Subgroups — C₇×Q₈×D₁₇ #14274161

Order 1904.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×D₁₇	C₂	1	3	yes	maximal
3	C₇×Dic₃₄	C₂	1	3	yes	maximal, complemented
4	C₂×C₇×D₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₁₇	C₂²	1	3	yes	—
6	C₇×Dic₁₇	C₂²	1	3	yes	—
7	Q₈×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
9	C₇×D₁₇	Q₈	1	2	yes	direct product factor
10	Q₈×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
11	C₄×D₁₇	C₂×C₇	1	3	yes	—
12	Dic₃₄	C₂×C₇	1	3	yes	complemented
13	C₇×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×Q₈	—	17	1	no	maximal, Hall
15	C₂×D₁₇	C₂²×C₇	1	1	yes	characteristic
16	C₄×C₁₇	C₂²×C₇	1	3	yes	—
17	Dic₁₇	C₂²×C₇	1	3	yes	—
18	C₇×Q₈	—	17	3	no	—
19	C₇×Q₈	D₁₇	1	1	yes	characteristic, direct product factor
20	C₂×C₄×C₇	—	17	3	no	—
21	C₂×C₁₇	C₂³×C₇	1	1	yes	characteristic
22	D₁₇	C₇×Q₈	1	2	yes	direct product factor
23	C₂²×C₇	—	17	1	no	—
24	C₄×C₇	—	17	3	no	—
25	C₄×C₇	C₂×D₁₇	1	3	yes	—
26	C₁₇	C₂×C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×Q₈	—	17	1	no	Sylow
28	C₂×C₇	—	17	2	no	—
29	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
30	Q₈	—	17	3	no	—
31	Q₈	C₇×D₁₇	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	17	3	no	—
33	C₇	Q₈×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	17	1	no	—
35	C₄	—	17	3	no	—
36	C₄	C₂×C₇×D₁₇	1	3	yes	—
37	C₂	—	17	2	no	—
38	C₂	C₂²×C₇×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂²×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₇
Fitting	C₇×Q₈×C₁₇	C₂
socle	C₂×C₇×C₁₇	C₂³
prime radical	C₂×C₇×D₁₇	C₂²
hypercenter	C₇×Q₈	D₁₇
hypocenter	C₁₇	C₂×C₇×Q₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₇ ◁ C₇×Q₈

Complements

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

N	H ≅ G/N	type
1. C₇×Q₈×C₁₇	C₂	semidirect
3. C₇×Dic₃₄	C₂	semidirect
7. Q₈×D₁₇	C₇	direct (N × H)
9. C₇×D₁₇	Q₈	direct (N × H)
10. Q₈×C₁₇	C₂×C₇	semidirect
12. Dic₃₄	C₂×C₇	semidirect
13. C₇×C₁₇	C₂×Q₈	semidirect
19. C₇×Q₈	D₁₇	direct (N × H)
22. D₁₇	C₇×Q₈	direct (N × H)
26. C₁₇	C₂×C₇×Q₈	semidirect
31. Q₈	C₇×D₁₇	direct (N × H)
33. C₇	Q₈×D₁₇	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×Q₈×C₁₇	2
C₄×C₇×D₁₇	2
C₇×Dic₃₄	2
Q₈×D₁₇	7
C₂×C₇×Q₈	17

Subgroups — C7×Q8×D17 #14274161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×Q₈×D₁₇ #14274161