Subgroups — C₁₁×#23360 #14600553

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3152	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1905	C₂	1	4	yes	maximal, complemented
3	C₁₁×#1902	C₂	1	4	yes	maximal, complemented
4	C₁₁×#1886	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1884	C₂	1	2	yes	maximal
6	C₁₁×#1841	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#137	C₂²	1	4	yes	—
8	C₁₁×#568	C₂²	1	2	yes	—
9	C₁₁×#532	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₁₁×#519	C₂²	1	2	yes	—
12	C₁₁×#497	C₄	1	4	yes	complemented
13	C₁₁×#494	C₄	1	2	yes	complemented
14	C₁₁×#492	C₄	1	2	yes	complemented
15	C₁₁×#421	C₂²	1	4	yes	—
16	C₁₁×#419	C₂²	1	4	yes	—
17	C₂×C₁₁×#101	C₂²	1	2	yes	—
18	C₁₁×#410	C₂²	1	2	yes	—
19	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₁₁×#344	C₂²	1	4	yes	—
21	C₁₁×#339	C₂²	1	4	yes	—
22	C₁₁×#338	C₂²	1	2	yes	—
23	C₁₁×H(3,ℤ/4)	C₂²	1	2	yes	—
24	C₂×C₁₁×#41	C₂³	1	2	yes	—
25	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
26	C₁₁×#137	—	4	4	no	—
27	C₁₁×#137	—	4	4	no	—
28	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	—
29	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	—
30	C₁₁×#131	—	4	4	no	—
31	C₂×C₁₁×M₁₆	—	4	2	no	—
32	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
33	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
34	C₁₁×C₄⋊Q₈	—	4	1	no	—
35	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
36	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
37	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
38	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
39	C₁₁×#124	C₂×C₄	1	2	yes	—
40	C₁₁×#121	—	4	1	no	—
41	C₄×Q₈×C₁₁	—	4	4	no	—
42	C₄×D₄×C₁₁	—	4	1	no	—
43	C₁₁×#117	—	4	2	no	—
44	C₁₁×#117	C₂³	1	4	yes	—
45	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#104	—	4	4	no	—
48	C₁₁×#103	—	4	4	no	—
49	C₁₁×#101	—	4	2	no	—
50	C₁₁×#99	—	4	2	no	—
51	C₁₁×#97	C₂×C₄	1	2	yes	—
52	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
53	#23360	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₁₁×#41	—	2	4	no	—
55	C₁₁×#41	—	2	4	no	—
56	C₂×Q₈×C₁₁	—	2	2	no	—
57	C₂×Q₈×C₁₁	—	2	4	no	—
58	C₂×Q₈×C₁₁	—	2	4	no	—
59	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
60	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
61	C₂×D₄×C₁₁	—	2	2	no	—
62	C₂×D₄×C₁₁	—	4	1	no	—
63	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	—	2	1	no	—
65	C₂²×C₄×C₁₁	—	2	2	no	—
66	C₂²×C₄×C₁₁	—	2	2	no	—
67	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
68	C₁₁×Q₁₆	—	4	8	no	—
69	C₁₁×SD₁₆	—	4	8	no	—
70	C₁₁×M₁₆	—	2	4	no	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	2	4	no	—
73	C₁₁×M₁₆	—	4	4	no	—
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	—	4	4	no	—
76	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
77	C₁₁×C₄⋊C₄	—	2	4	no	—
78	C₁₁×C₄⋊C₄	—	4	2	no	—
79	C₁₁×C₄⋊C₄	—	4	2	no	—
80	C₁₁×C₄⋊C₄	—	4	1	no	—
81	C₁₁×C₄⋊C₄	—	4	4	no	—
82	C₁₁×C₂²⋊C₄	—	2	4	no	—
83	C₁₁×C₂²⋊C₄	—	4	2	no	—
84	C₄²×C₁₁	—	2	1	no	—
85	C₄²×C₁₁	—	2	4	no	—
86	C₄²×C₁₁	—	4	4	no	—
87	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
88	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	#3152	C₂×C₁₁	1	1	yes	characteristic
90	#1905	C₂×C₁₁	1	4	yes	complemented
91	#1902	C₂×C₁₁	1	4	yes	complemented
92	#1886	C₂×C₁₁	1	2	yes	complemented
93	#1884	C₂×C₁₁	1	2	yes	—
94	#1841	C₂×C₁₁	1	2	yes	complemented
95	C₂³×C₁₁	—	2	2	no	—
96	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
97	Q₈×C₁₁	—	2	8	no	—
98	Q₈×C₁₁	—	2	4	no	—
99	Q₈×C₁₁	—	4	4	no	—
100	D₄×C₁₁	—	2	4	no	—
101	D₄×C₁₁	—	4	4	no	—
102	D₄×C₁₁	—	8	2	no	—
103	C₂×C₄×C₁₁	—	2	1	no	—
104	C₂×C₄×C₁₁	—	2	1	no	—
105	C₂×C₄×C₁₁	—	2	2	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	2	no	—
110	C₂×C₄×C₁₁	—	4	2	no	—
111	C₂×C₄×C₁₁	—	4	2	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
115	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
116	C₈×C₁₁	—	2	4	no	—
117	C₈×C₁₁	—	4	4	no	—
118	C₂×#137	C₂²×C₁₁	1	4	yes	—
119	#568	C₂²×C₁₁	1	2	yes	—
120	#532	C₂²×C₁₁	1	1	yes	characteristic
121	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
122	#519	C₂²×C₁₁	1	2	yes	—
123	#497	C₄×C₁₁	1	4	yes	complemented
