Subgroups — #28381649⋊C₂ #43246749

Order 28308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381657	C₂	1	1	yes	maximal, characteristic, complemented
2	#28381653	C₂	1	1	yes	maximal, characteristic, complemented
3	#28381649	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#20296697	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₃₅₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₃₃₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₃₃₇⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₃₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₃₇⋊C₃	—	7	1	no	—
12	D₃₃₇⋊C₃	—	7	1	no	—
13	D₃₃₇⋊C₃	—	14	1	no	—
14	C₂×D₃₃₇	—	7	1	no	Hall
15	C₃₃₇⋊C₃	—	14	1	no	Hall
16	C₂×C₃₃₇	—	7	1	no	—
17	D₃₃₇	—	7	1	no	—
18	D₃₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₃₃₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
20	C₂×AGL(1,𝔽₇)	—	337	1	no	maximal, Hall
21	C₂×ΓL(1,𝔽₈)	—	337	1	no	—
22	AGL(1,𝔽₇)	—	337	1	no	—
23	AGL(1,𝔽₇)	—	674	1	no	—
24	C₂×D₇	—	337	1	no	Hall
25	ΓL(1,𝔽₈)	—	674	1	no	Hall
26	C₂×C₇	—	337	1	no	—
27	D₇	—	337	1	no	—
28	D₇	D₃₃₇⋊C₃	1	1	yes	characteristic, complemented
29	C₂²×C₃	—	2359	1	no	Hall
30	C₇	C₂×D₃₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2359	1	no	—
32	C₂×C₃	—	2359	1	no	—
33	C₂×C₃	—	4718	1	no	—
34	C₂²	—	2359	1	no	Sylow
35	C₃	—	9436	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	2359	1	no	—
38	C₂	—	337	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₃₇	C₂²×C₃
LCS	G ▷ C₇×C₃₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #28381657	C₂	semidirect
2. #28381653	C₂	semidirect
3. #28381649	C₂	semidirect
4. D₇×D₃₃₇	C₃	semidirect
5. #20296697	C₂²	semidirect
6. D₂₃₅₉	C₂×C₃	semidirect
7. C₇×D₃₃₇	C₂×C₃	semidirect
8. D₇×C₃₃₇	C₂×C₃	semidirect
10. C₇×C₃₃₇	C₂²×C₃	semidirect
18. D₃₃₇	AGL(1,𝔽₇)	semidirect
19. C₃₃₇	C₂×AGL(1,𝔽₇)	semidirect
28. D₇	D₃₃₇⋊C₃	semidirect
30. C₇	C₂×D₃₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#28381657	2
#28381653	2
#28381649	2
D₇×D₃₃₇	3
C₂×D₃₃₇⋊C₃	7
C₂×AGL(1,𝔽₇)	337

Subgroups — #28381649⋊C2 #43246749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #28381649⋊C₂ #43246749