Subgroups — #14526985

Order 2176.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587465	C₂	1	1	yes	maximal, characteristic
2	#11762635	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
5	C₁₇×#107	—	2	1	no	—
6	#10587489	—	2	1	no	—
7	#10587465	C₄	1	2	yes	complemented
8	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₁₇	—	4	1	no	—
10	C₄⋊Dic₁₇	—	4	1	no	—
11	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₇	—	8	1	no	—
14	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
15	C₂×Dic₁₇	—	8	1	no	—
16	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₇	Q₁₆	1	1	yes	characteristic
18	#1424	—	17	1	no	maximal, Sylow
19	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
20	C₄×C₁₇	—	16	1	no	—
21	C₄×C₁₇	#107	1	1	yes	characteristic
22	C₄×C₁₇	Q₃₂	1	1	yes	characteristic
23	Dic₁₇	—	16	1	no	—
24	C₂×C₃₂	—	17	1	no	—
25	#366	—	17	1	no	—
26	#366	D₁₇	1	1	yes	characteristic
27	C₂×C₁₇	#366	1	1	yes	characteristic
28	C₂×C₁₇	SD₆₄	1	1	yes	characteristic
29	C₂×C₁₇	SD₆₄	1	1	yes	characteristic
30	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
31	#107	—	2	1	no	—
32	#107	—	34	1	no	—
33	C₃₂	—	17	2	no	—
34	C₁₇	#1424	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	68	1	no	—
38	C₁₆	Dic₃₄	1	1	yes	characteristic
39	C₁₆	C₄×D₁₇	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	136	1	no	—
42	C₂×C₄	#63228	1	1	yes	characteristic
43	C₈	#63225	1	1	yes	characteristic
44	C₈	#63231	1	1	yes	characteristic
45	C₂²	#10587497	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	272	1	no	—
48	C₄	#10587478	1	1	yes	characteristic
49	C₄	#10587500	1	1	yes	characteristic
50	C₂	#11762634	1	1	yes	characteristic
51	C₂	#11762646	1	1	yes	characteristic
52	C₂	#11762647	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587497
commutator	C₁₆×C₁₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₇
Fitting	C₁₇×#366	C₂
socle, prime radical	C₂²×C₁₇	D₁₆
cosocle	C₂×C₁₆×C₁₇	C₂²
hypercenter	#366	D₁₇
hypocenter	C₁₇	#1424
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
7. #10587465	C₄	semidirect
34. C₁₇	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587465	2
#11762635	2
C₁₇×#366	2
#1424	17