Subgroups — #17981487

Order 4352.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545887	C₂	1	2	yes	maximal
2	C₃₂×#595	C₂	1	1	yes	maximal, characteristic
3	#11763891	C₄	1	4	yes	complemented
4	#11763740	C₂²	1	1	yes	characteristic
5	C₁₆×#595	C₄	1	1	yes	characteristic
6	C₃₂×D₁₇	C₄	1	1	yes	characteristic
7	C₈×#595	C₈	1	1	yes	characteristic
8	#10587529	C₈	1	1	yes	characteristic
9	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
10	#10587467	C₂×C₄	1	2	yes	—
11	C₁₇×C₃₂	C₈	1	1	yes	characteristic
12	#10587465	C₈	1	1	yes	characteristic
13	C₄×#595	C₁₆	1	1	yes	characteristic
14	#63242	C₁₆	1	1	yes	characteristic
15	C₈×D₁₇	C₂×C₈	1	1	yes	characteristic
16	#63216	C₁₆	1	2	yes	—
17	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
18	#63214	C₄²	1	1	yes	characteristic
19	C₄×C₆₄	—	17	1	no	maximal, Sylow
20	C₂×#595	C₃₂	1	2	yes	—
21	C₄×D₁₇	C₂×C₁₆	1	1	yes	characteristic
22	#3624	C₃₂	1	2	yes	—
23	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
24	#3622	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₆₄	—	17	2	no	—
26	C₄×C₃₂	—	17	1	no	—
27	C₂×D₁₇	C₂×C₃₂	1	1	yes	characteristic
28	#595	C₆₄	1	4	yes	complemented
29	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
30	Dic₁₇	C₂×C₃₂	1	1	yes	characteristic
31	C₂×C₃₂	—	17	1	no	—
32	C₂×C₃₂	—	17	1	no	—
33	C₄×C₁₆	—	17	1	no	—
34	C₆₄	—	17	4	no	—
35	C₂×C₁₇	C₄×C₃₂	1	1	yes	characteristic
36	D₁₇	C₂×C₆₄	1	2	yes	—
37	C₂×C₁₆	—	17	1	no	—
38	C₂×C₁₆	—	17	1	no	—
39	C₄×C₈	—	17	1	no	—
40	C₃₂	—	17	2	no	—
41	C₃₂	—	17	1	no	—
42	C₃₂	#3633	1	1	yes	characteristic
43	C₁₇	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₈	—	17	1	no	—
45	C₂×C₈	—	17	1	no	—
46	C₄²	—	17	1	no	—
47	C₁₆	—	17	2	no	—
48	C₁₆	—	17	1	no	—
49	C₁₆	C₂×#3633	1	1	yes	characteristic
50	C₂×C₄	—	17	2	no	—
51	C₂×C₄	—	17	1	no	—
52	C₈	—	17	2	no	—
53	C₈	—	17	1	no	—
54	C₈	C₄×#3633	1	1	yes	characteristic
55	C₂²	—	17	1	no	—
56	C₄	—	17	4	no	—
57	C₄	—	17	1	no	—
58	C₄	#11763902	1	1	yes	characteristic
59	C₂	—	17	2	no	—
60	C₂	#14545868	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃₂	#3633
commutator, hypocenter	C₁₇	C₄×C₆₄
Frattini	C₁₆	C₂×#3633
Fitting	C₁₇×C₃₂	C₈
socle	C₂×C₁₇	C₄×C₃₂
prime radical	C₂×D₁₇	C₂×C₃₂
cosocle	#11763740	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
3. #11763891	C₄	semidirect
28. #595	C₆₄	semidirect
43. C₁₇	C₄×C₆₄	semidirect

Maximal subgroups

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

subgroup	index
#14545887	2
C₃₂×#595	2
C₄×C₆₄	17