Subgroups — C₂×#26044451 #37555439

Order 23548.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19154637	C₂	1	1	yes	maximal, characteristic, complemented
2	#26044451	C₂	1	2	yes	maximal, direct product factor
3	#19154637	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₉×D₂₉	—	7	1	no	maximal, Hall
5	C₂×C₂₉²	D₇	1	1	yes	characteristic, complemented
6	C₂₉×D₂₉	—	7	2	no	—
7	C₂₉²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₂₉⋊C₇	—	58	1	no	—
9	C₂₉⋊C₇	—	58	1	no	—
10	C₂²×C₂₉	—	203	1	no	—
11	C₂×D₂₉	—	7	1	no	—
12	C₂×C₂₉	—	2	1	no	—
13	C₂×C₂₉	—	7	1	no	—
14	C₂×C₂₉	—	14	1	no	—
15	C₂×C₂₉	—	14	1	no	—
16	C₂×C₂₉	—	203	2	no	—
17	D₂₉	—	7	2	no	—
18	C₂₉	—	2	1	no	—
19	C₂₉	—	7	1	no	—
20	C₂₉	—	14	1	no	—
21	C₂₉	—	14	1	no	—
22	C₂×D₇	—	841	1	no	maximal, Hall
23	C₂×C₇	—	1682	1	no	—
24	D₇	—	841	2	no	—
25	C₇	—	1682	1	no	Sylow
26	C₂²	—	203	1	no	Sylow
27	C₂	—	203	2	no	—
28	C₂	#26044451	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#26044451
commutator, cosocle, hypocenter	#19154637	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₂₉²	D₇
LCS	G ▷ #19154637
UCS	C₁ ◁ C₂

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.