Subgroups — C₁₆×#13062438 #36342189

Order 21568.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925032	C₂	1	1	yes	maximal, characteristic
2	C₈×#13062438	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₃₃₇	C₂	1	1	yes	maximal, characteristic
4	#19129193	C₄	1	1	yes	characteristic
5	C₄×#13062438	C₄	1	1	yes	characteristic
6	#19129188	C₄	1	2	yes	complemented
7	C₈×D₃₃₇	C₂²	1	1	yes	characteristic
8	#19129160	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#13062438	C₈	1	2	yes	—
11	#14582113	C₈	1	2	yes	—
12	C₄×D₃₃₇	C₂×C₄	1	1	yes	characteristic
13	#14582106	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₃₇	C₂×C₈	1	1	yes	characteristic
16	#13062438	C₁₆	1	4	yes	direct product factor
17	C₄×C₃₃₇	C₄²	1	1	yes	characteristic
18	Dic₃₃₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃₃₇	C₄×C₈	1	1	yes	characteristic
20	D₃₃₇	C₂×C₁₆	1	2	yes	—
21	C₃₃₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	337	1	no	maximal, Sylow
23	C₂×C₁₆	—	337	1	no	—
24	C₂×C₁₆	—	337	1	no	—
25	C₄×C₈	—	337	1	no	—
26	C₂×C₈	—	337	1	no	—
27	C₂×C₈	—	337	1	no	—
28	C₄²	—	337	1	no	—
29	C₁₆	—	337	2	no	—
30	C₁₆	—	337	1	no	—
31	C₁₆	#13062438	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	337	2	no	—
33	C₂×C₄	—	337	1	no	—
34	C₈	—	337	2	no	—
35	C₈	—	337	1	no	—
36	C₈	C₂×#13062438	1	1	yes	characteristic
37	C₂²	—	337	1	no	—
38	C₄	—	337	4	no	—
39	C₄	—	337	1	no	—
40	C₄	C₄×#13062438	1	1	yes	characteristic
41	C₂	—	337	2	no	—
42	C₂	C₈×#13062438	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#13062438
commutator, hypocenter	C₃₃₇	C₄×C₁₆
Frattini	C₈	C₂×#13062438
Fitting	C₁₆×C₃₃₇	C₄
socle	C₂×C₃₃₇	C₄×C₈
prime radical	C₂×D₃₃₇	C₂×C₈
cosocle	C₈×D₃₃₇	C₂²
LCS	G ▷ C₃₃₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #19129188	C₄	semidirect
8. #19129160	C₄	semidirect
9. C₁₆×C₃₃₇	C₄	semidirect
16. #13062438	C₁₆	direct (N × H)
21. C₃₃₇	C₄×C₁₆	semidirect
31. C₁₆	#13062438	direct (N × H)

Maximal subgroups

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

subgroup	index
#24925032	2
C₈×#13062438	2
C₁₆×D₃₃₇	2
C₄×C₁₆	337

Subgroups — C16×#13062438 #36342189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#13062438 #36342189