Subgroups — C₃₂×Dic₂₆₉ #46809016

Order 34432.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22575359	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#16864377	C₄	1	1	yes	characteristic
5	C₈×Dic₂₆₉	C₄	1	1	yes	characteristic
6	#22575359	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₆₉	C₄	1	2	yes	complemented
9	C₂×#14524130	C₈	1	1	yes	characteristic
10	C₄×Dic₂₆₉	C₈	1	1	yes	characteristic
11	#16864377	C₈	1	2	yes	—
12	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₂₆₉	C₁₆	1	2	yes	—
16	#14524130	C₁₆	1	2	yes	—
17	C₂×C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
18	C₈×C₂₆₉	C₄²	1	1	yes	characteristic
19	C₈×C₂₆₉	C₂×C₈	1	1	yes	characteristic
20	C₂²×C₂₆₉	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₂₆₉	C₄×C₈	1	1	yes	characteristic
22	C₄×C₂₆₉	C₂×C₁₆	1	1	yes	characteristic
23	Dic₂₆₉	C₃₂	1	4	yes	direct product factor
24	C₂×C₂₆₉	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₂₆₉	C₂×C₃₂	1	2	yes	—
26	C₂₆₉	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₃₂	—	269	1	no	maximal, Sylow
28	C₂×C₃₂	—	269	1	no	—
29	C₂×C₃₂	D₂₆₉	1	1	yes	characteristic
30	C₄×C₁₆	—	269	1	no	—
31	C₂×C₁₆	—	269	1	no	—
32	C₂×C₁₆	C₂×D₂₆₉	1	1	yes	characteristic
33	C₄×C₈	—	269	1	no	—
34	C₃₂	—	269	2	no	—
35	C₃₂	Dic₂₆₉	1	2	yes	direct product factor
36	C₂×C₈	—	269	1	no	—
37	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
38	C₄²	—	269	1	no	—
39	C₁₆	—	269	2	no	—
40	C₁₆	C₄×D₂₆₉	1	1	yes	characteristic
41	C₁₆	C₂×Dic₂₆₉	1	1	yes	characteristic
42	C₂×C₄	—	269	2	no	—
43	C₂×C₄	C₈×D₂₆₉	1	1	yes	characteristic
44	C₈	—	269	2	no	—
45	C₈	C₄×Dic₂₆₉	1	1	yes	characteristic
46	C₈	C₈×D₂₆₉	1	1	yes	characteristic
47	C₂²	C₁₆×D₂₆₉	1	1	yes	characteristic
48	C₄	—	269	4	no	—
49	C₄	C₈×Dic₂₆₉	1	1	yes	characteristic
50	C₄	C₁₆×D₂₆₉	1	1	yes	characteristic
51	C₂	C₁₆×Dic₂₆₉	1	1	yes	characteristic
52	C₂	C₃₂×D₂₆₉	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₂₆₉
commutator, hypocenter	C₂₆₉	C₄×C₃₂
Frattini	C₂×C₁₆	C₂×D₂₆₉
Fitting	C₂×C₃₂×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₆₉	C₂²
LCS	G ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. #22575359	C₄	semidirect
8. C₃₂×C₂₆₉	C₄	semidirect
23. Dic₂₆₉	C₃₂	direct (N × H)
26. C₂₆₉	C₄×C₃₂	semidirect
35. C₃₂	Dic₂₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22575359	2
C₁₆×Dic₂₆₉	2
C₂×C₃₂×C₂₆₉	2
C₄×C₃₂	269

Subgroups — C32×Dic269 #46809016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₂×Dic₂₆₉ #46809016