Subgroups — C₂×Dic₇×D₁₇ #14274142

Order 1904.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇×D₁₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₇×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₇×D₁₇	C₄	1	4	yes	complemented
7	C₂×C₇×D₁₇	C₂²	1	2	yes	—
8	Dic₁₁₉	C₂²	1	2	yes	complemented
9	C₁₇×Dic₇	C₂²	1	2	yes	complemented
10	C₂×C₄×D₁₇	—	7	1	no	maximal, Hall
11	C₂×C₇×C₁₇	C₂×C₄	1	2	yes	complemented
12	C₂×C₇×C₁₇	C₂³	1	1	yes	characteristic
13	C₇×D₁₇	C₂×C₄	1	4	yes	complemented
14	C₂²×D₁₇	D₇	1	1	yes	characteristic
15	C₂×C₄×C₁₇	—	7	1	no	—
16	C₂×Dic₁₇	—	7	1	no	—
17	C₄×D₁₇	—	7	4	no	—
18	C₇×C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂²×Dic₇	—	17	1	no	maximal, Hall
20	C₂²×C₁₇	C₂×D₇	1	1	yes	characteristic
21	C₂×D₁₇	Dic₇	1	4	yes	direct product factor
22	C₂×D₁₇	C₂×D₇	1	2	yes	—
23	C₄×C₁₇	—	7	2	no	—
24	Dic₁₇	—	7	2	no	—
25	C₂³×C₇	—	17	1	no	—
26	C₂×Dic₇	—	17	1	no	—
27	C₂×Dic₇	—	17	4	no	—
28	C₂×Dic₇	D₁₇	1	1	yes	characteristic, direct product factor
29	C₂×C₁₇	C₂×Dic₇	1	2	yes	complemented
30	C₂×C₁₇	C₂²×D₇	1	1	yes	characteristic
31	D₁₇	C₂×Dic₇	1	4	yes	direct product factor
32	C₂²×C₇	—	17	4	no	—
33	C₂²×C₇	—	17	2	no	—
34	C₂²×C₇	C₂×D₁₇	1	1	yes	characteristic
35	Dic₇	—	17	2	no	—
36	Dic₇	C₂×D₁₇	1	2	yes	direct product factor
37	C₁₇	C₂²×Dic₇	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	119	1	no	Sylow
39	C₂×C₇	—	17	4	no	—
40	C₂×C₇	C₄×D₁₇	1	2	yes	complemented
41	C₂×C₇	C₂²×D₁₇	1	1	yes	characteristic
42	C₂³	—	17	1	no	—
43	C₂×C₄	—	7	1	no	—
44	C₂×C₄	—	119	4	no	—
45	C₂×C₄	—	119	1	no	—
46	C₇	C₂×C₄×D₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	17	4	no	—
48	C₂²	—	17	2	no	—
49	C₂²	D₇×D₁₇	1	1	yes	characteristic
50	C₄	—	7	2	no	—
51	C₄	—	119	2	no	—
52	C₂	—	17	4	no	—
53	C₂	Dic₇×D₁₇	1	2	yes	direct product factor
54	C₂	C₂×D₇×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₇×D₁₇
commutator, hypocenter	C₇×C₁₇	C₂²×C₄
Frattini	C₂	C₂×D₇×D₁₇
Fitting, socle	C₂²×C₇×C₁₇	C₂²
prime radical	C₂²×C₇×D₁₇	C₂
cosocle	C₂×C₇×C₁₇	C₂³
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₁₉	C₂	semidirect
3. C₂×C₁₇×Dic₇	C₂	semidirect
4. Dic₇×D₁₇	C₂	direct (N × H)
6. C₂×C₇×D₁₇	C₄	semidirect
8. Dic₁₁₉	C₂²	semidirect
9. C₁₇×Dic₇	C₂²	semidirect
11. C₂×C₇×C₁₇	C₂×C₄	semidirect
13. C₇×D₁₇	C₂×C₄	semidirect
18. C₇×C₁₇	C₂²×C₄	semidirect
21. C₂×D₁₇	Dic₇	direct (N × H)
28. C₂×Dic₇	D₁₇	direct (N × H)
29. C₂×C₁₇	C₂×Dic₇	semidirect
31. D₁₇	C₂×Dic₇	direct (N × H)
36. Dic₇	C₂×D₁₇	direct (N × H)
37. C₁₇	C₂²×Dic₇	semidirect
40. C₂×C₇	C₄×D₁₇	semidirect
46. C₇	C₂×C₄×D₁₇	semidirect
53. C₂	Dic₇×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
C₂²×C₇×D₁₇	2
C₂×Dic₁₁₉	2
C₂×C₁₇×Dic₇	2
Dic₇×D₁₇	2
C₂×C₄×D₁₇	7
C₂²×Dic₇	17

Subgroups — C2×Dic7×D17 #14274142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₇×D₁₇ #14274142