Subgroups — #16922228

Order 4352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14526988	C₂	1	2	yes	maximal
2	C₂×C₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#11762639	—	2	2	no	—
4	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₇×C₆₄	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
7	#10587490	—	4	2	no	—
8	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₁₇×C₃₂	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
11	#63223	—	8	2	no	—
12	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₁₇	Q₁₆	1	1	yes	characteristic
14	#7547	—	17	1	no	maximal, Sylow
15	C₂×C₄×C₁₇	D₁₆	1	1	yes	characteristic
16	C₈×C₁₇	#107	1	1	yes	characteristic
17	C₈×C₁₇	Q₃₂	1	1	yes	characteristic
18	#3622	—	16	2	no	—
19	C₂×C₆₄	D₁₇	1	1	yes	characteristic
20	#1425	—	17	2	no	—
21	C₂²×C₁₇	Q₆₄	1	1	yes	characteristic
22	C₄×C₁₇	#366	1	1	yes	characteristic
23	C₄×C₁₇	D₃₂	1	1	yes	characteristic
24	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
25	#368	—	34	2	no	—
26	C₆₄	Dic₁₇	1	2	yes	—
27	C₂×C₁₇	—	2	1	no	—
28	C₂×C₁₇	#1423	1	1	yes	characteristic
29	C₂×C₁₆	D₆₈	1	1	yes	characteristic
30	#108	—	68	2	no	—
31	C₃₂	Dic₃₄	1	1	yes	characteristic
32	C₃₂	C₂×Dic₁₇	1	1	yes	characteristic
33	C₁₇	#7547	1	1	yes	characteristic, complemented, Sylow
34	M₁₆	—	136	2	no	—
35	C₂×C₈	D₁₃₆	1	1	yes	characteristic
36	C₁₆	Dic₆₈	1	1	yes	characteristic
37	C₁₆	C₄⋊Dic₁₇	1	1	yes	characteristic
38	C₂×C₄	D₂₇₂	1	1	yes	characteristic
39	C₈	—	272	2	no	—
40	C₈	Dic₁₃₆	1	1	yes	characteristic
41	C₈	#10587489	1	1	yes	characteristic
42	C₂²	Dic₂₇₂	1	1	yes	characteristic
43	C₄	#11762635	1	1	yes	characteristic
44	C₄	D₅₄₄	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14526984	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅₄₄
commutator	C₁₇×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₇
Fitting	C₂×C₁₇×C₆₄	C₂
socle	C₂×C₁₇	#1423
prime radical	C₂²×C₁₇	Q₆₄
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₇
hypocenter	C₁₇	#7547
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
33. C₁₇	#7547	semidirect

Maximal subgroups

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

subgroup	index
#14526988	2
C₂×C₁₇×C₆₄	2
#7547	17