Subgroups — C₂×C₇×D₃₉₁ #24926521

Order 10948.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₃₉₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₃₉₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
6	D₃₉₁	C₂×C₇	1	2	yes	direct product factor
7	C₂×C₇×D₂₃	—	17	1	no	maximal, Hall
8	C₂×C₇×D₁₇	—	23	1	no	maximal, Hall
9	C₁₇×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₂₃	D₁₇	1	1	yes	characteristic, complemented
11	C₇×D₂₃	—	17	2	no	—
12	C₂×C₇×C₁₇	D₂₃	1	1	yes	characteristic, complemented
13	C₇×D₁₇	—	23	2	no	—
14	C₇×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₇×C₁₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₂×D₂₃	—	17	1	no	Hall
17	C₂×D₁₇	—	23	1	no	Hall
18	C₂×C₂₃	C₇×D₁₇	1	1	yes	characteristic, complemented
19	D₂₃	—	17	2	no	—
20	C₂×C₁₇	C₇×D₂₃	1	1	yes	characteristic, complemented
21	D₁₇	—	23	2	no	—
22	C₂²×C₇	—	391	1	no	Hall
23	C₂₃	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₁₇	C₂×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	391	2	no	—
26	C₂×C₇	D₃₉₁	1	1	yes	characteristic, direct product factor
27	C₇	C₂×D₃₉₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	391	1	no	Sylow
29	C₂	—	391	2	no	—
30	C₂	C₇×D₃₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₃₉₁
commutator, cosocle, hypocenter	C₁₇×C₂₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₇×C₂₃	C₂
LCS	G ▷ C₁₇×C₂₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₃₉₁	C₂	direct (N × H)
2. C₂×C₇×C₁₇×C₂₃	C₂	semidirect
3. C₇×C₁₇×C₂₃	C₂²	semidirect
4. C₂×D₃₉₁	C₇	direct (N × H)
5. C₂×C₁₇×C₂₃	C₂×C₇	semidirect
6. D₃₉₁	C₂×C₇	direct (N × H)
9. C₁₇×C₂₃	C₂²×C₇	semidirect
10. C₂×C₇×C₂₃	D₁₇	semidirect
12. C₂×C₇×C₁₇	D₂₃	semidirect
14. C₇×C₂₃	C₂×D₁₇	semidirect
15. C₇×C₁₇	C₂×D₂₃	semidirect
18. C₂×C₂₃	C₇×D₁₇	semidirect
20. C₂×C₁₇	C₇×D₂₃	semidirect
23. C₂₃	C₂×C₇×D₁₇	semidirect
24. C₁₇	C₂×C₇×D₂₃	semidirect
26. C₂×C₇	D₃₉₁	direct (N × H)
27. C₇	C₂×D₃₉₁	direct (N × H)
30. C₂	C₇×D₃₉₁	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×D₃₉₁	2
C₂×C₇×C₁₇×C₂₃	2
C₂×D₃₉₁	7
C₂×C₇×D₂₃	17
C₂×C₇×D₁₇	23

Subgroups — C2×C7×D391 #24926521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₃₉₁ #24926521