95	C₂²	1	2	yes	—
36	C₁₁×#95	C₂²	1	2	yes	—
37	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
38	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
39	C₂×Q₈×C₁₁	—	2	2	no	—
40	C₂×Q₈×C₁₁	—	4	2	no	—
41	C₂×D₄×C₁₁	—	2	2	no	—
42	C₂×D₄×C₁₁	—	4	2	no	—
43	C₂²×C₄×C₁₁	—	4	2	no	—
44	C₂²×C₄×C₁₁	D₄	1	4	yes	—
45	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
50	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
54	C₁₁×C₄⋊C₄	—	2	2	no	—
55	C₁₁×C₄⋊C₄	—	2	4	no	—
56	C₁₁×C₄⋊C₄	—	2	2	no	—
57	C₁₁×C₄⋊C₄	—	2	2	no	—
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₂²⋊C₄	—	2	4	no	—
61	C₁₁×C₂²⋊C₄	—	2	2	no	—
62	C₁₁×C₂²⋊C₄	—	2	2	no	—
63	C₁₁×C₂²⋊C₄	—	2	2	no	—
64	C₁₁×C₂²⋊C₄	—	2	4	no	—
65	C₁₁×C₂²⋊C₄	—	2	4	no	—
66	C₁₁×C₂²⋊C₄	—	4	2	no	—
67	C₄²×C₁₁	—	4	2	no	—
68	#2663	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₁	—	2	2	no	—
70	C₂³×C₁₁	—	2	2	no	—
71	C₂³×C₁₁	—	2	1	no	—
72	C₂³×C₁₁	—	2	1	no	—
73	C₂³×C₁₁	—	2	1	no	—
74	C₂³×C₁₁	—	2	2	no	—
75	C₂³×C₁₁	—	2	2	no	—
76	C₂³×C₁₁	—	2	1	no	—
77	C₂³×C₁₁	—	2	1	no	—
78	C₂³×C₁₁	C₂×D₄	1	2	yes	—
79	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
80	Q₈×C₁₁	—	4	4	no	—
81	D₄×C₁₁	—	4	4	no	—
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	1	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	4	4	no	—
103	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
105	C₂×C₄×C₁₁	#41	1	4	yes	—
106	C₂×#123	C₂×C₁₁	1	1	yes	characteristic
107	C₂×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
108	#400	C₂×C₁₁	1	1	yes	characteristic, complemented
109	#399	C₂×C₁₁	1	1	yes	characteristic, complemented
110	#397	C₂×C₁₁	1	2	yes	complemented
111	#395	C₂×C₁₁	1	1	yes	characteristic, complemented
112	#394	C₂×C₁₁	1	2	yes	—
113	#393	C₂×C₁₁	1	1	yes	characteristic, complemented
114	#389	C₂×C₁₁	1	2	yes	complemented
115	#388	C₂×C₁₁	1	2	yes	complemented
116	C₄×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
117	C₂²×C₁₁	—	2	2	no	—
118	C₂²×C₁₁	—	2	2	no	—
119	C₂²×C₁₁	—	2	2	no	—
120	C₂²×C₁₁	—	4	2	no	—
121	C₂²×C₁₁	—	4	2	no	—
122	C₂²×C₁₁	—	4	1	no	—
123	C₂²×C₁₁	—	4	1	no	—
124	C₂²×C₁₁	—	4	1	no	—
125	C₂²×C₁₁	—	4	2	no	—
126	C₂²×C₁₁	—	4	2	no	—
127	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
128	C₂²×C₁₁	C₂×#41	1	2	yes	—
129	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
130	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
131	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	—	2	4	no	—
135	C₄×C₁₁	—	4	1	no	—
136	C₄×C₁₁	—	4	2	no	—
137	C₄×C₁₁	—	4	1	no	—
138	C₄×C₁₁	—	4	2	no	—
139	C₄×C₁₁	—	4	1	no	—
140	C₄×C₁₁	—	4	2	no	—
141	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
142	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic
143	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic
144	#123	—	2	4	no	—
145	C₂²⋊Q₈	—	2	4	no	—
146	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
147	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
149	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
152	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
153	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
156	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
157	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
158	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
159	C₂×C₄²	C₂²×C₁₁	1	2	yes	—
