Subgroups — C₁₆×#11757210 #29508601

Order 15424.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440715	C₂	1	1	yes	maximal, characteristic
2	C₈×#11757210	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#16838778	C₄	1	1	yes	characteristic
5	C₄×#11757210	C₄	1	1	yes	characteristic
6	#16838773	C₄	1	2	yes	complemented
7	C₈×D₂₄₁	C₂²	1	1	yes	characteristic
8	#16838745	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₂₄₁	C₄	1	1	yes	characteristic, complemented
10	C₂×#11757210	C₈	1	2	yes	—
11	#14515356	C₈	1	2	yes	—
12	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
13	#14515349	C₂×C₄	1	1	yes	characteristic
14	C₈×C₂₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×D₂₄₁	C₂×C₈	1	1	yes	characteristic
16	#11757210	C₁₆	1	4	yes	direct product factor
17	C₄×C₂₄₁	C₄²	1	1	yes	characteristic
18	Dic₂₄₁	C₂×C₈	1	1	yes	characteristic
19	C₂×C₂₄₁	C₄×C₈	1	1	yes	characteristic
20	D₂₄₁	C₂×C₁₆	1	2	yes	—
21	C₂₄₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	241	1	no	maximal, Sylow
23	C₂×C₁₆	—	241	1	no	—
24	C₂×C₁₆	—	241	1	no	—
25	C₄×C₈	—	241	1	no	—
26	C₂×C₈	—	241	1	no	—
27	C₂×C₈	—	241	1	no	—
28	C₄²	—	241	1	no	—
29	C₁₆	—	241	2	no	—
30	C₁₆	—	241	1	no	—
31	C₁₆	#11757210	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	241	2	no	—
33	C₂×C₄	—	241	1	no	—
34	C₈	—	241	2	no	—
35	C₈	—	241	1	no	—
36	C₈	C₂×#11757210	1	1	yes	characteristic
37	C₂²	—	241	1	no	—
38	C₄	—	241	4	no	—
39	C₄	—	241	1	no	—
40	C₄	C₄×#11757210	1	1	yes	characteristic
41	C₂	—	241	2	no	—
42	C₂	C₈×#11757210	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#11757210
commutator, hypocenter	C₂₄₁	C₄×C₁₆
Frattini	C₈	C₂×#11757210
Fitting	C₁₆×C₂₄₁	C₄
socle	C₂×C₂₄₁	C₄×C₈
prime radical	C₂×D₂₄₁	C₂×C₈
cosocle	C₈×D₂₄₁	C₂²
LCS	G ▷ C₂₄₁
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #16838773	C₄	semidirect
8. #16838745	C₄	semidirect
9. C₁₆×C₂₄₁	C₄	semidirect
16. #11757210	C₁₆	direct (N × H)
21. C₂₄₁	C₄×C₁₆	semidirect
31. C₁₆	#11757210	direct (N × H)

Maximal subgroups

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

subgroup	index
#21440715	2
C₈×#11757210	2
C₁₆×D₂₄₁	2
C₄×C₁₆	241

Subgroups — C16×#11757210 #29508601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#11757210 #29508601