Subgroups — #17981507

Order 4352.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545782	C₂	1	2	yes	maximal, complemented
2	C₂×#11763648	C₂	1	1	yes	maximal, characteristic
3	#11763648	C₄	1	1	yes	characteristic
4	#11763648	C₂²	1	1	yes	characteristic
5	C₂×#10587465	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
7	#10587465	C₈	1	1	yes	characteristic
8	#10587465	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
10	C₁₆×C₁₇	C₁₆	1	1	yes	characteristic
11	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
12	M₂₅₆	—	17	1	no	maximal, Sylow
13	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
14	C₈×C₁₇	C₃₂	1	1	yes	characteristic
15	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₆₄	—	17	1	no	—
17	C₁₂₈	—	17	2	no	—
18	C₂²×C₁₇	C₆₄	1	1	yes	characteristic
19	C₄×C₁₇	C₆₄	1	1	yes	characteristic
20	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
21	C₂×C₃₂	—	17	1	no	—
22	C₆₄	—	17	1	no	—
23	C₆₄	—	17	1	no	—
24	C₂×C₁₇	—	2	1	no	—
25	C₂×C₁₇	C₂×C₆₄	1	1	yes	characteristic
26	C₂×C₁₆	#3633	1	1	yes	characteristic
27	C₃₂	—	17	1	no	—
28	C₃₂	—	17	1	no	—
29	C₁₇	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	#63241	1	1	yes	characteristic
31	C₁₆	#63241	1	1	yes	characteristic
32	C₁₆	C₂×#3633	1	1	yes	characteristic
33	C₂×C₄	#10587528	1	1	yes	characteristic
34	C₈	#10587528	1	1	yes	characteristic
35	C₈	C₂×#63241	1	1	yes	characteristic
36	C₂²	#11763891	1	1	yes	characteristic
37	C₄	#11763891	1	1	yes	characteristic
38	C₄	C₂×#10587528	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×#11763891	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂×#3633
commutator, socle	C₂×C₁₇	C₂×C₆₄
Fitting	C₂×C₁₆×C₁₇	C₈
prime radical	C₂²×C₁₇	C₆₄
cosocle	#11763648	C₂²
hypercenter	C₂×C₁₆	#3633
hypocenter	C₁₇	M₂₅₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #14545782	C₂	semidirect
29. C₁₇	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
#14545782	2
C₂×#11763648	2
M₂₅₆	17