Subgroups — #17949625

Order 4352.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543948	C₂	1	1	yes	maximal, characteristic
2	#14543946	C₂	1	1	yes	maximal, characteristic
3	#14526994	C₂	1	1	yes	maximal, characteristic
4	#11763737	—	2	1	no	—
5	#11763735	—	2	1	no	—
6	C₃₂×D₁₇	C₂²	1	1	yes	characteristic
7	#11762528	C₄	1	1	yes	characteristic, complemented
8	C₁₇×C₆₄	C₄	1	1	yes	characteristic, complemented
9	#10587536	—	4	1	no	—
10	#10587534	—	4	1	no	—
11	C₁₆×D₁₇	D₄	1	1	yes	characteristic
12	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
13	#10587465	Q₈	1	1	yes	characteristic
14	C₄⋊#595	—	8	1	no	—
15	#63243	—	8	1	no	—
16	C₈×D₁₇	D₈	1	1	yes	characteristic
17	C₁₆×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	#63214	Q₁₆	1	1	yes	characteristic
19	#7548	—	17	1	no	maximal, Sylow
20	C₂×#595	—	16	1	no	—
21	C₄×D₁₇	D₁₆	1	1	yes	characteristic
22	#3624	—	16	1	no	—
23	C₈×C₁₇	#107	1	1	yes	characteristic
24	#3622	Q₃₂	1	1	yes	characteristic
25	M₁₂₈	—	17	1	no	—
26	#1425	—	17	1	no	—
27	#1424	—	17	1	no	—
28	C₂×D₁₇	SD₆₄	1	1	yes	characteristic
29	#595	—	32	1	no	—
30	C₄×C₁₇	#366	1	1	yes	characteristic
31	Dic₁₇	SD₆₄	1	1	yes	characteristic
32	C₂×C₃₂	—	17	1	no	—
33	#368	—	34	1	no	—
34	#366	—	34	1	no	—
35	C₆₄	—	17	1	no	—
36	C₆₄	#595	1	1	yes	characteristic, complemented
37	C₂×C₁₇	#1424	1	1	yes	characteristic
38	D₁₇	—	2	1	no	—
39	C₂×C₁₆	—	17	1	no	—
40	#108	—	68	1	no	—
41	#107	—	68	1	no	—
42	C₃₂	—	17	1	no	—
43	C₃₂	C₂×#595	1	1	yes	characteristic
44	C₁₇	#7548	1	1	yes	characteristic, complemented, Sylow
45	M₁₆	—	136	1	no	—
46	C₂×C₈	—	17	1	no	—
47	C₄⋊C₄	—	136	1	no	—
48	C₁₆	—	17	1	no	—
49	C₁₆	C₄⋊#595	1	1	yes	characteristic
50	C₂×C₄	—	272	1	no	—
51	C₂×C₄	—	17	1	no	—
52	C₈	—	272	1	no	—
53	C₈	—	17	1	no	—
54	C₈	#10587534	1	1	yes	characteristic
55	C₂²	—	17	1	no	—
56	C₄	—	17	1	no	—
57	C₄	—	544	1	no	—
58	C₄	#11763735	1	1	yes	characteristic
59	C₂	—	34	1	no	—
60	C₂	#14543946	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14543946
commutator	C₁₇×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#595
Fitting	C₁₇×C₆₄	C₄
socle	C₂×C₁₇	#1424
prime radical	C₂×D₁₇	SD₆₄
cosocle	C₃₂×D₁₇	C₂²
hypercenter	C₆₄	#595
hypocenter	C₁₇	#7548
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
7. #11762528	C₄	semidirect
8. C₁₇×C₆₄	C₄	semidirect
36. C₆₄	#595	semidirect
44. C₁₇	#7548	semidirect

Maximal subgroups

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

subgroup	index
#14543948	2
#14543946	2
#14526994	2
#7548	17