Subgroups — #17949618

Order 4352.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	2	yes	maximal
2	C₄×#10587465	C₂	1	1	yes	maximal, characteristic
3	#11763648	—	2	2	no	—
4	C₂×#10587465	C₄	1	1	yes	characteristic
5	C₂×#10587465	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
10	#10587465	—	2	1	no	—
11	#10587465	D₄	1	1	yes	characteristic
12	#10587465	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₇	C₁₆	1	1	yes	characteristic
16	C₁₆×C₁₇	—	2	1	no	—
17	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
19	#7544	—	17	1	no	maximal, Sylow
20	C₂×C₄×C₁₇	—	2	1	no	—
21	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
22	C₈×C₁₇	C₃₂	1	2	yes	—
23	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₁₇	M₃₂	1	1	yes	characteristic
25	M₁₂₈	—	17	2	no	—
26	C₄×C₃₂	—	17	1	no	—
27	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
28	C₄×C₁₇	—	2	2	no	—
29	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
30	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
31	C₂×C₃₂	—	17	1	no	—
32	C₂×C₃₂	—	17	1	no	—
33	C₄×C₁₆	#595	1	1	yes	characteristic
34	C₆₄	—	34	2	no	—
35	C₂×C₁₇	—	2	1	no	—
36	C₂×C₁₇	C₄⋊C₃₂	1	1	yes	characteristic
37	C₂×C₁₆	#3624	1	1	yes	characteristic
38	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
39	C₄×C₈	#3624	1	1	yes	characteristic
40	C₃₂	—	17	1	no	—
41	C₃₂	—	17	1	no	—
42	C₃₂	—	34	1	no	—
43	C₁₇	#7544	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₈	#63216	1	1	yes	characteristic
45	C₂×C₈	C₂×#3624	1	1	yes	characteristic
46	C₄²	#63216	1	1	yes	characteristic
47	C₁₆	—	2	1	no	—
48	C₁₆	#63243	1	1	yes	characteristic
49	C₁₆	C₄⋊#595	1	1	yes	characteristic
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂×#63216	1	1	yes	characteristic
52	C₈	#10587467	1	2	yes	—
53	C₈	#10587538	1	1	yes	characteristic
54	C₈	C₄⋊#3624	1	1	yes	characteristic
55	C₂²	#11763741	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	C₄⋊#63216	1	1	yes	characteristic
58	C₄	C₂×#10587467	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄⋊#10587467	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄⋊#595
commutator	C₄×C₁₇	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₄⋊C₃₂
prime radical	C₂²×C₁₇	M₆₄
cosocle	C₂×#10587465	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7544
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
43. C₁₇	#7544	semidirect

Maximal subgroups

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

subgroup	index
#14543953	2
C₄×#10587465	2
#7544	17