Subgroups — #17981464

Order 4352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545851	C₂	1	2	yes	maximal
2	#14543890	C₂	1	1	yes	maximal, characteristic
3	#11763899	—	2	2	no	—
4	#11763740	C₄	1	1	yes	characteristic
5	C₁₆×#595	C₂²	1	1	yes	characteristic
6	C₃₂×D₁₇	C₄	1	1	yes	characteristic
7	C₄⋊#3633	—	4	2	no	—
8	C₈×#595	D₄	1	1	yes	characteristic
9	#10587529	Q₈	1	1	yes	characteristic
10	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
11	#10587467	—	2	1	no	—
12	C₁₇×C₃₂	C₈	1	1	yes	characteristic, complemented
13	#10587465	C₈	1	1	yes	characteristic, complemented
14	C₂×#3633	—	8	2	no	—
15	C₄×#595	D₈	1	1	yes	characteristic
16	#63242	Q₁₆	1	1	yes	characteristic
17	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
18	#63216	—	2	1	no	—
19	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
20	#63214	M₁₆	1	1	yes	characteristic
21	#7463	—	17	1	no	maximal, Sylow
22	C₂×#595	SD₃₂	1	2	yes	—
23	#3633	—	16	2	no	—
24	C₄×D₁₇	#107	1	1	yes	characteristic
25	#3624	—	2	1	no	—
26	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
27	#3622	#108	1	1	yes	characteristic
28	#1397	—	17	1	no	—
29	#1372	—	17	2	no	—
30	C₂×D₁₇	#367	1	1	yes	characteristic
31	#595	—	2	2	no	—
32	C₄×C₁₇	#335	1	1	yes	characteristic
33	Dic₁₇	#368	1	1	yes	characteristic
34	C₂×C₃₂	—	17	1	no	—
35	C₂×C₃₂	—	17	1	no	—
36	C₄×C₁₆	—	17	1	no	—
37	#335	—	34	2	no	—
38	C₂×C₁₇	#1372	1	1	yes	characteristic
39	D₁₇	#1426	1	2	yes	—
40	C₂×C₁₆	—	17	1	no	—
41	C₂×C₁₆	—	17	1	no	—
42	C₄⋊C₈	—	68	2	no	—
43	C₄×C₈	—	17	1	no	—
44	C₃₂	—	17	1	no	—
45	C₃₂	—	34	1	no	—
46	C₃₂	#3633	1	1	yes	characteristic, complemented
47	C₁₇	#7463	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	136	2	no	—
51	C₄²	—	17	1	no	—
52	C₁₆	—	17	1	no	—
53	C₁₆	—	34	1	no	—
54	C₁₆	C₂×#3633	1	1	yes	characteristic
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	17	2	no	—
57	C₈	—	272	2	no	—
58	C₈	—	17	1	no	—
59	C₈	—	34	1	no	—
60	C₈	C₄⋊#3633	1	1	yes	characteristic
61	C₂²	—	17	1	no	—
62	C₄	—	17	1	no	—
63	C₄	—	34	2	no	—
64	C₄	#11763899	1	1	yes	characteristic
65	C₂	—	17	2	no	—
66	C₂	#14545851	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14545851
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₁₆	C₂×#3633
Fitting	C₁₇×C₃₂	C₈
socle	C₂×C₁₇	#1372
prime radical	C₂×D₁₇	#367
cosocle	C₁₆×#595	C₂²
hypercenter	C₃₂	#3633
hypocenter	C₁₇	#7463
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
12. C₁₇×C₃₂	C₈	semidirect
13. #10587465	C₈	semidirect
46. C₃₂	#3633	semidirect
47. C₁₇	#7463	semidirect

Maximal subgroups

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

subgroup	index
#14545851	2
#14543890	2
#7463	17