Subgroups — C₂⁶×D₂₈₃ #49136075

Order 36224.

58424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₂₈₃	C₂	1	126	yes	maximal, direct product factor
2	C₂⁶×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×D₂₈₃	C₂²	1	2604	yes	direct product factor
4	C₂⁵×C₂₈₃	C₂²	1	63	yes	complemented
5	C₂³×D₂₈₃	C₂³	1	11160	yes	direct product factor
6	C₂⁴×C₂₈₃	C₂³	1	651	yes	complemented
7	C₂²×D₂₈₃	C₂⁴	1	10416	yes	direct product factor
8	C₂³×C₂₈₃	C₂⁴	1	1395	yes	complemented
9	C₂²×C₂₈₃	C₂⁵	1	651	yes	complemented
10	C₂×D₂₈₃	C₂⁵	1	2016	yes	direct product factor
11	C₂×C₂₈₃	C₂⁶	1	63	yes	complemented
12	D₂₈₃	C₂⁶	1	64	yes	direct product factor
13	C₂₈₃	C₂⁷	1	1	yes	characteristic, complemented, Sylow
14	C₂⁷	—	283	1	no	maximal, Sylow
15	C₂⁶	—	283	126	no	—
16	C₂⁶	D₂₈₃	1	1	yes	characteristic, direct product factor
17	C₂⁵	—	283	2604	no	—
18	C₂⁵	C₂×D₂₈₃	1	63	yes	direct product factor
19	C₂⁴	—	283	11160	no	—
20	C₂⁴	C₂²×D₂₈₃	1	651	yes	direct product factor
21	C₂³	—	283	10416	no	—
22	C₂³	C₂³×D₂₈₃	1	1395	yes	direct product factor
23	C₂²	—	283	2016	no	—
24	C₂²	C₂⁴×D₂₈₃	1	651	yes	direct product factor
25	C₂	—	283	64	no	—
26	C₂	C₂⁵×D₂₈₃	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	D₂₈₃
commutator, cosocle, hypocenter	C₂₈₃	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₂₈₃	C₂
LCS	G ▷ C₂₈₃
UCS	C₁ ◁ C₂⁶

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

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