124	#494	C₄×C₁₁	1	2	yes	complemented
125	#492	C₄×C₁₁	1	2	yes	complemented
126	#421	C₂²×C₁₁	1	4	yes	—
127	#419	C₂²×C₁₁	1	4	yes	—
128	C₂×#101	C₂²×C₁₁	1	2	yes	—
129	#410	C₂²×C₁₁	1	2	yes	—
130	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
131	#344	C₂²×C₁₁	1	4	yes	—
132	#339	C₂²×C₁₁	1	4	yes	—
133	#338	C₂²×C₁₁	1	2	yes	—
134	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	—
135	C₂²×C₁₁	—	4	1	no	—
136	C₂²×C₁₁	—	4	2	no	—
137	C₂²×C₁₁	—	8	2	no	—
138	C₂²×C₁₁	#518	1	1	yes	characteristic
139	C₂²×C₁₁	#560	1	2	yes	—
140	C₄×C₁₁	—	2	2	no	—
141	C₄×C₁₁	—	4	1	no	—
142	C₄×C₁₁	—	4	2	no	—
143	C₄×C₁₁	—	4	4	no	—
144	C₄×C₁₁	—	8	4	no	—
145	C₄×C₁₁	#518	1	2	yes	—
146	C₄×C₁₁	#560	1	2	yes	—
147	C₂×#41	C₂³×C₁₁	1	2	yes	—
148	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
149	#137	—	4	4	no	—
150	#137	—	4	4	no	—
151	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	—
152	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	—
153	#131	—	4	4	no	—
154	C₂×M₁₆	—	4	2	no	—
155	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
156	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
157	C₄⋊Q₈	—	4	1	no	—
158	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
159	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
160	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
161	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
162	#124	C₂×C₄×C₁₁	1	2	yes	—
163	#121	—	4	1	no	—
164	C₄×Q₈	—	4	4	no	—
165	C₄×D₄	—	4	1	no	—
166	#117	—	4	2	no	—
167	#117	C₂³×C₁₁	1	4	yes	—
168	C₂×C₄⋊C₄	—	4	1	no	—
169	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
170	#104	—	4	4	no	—
171	#103	—	4	4	no	—
172	#101	—	4	2	no	—
173	#99	—	4	2	no	—
174	#97	C₂×C₄×C₁₁	1	2	yes	—
175	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
176	C₂×C₁₁	—	2	1	no	—
177	C₂×C₁₁	—	2	2	no	—
178	C₂×C₁₁	—	8	2	no	—
179	C₂×C₁₁	#2380	1	1	yes	characteristic
180	#41	—	2	4	no	—
181	#41	—	2	4	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	2	4	no	—
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
186	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
194	Q₁₆	—	4	8	no	—
195	SD₁₆	—	4	8	no	—
196	M₁₆	—	2	4	no	—
197	M₁₆	—	2	4	no	—
198	M₁₆	—	2	4	no	—
199	M₁₆	—	4	4	no	—
200	C₂×C₈	—	2	4	no	—
201	C₂×C₈	—	4	4	no	—
202	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄⋊C₄	—	4	4	no	—
208	C₂²⋊C₄	—	2	4	no	—
209	C₂²⋊C₄	—	4	2	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	4	no	—
212	C₄²	—	4	4	no	—
213	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
214	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
215	C₁₁	#23360	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	2	no	—
217	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
218	Q₈	—	2	8	no	—
219	Q₈	—	2	4	no	—
220	Q₈	—	4	4	no	—
221	D₄	—	2	4	no	—
222	D₄	—	4	4	no	—
223	D₄	—	8	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
235	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
236	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
237	C₈	—	2	4	no	—
238	C₈	—	4	4	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	8	2	no	—
242	C₂²	C₁₁×#518	1	1	yes	characteristic
243	C₂²	C₁₁×#560	1	2	yes	—
244	C₄	—	2	2	no	—
245	C₄	—	4	1	no	—
246	C₄	—	4	2	no	—
247	C₄	—	4	4	no	—
248	C₄	—	8	4	no	—
249	C₄	C₁₁×#518	1	2	yes	—
250	C₄	C₁₁×#560	1	2	yes	—
251	C₂	—	2	1	no	—
252	C₂	—	2	2	no	—
253	C₂	—	8	2	no	—
254	C₂	C₁₁×#2380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#2380
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#1905	C₂	semidirect
3. C₁₁×#1902	C₂	semidirect
4. C₁₁×#1886	C₂	semidirect
6. C₁₁×#1841	C₂	semidirect
12. C₁₁×#497	C₄	semidirect
13. C₁₁×#494	C₄	semidirect
14. C₁₁×#492	C₄	semidirect
53. #23360	C₁₁	direct (N × H)
90. #1905	C₂×C₁₁	semidirect
91. #1902	C₂×C₁₁	semidirect
92. #1886	C₂×C₁₁	semidirect
94. #1841	C₂×C₁₁	semidirect
123. #497	C₄×C₁₁	semidirect
124. #494	C₄×C₁₁	semidirect
125. #492	C₄×C₁₁	semidirect
215. C₁₁	#23360	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3152	2
C₁₁×#1905	2
C₁₁×#1902	2
C₁₁×#1886	2
C₁₁×#1884	2
C₁₁×#1841	2
#23360	11

Subgroups — C11×#23360 #14600553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23360 #14600553