Subgroups — C₂²×C₁₁×C₄⋊C₁₆ #14610587

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×C₁₆	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₄⋊C₁₆	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
5	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₁	C₄	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₆	—	2	8	no	—
8	C₂²×C₁₁×C₁₆	C₂²	1	12	yes	—
9	C₂×C₄×C₈×C₁₁	C₄	1	6	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	6	yes	—
11	C₁₁×C₄⋊C₁₆	C₂²	1	16	yes	direct product factor
12	C₂³×C₄×C₁₁	C₈	1	1	yes	characteristic
13	C₂³×C₄×C₁₁	C₈	1	1	yes	characteristic
14	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	—	2	4	no	—
16	C₂²×C₈×C₁₁	C₂×C₄	1	6	yes	—
17	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
18	C₂²×C₈×C₁₁	D₄	1	4	yes	—
19	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
20	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
21	C₂×C₄²×C₁₁	C₈	1	6	yes	—
22	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
23	C₂×C₁₁×C₁₆	—	2	24	no	—
24	C₂×C₁₁×C₁₆	C₂³	1	8	yes	—
25	C₄×C₈×C₁₁	C₂×C₄	1	12	yes	—
26	C₄×C₈×C₁₁	C₂³	1	4	yes	—
27	C₂²×C₄⋊C₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
29	C₂²×C₄×C₁₁	—	2	4	no	—
30	C₂²×C₄×C₁₁	C₁₆	1	8	yes	complemented
31	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
32	C₂²×C₄×C₁₁	C₂×C₈	1	6	yes	—
33	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
34	C₂²×C₄×C₁₁	C₂×C₈	1	6	yes	—
35	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
36	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
37	C₂×C₈×C₁₁	—	2	12	no	—
38	C₂×C₈×C₁₁	C₄⋊C₄	1	12	yes	—
39	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
40	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
41	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
42	C₂×C₈×C₁₁	C₂×Q₈	1	6	yes	—
43	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
44	C₄²×C₁₁	C₂×C₈	1	12	yes	—
45	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
46	C₁₁×C₁₆	—	2	8	no	—
47	C₂³×C₁₆	C₂×C₁₁	1	2	yes	—
48	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
49	C₂×C₄⋊C₁₆	C₂×C₁₁	1	12	yes	direct product factor
50	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
51	C₂³×C₁₁	C₂×C₁₆	1	4	yes	—
52	C₂³×C₁₁	M₃₂	1	4	yes	—
53	C₂³×C₁₁	C₂²×C₈	1	3	yes	—
54	C₂×C₄×C₁₁	—	2	12	no	—
55	C₂×C₄×C₁₁	C₄⋊C₈	1	12	yes	—
56	C₂×C₄×C₁₁	C₂×C₁₆	1	24	yes	complemented
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
58	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
59	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
60	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
61	C₂×C₄×C₁₁	C₂×M₁₆	1	6	yes	—
62	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
63	C₈×C₁₁	—	2	4	no	—
64	C₈×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
65	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
66	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
67	C₂³×C₈	C₄×C₁₁	1	1	yes	characteristic
68	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
69	C₂²×C₄²	C₄×C₁₁	1	1	yes	characteristic
70	C₂²×C₁₆	—	2	8	no	—
71	C₂²×C₁₆	C₂²×C₁₁	1	12	yes	—
72	C₂×C₄×C₈	C₄×C₁₁	1	6	yes	—
73	C₂×C₄×C₈	C₂²×C₁₁	1	6	yes	—
74	C₄⋊C₁₆	C₂²×C₁₁	1	16	yes	direct product factor
75	C₂²×C₁₁	C₄⋊C₁₆	1	16	yes	direct product factor
76	C₂²×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
77	C₂²×C₁₁	C₂²×C₁₆	1	6	yes	—
78	C₂²×C₁₁	C₂×M₃₂	1	6	yes	—
79	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
80	C₄×C₁₁	—	2	4	no	—
81	C₄×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
82	C₄×C₁₁	C₂²×C₁₆	1	8	yes	complemented
83	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
84	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
85	C₂³×C₄	C₈×C₁₁	1	1	yes	characteristic
86	C₂³×C₄	C₈×C₁₁	1	1	yes	characteristic
87	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
88	C₂²×C₈	—	2	4	no	—
