Subgroups — C₇×Dic₃⋊C₄ #66613

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×C₇×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₇×C₄⋊C₄	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₇	—	2	1	no	—
7	C₇×Dic₃	—	2	1	no	—
8	C₇×Dic₃	C₄	1	2	yes	complemented
9	C₂×C₄×C₇	—	3	1	no	—
10	C₂×C₄×C₇	—	3	1	no	—
11	C₂×C₄×C₇	D₃	1	1	yes	characteristic
12	Dic₃⋊C₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₇	D₄	1	1	yes	characteristic
15	C₂×C₃×C₇	Q₈	1	1	yes	characteristic
16	C₂²×C₇	C₂×D₃	1	1	yes	characteristic
17	C₄×C₇	—	2	1	no	—
18	C₄×C₇	—	3	2	no	—
19	C₄×C₇	—	6	1	no	—
20	C₂×C₃×C₄	C₂×C₇	1	1	yes	characteristic
21	C₂×Dic₃	C₂×C₇	1	1	yes	characteristic
22	C₂×Dic₃	C₂×C₇	1	1	yes	characteristic
23	C₃×C₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
24	C₄⋊C₄	—	3	1	no	Sylow
25	C₂×C₇	Dic₆	1	1	yes	characteristic
26	C₂×C₇	C₄×D₃	1	1	yes	characteristic
27	C₂×C₇	#67	1	1	yes	characteristic
28	C₂²×C₃	C₂²×C₇	1	1	yes	characteristic
29	C₃×C₄	—	2	1	no	—
30	Dic₃	—	2	1	no	—
31	Dic₃	C₄×C₇	1	2	yes	complemented
32	C₂×C₄	—	3	1	no	—
33	C₂×C₄	—	3	1	no	—
34	C₂×C₄	D₃×C₇	1	1	yes	characteristic
35	C₇	Dic₃⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃	C₂×C₄×C₇	1	1	yes	characteristic
37	C₂×C₃	C₇×D₄	1	1	yes	characteristic
38	C₂×C₃	C₇×Q₈	1	1	yes	characteristic
39	C₂²	C₂×D₃×C₇	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	3	2	no	—
42	C₄	—	6	1	no	—
43	C₃	C₇×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
44	C₂	C₇×Dic₆	1	1	yes	characteristic
45	C₂	C₄×D₃×C₇	1	1	yes	characteristic
46	C₂	C₇×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₇
Frattini	C₂²	C₂×D₃×C₇
Fitting	C₂×C₃×C₄×C₇	C₂
socle, prime radical	C₂²×C₃×C₇	C₂²
cosocle	C₂²×C₃	C₂²×C₇
hypercenter	C₂×C₄×C₇	D₃
hypocenter	C₃	C₇×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
8. C₇×Dic₃	C₄	semidirect
12. Dic₃⋊C₄	C₇	direct (N × H)
23. C₃×C₇	C₄⋊C₄	semidirect
31. Dic₃	C₄×C₇	semidirect
35. C₇	Dic₃⋊C₄	direct (N × H)
43. C₃	C₇×C₄⋊C₄	semidirect

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×C₇×Dic₃	2
C₇×C₄⋊C₄	3
Dic₃⋊C₄	7

Subgroups — C7×Dic3⋊C4 #66613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Dic₃⋊C₄ #66613