Subgroups — C₁₇×#1726 #14524732

Order 2176.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#97	C₂	1	3	yes	maximal
2	C₂×C₄×C₈×C₁₇	C₂	1	3	yes	maximal
3	C₁₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₇	C₂²	1	3	yes	—
5	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₁₇	C₂²	1	3	yes	—
7	C₁₇×#97	C₄	1	12	yes	complemented
8	C₄×C₈×C₁₇	C₄	1	12	yes	complemented
9	C₁₇×#95	C₄	1	4	yes	—
10	C₂²×C₄×C₁₇	C₂×C₄	1	6	yes	—
11	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₁₇	C₂×C₄	1	6	yes	—
13	C₂×C₈×C₁₇	C₂×C₄	1	12	yes	—
14	C₂×C₈×C₁₇	C₂×C₄	1	6	yes	—
15	C₄²×C₁₇	C₂×C₄	1	6	yes	—
16	C₄²×C₁₇	C₂×C₄	1	6	yes	—
17	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₇	—	2	12	no	—
19	C₂×C₄×C₁₇	C₄²	1	12	yes	—
20	C₂×C₄×C₁₇	C₂²×C₄	1	3	yes	—
21	C₂×C₄×C₁₇	C₂²×C₄	1	3	yes	—
22	C₈×C₁₇	C₄²	1	12	yes	—
23	C₈×C₁₇	C₄²	1	4	yes	—
24	#1726	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₇	C₂×C₄²	1	3	yes	—
26	C₂²×C₁₇	#131	1	4	yes	—
27	C₄×C₁₇	—	2	12	no	—
28	C₄×C₁₇	C₂×C₄²	1	3	yes	—
29	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
30	C₂×#97	C₂×C₁₇	1	3	yes	—
31	C₂×C₄×C₈	C₂×C₁₇	1	3	yes	—
32	#376	C₂×C₁₇	1	1	yes	characteristic
33	C₂×C₁₇	C₄³	1	1	yes	characteristic
34	C₂×C₁₇	#405	1	6	yes	—
35	C₂²×C₈	C₂²×C₁₇	1	3	yes	—
36	C₂²×C₈	C₂²×C₁₇	1	1	yes	characteristic
37	C₂×C₄²	C₂²×C₁₇	1	3	yes	—
38	#97	C₄×C₁₇	1	12	yes	complemented
39	C₄×C₈	C₄×C₁₇	1	12	yes	complemented
40	#95	C₄×C₁₇	1	4	yes	—
41	C₁₇	#1726	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₄	C₂×C₄×C₁₇	1	6	yes	—
43	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
44	C₂×C₈	C₂×C₄×C₁₇	1	6	yes	—
45	C₂×C₈	C₂×C₄×C₁₇	1	6	yes	—
46	C₂×C₈	C₂×C₄×C₁₇	1	12	yes	—
47	C₄²	C₂×C₄×C₁₇	1	6	yes	—
48	C₄²	C₂×C₄×C₁₇	1	6	yes	—
49	C₂³	C₂²×C₄×C₁₇	1	1	yes	characteristic
50	C₂×C₄	—	2	12	no	—
51	C₂×C₄	C₄²×C₁₇	1	12	yes	—
52	C₂×C₄	C₂²×C₄×C₁₇	1	3	yes	—
53	C₂×C₄	C₂²×C₄×C₁₇	1	3	yes	—
54	C₈	C₄²×C₁₇	1	4	yes	—
55	C₈	C₄²×C₁₇	1	12	yes	—
56	C₂²	C₂×C₄²×C₁₇	1	3	yes	—
57	C₂²	C₁₇×#131	1	4	yes	—
58	C₄	—	2	12	no	—
59	C₄	C₂×C₄²×C₁₇	1	1	yes	characteristic
60	C₄	C₂×C₄²×C₁₇	1	3	yes	—
61	C₂	C₄³×C₁₇	1	1	yes	characteristic
62	C₂	C₁₇×#405	1	6	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₇	C₂²
commutator	C₂	C₄³×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle, prime radical	C₂³×C₁₇	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₇×#97	C₄	semidirect
8. C₄×C₈×C₁₇	C₄	semidirect
24. #1726	C₁₇	direct (N × H)
38. #97	C₄×C₁₇	semidirect
39. C₄×C₈	C₄×C₁₇	semidirect
41. C₁₇	#1726	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×C₁₇×#97	2
C₂×C₄×C₈×C₁₇	2
C₁₇×#376	2
#1726	17

Subgroups — C17×#1726 #14524732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1726 #14524732