Subgroups — C₂×Dic₃⋊C₄ #923

Order 96.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄⋊C₄	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄	—	2	2	no	—
8	C₂×C₃×C₄	C₂²	1	2	yes	—
9	C₂×Dic₃	—	2	2	no	—
10	C₂×Dic₃	C₄	1	4	yes	complemented
11	C₂×Dic₃	C₂²	1	2	yes	—
12	C₂×Dic₃	C₂²	1	2	yes	—
13	C₂²×C₄	—	3	1	no	—
14	C₂²×C₄	—	3	1	no	—
15	C₂²×C₄	D₃	1	1	yes	characteristic
16	C₄⋊C₄	—	3	4	no	—
17	C₂²×C₃	C₂×C₄	1	2	yes	—
18	C₂²×C₃	D₄	1	2	yes	—
19	C₂²×C₃	Q₈	1	2	yes	—
20	C₂²×C₃	C₂³	1	1	yes	characteristic
21	C₃×C₄	—	2	2	no	—
22	Dic₃	—	2	2	no	—
23	Dic₃	C₂×C₄	1	4	yes	complemented
24	C₂³	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	3	4	no	—
27	C₂×C₄	—	3	2	no	—
28	C₂×C₄	—	3	2	no	—
29	C₂×C₄	—	6	2	no	—
30	C₂×C₄	C₂×D₃	1	2	yes	—
31	C₂×C₃	C₄⋊C₄	1	4	yes	complemented
32	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
35	C₂²	Dic₆	1	2	yes	—
36	C₂²	C₄×D₃	1	2	yes	—
37	C₂²	#67	1	2	yes	—
38	C₂²	C₂²×D₃	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	3	4	no	—
41	C₄	—	6	2	no	—
42	C₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
43	C₂	Dic₃⋊C₄	1	4	yes	direct product factor
44	C₂	C₂×Dic₆	1	1	yes	characteristic
45	C₂	C₂×C₄×D₃	1	1	yes	characteristic
46	C₂	C₂×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. Dic₃⋊C₄	C₂	direct (N × H)
10. C₂×Dic₃	C₄	semidirect
23. Dic₃	C₂×C₄	semidirect
31. C₂×C₃	C₄⋊C₄	semidirect
42. C₃	C₂×C₄⋊C₄	semidirect
43. C₂	Dic₃⋊C₄	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×C₃×C₄	2
C₂²×Dic₃	2
Dic₃⋊C₄	2
C₂×C₄⋊C₄	3

Subgroups — C2×Dic3⋊C4 #923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃⋊C₄ #923