Subgroups — C₃×C₄⋊Dic₇ #66598

Order 336.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₇	C₂	1	2	yes	maximal
3	C₄⋊Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	C₄	1	2	yes	complemented
6	C₃×Dic₇	—	2	2	no	—
7	C₂×C₄×C₇	C₂×C₃	1	1	yes	characteristic
8	C₂×Dic₇	C₂×C₃	1	2	yes	—
9	C₃×C₄⋊C₄	—	7	1	no	maximal, Hall
10	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₇	D₄	1	1	yes	characteristic
12	C₂×C₃×C₇	Q₈	1	1	yes	characteristic
13	C₂²×C₇	C₂²×C₃	1	1	yes	characteristic
14	C₄×C₇	C₃×C₄	1	2	yes	complemented
15	Dic₇	—	2	2	no	—
16	C₂×C₃×C₄	—	7	2	no	—
17	C₂×C₃×C₄	D₇	1	1	yes	characteristic
18	C₃×C₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
19	C₄⋊C₄	—	7	1	no	Sylow
20	C₂×C₇	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂×C₇	C₃×D₄	1	1	yes	characteristic
22	C₂×C₇	C₃×Q₈	1	1	yes	characteristic
23	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
24	C₃×C₄	—	14	2	no	—
25	C₃×C₄	Dic₇	1	2	yes	complemented
26	C₂×C₄	—	7	2	no	—
27	C₂×C₄	C₃×D₇	1	1	yes	characteristic
28	C₇	C₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	Dic₁₄	1	1	yes	characteristic
30	C₂×C₃	D₂₈	1	1	yes	characteristic
31	C₂×C₃	C₂×Dic₇	1	1	yes	characteristic
32	C₂²	C₂×C₃×D₇	1	1	yes	characteristic
33	C₄	—	14	2	no	—
34	C₄	C₃×Dic₇	1	2	yes	complemented
35	C₃	C₄⋊Dic₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	C₃×Dic₁₄	1	1	yes	characteristic
37	C₂	C₃×D₂₈	1	1	yes	characteristic
38	C₂	C₂×C₃×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₇
commutator	C₂×C₇	C₂×C₃×C₄
Frattini	C₂²	C₂×C₃×D₇
Fitting	C₂×C₃×C₄×C₇	C₂
socle, prime radical	C₂²×C₃×C₇	C₂²
cosocle	C₂²×C₇	C₂²×C₃
hypercenter	C₂×C₃×C₄	D₇
hypocenter	C₇	C₃×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊Dic₇	C₃	direct (N × H)
5. C₃×C₄×C₇	C₄	semidirect
14. C₄×C₇	C₃×C₄	semidirect
18. C₃×C₇	C₄⋊C₄	semidirect
25. C₃×C₄	Dic₇	semidirect
28. C₇	C₃×C₄⋊C₄	semidirect
34. C₄	C₃×Dic₇	semidirect
35. C₃	C₄⋊Dic₇	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×C₄×C₇	2
C₂×C₃×Dic₇	2
C₄⋊Dic₇	3
C₃×C₄⋊C₄	7

Subgroups — C3×C4⋊Dic7 #66598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄⋊Dic₇ #66598