Subgroups — C₁₁×#22281 #14599474

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3150	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2931	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1963	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1876	C₂	1	8	yes	maximal, complemented
5	C₁₁×#1838	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#135	C₂²	1	4	yes	—
8	C₂×C₁₁×#131	C₂²	1	4	yes	—
9	C₁₁×#532	C₂²	1	2	yes	—
10	C₁₁×#497	C₄	1	4	yes	complemented
11	C₁₁×#496	C₄	1	4	yes	complemented
12	C₁₁×#436	—	2	2	no	—
13	C₁₁×#436	—	2	2	no	—
14	C₈×D₄×C₁₁	—	2	2	no	—
15	C₈×D₄×C₁₁	—	2	2	no	—
16	C₁₁×#423	C₂²	1	2	yes	—
17	C₂×C₁₁×#104	C₂²	1	8	yes	—
18	C₁₁×#408	C₂²	1	4	yes	—
19	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#376	C₂²	1	1	yes	characteristic
22	C₁₁×#341	C₂²	1	4	yes	—
23	C₁₁×#336	C₂²	1	4	yes	—
24	C₂×C₁₁×#41	C₂³	1	4	yes	—
25	C₁₁×#135	—	4	8	no	—
26	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	—
28	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
29	C₁₁×#131	—	4	8	no	—
30	C₂×C₁₁×M₁₆	—	2	4	no	—
31	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
32	C₂²×C₈×C₁₁	—	2	4	no	—
33	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
35	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
36	C₁₁×#127	C₂×C₄	1	2	yes	—
37	C₁₁×#124	C₂×C₄	1	4	yes	—
38	C₁₁×#121	—	2	2	no	—
39	C₁₁×#121	—	2	2	no	—
40	C₄×D₄×C₁₁	—	2	2	no	—
41	C₄×D₄×C₁₁	—	2	2	no	—
42	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×C₄⋊C₈	—	2	2	no	—
45	C₁₁×C₄⋊C₈	—	2	2	no	—
46	C₁₁×#104	—	4	8	no	—
47	C₁₁×C₂²⋊C₈	—	2	4	no	—
48	C₁₁×C₂²⋊C₈	—	2	4	no	—
49	C₁₁×#97	C₂×C₄	1	4	yes	—
50	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
51	C₄×C₈×C₁₁	D₄	1	2	yes	—
52	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₁₁×#95	—	2	2	no	—
54	#22281	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₁₁×#41	—	2	8	no	—
56	C₁₁×#41	—	2	8	no	—
57	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
58	C₂×D₄×C₁₁	—	2	4	no	—
59	C₂×D₄×C₁₁	—	2	2	no	—
60	C₂×D₄×C₁₁	—	2	2	no	—
61	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
62	C₂²×C₄×C₁₁	—	2	4	no	—
63	C₂²×C₄×C₁₁	—	2	2	no	—
64	C₂²×C₄×C₁₁	#41	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
66	C₁₁×Q₁₆	—	4	4	no	—
67	C₁₁×SD₁₆	—	4	8	no	—
68	C₁₁×D₈	—	4	4	no	—
69	C₁₁×M₁₆	—	2	8	no	—
70	C₁₁×M₁₆	—	4	8	no	—
71	C₂×C₈×C₁₁	—	2	4	no	—
72	C₂×C₈×C₁₁	—	2	4	no	—
73	C₂×C₈×C₁₁	—	2	4	no	—
74	C₂×C₈×C₁₁	—	4	8	no	—
75	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
76	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
78	C₁₁×C₄⋊C₄	—	2	2	no	—
79	C₁₁×C₄⋊C₄	—	2	2	no	—
80	C₁₁×C₂²⋊C₄	—	2	4	no	—
81	C₁₁×C₂²⋊C₄	—	2	4	no	—
82	C₄²×C₁₁	—	2	4	no	—
83	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
84	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
86	#3150	C₂×C₁₁	1	1	yes	characteristic
87	#2931	C₂×C₁₁	1	2	yes	complemented
88	#1963	C₂×C₁₁	1	2	yes	complemented
89	#1876	C₂×C₁₁	1	8	yes	complemented
90	#1838	C₂×C₁₁	1	1	yes	characteristic, complemented
91	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
92	C₂³×C₁₁	—	2	4	no	—
93	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
94	Q₈×C₁₁	—	2	8	no	—
95	D₄×C₁₁	—	2	8	no	—
96	D₄×C₁₁	—	4	4	no	—
97	D₄×C₁₁	—	4	4	no	—
98	D₄×C₁₁	—	4	8	no	—
99	C₂×C₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	4	4	no	—
102	C₂×C₄×C₁₁	—	4	4	no	—
103	C₂×C₄×C₁₁	—	4	4	no	—
104	C₂×C₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
106	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
107	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
110	C₈×C₁₁	—	2	4	no	—
111	C₈×C₁₁	—	2	2	no	—
112	C₈×C₁₁	—	2	2	no	—
113	C₈×C₁₁	—	4	4	no	—
114	C₂×#135	C₂²×C₁₁	1	4	yes	—
115	C₂×#131	C₂²×C₁₁	1	4	yes	—
116	#532	C₂²×C₁₁	1	2	yes	—
117	#497	C₄×C₁₁	1	4	yes	complemented
118	#496	C₄×C₁₁	1	4	yes	complemented
119	#436	—	2	2	no	—
120	#436	—	2	2	no	—
121	C₈×D₄	—	2	2	no	—
122	C₈×D₄	—	2	2	no	—
123	#423	C₂²×C₁₁	1	2	yes	—
124	C₂×#104	C₂²×C₁₁	1	8	yes	—
125	#408	C₂²×C₁₁	1	4	yes	—
126	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
128	#376	C₂²×C₁₁	1	1	yes	characteristic
129	#341	C₂²×C₁₁	1	4	yes	—
130	#336	C₂²×C₁₁	1	4	yes	—
131	C₂²×C₁₁	—	2	2	no	—
132	C₂²×C₁₁	—	4	4	no	—
133	C₂²×C₁₁	—	4	4	no	—
134	C₂²×C₁₁	—	4	4	no	—
