Subgroups — C₂×C₁₁×#2161 #14610606

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#108	C₂	1	2	yes	maximal
3	C₁₁×#2161	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₁×#368	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₁×M₁₆	—	2	2	no	—
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×M₃₂	C₄	1	4	yes	—
8	C₂×C₁₁×M₃₂	C₄	1	4	yes	—
9	C₂×C₁₁×M₃₂	C₂²	1	4	yes	—
10	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
11	C₂×C₁₁×#108	—	2	4	no	—
12	C₂×C₁₁×#108	—	2	2	no	—
13	C₂×C₁₁×#108	C₂²	1	4	yes	—
14	C₂×C₁₁×#108	C₂²	1	8	yes	—
15	C₁₁×#368	C₂²	1	16	yes	complemented
16	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₁₁×M₁₆	—	2	8	no	—
18	C₂×C₁₁×M₁₆	—	2	4	no	—
19	C₂×C₁₁×M₁₆	—	4	4	no	—
20	C₂×C₁₁×M₁₆	—	4	2	no	—
21	C₂²×C₈×C₁₁	—	4	2	no	—
22	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₁	D₄	1	2	yes	—
25	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
27	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
30	C₁₁×M₃₂	C₂×C₄	1	16	yes	—
31	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
34	C₁₁×#108	—	2	4	no	—
35	C₁₁×#108	—	2	8	no	—
36	C₁₁×#108	C₂³	1	8	yes	—
37	C₂×#2161	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂⁴×C₁₁	Q₁₆	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₁	D₈	1	2	yes	—
42	C₂²×C₄×C₁₁	D₈	1	2	yes	—
43	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₁₁×M₁₆	—	2	8	no	—
48	C₁₁×M₁₆	—	4	8	no	—
49	C₁₁×M₁₆	—	4	4	no	—
50	C₂×C₈×C₁₁	—	4	8	no	—
51	C₂×C₈×C₁₁	—	4	4	no	—
52	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
53	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
54	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
59	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
64	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₁₁×C₁₆	C₂²×C₄	1	8	yes	—
66	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic
67	C₂²×#108	C₂×C₁₁	1	2	yes	—
68	#2161	C₂×C₁₁	1	8	yes	direct product factor
69	C₂×#368	C₂×C₁₁	1	4	yes	complemented
70	C₂³×C₁₁	—	4	2	no	—
71	C₂³×C₁₁	#107	1	2	yes	—
72	C₂³×C₁₁	#107	1	2	yes	—
73	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
74	C₂³×C₁₁	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₁	#107	1	2	yes	—
76	C₂×C₄×C₁₁	#107	1	4	yes	—
77	C₂×C₄×C₁₁	#107	1	2	yes	—
78	C₂×C₄×C₁₁	#107	1	4	yes	—
79	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
80	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
83	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
88	C₈×C₁₁	—	4	8	no	—
89	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
92	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
93	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
94	C₂²×M₁₆	—	2	2	no	—
95	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
96	C₂×M₃₂	C₄×C₁₁	1	4	yes	—
97	C₂×M₃₂	C₄×C₁₁	1	4	yes	—
98	C₂×M₃₂	C₂²×C₁₁	1	4	yes	—
99	C₂²×C₁₆	C₂²×C₁₁	1	2	yes	—
100	C₂×#108	—	2	4	no	—
101	C₂×#108	—	2	2	no	—
102	C₂×#108	C₂²×C₁₁	1	4	yes	—
103	C₂×#108	C₂²×C₁₁	1	8	yes	—
104	#368	C₂²×C₁₁	1	16	yes	complemented
105	C₂²×C₁₁	—	2	4	no	—
106	C₂²×C₁₁	—	2	2	no	—
107	C₂²×C₁₁	—	4	2	no	—
108	C₂²×C₁₁	—	4	2	no	—
109	C₂²×C₁₁	C₂×#107	1	4	yes	—
110	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
111	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
112	C₂²×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
113	C₄×C₁₁	C₂×#107	1	4	yes	—
114	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
115	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
116	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
117	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
118	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
119	C₂×M₁₆	—	2	4	no	—
120	C₂×M₁₆	—	2	8	no	—
121	C₂×M₁₆	—	4	2	no	—
122	C₂×M₁₆	—	4	4	no	—
123	C₂²×C₈	—	4	2	no	—
124	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
125	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
126	C₂²×C₈	D₄×C₁₁	1	2	yes	—
127	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
128	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
129	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
