Subgroups — C₂²×C₇×Dic₃ #66723

Order 336.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Dic₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₇	C₄	1	4	yes	complemented
5	C₂²×C₃×C₇	C₂²	1	3	yes	—
6	C₇×Dic₃	C₂²	1	4	yes	direct product factor
7	C₂³×C₇	D₃	1	1	yes	characteristic
8	C₂×C₄×C₇	—	3	6	no	—
9	C₂²×Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₇	C₂×C₄	1	6	yes	complemented
11	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
12	C₂²×C₇	Dic₃	1	4	yes	direct product factor
13	C₂²×C₇	C₂×D₃	1	3	yes	—
14	C₄×C₇	—	3	4	no	—
15	C₂³×C₃	C₂×C₇	1	1	yes	characteristic
16	C₂×Dic₃	C₂×C₇	1	6	yes	direct product factor
17	C₃×C₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₄	—	3	1	no	Sylow
19	C₂×C₇	C₂×Dic₃	1	6	yes	direct product factor
20	C₂×C₇	C₂²×D₃	1	1	yes	characteristic
21	C₂²×C₃	C₄×C₇	1	4	yes	complemented
22	C₂²×C₃	C₂²×C₇	1	3	yes	—
23	Dic₃	C₂²×C₇	1	4	yes	direct product factor
24	C₂³	D₃×C₇	1	1	yes	characteristic
25	C₂×C₄	—	3	6	no	—
26	C₇	C₂²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂×C₄×C₇	1	6	yes	complemented
28	C₂×C₃	C₂³×C₇	1	1	yes	characteristic
29	C₂²	C₇×Dic₃	1	4	yes	direct product factor
30	C₂²	C₂×D₃×C₇	1	3	yes	—
31	C₄	—	3	4	no	—
32	C₃	C₂²×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂×C₇×Dic₃	1	6	yes	direct product factor
34	C₂	C₂²×D₃×C₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₇	D₃
commutator, hypocenter	C₃	C₂²×C₄×C₇
Frattini	C₂	C₂²×D₃×C₇
Fitting, socle, prime radical	C₂³×C₃×C₇	C₂
cosocle	C₂×C₃	C₂³×C₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₇

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×Dic₃	C₂	direct (N × H)
4. C₂²×C₃×C₇	C₄	semidirect
6. C₇×Dic₃	C₂²	direct (N × H)
9. C₂²×Dic₃	C₇	direct (N × H)
10. C₂×C₃×C₇	C₂×C₄	semidirect
12. C₂²×C₇	Dic₃	direct (N × H)
16. C₂×Dic₃	C₂×C₇	direct (N × H)
17. C₃×C₇	C₂²×C₄	semidirect
19. C₂×C₇	C₂×Dic₃	direct (N × H)
21. C₂²×C₃	C₄×C₇	semidirect
23. Dic₃	C₂²×C₇	direct (N × H)
26. C₇	C₂²×Dic₃	direct (N × H)
27. C₂×C₃	C₂×C₄×C₇	semidirect
29. C₂²	C₇×Dic₃	direct (N × H)
32. C₃	C₂²×C₄×C₇	semidirect
33. C₂	C₂×C₇×Dic₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₇	2
C₂×C₇×Dic₃	2
C₂²×C₄×C₇	3
C₂²×Dic₃	7

Subgroups — C22×C7×Dic3 #66723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×Dic₃ #66723