Subgroups — C₁₁×#33657 #14610850

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3058	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2238	C₂	1	8	yes	maximal, complemented
4	C₁₁×#2155	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#361	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
8	C₁₁×#568	—	2	1	no	—
9	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
10	C₁₁×#535	—	2	1	no	—
11	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
12	C₁₁×#469	C₂²	1	4	yes	—
13	C₁₁×#466	—	2	2	no	—
14	C₁₁×#430	—	2	1	no	—
15	C₁₁×#430	C₂²	1	4	yes	complemented
16	C₂×C₁₁×#108	—	2	2	no	—
17	C₂×C₁₁×#108	C₂²	1	2	yes	—
18	C₁₁×#427	C₂²	1	1	yes	characteristic
19	C₁₁×#418	—	2	1	no	—
20	C₁₁×#365	C₂²	1	8	yes	complemented
21	C₁₁×#361	C₂²	1	8	yes	—
22	C₁₁×#349	C₂²	1	4	yes	complemented
23	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
24	C₂²×D₄×C₁₁	—	2	1	no	—
25	C₂×C₁₁×D₈	—	2	1	no	—
26	C₂×C₁₁×D₈	—	2	2	no	—
27	C₂×C₁₁×D₈	—	2	2	no	—
28	C₂×C₁₁×D₈	C₂³	1	2	yes	—
29	C₁₁×#131	—	2	2	no	—
30	C₁₁×#131	—	2	2	no	—
31	C₁₁×#131	—	4	4	no	—
32	C₂×C₁₁×M₁₆	—	2	4	no	—
33	C₂×C₁₁×M₁₆	—	2	2	no	—
34	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
35	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	2	yes	—
37	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₁₁×#127	—	4	1	no	—
39	C₁₁×#124	—	4	1	no	—
40	C₁₁×#121	—	2	4	no	—
41	C₁₁×#120	—	4	2	no	—
42	C₁₁×#117	—	2	1	no	—
43	C₁₁×M₃₂	—	2	2	no	—
44	C₁₁×M₃₂	C₂³	1	4	yes	—
45	C₂×C₁₁×C₁₆	—	2	2	no	—
46	C₁₁×#108	—	2	2	no	—
47	C₁₁×#108	—	2	4	no	—
48	C₁₁×#108	C₂³	1	4	yes	—
49	C₁₁×#107	—	2	1	no	—
50	C₁₁×#106	C₂³	1	2	yes	—
51	C₁₁×#102	—	2	4	no	—
52	#33657	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₁	—	4	1	no	—
54	C₁₁×#41	—	2	2	no	—
55	C₁₁×#41	—	2	2	no	—
56	C₂×Q₈×C₁₁	SD₁₆	1	1	yes	characteristic
57	C₂×D₄×C₁₁	—	2	2	no	—
58	C₂×D₄×C₁₁	—	4	4	no	—
59	C₂×D₄×C₁₁	—	4	2	no	—
60	C₂×D₄×C₁₁	—	4	1	no	—
61	C₂×D₄×C₁₁	—	4	2	no	—
62	C₂×D₄×C₁₁	SD₁₆	1	2	yes	—
63	C₂×D₄×C₁₁	SD₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₁₁×D₈	—	2	4	no	—
67	C₁₁×D₈	—	4	1	no	—
68	C₁₁×D₈	—	4	1	no	—
69	C₁₁×M₁₆	—	2	4	no	—
70	C₁₁×M₁₆	—	2	2	no	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	4	4	no	—
73	C₁₁×M₁₆	—	4	2	no	—
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	—	2	2	no	—
76	C₂×C₈×C₁₁	—	4	4	no	—
77	C₂×C₈×C₁₁	—	4	2	no	—
78	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₁₁	#41	1	2	yes	—
81	C₂×C₈×C₁₁	#41	1	2	yes	—
82	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
83	C₁₁×C₄⋊C₄	—	2	2	no	—
84	C₁₁×C₂²⋊C₄	—	4	1	no	—
85	C₁₁×C₂²⋊C₄	—	4	4	no	—
86	C₄²×C₁₁	—	4	1	no	—
87	C₁₁×C₁₆	—	2	4	no	—
88	#3058	C₂×C₁₁	1	1	yes	characteristic
89	#2916	C₂×C₁₁	1	1	yes	characteristic, complemented
90	#2238	C₂×C₁₁	1	8	yes	complemented
91	#2155	C₂×C₁₁	1	2	yes	complemented
92	C₂×#361	C₂×C₁₁	1	2	yes	complemented
93	#2115	C₂×C₁₁	1	1	yes	characteristic, complemented