130	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
132	M₃₂	C₂×C₄×C₁₁	1	16	yes	—
133	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
134	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
135	C₂×C₁₆	C₂³×C₁₁	1	4	yes	—
136	#108	—	2	4	no	—
137	#108	—	2	8	no	—
138	#108	C₂³×C₁₁	1	8	yes	—
139	C₂×C₁₁	—	2	1	no	—
140	C₂×C₁₁	—	2	4	no	—
141	C₂×C₁₁	—	2	1	no	—
142	C₂×C₁₁	#2161	1	2	yes	direct product factor
143	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
144	C₂⁴	C₁₁×Q₁₆	1	1	yes	characteristic
145	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
146	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
147	C₂²×C₄	C₁₁×D₈	1	2	yes	—
148	C₂²×C₄	C₁₁×D₈	1	2	yes	—
149	C₂²×C₄	C₁₁×Q₁₆	1	1	yes	characteristic
150	C₂²×C₄	C₁₁×Q₁₆	1	2	yes	—
151	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
152	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
153	M₁₆	—	2	8	no	—
154	M₁₆	—	4	8	no	—
155	M₁₆	—	4	4	no	—
156	C₂×C₈	—	4	8	no	—
157	C₂×C₈	—	4	4	no	—
158	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
159	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
160	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
161	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
162	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
164	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
165	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
166	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
167	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
168	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
169	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
170	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
171	C₁₆	C₂²×C₄×C₁₁	1	8	yes	—
172	C₁₁	C₂×#2161	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³	—	4	2	no	—
174	C₂³	C₁₁×#107	1	2	yes	—
175	C₂³	C₁₁×#107	1	2	yes	—
176	C₂³	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
177	C₂³	C₂×C₁₁×Q₁₆	1	2	yes	—
178	C₂×C₄	C₁₁×#107	1	4	yes	—
179	C₂×C₄	C₁₁×#107	1	2	yes	—
180	C₂×C₄	C₁₁×#107	1	4	yes	—
181	C₂×C₄	C₁₁×#107	1	2	yes	—
182	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
184	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
186	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
187	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
188	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
189	C₂×C₄	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
190	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
191	C₈	—	4	8	no	—
192	C₈	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
193	C₈	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
194	C₈	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
195	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
196	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
197	C₂²	—	2	4	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	—	4	2	no	—
201	C₂²	C₂×C₁₁×#107	1	4	yes	—
202	C₂²	C₂×C₁₁×#107	1	1	yes	characteristic
203	C₂²	C₂×C₁₁×#107	1	1	yes	characteristic
204	C₂²	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
205	C₄	C₂×C₁₁×#107	1	4	yes	—
206	C₄	C₂×C₁₁×#107	1	1	yes	characteristic
207	C₄	C₂×C₁₁×#107	1	1	yes	characteristic
208	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
209	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
210	C₂	—	2	4	no	—
211	C₂	—	2	1	no	—
212	C₂	—	2	1	no	—
213	C₂	C₁₁×#2161	1	2	yes	direct product factor
214	C₂	C₂²×C₁₁×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂⁴×C₁₁	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2161	C₂	direct (N × H)
4. C₂×C₁₁×#368	C₂	semidirect
15. C₁₁×#368	C₂²	semidirect
37. C₂×#2161	C₁₁	direct (N × H)
68. #2161	C₂×C₁₁	direct (N × H)
69. C₂×#368	C₂×C₁₁	semidirect
104. #368	C₂²×C₁₁	semidirect
142. C₂×C₁₁	#2161	direct (N × H)
172. C₁₁	C₂×#2161	direct (N × H)
213. C₂	C₁₁×#2161	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×M₃₂	2
C₂²×C₁₁×#108	2
C₁₁×#2161	2
C₂×C₁₁×#368	2
C₂×#2161	11

Subgroups — C2×C11×#2161 #14610606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2161 #14610606