Subgroups — C₂×C₄×C₃⋊C₈ #4920

Order 192.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₄×C₃⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₈	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₄	C₄	1	2	yes	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃×C₄²	C₄	1	2	yes	—
8	C₃×C₄²	C₂²	1	2	yes	—
9	C₂×C₃⋊C₈	C₄	1	8	yes	direct product factor
10	C₂×C₃⋊C₈	C₂²	1	4	yes	—
11	C₂²×C₈	—	3	2	no	—
12	C₂×C₄²	D₃	1	1	yes	characteristic
13	C₄×C₈	—	3	4	no	—
14	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₄	C₈	1	8	yes	complemented
16	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
17	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
19	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
20	C₃⋊C₈	C₂×C₄	1	8	yes	direct product factor
21	C₂²×C₄	Dic₃	1	2	yes	—
22	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
23	C₂×C₈	—	3	8	no	—
24	C₂×C₈	—	3	4	no	—
25	C₄²	Dic₃	1	2	yes	—
26	C₄²	C₂×D₃	1	2	yes	—
27	C₂²×C₃	C₄²	1	2	yes	—
28	C₂²×C₃	C₂×C₈	1	4	yes	—
29	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
30	C₃×C₄	C₄²	1	2	yes	—
31	C₃×C₄	C₂×C₈	1	8	yes	complemented
32	C₃×C₄	C₂²×C₄	1	2	yes	—
33	C₂³	C₂×Dic₃	1	1	yes	characteristic
34	C₂×C₄	C₃⋊C₈	1	8	yes	direct product factor
35	C₂×C₄	C₄×D₃	1	4	yes	—
36	C₂×C₄	C₂×Dic₃	1	4	yes	—
37	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
38	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
39	C₈	—	3	8	no	—
40	C₂×C₃	C₄×C₈	1	4	yes	complemented
41	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₃	C₂²×C₈	1	2	yes	—
43	C₂²	C₂×C₃⋊C₈	1	4	yes	—
44	C₂²	C₄×Dic₃	1	2	yes	—
45	C₂²	C₂²×Dic₃	1	1	yes	characteristic
46	C₄	C₂×C₃⋊C₈	1	8	yes	direct product factor
47	C₄	C₄×Dic₃	1	2	yes	—
48	C₄	C₂×C₄×D₃	1	2	yes	—
49	C₃	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
50	C₂	C₄×C₃⋊C₈	1	4	yes	direct product factor
51	C₂	C₂²×C₃⋊C₈	1	2	yes	—
52	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₃
commutator, hypocenter	C₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical	C₂³×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×C₃⋊C₈	C₂	direct (N × H)
9. C₂×C₃⋊C₈	C₄	direct (N × H)
15. C₂×C₃×C₄	C₈	semidirect
20. C₃⋊C₈	C₂×C₄	direct (N × H)
31. C₃×C₄	C₂×C₈	semidirect
34. C₂×C₄	C₃⋊C₈	direct (N × H)
40. C₂×C₃	C₄×C₈	semidirect
46. C₄	C₂×C₃⋊C₈	direct (N × H)
49. C₃	C₂×C₄×C₈	semidirect
50. C₂	C₄×C₃⋊C₈	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×C₃×C₄²	2
C₂²×C₃⋊C₈	2
C₄×C₃⋊C₈	2
C₂×C₄×C₈	3

Subgroups — C2×C4×C3⋊C8 #4920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃⋊C₈ #4920