Subgroups — C₆₇×C₃⋊Dic₃₉ #44535679

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×Dic₃₉	—	3	4	no	maximal
3	C₃²×C₁₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₆₇	D₃	1	4	yes	—
5	Dic₁₃×C₆₇	—	9	1	no	Hall
6	C₃×C₁₃×C₆₇	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₃×C₆₇	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₆₇	C₃⋊D₃	1	1	yes	characteristic
9	C₂×C₃²×C₆₇	D₁₃	1	1	yes	characteristic
10	C₁₃×C₆₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	Dic₃×C₆₇	—	39	4	no	—
12	C₃²×C₆₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊Dic₃₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₆₇	D₃₉	1	4	yes	—
15	C₄×C₆₇	—	117	1	no	Hall
16	C₂×C₃²×C₁₃	C₂×C₆₇	1	1	yes	characteristic
17	C₃×C₆₇	Dic₃₉	1	4	yes	complemented
18	Dic₃₉	—	3	4	no	—
19	C₂×C₆₇	C₃⋊D₃₉	1	1	yes	characteristic
20	C₃²×C₁₃	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	D₃×C₆₇	1	4	yes	—
22	C₆₇	C₃⋊Dic₃₉	1	1	yes	characteristic, direct product factor, Sylow
23	Dic₁₃	—	9	1	no	Hall
24	C₃×C₁₃	Dic₃×C₆₇	1	4	yes	complemented
25	C₃⋊Dic₃	—	13	1	no	Hall
26	C₂×C₁₃	C₃⋊D₃×C₆₇	1	1	yes	characteristic
27	C₂×C₃²	D₁₃×C₆₇	1	1	yes	characteristic
28	C₁₃	C₃⋊Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	39	4	no	—
30	C₃²	Dic₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₆₇×D₃₉	1	4	yes	—
32	C₄	—	117	1	no	Sylow
33	C₃	C₆₇×Dic₃₉	1	4	yes	complemented
34	C₂	C₆₇×C₃⋊D₃₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₆₇	C₃⋊D₃₉
commutator, hypocenter	C₃²×C₁₃	C₄×C₆₇
Frattini	C₂	C₆₇×C₃⋊D₃₉
Fitting, socle, prime radical	C₂×C₃²×C₁₃×C₆₇	C₂
cosocle	C₂×C₃²×C₁₃	C₂×C₆₇
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂×C₆₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₁₃×C₆₇	C₄	semidirect
6. C₃×C₁₃×C₆₇	Dic₃	semidirect
10. C₁₃×C₆₇	C₃⋊Dic₃	semidirect
12. C₃²×C₆₇	Dic₁₃	semidirect
13. C₃⋊Dic₃₉	C₆₇	direct (N × H)
17. C₃×C₆₇	Dic₃₉	semidirect
20. C₃²×C₁₃	C₄×C₆₇	semidirect
22. C₆₇	C₃⋊Dic₃₉	direct (N × H)
24. C₃×C₁₃	Dic₃×C₆₇	semidirect
28. C₁₃	C₃⋊Dic₃×C₆₇	semidirect
30. C₃²	Dic₁₃×C₆₇	semidirect
33. C₃	C₆₇×Dic₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₃×C₆₇	2
C₆₇×Dic₃₉	3
C₃⋊Dic₃×C₆₇	13
C₃⋊Dic₃₉	67

Subgroups — C67×C3⋊Dic39 #44535679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×C₃⋊Dic₃₉ #44535679