Subgroups — C₃×D₇×C₁₆ #10620554

Order 672.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×D₇	C₄	1	1	yes	characteristic
6	C₃×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₃×C₇⋊C₈	C₄	1	1	yes	characteristic
8	C₈×D₇	C₂×C₃	1	1	yes	characteristic
9	C₇×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
10	C₇⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₆	—	7	1	no	maximal, Hall
12	C₂×C₃×D₇	C₈	1	1	yes	characteristic
13	C₃×C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₃×Dic₇	C₈	1	1	yes	characteristic
15	C₄×D₇	C₃×C₄	1	1	yes	characteristic
16	C₇×C₈	C₂²×C₃	1	1	yes	characteristic
17	C₇⋊C₈	C₃×C₄	1	1	yes	characteristic
18	C₂×C₃×C₈	—	7	1	no	—
19	C₃×C₁₆	—	7	1	no	—
20	C₃×C₁₆	D₇	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₇	C₂×C₈	1	1	yes	characteristic
22	C₃×D₇	C₁₆	1	2	yes	direct product factor
23	C₂×C₁₆	—	7	1	no	Sylow
24	C₂×D₇	C₃×C₈	1	1	yes	characteristic
25	C₄×C₇	C₂×C₃×C₄	1	1	yes	characteristic
26	Dic₇	C₃×C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	—	7	1	no	—
28	C₃×C₈	—	7	1	no	—
29	C₃×C₈	C₂×D₇	1	1	yes	characteristic
30	C₃×C₇	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
31	C₂×C₈	—	7	1	no	—
32	C₁₆	—	7	1	no	—
33	C₁₆	C₃×D₇	1	1	yes	characteristic, direct product factor
34	C₂×C₇	C₂×C₃×C₈	1	1	yes	characteristic
35	D₇	C₃×C₁₆	1	2	yes	direct product factor
36	C₂²×C₃	—	7	1	no	—
37	C₃×C₄	—	7	1	no	—
38	C₃×C₄	C₄×D₇	1	1	yes	characteristic
39	C₂×C₄	—	7	1	no	—
40	C₈	—	7	1	no	—
41	C₈	C₂×C₃×D₇	1	1	yes	characteristic
42	C₇	C₂×C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	2	no	—
44	C₂×C₃	C₈×D₇	1	1	yes	characteristic
45	C₂²	—	7	1	no	—
46	C₄	—	7	1	no	—
47	C₄	C₃×C₄×D₇	1	1	yes	characteristic
48	C₃	D₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	7	2	no	—
50	C₂	C₃×C₈×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₁₆	D₇
commutator, hypocenter	C₇	C₂×C₃×C₁₆
Frattini	C₈	C₂×C₃×D₇
Fitting	C₃×C₇×C₁₆	C₂
socle	C₂×C₃×C₇	C₂×C₈
prime radical	C₂×C₃×D₇	C₈
cosocle	C₇×C₈	C₂²×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₁₆	C₂	semidirect
3. C₃×C₇⋊C₁₆	C₂	semidirect
4. D₇×C₁₆	C₃	direct (N × H)
9. C₇×C₁₆	C₂×C₃	semidirect
10. C₇⋊C₁₆	C₂×C₃	semidirect
20. C₃×C₁₆	D₇	direct (N × H)
22. C₃×D₇	C₁₆	direct (N × H)
30. C₃×C₇	C₂×C₁₆	semidirect
33. C₁₆	C₃×D₇	direct (N × H)
35. D₇	C₃×C₁₆	direct (N × H)
42. C₇	C₂×C₃×C₁₆	semidirect
48. C₃	D₇×C₁₆	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×C₈×D₇	2
C₃×C₇×C₁₆	2
C₃×C₇⋊C₁₆	2
D₇×C₁₆	3
C₂×C₃×C₁₆	7

Subgroups — C3×D7×C16 #10620554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×C₁₆ #10620554