Subgroups — C₂×C₆₇⋊#3862 #34089192

Order 19698.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇⋊#3862	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#13064104	—	7	1	no	maximal
5	C₂×#13064105	—	7	1	no	maximal
6	#13064105	—	7	1	no	—
7	#13064104	—	7	1	no	—
8	C₂×C₇×C₆₇	—	3	2	no	—
9	C₂×C₇×C₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
10	C₂×C₇×C₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₇×C₆₇	—	3	2	no	—
12	C₇×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₇×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₂×C₆₇⋊C₃	—	49	1	no	Hall
15	C₂×#3862	—	67	1	no	maximal, Hall
16	C₆₇⋊C₃	—	49	1	no	Hall
17	#3862	—	67	1	no	Hall
18	C₂×C₆₇	#3862	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇²	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₆₇	C₂×#3862	1	1	yes	characteristic, complemented, Sylow
21	C₇²	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×ΓL(1,𝔽₈)	—	469	1	no	—
23	C₂×ΓL(1,𝔽₈)	—	469	1	no	—
24	ΓL(1,𝔽₈)	—	469	1	no	—
25	ΓL(1,𝔽₈)	—	469	1	no	—
26	C₂×C₇	—	3	2	no	—
27	C₂×C₇	#13064104	1	1	yes	characteristic, complemented
28	C₂×C₇	#13064105	1	1	yes	characteristic, complemented
29	C₇	—	3	2	no	—
30	C₇	C₂×#13064105	1	1	yes	characteristic, complemented
31	C₇	C₂×#13064104	1	1	yes	characteristic, complemented
32	C₂×C₃	—	3283	1	no	Hall
33	C₃	—	3283	1	no	Sylow
34	C₂	C₆₇⋊#3862	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₆₇⋊#3862
commutator, cosocle, hypocenter	C₇²×C₆₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₆₇	C₃
LCS	G ▷ C₇²×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₆₇⋊#3862	C₂	direct (N × H)
2. C₂×C₇²×C₆₇	C₃	semidirect
3. C₇²×C₆₇	C₂×C₃	semidirect
9. C₂×C₇×C₆₇	ΓL(1,𝔽₈)	semidirect
10. C₂×C₇×C₆₇	ΓL(1,𝔽₈)	semidirect
12. C₇×C₆₇	C₂×ΓL(1,𝔽₈)	semidirect
13. C₇×C₆₇	C₂×ΓL(1,𝔽₈)	semidirect
18. C₂×C₆₇	#3862	semidirect
19. C₂×C₇²	C₆₇⋊C₃	semidirect
20. C₆₇	C₂×#3862	semidirect
21. C₇²	C₂×C₆₇⋊C₃	semidirect
27. C₂×C₇	#13064104	semidirect
28. C₂×C₇	#13064105	semidirect
30. C₇	C₂×#13064105	semidirect
31. C₇	C₂×#13064104	semidirect
34. C₂	C₆₇⋊#3862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇⋊#3862	2
C₂×C₇²×C₆₇	3
C₂×#13064104	7
C₂×#13064105	7
C₂×#3862	67

Subgroups — C2×C67⋊#3862 #34089192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇⋊#3862 #34089192