Subgroups — C₁₇×#1712 #14524718

Order 2176.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#493	C₂	1	6	yes	maximal, complemented
2	C₈²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×C₁₇	—	2	12	no	—
4	C₁₇×#127	C₂²	1	4	yes	—
5	C₄×C₈×C₁₇	C₂²	1	3	yes	—
6	C₂×D₄×C₁₇	—	2	12	no	—
7	D₈×C₁₇	—	4	24	no	—
8	C₂×C₈×C₁₇	D₄	1	6	yes	—
9	C₄²×C₁₇	C₂³	1	1	yes	characteristic
10	C₂³×C₁₇	—	4	4	no	—
11	D₄×C₁₇	—	4	24	no	—
12	C₂×C₄×C₁₇	C₂×D₄	1	3	yes	—
13	C₈×C₁₇	D₈	1	12	yes	complemented
14	#1712	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₁₇	—	8	12	no	—
16	C₂²×C₁₇	#127	1	1	yes	characteristic
17	C₄×C₁₇	C₂×D₈	1	6	yes	—
18	#493	C₂×C₁₇	1	6	yes	complemented
19	C₈²	C₂×C₁₇	1	1	yes	characteristic, complemented
20	C₂×C₁₇	—	16	4	no	—
21	C₂×C₁₇	#493	1	3	yes	—
22	C₂×D₈	—	2	12	no	—
23	#127	C₂²×C₁₇	1	4	yes	—
24	C₄×C₈	C₂²×C₁₇	1	3	yes	—
25	C₁₇	#1712	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×D₄	—	2	12	no	—
27	D₈	—	4	24	no	—
28	C₂×C₈	D₄×C₁₇	1	6	yes	—
29	C₄²	C₂³×C₁₇	1	1	yes	characteristic
30	C₂³	—	4	4	no	—
31	D₄	—	4	24	no	—
32	C₂×C₄	C₂×D₄×C₁₇	1	3	yes	—
33	C₈	D₈×C₁₇	1	12	yes	complemented
34	C₂²	—	8	12	no	—
35	C₂²	C₁₇×#127	1	1	yes	characteristic
36	C₄	C₂×D₈×C₁₇	1	6	yes	—
37	C₂	—	16	4	no	—
38	C₂	C₁₇×#493	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

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