89	C₂²×C₈	C₂×C₄×C₁₁	1	6	yes	—
90	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
91	C₂²×C₈	D₄×C₁₁	1	4	yes	—
92	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
93	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
94	C₂×C₄²	C₈×C₁₁	1	6	yes	—
95	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
96	C₂×C₁₆	—	2	24	no	—
97	C₂×C₁₆	C₂³×C₁₁	1	8	yes	—
98	C₄×C₈	C₂×C₄×C₁₁	1	12	yes	—
99	C₄×C₈	C₂³×C₁₁	1	4	yes	—
100	C₂×C₁₁	C₂×C₄⋊C₁₆	1	12	yes	direct product factor
101	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
102	C₂×C₁₁	C₂³×C₁₆	1	1	yes	characteristic
103	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
104	C₂⁴	C₂×C₈×C₁₁	1	1	yes	characteristic
105	C₂²×C₄	—	2	4	no	—
106	C₂²×C₄	C₁₁×C₁₆	1	8	yes	complemented
107	C₂²×C₄	C₁₁×C₄⋊C₄	1	4	yes	—
108	C₂²×C₄	C₂×C₈×C₁₁	1	6	yes	—
109	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
110	C₂²×C₄	C₂×C₈×C₁₁	1	6	yes	—
111	C₂²×C₄	C₁₁×M₁₆	1	4	yes	—
112	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
113	C₂×C₈	—	2	12	no	—
114	C₂×C₈	C₁₁×C₄⋊C₄	1	12	yes	—
115	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
116	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
117	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
118	C₂×C₈	C₂×Q₈×C₁₁	1	6	yes	—
119	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
120	C₄²	C₂×C₈×C₁₁	1	12	yes	—
121	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
122	C₁₆	—	2	8	no	—
123	C₁₁	C₂²×C₄⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³	C₁₁×C₄⋊C₈	1	4	yes	—
125	C₂³	C₂×C₁₁×C₁₆	1	4	yes	—
126	C₂³	C₁₁×M₃₂	1	4	yes	—
127	C₂³	C₂²×C₈×C₁₁	1	3	yes	—
128	C₂×C₄	—	2	12	no	—
129	C₂×C₄	C₁₁×C₄⋊C₈	1	12	yes	—
130	C₂×C₄	C₂×C₁₁×C₁₆	1	24	yes	complemented
131	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
132	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
133	C₂×C₄	C₂²×C₈×C₁₁	1	4	yes	—
134	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
135	C₂×C₄	C₂×C₁₁×M₁₆	1	6	yes	—
136	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
137	C₈	—	2	4	no	—
138	C₈	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
139	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
140	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
141	C₂²	C₁₁×C₄⋊C₁₆	1	16	yes	direct product factor
142	C₂²	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
143	C₂²	C₂²×C₁₁×C₁₆	1	6	yes	—
144	C₂²	C₂×C₁₁×M₃₂	1	6	yes	—
145	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
146	C₄	—	2	4	no	—
147	C₄	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
148	C₄	C₂²×C₁₁×C₁₆	1	8	yes	complemented
149	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
150	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
151	C₂	C₂×C₁₁×C₄⋊C₁₆	1	12	yes	direct product factor
152	C₂	C₂²×C₁₁×C₄⋊C₈	1	1	yes	characteristic
153	C₂	C₂³×C₁₁×C₁₆	1	1	yes	characteristic
154	C₂	C₂²×C₁₁×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₈×C₁₁	C₂²
commutator	C₂	C₂³×C₁₁×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle, prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₁×C₄⋊C₁₆	C₂	direct (N × H)
11. C₁₁×C₄⋊C₁₆	C₂²	direct (N × H)
27. C₂²×C₄⋊C₁₆	C₁₁	direct (N × H)
30. C₂²×C₄×C₁₁	C₁₆	semidirect
49. C₂×C₄⋊C₁₆	C₂×C₁₁	direct (N × H)
56. C₂×C₄×C₁₁	C₂×C₁₆	semidirect
74. C₄⋊C₁₆	C₂²×C₁₁	direct (N × H)
75. C₂²×C₁₁	C₄⋊C₁₆	direct (N × H)
82. C₄×C₁₁	C₂²×C₁₆	semidirect
100. C₂×C₁₁	C₂×C₄⋊C₁₆	direct (N × H)
106. C₂²×C₄	C₁₁×C₁₆	semidirect
123. C₁₁	C₂²×C₄⋊C₁₆	direct (N × H)
130. C₂×C₄	C₂×C₁₁×C₁₆	semidirect
141. C₂²	C₁₁×C₄⋊C₁₆	direct (N × H)
148. C₄	C₂²×C₁₁×C₁₆	semidirect
151. C₂	C₂×C₁₁×C₄⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×C₁₆	2
C₂²×C₄×C₈×C₁₁	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂²×C₄⋊C₁₆	11

Subgroups — C22×C11×C4⋊C16 #14610587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₄⋊C₁₆ #14610587