Subgroups — C₃×C₇×SD₁₆ #66643

Order 336.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₇	—	2	1	no	—
6	C₃×C₄×C₇	—	2	1	no	—
7	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×D₄	C₂×C₃	1	1	yes	characteristic
10	C₇×C₈	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×SD₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₇	—	4	1	no	—
13	C₂×C₃×C₇	D₄	1	1	yes	characteristic
14	C₂²×C₇	—	2	1	no	—
15	C₄×C₇	—	2	1	no	—
16	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
17	C₃×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
18	C₃×D₄	C₂×C₇	1	1	yes	characteristic
19	C₃×C₈	C₂×C₇	1	1	yes	characteristic, complemented
20	C₃×C₇	SD₁₆	1	1	yes	characteristic, direct product factor, Hall
21	SD₁₆	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₇	—	4	1	no	—
23	C₂×C₇	C₃×D₄	1	1	yes	characteristic
24	C₂²×C₃	—	2	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂²×C₇	1	1	yes	characteristic
27	Q₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
28	D₄	C₂×C₃×C₇	1	1	yes	characteristic
29	C₈	C₂×C₃×C₇	1	1	yes	characteristic, complemented
30	C₇	C₃×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	4	1	no	—
32	C₂×C₃	C₇×D₄	1	1	yes	characteristic
33	C₂²	—	2	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂²×C₃×C₇	1	1	yes	characteristic
36	C₃	C₇×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	4	1	no	—
38	C₂	C₃×C₇×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₇	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₇
prime radical	C₃×C₇×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₇ ◁ C₃×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×Q₈	C₂	semidirect
3. C₃×C₇×C₈	C₂	semidirect
4. C₇×SD₁₆	C₃	direct (N × H)
8. C₇×Q₈	C₂×C₃	semidirect
10. C₇×C₈	C₂×C₃	semidirect
11. C₃×SD₁₆	C₇	direct (N × H)
17. C₃×Q₈	C₂×C₇	semidirect
19. C₃×C₈	C₂×C₇	semidirect
20. C₃×C₇	SD₁₆	direct (N × H)
21. SD₁₆	C₃×C₇	direct (N × H)
27. Q₈	C₂×C₃×C₇	semidirect
29. C₈	C₂×C₃×C₇	semidirect
30. C₇	C₃×SD₁₆	direct (N × H)
36. C₃	C₇×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×Q₈	2
C₃×C₇×D₄	2
C₃×C₇×C₈	2
C₇×SD₁₆	3
C₃×SD₁₆	7

Subgroups — C3×C7×SD16 #66643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×SD₁₆ #66643