Subgroups — C₇×#16812968 #37613113

Order 24738.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#13183714	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#16812968	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	#13183714	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₇×D₃₁⋊C₃	—	19	1	no	maximal, Hall
7	C₁₉×D₃₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₁₉⋊C₃	—	31	1	no	maximal, Hall
9	C₇×C₃₁⋊C₃	—	19	1	no	Hall
10	C₁₉×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×D₃₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₉⋊C₃	—	31	1	no	Hall
13	C₂×C₇×C₁₉	—	31	1	no	Hall
14	C₇×C₃₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	D₃₁⋊C₃	—	19	1	no	Hall
16	C₇×C₁₉	D₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₉⋊C₃	—	31	1	no	Hall
18	C₃₁⋊C₃	—	19	1	no	Hall
19	D₃₁	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₁₉⋊C₃	—	31	1	no	Hall
21	C₂×C₃×C₇	—	589	1	no	Hall
22	C₂×C₁₉	—	31	1	no	Hall
23	C₃₁	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	589	1	no	Hall
25	C₁₉	C₇×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	31	1	no	Hall
27	C₇	#16812968	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	589	1	no	Hall
29	C₃	—	589	1	no	Sylow
30	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	#16812968
commutator, cosocle, hypocenter	C₁₉×C₃₁	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₃₁	C₂×C₃
LCS	G ▷ C₁₉×C₃₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#13183714	C₂	semidirect
2. C₇×C₁₉×D₃₁	C₃	semidirect
3. C₇×C₁₉×C₃₁	C₂×C₃	semidirect
4. #16812968	C₇	direct (N × H)
5. #13183714	C₂×C₇	semidirect
7. C₁₉×D₃₁	C₃×C₇	semidirect
10. C₁₉×C₃₁	C₂×C₃×C₇	semidirect
11. C₇×D₃₁	C₁₉⋊C₃	semidirect
14. C₇×C₃₁	C₂×C₁₉⋊C₃	semidirect
16. C₇×C₁₉	D₃₁⋊C₃	semidirect
19. D₃₁	C₇×C₁₉⋊C₃	semidirect
23. C₃₁	C₂×C₇×C₁₉⋊C₃	semidirect
25. C₁₉	C₇×D₃₁⋊C₃	semidirect
27. C₇	#16812968	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#13183714	2
C₇×C₁₉×D₃₁	3
#16812968	7
C₇×D₃₁⋊C₃	19
C₂×C₇×C₁₉⋊C₃	31

Subgroups — C7×#16812968 #37613113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#16812968 #37613113