Subgroups — C₂×C₃×D₉₁₇ #24927016

Order 11004.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₉₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₉₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented
6	D₉₁₇	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×D₁₃₁	—	7	1	no	maximal, Hall
8	C₇×C₁₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₃₁	D₇	1	1	yes	characteristic, complemented
10	C₃×D₁₃₁	—	7	2	no	—
11	C₂×D₁₃₁	—	7	1	no	Hall
12	C₃×C₁₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃₁	C₃×D₇	1	1	yes	characteristic, complemented
14	D₁₃₁	—	7	2	no	—
15	C₁₃₁	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₇	—	131	1	no	maximal, Hall
17	C₂×C₃×C₇	D₁₃₁	1	1	yes	characteristic, complemented
18	C₃×D₇	—	131	2	no	—
19	C₂×D₇	—	131	1	no	Hall
20	C₃×C₇	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇	C₃×D₁₃₁	1	1	yes	characteristic, complemented
22	D₇	—	131	2	no	—
23	C₂²×C₃	—	917	1	no	Hall
24	C₇	C₂×C₃×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	917	2	no	—
26	C₂×C₃	D₉₁₇	1	1	yes	characteristic, direct product factor
27	C₂²	—	917	1	no	Sylow
28	C₃	C₂×D₉₁₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	917	2	no	—
30	C₂	C₃×D₉₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₉₁₇
commutator, cosocle, hypocenter	C₇×C₁₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃₁	C₂
LCS	G ▷ C₇×C₁₃₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₉₁₇	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₃₁	C₂	semidirect
3. C₂×D₉₁₇	C₃	direct (N × H)
4. C₃×C₇×C₁₃₁	C₂²	semidirect
5. C₂×C₇×C₁₃₁	C₂×C₃	semidirect
6. D₉₁₇	C₂×C₃	direct (N × H)
8. C₇×C₁₃₁	C₂²×C₃	semidirect
9. C₂×C₃×C₁₃₁	D₇	semidirect
12. C₃×C₁₃₁	C₂×D₇	semidirect
13. C₂×C₁₃₁	C₃×D₇	semidirect
15. C₁₃₁	C₂×C₃×D₇	semidirect
17. C₂×C₃×C₇	D₁₃₁	semidirect
20. C₃×C₇	C₂×D₁₃₁	semidirect
21. C₂×C₇	C₃×D₁₃₁	semidirect
24. C₇	C₂×C₃×D₁₃₁	semidirect
26. C₂×C₃	D₉₁₇	direct (N × H)
28. C₃	C₂×D₉₁₇	direct (N × H)
30. C₂	C₃×D₉₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₉₁₇	2
C₂×C₃×C₇×C₁₃₁	2
C₂×D₉₁₇	3
C₂×C₃×D₁₃₁	7
C₂×C₃×D₇	131

Subgroups — C2×C3×D917 #24927016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₉₁₇ #24927016