Subgroups — C₂×C₃×Dic₁₄ #66705

Order 336.

76 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	C₃×Dic₁₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₇	C₂²	1	2	yes	—
7	C₃×Dic₇	C₂²	1	4	yes	—
8	C₂×C₄×C₇	C₂×C₃	1	1	yes	characteristic
9	C₂×Dic₇	C₂×C₃	1	2	yes	—
10	Dic₁₄	C₂×C₃	1	4	yes	direct product factor
11	C₂×C₃×Q₈	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	Q₈	1	2	yes	complemented
13	C₂×C₃×C₇	C₂³	1	1	yes	characteristic
14	C₂²×C₇	C₂²×C₃	1	1	yes	characteristic
15	C₄×C₇	C₂²×C₃	1	2	yes	—
16	Dic₇	C₂²×C₃	1	4	yes	—
17	C₃×Q₈	—	7	4	no	—
18	C₂×C₃×C₄	—	7	2	no	—
19	C₂×C₃×C₄	D₇	1	1	yes	characteristic
20	C₃×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
21	C₂×Q₈	—	7	1	no	Sylow
22	C₂×C₇	C₃×Q₈	1	2	yes	complemented
23	C₂×C₇	C₂³×C₃	1	1	yes	characteristic
24	C₂²×C₃	C₂×D₇	1	1	yes	characteristic
25	C₃×C₄	—	7	4	no	—
26	C₃×C₄	C₂×D₇	1	2	yes	—
27	Q₈	—	7	4	no	—
28	C₂×C₄	—	7	2	no	—
29	C₂×C₄	C₃×D₇	1	1	yes	characteristic
30	C₇	C₂×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	Dic₁₄	1	2	yes	direct product factor
32	C₂×C₃	C₂²×D₇	1	1	yes	characteristic
33	C₂²	C₂×C₃×D₇	1	1	yes	characteristic
34	C₄	—	7	4	no	—
35	C₄	C₂×C₃×D₇	1	2	yes	—
36	C₃	C₂×Dic₁₄	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	C₃×Dic₁₄	1	2	yes	direct product factor
38	C₂	C₂²×C₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₇
commutator, cosocle	C₂×C₇	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₇
Fitting	C₂×C₃×C₄×C₇	C₂
socle, prime radical	C₂²×C₃×C₇	C₂²
hypercenter	C₂×C₃×C₄	D₇
hypocenter	C₇	C₂×C₃×Q₈
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. C₃×Dic₁₄	C₂	direct (N × H)
4. C₂×Dic₁₄	C₃	direct (N × H)
10. Dic₁₄	C₂×C₃	direct (N × H)
12. C₂×C₃×C₇	Q₈	semidirect
20. C₃×C₇	C₂×Q₈	semidirect
22. C₂×C₇	C₃×Q₈	semidirect
30. C₇	C₂×C₃×Q₈	semidirect
31. C₂×C₃	Dic₁₄	direct (N × H)
36. C₃	C₂×Dic₁₄	direct (N × H)
37. C₂	C₃×Dic₁₄	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
C₃×Dic₁₄	2
C₂×Dic₁₄	3
C₂×C₃×Q₈	7

Subgroups — C2×C3×Dic14 #66705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₁₄ #66705