Subgroups — #14543890

Order 2176.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763740	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#595	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₈×#595	C₄	1	1	yes	characteristic
5	#10587529	C₄	1	1	yes	characteristic
6	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
7	#10587467	C₄	1	2	yes	complemented
8	C₁₇×C₃₂	C₄	1	1	yes	characteristic, complemented
9	#10587465	C₄	1	1	yes	characteristic, complemented
10	C₄×#595	C₈	1	1	yes	characteristic
11	#63242	C₈	1	1	yes	characteristic
12	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
13	#63216	C₈	1	2	yes	—
14	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
15	#63214	C₂×C₄	1	1	yes	characteristic
16	C₂×#595	C₁₆	1	2	yes	—
17	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
18	#3624	C₁₆	1	2	yes	—
19	C₈×C₁₇	C₄²	1	1	yes	characteristic
20	#3622	C₂×C₈	1	1	yes	characteristic
21	#1397	—	17	1	no	maximal, Sylow
22	C₂×D₁₇	C₂×C₁₆	1	1	yes	characteristic
23	#595	—	2	2	no	—
24	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
25	Dic₁₇	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₃₂	—	17	1	no	—
27	C₂×C₃₂	—	17	1	no	—
28	C₄×C₁₆	—	17	1	no	—
29	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
30	D₁₇	M₆₄	1	2	yes	—
31	C₂×C₁₆	—	17	1	no	—
32	C₂×C₁₆	—	17	1	no	—
33	C₄×C₈	—	17	1	no	—
34	C₃₂	—	17	2	no	—
35	C₃₂	—	17	1	no	—
36	C₃₂	#595	1	1	yes	characteristic, complemented
37	C₁₇	#1397	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	—	17	1	no	—
39	C₂×C₈	—	17	1	no	—
40	C₄²	—	17	1	no	—
41	C₁₆	—	17	2	no	—
42	C₁₆	—	17	1	no	—
43	C₁₆	C₂×#595	1	1	yes	characteristic
44	C₂×C₄	—	17	1	no	—
45	C₂×C₄	—	17	2	no	—
46	C₈	—	17	2	no	—
47	C₈	—	17	1	no	—
48	C₈	C₄×#595	1	1	yes	characteristic
49	C₂²	—	17	1	no	—
50	C₄	—	17	1	no	—
51	C₄	—	34	2	no	—
52	C₄	C₈×#595	1	1	yes	characteristic
53	C₂	—	17	2	no	—
54	C₂	C₁₆×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂×#595
commutator, socle	C₂×C₁₇	C₄×C₁₆
Fitting	C₁₇×C₃₂	C₄
prime radical	C₂×D₁₇	C₂×C₁₆
cosocle	C₁₆×D₁₇	C₂²
hypercenter	C₃₂	#595
hypocenter	C₁₇	#1397
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #10587467	C₄	semidirect
8. C₁₇×C₃₂	C₄	semidirect
9. #10587465	C₄	semidirect
36. C₃₂	#595	semidirect
37. C₁₇	#1397	semidirect

Maximal subgroups

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

subgroup	index
#11763740	2
C₁₆×#595	2
C₃₂×D₁₇	2
#1397	17