Subgroups — C₁₇×#1420 #14524426

Order 2176.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₇×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₇	—	2	1	no	—
5	C₁₇×Q₃₂	—	2	1	no	—
6	C₁₇×Q₃₂	C₄	1	2	yes	—
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#108	—	2	1	no	—
9	C₁₇×C₃₂	—	2	1	no	—
10	C₂×Q₈×C₁₇	—	4	1	no	—
11	Q₁₆×C₁₇	—	2	2	no	—
12	Q₁₆×C₁₇	—	4	1	no	—
13	M₁₆×C₁₇	—	4	1	no	—
14	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
15	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₇	D₄	1	1	yes	characteristic
17	Q₈×C₁₇	—	4	2	no	—
18	Q₈×C₁₇	—	8	1	no	—
19	C₂×C₄×C₁₇	—	8	1	no	—
20	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
21	C₈×C₁₇	—	8	1	no	—
22	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₇	SD₁₆	1	1	yes	characteristic
24	#1420	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₇	SD₃₂	1	1	yes	characteristic
26	C₄×C₁₇	—	8	2	no	—
27	C₄×C₁₇	#102	1	1	yes	characteristic
28	C₄×C₁₇	D₁₆	1	1	yes	characteristic
29	C₂×Q₃₂	C₂×C₁₇	1	1	yes	characteristic
30	M₆₄	C₂×C₁₇	1	1	yes	characteristic
31	#368	C₂×C₁₇	1	1	yes	characteristic
32	C₂×C₁₇	—	2	1	no	—
33	C₂×C₁₇	#357	1	1	yes	characteristic
34	C₂×Q₁₆	—	2	1	no	—
35	Q₃₂	—	2	1	no	—
36	Q₃₂	C₄×C₁₇	1	2	yes	—
37	C₂×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
38	#108	—	2	1	no	—
39	C₃₂	—	2	1	no	—
40	C₁₇	#1420	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
46	C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
47	C₁₆	D₄×C₁₇	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	D₈×C₁₇	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
54	C₈	SD₁₆×C₁₇	1	1	yes	characteristic
55	C₂²	C₁₇×SD₃₂	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	C₁₇×#102	1	1	yes	characteristic
58	C₄	C₁₇×D₁₆	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₁₇×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#357
commutator	C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₇
prime radical	C₂²×C₁₇	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₆×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
24. #1420	C₁₇	direct (N × H)
40. C₁₇	#1420	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×Q₃₂	2
C₁₇×M₆₄	2
C₁₇×#368	2
#1420	17

Subgroups — C17×#1420 #14524426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1420 #14524426