Subgroups — #16922227

Order 4352.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762528	C₂	1	1	yes	maximal, characteristic
2	#14526988	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#1425	C₂	1	1	yes	maximal, characteristic
4	#11762639	—	2	1	no	—
5	#11762528	C₄	1	2	yes	—
6	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₇×#368	—	2	1	no	—
8	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
9	C₁₇×#108	—	4	1	no	—
10	#10587490	—	4	1	no	—
11	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₇×C₃₂	Q₈	1	1	yes	characteristic
13	M₁₆×C₁₇	—	8	1	no	—
14	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
15	#63223	—	8	1	no	—
16	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₁₇	Q₁₆	1	1	yes	characteristic
18	#7547	—	17	1	no	maximal, Sylow
19	C₂×C₄×C₁₇	D₁₆	1	1	yes	characteristic
20	C₈×C₁₇	—	16	1	no	—
21	C₈×C₁₇	#107	1	1	yes	characteristic
22	C₈×C₁₇	Q₃₂	1	1	yes	characteristic
23	#3622	—	16	1	no	—
24	C₂×C₆₄	—	17	1	no	—
25	#1425	—	17	1	no	—
26	#1425	D₁₇	1	1	yes	characteristic
27	C₂²×C₁₇	Q₆₄	1	1	yes	characteristic
28	C₄×C₁₇	#366	1	1	yes	characteristic
29	C₄×C₁₇	D₃₂	1	1	yes	characteristic
30	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
31	#368	—	2	1	no	—
32	#368	—	34	1	no	—
33	C₆₄	—	17	2	no	—
34	C₂×C₁₇	—	2	1	no	—
35	C₂×C₁₇	#1423	1	1	yes	characteristic
36	C₂×C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
37	#108	—	4	1	no	—
38	#108	—	68	1	no	—
39	C₃₂	Dic₃₄	1	1	yes	characteristic
40	C₃₂	C₄×D₁₇	1	1	yes	characteristic
41	C₁₇	#7547	1	1	yes	characteristic, complemented, Sylow
42	M₁₆	—	8	1	no	—
43	M₁₆	—	136	1	no	—
44	C₂×C₈	#63228	1	1	yes	characteristic
45	C₁₆	#63225	1	1	yes	characteristic
46	C₁₆	#63231	1	1	yes	characteristic
47	C₂×C₄	#10587497	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	272	1	no	—
50	C₈	#10587478	1	1	yes	characteristic
51	C₈	#10587500	1	1	yes	characteristic
52	C₂²	#11762649	1	1	yes	characteristic
53	C₄	#11762634	1	1	yes	characteristic
54	C₄	#11762644	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#14526983	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11762644
commutator	C₁₇×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₇
Fitting	C₁₇×#1425	C₂
socle	C₂×C₁₇	#1423
prime radical	C₂²×C₁₇	Q₆₄
cosocle	C₂×C₁₇×C₃₂	C₂²
hypercenter	#1425	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 ◁ #1425

Complements

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

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

Maximal subgroups

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

subgroup	index
C₂×#11762528	2
#14526988	2
C₁₇×#1425	2
#7547	17