94	C₂³×C₁₁	—	4	2	no	—
95	C₂³×C₁₁	—	8	2	no	—
96	C₂³×C₁₁	—	16	2	no	—
97	C₂³×C₁₁	C₂×SD₁₆	1	2	yes	—
98	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
99	Q₈×C₁₁	—	2	2	no	—
100	D₄×C₁₁	—	2	4	no	—
101	D₄×C₁₁	—	2	2	no	—
102	D₄×C₁₁	—	4	2	no	—
103	D₄×C₁₁	—	4	2	no	—
104	D₄×C₁₁	—	8	2	no	—
105	D₄×C₁₁	—	16	4	no	—
106	C₂×C₄×C₁₁	—	2	2	no	—
107	C₂×C₄×C₁₁	—	2	2	no	—
108	C₂×C₄×C₁₁	—	4	2	no	—
109	C₂×C₄×C₁₁	#123	1	2	yes	—
110	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
111	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
113	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
114	C₈×C₁₁	—	2	2	no	—
115	C₈×C₁₁	—	4	4	no	—
116	C₈×C₁₁	#123	1	1	yes	characteristic
117	C₈×C₁₁	#123	1	1	yes	characteristic
118	C₈×C₁₁	C₂×#41	1	2	yes	—
119	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
120	#568	—	2	1	no	—
121	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
122	#535	—	2	1	no	—
123	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
124	#469	C₂²×C₁₁	1	4	yes	—
125	#466	—	2	2	no	—
126	#430	—	2	1	no	—
127	#430	C₂²×C₁₁	1	4	yes	complemented
128	C₂×#108	—	2	2	no	—
129	C₂×#108	C₂²×C₁₁	1	2	yes	—
130	#427	C₂²×C₁₁	1	1	yes	characteristic
131	#418	—	2	1	no	—
132	#365	C₂²×C₁₁	1	8	yes	complemented
133	#361	C₂²×C₁₁	1	8	yes	—
134	#349	C₂²×C₁₁	1	4	yes	complemented
135	C₂²×C₁₁	—	2	2	no	—
136	C₂²×C₁₁	—	4	1	no	—
137	C₂²×C₁₁	—	4	2	no	—
138	C₂²×C₁₁	—	8	4	no	—
139	C₂²×C₁₁	—	8	2	no	—
140	C₂²×C₁₁	—	16	4	no	—
141	C₂²×C₁₁	#481	1	2	yes	—
142	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
143	C₄×C₁₁	—	2	2	no	—
144	C₄×C₁₁	—	8	2	no	—
145	C₄×C₁₁	#481	1	2	yes	—
146	C₄×C₁₁	C₂×#123	1	1	yes	characteristic
147	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×#41	D₄×C₁₁	1	1	yes	characteristic
149	C₂²×D₄	—	2	1	no	—
150	C₂×D₈	—	2	1	no	—
151	C₂×D₈	—	2	2	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	C₂³×C₁₁	1	2	yes	—
154	#131	—	2	2	no	—
155	#131	—	2	2	no	—
156	#131	—	4	4	no	—
157	C₂×M₁₆	—	2	4	no	—
158	C₂×M₁₆	—	2	2	no	—
159	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
160	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
161	C₂²×C₈	D₄×C₁₁	1	2	yes	—
162	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
163	#127	—	4	1	no	—
164	#124	—	4	1	no	—
165	#121	—	2	4	no	—
166	#120	—	4	2	no	—
167	#117	—	2	1	no	—
168	M₃₂	—	2	2	no	—
169	M₃₂	C₂³×C₁₁	1	4	yes	—
170	C₂×C₁₆	—	2	2	no	—
171	#108	—	2	2	no	—
172	#108	—	2	4	no	—
173	#108	C₂³×C₁₁	1	4	yes	—
174	#107	—	2	1	no	—
175	#106	C₂³×C₁₁	1	2	yes	—
176	#102	—	2	4	no	—
177	C₂×C₁₁	—	2	1	no	—
178	C₂×C₁₁	—	2	2	no	—
179	C₂×C₁₁	—	4	2	no	—
180	C₂×C₁₁	—	16	2	no	—
181	C₂×C₁₁	C₂×#481	1	1	yes	characteristic
182	C₂⁴	—	4	1	no	—
183	#41	—	2	2	no	—
184	#41	—	2	2	no	—
185	C₂×Q₈	C₁₁×SD₁₆	1	1	yes	characteristic
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	4	4	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	1	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	C₁₁×SD₁₆	1	2	yes	—
