Subgroups — C₇×Dic₁₀₁₇ #43249757

Order 28476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₃₉	—	3	1	no	maximal
3	C₇×C₉×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₁₃	D₃	1	1	yes	characteristic
5	Dic₁₀₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×Dic₁₁₃	—	9	1	no	Hall
7	C₃×C₇×C₁₁₃	Dic₃	1	1	yes	characteristic
8	C₂×C₉×C₁₁₃	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₁₁₃	D₉	1	1	yes	characteristic
10	Dic₃₃₉	—	3	1	no	—
11	C₉×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₁₃	D₃×C₇	1	1	yes	characteristic
14	Dic₁₁₃	—	9	1	no	Hall
15	C₃×C₁₁₃	C₇×Dic₃	1	1	yes	characteristic
16	C₇×Dic₉	—	113	1	no	maximal, Hall
17	C₂×C₁₁₃	C₇×D₉	1	1	yes	characteristic
18	C₂×C₇×C₉	D₁₁₃	1	1	yes	characteristic
19	C₁₁₃	C₇×Dic₉	1	1	yes	characteristic, complemented, Sylow
20	C₇×Dic₃	—	339	1	no	—
21	C₇×C₉	Dic₁₁₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₃₃₉	1	1	yes	characteristic
23	Dic₉	—	113	1	no	Hall
24	C₄×C₇	—	1017	1	no	Hall
25	C₃×C₇	Dic₃₃₉	1	1	yes	characteristic
26	C₂×C₉	C₇×D₁₁₃	1	1	yes	characteristic
27	C₂×C₇	D₁₀₁₇	1	1	yes	characteristic
28	Dic₃	—	339	1	no	—
29	C₉	C₇×Dic₁₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₇	Dic₁₀₁₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₇×D₃₃₉	1	1	yes	characteristic
32	C₄	—	1017	1	no	Sylow
33	C₃	C₇×Dic₃₃₉	1	1	yes	characteristic
34	C₂	C₇×D₁₀₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₀₁₇
commutator, hypocenter	C₉×C₁₁₃	C₄×C₇
Frattini	C₂×C₃	C₇×D₃₃₉
Fitting	C₂×C₇×C₉×C₁₁₃	C₂
socle, prime radical	C₂×C₃×C₇×C₁₁₃	D₃
cosocle	C₂×C₉×C₁₁₃	C₂×C₇
LCS	G ▷ C₉×C₁₁₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₁₁₃	C₄	semidirect
5. Dic₁₀₁₇	C₇	direct (N × H)
11. C₉×C₁₁₃	C₄×C₇	semidirect
12. C₇×C₁₁₃	Dic₉	semidirect
19. C₁₁₃	C₇×Dic₉	semidirect
21. C₇×C₉	Dic₁₁₃	semidirect
29. C₉	C₇×Dic₁₁₃	semidirect
30. C₇	Dic₁₀₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₉×C₁₁₃	2
C₇×Dic₃₃₉	3
Dic₁₀₁₇	7
C₇×Dic₉	113

Subgroups — C7×Dic1017 #43249757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Dic₁₀₁₇ #43249757