Subgroups — #17962905

Order 4352.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	3	yes	maximal, complemented
2	C₂×#11763648	C₂	1	3	yes	maximal, complemented
3	#14531078	C₂	1	1	yes	maximal, characteristic
4	#11763648	C₂²	1	1	yes	characteristic
5	#11763648	C₂²	1	3	yes	—
6	#11762643	C₄	1	3	yes	—
7	C₂×#10587465	C₂²	1	3	yes	—
8	C₁₇×#504	C₄	1	1	yes	characteristic
9	C₁₇×#131	C₈	1	1	yes	characteristic
10	C₁₇×M₃₂	C₈	1	3	yes	—
11	C₂×C₁₆×C₁₇	C₂×C₄	1	3	yes	—
12	#10587465	C₂×C₄	1	3	yes	—
13	#10587465	C₂³	1	1	yes	characteristic
14	#41×C₁₇	C₁₆	1	1	yes	characteristic
15	M₁₆×C₁₇	C₁₆	1	3	yes	—
16	C₂×C₈×C₁₇	C₂×C₈	1	3	yes	—
17	C₁₆×C₁₇	C₂×C₈	1	3	yes	—
18	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
19	#13737	—	17	1	no	maximal, Sylow
20	Q₈×C₁₇	C₃₂	1	1	yes	characteristic
21	D₄×C₁₇	C₃₂	1	3	yes	—
22	C₂×C₄×C₁₇	C₂×C₁₆	1	3	yes	—
23	C₈×C₁₇	C₂×C₁₆	1	3	yes	—
24	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
25	#2258	—	17	1	no	—
26	M₁₂₈	—	17	3	no	—
27	C₂×C₆₄	—	17	3	no	—
28	C₂²×C₁₇	C₂×C₃₂	1	3	yes	—
29	C₄×C₁₇	C₂×C₃₂	1	3	yes	—
30	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
31	#504	#595	1	1	yes	characteristic
32	M₆₄	—	17	3	no	—
33	C₂×C₃₂	—	17	3	no	—
34	C₆₄	—	17	1	no	—
35	C₆₄	—	17	3	no	—
36	C₂×C₁₇	—	2	3	no	—
37	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
38	#131	#3624	1	1	yes	characteristic
39	M₃₂	#3624	1	3	yes	—
40	C₂×C₁₆	C₂×#595	1	3	yes	—
41	C₃₂	—	17	1	no	—
42	C₃₂	—	17	3	no	—
43	C₁₇	#13737	1	1	yes	characteristic, complemented, Sylow
44	#41	#63216	1	1	yes	characteristic
45	M₁₆	#63216	1	3	yes	—
46	C₂×C₈	C₂×#3624	1	3	yes	—
47	C₁₆	C₂×#3624	1	3	yes	—
48	C₁₆	C₂²×#595	1	1	yes	characteristic
49	Q₈	#10587467	1	1	yes	characteristic
50	D₄	#10587467	1	3	yes	—
51	C₂×C₄	C₂×#63216	1	3	yes	—
52	C₈	C₂×#63216	1	3	yes	—
53	C₈	C₂²×#3624	1	1	yes	characteristic
54	C₂²	C₂×#10587467	1	3	yes	—
55	C₄	C₂×#10587467	1	3	yes	—
56	C₄	C₂²×#63216	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×#10587467	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×#595
commutator, socle	C₂×C₁₇	C₂²×C₃₂
Fitting	C₁₇×#504	C₄
prime radical	#41×C₁₇	C₁₆
cosocle	#10587465	C₂³
hypercenter	#504	#595
hypocenter	C₁₇	#13737
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #14543953	C₂	semidirect
2. C₂×#11763648	C₂	semidirect
43. C₁₇	#13737	semidirect

Maximal subgroups

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

subgroup	index
#14543953	2
C₂×#11763648	2
#14531078	2
#13737	17