192	C₂×D₄	C₁₁×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
194	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
195	D₈	—	2	4	no	—
196	D₈	—	4	1	no	—
197	D₈	—	4	1	no	—
198	M₁₆	—	2	2	no	—
199	M₁₆	—	2	4	no	—
200	M₁₆	—	2	4	no	—
201	M₁₆	—	4	4	no	—
202	M₁₆	—	4	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	4	4	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
208	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
209	C₂×C₈	C₁₁×#41	1	2	yes	—
210	C₂×C₈	C₁₁×#41	1	2	yes	—
211	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
212	C₄⋊C₄	—	2	2	no	—
213	C₂²⋊C₄	—	4	1	no	—
214	C₂²⋊C₄	—	4	4	no	—
215	C₄²	—	4	1	no	—
216	C₁₆	—	2	4	no	—
217	C₁₁	#33657	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³	—	4	2	no	—
219	C₂³	—	8	2	no	—
220	C₂³	—	16	2	no	—
221	C₂³	C₂×C₁₁×SD₁₆	1	2	yes	—
222	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
223	Q₈	—	2	2	no	—
224	D₄	—	2	4	no	—
225	D₄	—	2	2	no	—
226	D₄	—	4	2	no	—
227	D₄	—	4	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	16	4	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	C₁₁×#123	1	2	yes	—
234	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
235	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
236	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
238	C₈	—	2	2	no	—
239	C₈	—	4	4	no	—
240	C₈	C₁₁×#123	1	1	yes	characteristic
241	C₈	C₁₁×#123	1	1	yes	characteristic
242	C₈	C₂×C₁₁×#41	1	2	yes	—
243	C₂²	—	2	2	no	—
244	C₂²	—	4	1	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	8	4	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	16	4	no	—
249	C₂²	C₁₁×#481	1	2	yes	—
250	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	8	2	no	—
253	C₄	C₁₁×#481	1	2	yes	—
254	C₄	C₂×C₁₁×#123	1	1	yes	characteristic
255	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂	—	2	1	no	—
257	C₂	—	2	2	no	—
258	C₂	—	4	2	no	—
259	C₂	—	16	2	no	—
260	C₂	C₂×C₁₁×#481	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	C₂×#481
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₁₁×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2916	C₂	semidirect
3. C₁₁×#2238	C₂	semidirect
4. C₁₁×#2155	C₂	semidirect
5. C₂×C₁₁×#361	C₂	semidirect
6. C₁₁×#2115	C₂	semidirect
15. C₁₁×#430	C₂²	semidirect
20. C₁₁×#365	C₂²	semidirect
22. C₁₁×#349	C₂²	semidirect
52. #33657	C₁₁	direct (N × H)
89. #2916	C₂×C₁₁	semidirect
90. #2238	C₂×C₁₁	semidirect
91. #2155	C₂×C₁₁	semidirect
92. C₂×#361	C₂×C₁₁	semidirect
93. #2115	C₂×C₁₁	semidirect
127. #430	C₂²×C₁₁	semidirect
132. #365	C₂²×C₁₁	semidirect
134. #349	C₂²×C₁₁	semidirect
217. C₁₁	#33657	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×#3058	2
C₁₁×#2916	2
C₁₁×#2238	2
C₁₁×#2155	2
C₂×C₁₁×#361	2
C₁₁×#2115	2
#33657	11

Subgroups — C11×#33657 #14610850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33657 #14610850