Subgroups — C₂×A₄×C₁₆ #73273

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×A₄	C₂	1	1	yes	maximal, characteristic
2	A₄×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂³×C₁₆	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×C₄×A₄	C₄	1	1	yes	characteristic
5	C₈×A₄	C₄	1	1	yes	characteristic
6	C₈×A₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₆	—	4	1	no	maximal
8	C₂³×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₁₆	—	3	1	no	—
10	C₂²×C₁₆	—	3	1	no	—
11	C₂²×C₁₆	—	3	2	no	—
12	C₂²×C₁₆	C₂×C₃	1	2	yes	complemented
13	C₂²×A₄	C₈	1	1	yes	characteristic
14	C₄×A₄	C₈	1	1	yes	characteristic
15	C₄×A₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₈	—	4	1	no	—
17	C₃×C₁₆	—	4	2	no	—
18	C₂³×C₄	C₃×C₄	1	1	yes	characteristic
19	C₂²×C₈	—	3	1	no	—
20	C₂²×C₈	—	3	1	no	—
21	C₂²×C₈	—	3	1	no	—
22	C₂²×C₈	—	3	1	no	—
23	C₂²×C₈	C₃×C₄	1	1	yes	characteristic
24	C₂²×C₈	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₁₆	—	3	2	no	—
26	C₂×C₁₆	—	3	1	no	—
27	C₂×C₁₆	—	3	2	no	—
28	C₂×C₁₆	—	3	2	no	—
29	C₂×C₁₆	—	3	2	no	—
30	C₂×C₁₆	A₄	1	1	yes	characteristic, direct product factor
31	C₂×A₄	C₁₆	1	2	yes	direct product factor
32	C₂×A₄	C₂×C₈	1	1	yes	characteristic
33	C₂×C₃×C₄	—	4	1	no	—
34	C₃×C₈	—	4	1	no	—
35	C₃×C₈	—	4	1	no	—
36	C₂⁴	C₃×C₈	1	1	yes	characteristic
37	C₂²×C₄	—	3	1	no	—
38	C₂²×C₄	—	3	1	no	—
39	C₂²×C₄	—	3	1	no	—
40	C₂²×C₄	—	3	1	no	—
41	C₂²×C₄	C₃×C₈	1	1	yes	characteristic
42	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
43	C₂×C₈	—	3	2	no	—
44	C₂×C₈	—	3	1	no	—
45	C₂×C₈	—	3	1	no	—
46	C₂×C₈	—	3	1	no	—
47	C₂×C₈	—	3	1	no	—
48	C₂×C₈	—	3	1	no	—
49	C₂×C₈	—	3	1	no	—
50	C₂×C₈	—	3	1	no	—
51	C₂×C₈	C₂×A₄	1	1	yes	characteristic
52	C₁₆	—	3	2	no	—
53	C₁₆	C₂×A₄	1	2	yes	direct product factor
54	C₂²×C₃	—	4	1	no	—
55	A₄	C₂×C₁₆	1	1	yes	characteristic, direct product factor
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	4	1	no	—
58	C₂³	—	3	1	no	—
59	C₂³	—	3	2	no	—
60	C₂³	—	3	1	no	—
61	C₂³	C₃×C₁₆	1	2	yes	complemented
62	C₂³	C₂×C₃×C₈	1	1	yes	characteristic
63	C₂×C₄	—	3	2	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	C₄×A₄	1	1	yes	characteristic
72	C₈	—	3	1	no	—
73	C₈	—	3	1	no	—
74	C₈	C₄×A₄	1	1	yes	characteristic
75	C₈	C₂²×A₄	1	1	yes	characteristic
76	C₂×C₃	—	4	2	no	—
77	C₂×C₃	—	4	1	no	—
78	C₂²	—	3	2	no	—
79	C₂²	—	3	1	no	—
80	C₂²	—	3	2	no	—
81	C₂²	—	3	2	no	—
82	C₂²	—	3	2	no	—
83	C₂²	—	3	1	no	—
84	C₂²	—	3	1	no	—
85	C₂²	C₂×C₃×C₁₆	1	1	yes	characteristic, complemented
86	C₂²	C₈×A₄	1	1	yes	characteristic
87	C₄	—	3	1	no	—
88	C₄	—	3	1	no	—
89	C₄	C₈×A₄	1	1	yes	characteristic
90	C₄	C₂×C₄×A₄	1	1	yes	characteristic
91	C₃	—	4	1	no	Sylow
92	C₂	—	3	2	no	—
93	C₂	—	3	1	no	—
94	C₂	—	3	1	no	—
95	C₂	A₄×C₁₆	1	2	yes	direct product factor
96	C₂	C₂×C₈×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	A₄
commutator, hypocenter	C₂²	C₂×C₃×C₁₆
Frattini	C₈	C₂²×A₄
Fitting	C₂³×C₁₆	C₃
socle	C₂⁴	C₃×C₈
prime radical	C₂²×A₄	C₈
cosocle	C₂²×C₈	C₂²×C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. A₄×C₁₆	C₂	direct (N × H)
3. C₂³×C₁₆	C₃	semidirect
12. C₂²×C₁₆	C₂×C₃	semidirect
30. C₂×C₁₆	A₄	direct (N × H)
31. C₂×A₄	C₁₆	direct (N × H)
53. C₁₆	C₂×A₄	direct (N × H)
55. A₄	C₂×C₁₆	direct (N × H)
61. C₂³	C₃×C₁₆	semidirect
85. C₂²	C₂×C₃×C₁₆	semidirect
95. C₂	A₄×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
C₂×C₈×A₄	2
A₄×C₁₆	2
C₂³×C₁₆	3
C₂×C₃×C₁₆	4

Subgroups — C2×A4×C16 #73273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄×C₁₆ #73273