135	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
136	C₂²×C₁₁	#540	1	2	yes	—
137	C₄×C₁₁	—	2	2	no	—
138	C₄×C₁₁	—	2	2	no	—
139	C₄×C₁₁	—	4	4	no	—
140	C₄×C₁₁	—	8	2	no	—
141	C₄×C₁₁	#518	1	2	yes	—
142	C₄×C₁₁	#535	1	2	yes	—
143	C₂×#41	C₂³×C₁₁	1	4	yes	—
144	#135	—	4	8	no	—
145	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
146	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	—
147	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
148	#131	—	4	8	no	—
149	C₂×M₁₆	—	2	4	no	—
150	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
151	C₂²×C₈	—	2	4	no	—
152	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
153	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
154	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
155	#127	C₂×C₄×C₁₁	1	2	yes	—
156	#124	C₂×C₄×C₁₁	1	4	yes	—
157	#121	—	2	2	no	—
158	#121	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₄×D₄	—	2	2	no	—
161	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
162	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	#104	—	4	8	no	—
166	C₂²⋊C₈	—	2	4	no	—
167	C₂²⋊C₈	—	2	4	no	—
168	#97	C₂×C₄×C₁₁	1	4	yes	—
169	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
170	C₄×C₈	D₄×C₁₁	1	2	yes	—
171	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
172	#95	—	2	2	no	—
173	C₂×C₁₁	—	2	2	no	—
174	C₂×C₁₁	—	8	4	no	—
175	C₂×C₁₁	#2328	1	1	yes	characteristic
176	C₂×C₁₁	#2955	1	2	yes	—
177	#41	—	2	8	no	—
178	#41	—	2	8	no	—
179	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
180	C₂×D₄	—	2	4	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
184	C₂²×C₄	—	2	4	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	C₁₁×#41	1	2	yes	—
187	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
188	Q₁₆	—	4	4	no	—
189	SD₁₆	—	4	8	no	—
190	D₈	—	4	4	no	—
191	M₁₆	—	2	8	no	—
192	M₁₆	—	4	8	no	—
193	C₂×C₈	—	2	4	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	2	4	no	—
196	C₂×C₈	—	4	8	no	—
197	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
198	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
199	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
200	C₄⋊C₄	—	2	2	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₄²	—	2	4	no	—
205	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
206	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
207	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
208	C₁₁	#22281	1	1	yes	characteristic, direct product factor, Sylow
209	C₂³	—	2	4	no	—
210	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
211	Q₈	—	2	8	no	—
212	D₄	—	2	8	no	—
213	D₄	—	4	4	no	—
214	D₄	—	4	4	no	—
215	D₄	—	4	8	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	4	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
223	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
224	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
225	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
226	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
227	C₈	—	2	4	no	—
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	4	4	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	4	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	4	4	no	—
235	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
236	C₂²	C₁₁×#540	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	4	4	no	—
240	C₄	—	8	2	no	—
241	C₄	C₁₁×#518	1	2	yes	—
242	C₄	C₁₁×#535	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	8	4	no	—
245	C₂	C₁₁×#2328	1	1	yes	characteristic
246	C₂	C₁₁×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2931	C₂	semidirect
3. C₁₁×#1963	C₂	semidirect
4. C₁₁×#1876	C₂	semidirect
5. C₁₁×#1838	C₂	semidirect
6. C₁₁×#1746	C₂	semidirect
10. C₁₁×#497	C₄	semidirect
11. C₁₁×#496	C₄	semidirect
54. #22281	C₁₁	direct (N × H)
87. #2931	C₂×C₁₁	semidirect
88. #1963	C₂×C₁₁	semidirect
89. #1876	C₂×C₁₁	semidirect
90. #1838	C₂×C₁₁	semidirect
91. #1746	C₂×C₁₁	semidirect
117. #497	C₄×C₁₁	semidirect
118. #496	C₄×C₁₁	semidirect
208. C₁₁	#22281	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×#3150	2
C₁₁×#2931	2
C₁₁×#1963	2
C₁₁×#1876	2
C₁₁×#1838	2
C₁₁×#1746	2
#22281	11

Subgroups — C11×#22281 #14599474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22281 #14599474