160	#95	C₂²×C₁₁	1	1	yes	characteristic
161	#95	C₂²×C₁₁	1	1	yes	characteristic
162	#95	C₂²×C₁₁	1	2	yes	—
163	#95	C₂²×C₁₁	1	2	yes	—
164	#95	C₂²×C₁₁	1	2	yes	—
165	#95	C₂²×C₁₁	1	2	yes	—
166	C₂×C₁₁	—	4	2	no	—
167	C₂×C₁₁	—	8	1	no	—
168	C₂×C₁₁	#532	1	1	yes	characteristic
169	C₂×C₁₁	#534	1	1	yes	characteristic
170	C₂×C₁₁	#536	1	1	yes	characteristic
171	C₂×C₁₁	#539	1	2	yes	—
172	C₂×C₁₁	#542	1	2	yes	—
173	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
174	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	D₄×C₁₁	1	4	yes	—
181	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
182	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
183	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
184	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
185	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
186	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
187	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
188	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
189	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₂²⋊C₄	—	2	4	no	—
197	C₂²⋊C₄	—	2	2	no	—
198	C₂²⋊C₄	—	2	2	no	—
199	C₂²⋊C₄	—	2	2	no	—
200	C₂²⋊C₄	—	2	4	no	—
201	C₂²⋊C₄	—	2	4	no	—
202	C₂²⋊C₄	—	4	2	no	—
203	C₄²	—	4	2	no	—
204	C₁₁	#2663	1	1	yes	characteristic, direct product factor, Sylow
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	2	1	no	—
213	C₂³	—	2	1	no	—
214	C₂³	C₂×D₄×C₁₁	1	2	yes	—
215	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
216	Q₈	—	4	4	no	—
217	D₄	—	4	4	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	4	4	no	—
239	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
240	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
241	C₂×C₄	C₁₁×#41	1	4	yes	—
242	C₂²	—	2	2	no	—
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	4	1	no	—
249	C₂²	—	4	1	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
253	C₂²	C₂×C₁₁×#41	1	2	yes	—
254	C₂²	C₁₁×H(5,𝔽₂)	1	2	yes	—
255	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
256	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	4	no	—
260	C₄	—	4	1	no	—
261	C₄	—	4	2	no	—
262	C₄	—	4	1	no	—
263	C₄	—	4	2	no	—
264	C₄	—	4	1	no	—
265	C₄	—	4	2	no	—
266	C₂	—	4	2	no	—
267	C₂	—	8	1	no	—
268	C₂	C₁₁×#532	1	1	yes	characteristic
269	C₂	C₁₁×#534	1	1	yes	characteristic
270	C₂	C₁₁×#536	1	1	yes	characteristic
271	C₂	C₁₁×#539	1	2	yes	—
272	C₂	C₁₁×#542	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₂²⋊Q₈	C₂	semidirect
3. C₁₁×#400	C₂	semidirect
4. C₁₁×#399	C₂	semidirect
5. C₁₁×#397	C₂	semidirect
6. C₁₁×#395	C₂	semidirect
8. C₁₁×#393	C₂	semidirect
9. C₁₁×#389	C₂	semidirect
10. C₁₁×#388	C₂	semidirect
11. C₄×C₁₁×C₂²⋊C₄	C₂	semidirect
68. #2663	C₁₁	direct (N × H)
107. C₂×C₂²⋊Q₈	C₂×C₁₁	semidirect
108. #400	C₂×C₁₁	semidirect
109. #399	C₂×C₁₁	semidirect
110. #397	C₂×C₁₁	semidirect
111. #395	C₂×C₁₁	semidirect
113. #393	C₂×C₁₁	semidirect
114. #389	C₂×C₁₁	semidirect
115. #388	C₂×C₁₁	semidirect
116. C₄×C₂²⋊C₄	C₂×C₁₁	semidirect
204. C₁₁	#2663	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×#123	2
C₂×C₁₁×C₂²⋊Q₈	2
C₁₁×#400	2
C₁₁×#399	2
C₁₁×#397	2
C₁₁×#395	2
C₁₁×#394	2
C₁₁×#393	2
C₁₁×#389	2
C₁₁×#388	2
C₄×C₁₁×C₂²⋊C₄	2
#2663	11

Subgroups — C11×#2663 #13065501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2663 #13065501