Subgroups — #29507096⋊C₂ #44502829

Order 30828.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29507104	C₂	1	1	yes	maximal, characteristic, complemented
2	#29507100	C₂	1	1	yes	maximal, characteristic, complemented
3	#29507096	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#21440474	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₅₆₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₆₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₃₆₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₃₆₇⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₃₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₆₇⋊C₃	—	7	1	no	—
12	D₃₆₇⋊C₃	—	7	1	no	—
13	D₃₆₇⋊C₃	—	7	1	no	—
14	C₂×D₃₆₇	—	7	1	no	Hall
15	C₃₆₇⋊C₃	—	7	1	no	Hall
16	C₂×C₃₆₇	—	7	1	no	—
17	D₃₆₇	—	7	1	no	—
18	D₃₆₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
19	C₃₆₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
20	C₂×AGL(1,𝔽₇)	—	367	1	no	maximal, Hall
21	C₂×ΓL(1,𝔽₈)	—	367	1	no	—
22	AGL(1,𝔽₇)	—	367	1	no	—
23	AGL(1,𝔽₇)	—	367	1	no	—
24	C₂×D₇	—	367	1	no	Hall
25	ΓL(1,𝔽₈)	—	367	1	no	Hall
26	C₂×C₇	—	367	1	no	—
27	D₇	—	367	1	no	—
28	D₇	D₃₆₇⋊C₃	1	1	yes	characteristic, complemented
29	C₂²×C₃	—	2569	1	no	Hall
30	C₇	C₂×D₃₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2569	1	no	—
32	C₂×C₃	—	2569	1	no	—
33	C₂×C₃	—	2569	1	no	—
34	C₂²	—	2569	1	no	Sylow
35	C₃	—	2569	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	2569	1	no	—
38	C₂	—	367	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₆₇	C₂²×C₃
LCS	G ▷ C₇×C₃₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #29507104	C₂	semidirect
2. #29507100	C₂	semidirect
3. #29507096	C₂	semidirect
4. D₇×D₃₆₇	C₃	semidirect
5. #21440474	C₂²	semidirect
6. D₂₅₆₉	C₂×C₃	semidirect
7. C₇×D₃₆₇	C₂×C₃	semidirect
8. D₇×C₃₆₇	C₂×C₃	semidirect
10. C₇×C₃₆₇	C₂²×C₃	semidirect
18. D₃₆₇	AGL(1,𝔽₇)	semidirect
19. C₃₆₇	C₂×AGL(1,𝔽₇)	semidirect
28. D₇	D₃₆₇⋊C₃	semidirect
30. C₇	C₂×D₃₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#29507104	2
#29507100	2
#29507096	2
D₇×D₃₆₇	3
C₂×D₃₆₇⋊C₃	7
C₂×AGL(1,𝔽₇)	367

Subgroups — #29507096⋊C2 #44502829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #29507096⋊C₂ #44502829