Subgroups — #17981462

Order 4352.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545852	C₂	1	2	yes	maximal
2	C₃₂×#595	C₂	1	1	yes	maximal, characteristic
3	#11763914	—	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	#10587666	—	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
13	#10587465	C₈	1	1	yes	characteristic
14	C₄×#595	Q₁₆	1	1	yes	characteristic
15	#63242	D₈	1	1	yes	characteristic
16	#63241	—	8	2	no	—
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	#7462	—	17	1	no	maximal, Sylow
22	C₂×#595	—	2	1	no	—
23	C₄×D₁₇	#107	1	1	yes	characteristic
24	#3624	D₁₆	1	1	yes	characteristic
25	#3624	Q₃₂	1	1	yes	characteristic
26	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
27	#3622	#108	1	1	yes	characteristic
28	C₄×C₃₂	—	17	1	no	—
29	#1373	—	17	2	no	—
30	C₂×D₁₇	#368	1	1	yes	characteristic
31	#595	—	2	2	no	—
32	C₄×C₁₇	#335	1	1	yes	characteristic
33	Dic₁₇	#366	1	1	yes	characteristic
34	C₂×C₃₂	—	17	1	no	—
35	C₂×C₃₂	—	17	1	no	—
36	#364	—	34	2	no	—
37	C₄×C₁₆	—	17	1	no	—
38	C₂×C₁₇	#1371	1	1	yes	characteristic
39	D₁₇	—	2	1	no	—
40	M₃₂	—	68	2	no	—
41	C₂×C₁₆	—	17	1	no	—
42	C₂×C₁₆	—	17	1	no	—
43	C₄×C₈	—	17	1	no	—
44	C₃₂	—	17	1	no	—
45	C₃₂	—	34	1	no	—
46	C₃₂	#3633	1	1	yes	characteristic
47	C₁₇	#7462	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	17	1	no	—
50	C₄²	—	17	1	no	—
51	C₁₆	—	17	1	no	—
52	C₁₆	—	34	1	no	—
53	C₁₆	—	136	2	no	—
54	C₁₆	C₂×#3633	1	1	yes	characteristic
55	C₂×C₄	—	17	1	no	—
56	C₂×C₄	—	34	1	no	—
57	C₈	—	17	1	no	—
58	C₈	—	17	1	no	—
59	C₈	—	17	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	—	34	1	no	—
66	C₂	#14545850	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14545850
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₁₆	C₂×#3633
Fitting	C₁₇×C₃₂	C₈
socle	C₂×C₁₇	#1371
prime radical	C₂×D₁₇	#368
cosocle	C₁₆×#595	C₂²
hypercenter	C₃₂	#3633
hypocenter	C₁₇	#7462
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
47. C₁₇	#7462	semidirect

Maximal subgroups

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

subgroup	index
#14545852	2
C₃₂×#595	2
#7462	17