Subgroups — C₃²×Dic₉₇₃ #46856074

Order 35028.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₉₇₃	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×C₁₃₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₃₉	C₂×C₃	1	4	yes	—
5	C₃²×Dic₁₃₉	—	7	1	no	maximal, Hall
6	Dic₉₇₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₃₉	C₃×C₄	1	4	yes	complemented
8	C₂×C₃²×C₁₃₉	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₃₉	C₂×C₃²	1	1	yes	characteristic
10	C₃×Dic₁₃₉	—	7	4	no	—
11	C₃²×C₁₃₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₃₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₃₉	C₃×D₇	1	4	yes	—
14	Dic₁₃₉	—	7	1	no	Hall
15	C₃×C₁₃₉	C₃×Dic₇	1	4	yes	complemented
16	C₂×C₁₃₉	C₃²×D₇	1	1	yes	characteristic
17	C₃²×Dic₇	—	139	1	no	maximal, Hall
18	C₁₃₉	C₃²×Dic₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₇	D₁₃₉	1	1	yes	characteristic
20	C₃×Dic₇	—	139	4	no	—
21	C₃²×C₇	Dic₁₃₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	C₃×D₁₃₉	1	4	yes	—
23	C₃²×C₄	—	973	1	no	Hall
24	Dic₇	—	139	1	no	Hall
25	C₃×C₇	C₃×Dic₁₃₉	1	4	yes	complemented
26	C₂×C₃²	D₉₇₃	1	1	yes	characteristic
27	C₂×C₇	C₃²×D₁₃₉	1	1	yes	characteristic
28	C₃×C₄	—	973	4	no	—
29	C₃²	Dic₉₇₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×Dic₁₃₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₃×D₉₇₃	1	4	yes	—
32	C₄	—	973	1	no	Sylow
33	C₃	C₃×Dic₉₇₃	1	4	yes	direct product factor
34	C₂	C₃²×D₉₇₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₉₇₃
commutator, hypocenter	C₇×C₁₃₉	C₃²×C₄
Frattini	C₂	C₃²×D₉₇₃
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₃₉	C₂
cosocle	C₂×C₇×C₁₃₉	C₂×C₃²
LCS	G ▷ C₇×C₁₃₉
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₉₇₃	C₃	direct (N × H)
3. C₃²×C₇×C₁₃₉	C₄	semidirect
6. Dic₉₇₃	C₃²	direct (N × H)
7. C₃×C₇×C₁₃₉	C₃×C₄	semidirect
11. C₃²×C₁₃₉	Dic₇	semidirect
12. C₇×C₁₃₉	C₃²×C₄	semidirect
15. C₃×C₁₃₉	C₃×Dic₇	semidirect
18. C₁₃₉	C₃²×Dic₇	semidirect
21. C₃²×C₇	Dic₁₃₉	semidirect
25. C₃×C₇	C₃×Dic₁₃₉	semidirect
29. C₃²	Dic₉₇₃	direct (N × H)
30. C₇	C₃²×Dic₁₃₉	semidirect
33. C₃	C₃×Dic₉₇₃	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×C₃²×C₇×C₁₃₉	2
C₃×Dic₉₇₃	3
C₃²×Dic₁₃₉	7
C₃²×Dic₇	139

Subgroups — C32×Dic973 #46856074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₉₇₃ #46856074