Subgroups — C₂×C₈×A₄ #5451

Order 192.

93 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×A₄	C₂	1	1	yes	maximal, characteristic
2	C₈×A₄	C₂	1	2	yes	maximal, direct product factor
3	C₂³×C₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂²×A₄	C₄	1	1	yes	characteristic
5	C₄×A₄	C₄	1	1	yes	characteristic
6	C₄×A₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	—	4	1	no	maximal
8	C₂³×C₄	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₈	—	3	1	no	—
10	C₂²×C₈	—	3	1	no	—
11	C₂²×C₈	—	3	2	no	—
12	C₂²×C₈	C₂×C₃	1	2	yes	complemented
13	C₂×A₄	C₈	1	2	yes	direct product factor
14	C₂×A₄	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₄	—	4	1	no	—
16	C₃×C₈	—	4	2	no	—
17	C₂⁴	C₃×C₄	1	1	yes	characteristic
18	C₂²×C₄	—	3	1	no	—
19	C₂²×C₄	—	3	1	no	—
20	C₂²×C₄	—	3	1	no	—
21	C₂²×C₄	—	3	1	no	—
22	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
23	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₈	—	3	2	no	—
25	C₂×C₈	—	3	1	no	—
26	C₂×C₈	—	3	2	no	—
27	C₂×C₈	—	3	2	no	—
28	C₂×C₈	—	3	2	no	—
29	C₂×C₈	A₄	1	1	yes	characteristic, direct product factor
30	C₂²×C₃	—	4	1	no	—
31	A₄	C₂×C₈	1	1	yes	characteristic, direct product factor
32	C₃×C₄	—	4	1	no	—
33	C₃×C₄	—	4	1	no	—
34	C₂³	—	3	1	no	—
35	C₂³	—	3	2	no	—
36	C₂³	—	3	1	no	—
37	C₂³	C₃×C₈	1	2	yes	complemented
38	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
39	C₂×C₄	—	3	2	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	3	1	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	C₂×A₄	1	1	yes	characteristic
48	C₈	—	3	2	no	—
49	C₈	C₂×A₄	1	2	yes	direct product factor
50	C₂×C₃	—	4	2	no	—
51	C₂×C₃	—	4	1	no	—
52	C₂²	—	3	2	no	—
53	C₂²	—	3	1	no	—
54	C₂²	—	3	2	no	—
55	C₂²	—	3	2	no	—
56	C₂²	—	3	2	no	—
57	C₂²	—	3	1	no	—
58	C₂²	—	3	1	no	—
59	C₂²	C₂×C₃×C₈	1	1	yes	characteristic, complemented
60	C₂²	C₄×A₄	1	1	yes	characteristic
61	C₄	—	3	1	no	—
62	C₄	—	3	1	no	—
63	C₄	C₄×A₄	1	1	yes	characteristic
64	C₄	C₂²×A₄	1	1	yes	characteristic
65	C₃	—	4	1	no	Sylow
66	C₂	—	3	2	no	—
67	C₂	—	3	1	no	—
68	C₂	—	3	1	no	—
69	C₂	C₈×A₄	1	2	yes	direct product factor
70	C₂	C₂×C₄×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	A₄
commutator, hypocenter	C₂²	C₂×C₃×C₈
Frattini	C₄	C₂²×A₄
Fitting	C₂³×C₈	C₃
socle	C₂⁴	C₃×C₄
prime radical	C₂²×A₄	C₄
cosocle	C₂²×C₄	C₂²×C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×A₄	C₂	direct (N × H)
3. C₂³×C₈	C₃	semidirect
12. C₂²×C₈	C₂×C₃	semidirect
13. C₂×A₄	C₈	direct (N × H)
29. C₂×C₈	A₄	direct (N × H)
31. A₄	C₂×C₈	direct (N × H)
37. C₂³	C₃×C₈	semidirect
49. C₈	C₂×A₄	direct (N × H)
59. C₂²	C₂×C₃×C₈	semidirect
69. C₂	C₈×A₄	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×C₄×A₄	2
C₈×A₄	2
C₂³×C₈	3
C₂×C₃×C₈	4

Subgroups — C2×C8×A4 #5451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×A₄ #5451