Subgroups — C₂²×D₆₃ #92639

Order 504.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₆₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₂₁	—	3	1	no	maximal
4	C₂×C₇×C₉	C₂²	1	3	yes	complemented
5	D₆₃	C₂²	1	4	yes	direct product factor
6	C₂²×C₃×C₇	D₃	1	1	yes	characteristic
7	C₂×D₂₁	—	3	6	no	—
8	C₂²×D₉	—	7	1	no	maximal, Hall
9	C₇×C₉	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×D₇	—	9	1	no	Hall
11	C₂×C₃×C₇	C₂×D₃	1	3	yes	—
12	D₂₁	—	3	4	no	—
13	C₂²×C₉	D₇	1	1	yes	characteristic, complemented
14	C₂×D₉	—	7	6	no	—
15	C₂²×C₇	D₉	1	1	yes	characteristic, complemented
16	C₂×D₇	—	9	6	no	—
17	C₂²×D₃	—	21	1	no	—
18	C₃×C₇	C₂²×D₃	1	1	yes	characteristic
19	C₂×C₉	C₂×D₇	1	3	yes	complemented
20	D₉	—	7	4	no	—
21	C₂×C₇	C₂×D₉	1	3	yes	complemented
22	D₇	—	9	4	no	—
23	C₂²×C₃	D₂₁	1	1	yes	characteristic
24	C₂×D₃	—	21	6	no	—
25	C₉	C₂²×D₇	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	63	1	no	Sylow
27	C₇	C₂²×D₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	C₂×D₂₁	1	3	yes	—
29	D₃	—	21	4	no	—
30	C₂²	—	63	6	no	—
31	C₂²	D₆₃	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×D₂₁	1	1	yes	characteristic
33	C₂	—	63	4	no	—
34	C₂	C₂×D₆₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂³
Frattini	C₃	C₂²×D₂₁
Fitting	C₂²×C₇×C₉	C₂
socle	C₂²×C₃×C₇	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₂²

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.