Subgroups — #27166316⋊C₂ #38788643

Order 25788.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27166324	C₂	1	1	yes	maximal, characteristic, complemented
2	#27166320	C₂	1	1	yes	maximal, characteristic, complemented
3	#27166316	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#20264517	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₀₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₃₀₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₃₀₇⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₃₀₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₀₇⋊C₃	—	7	1	no	—
12	D₃₀₇⋊C₃	—	7	1	no	—
13	D₃₀₇⋊C₃	—	14	1	no	—
14	C₂×D₃₀₇	—	7	1	no	Hall
15	C₃₀₇⋊C₃	—	14	1	no	Hall
16	C₂×C₃₀₇	—	7	1	no	—
17	D₃₀₇	—	7	1	no	—
18	D₃₀₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₃₀₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
20	C₂×AGL(1,𝔽₇)	—	307	1	no	maximal, Hall
21	C₂×ΓL(1,𝔽₈)	—	307	1	no	—
22	AGL(1,𝔽₇)	—	307	1	no	—
23	AGL(1,𝔽₇)	—	614	1	no	—
24	C₂×D₇	—	307	1	no	Hall
25	ΓL(1,𝔽₈)	—	614	1	no	Hall
26	C₂×C₇	—	307	1	no	—
27	D₇	—	307	1	no	—
28	D₇	D₃₀₇⋊C₃	1	1	yes	characteristic, complemented
29	C₂²×C₃	—	2149	1	no	Hall
30	C₇	C₂×D₃₀₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2149	1	no	—
32	C₂×C₃	—	4298	1	no	—
33	C₂×C₃	—	4298	1	no	—
34	C₂²	—	2149	1	no	Sylow
35	C₃	—	8596	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	307	1	no	—
38	C₂	—	2149	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₀₇	C₂²×C₃
LCS	G ▷ C₇×C₃₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #27166324	C₂	semidirect
2. #27166320	C₂	semidirect
3. #27166316	C₂	semidirect
4. D₇×D₃₀₇	C₃	semidirect
5. #20264517	C₂²	semidirect
6. D₂₁₄₉	C₂×C₃	semidirect
7. C₇×D₃₀₇	C₂×C₃	semidirect
8. D₇×C₃₀₇	C₂×C₃	semidirect
10. C₇×C₃₀₇	C₂²×C₃	semidirect
18. D₃₀₇	AGL(1,𝔽₇)	semidirect
19. C₃₀₇	C₂×AGL(1,𝔽₇)	semidirect
28. D₇	D₃₀₇⋊C₃	semidirect
30. C₇	C₂×D₃₀₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#27166324	2
#27166320	2
#27166316	2
D₇×D₃₀₇	3
C₂×D₃₀₇⋊C₃	7
C₂×AGL(1,𝔽₇)	307

Subgroups — #27166316⋊C2 #38788643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #27166316⋊C₂ #38788643