Subgroups — #126×C₄₅₇ #28410439

Order 14624.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×C₄₅₇	C₂	1	3	yes	maximal, complemented
2	C₂²⋊C₄×C₄₅₇	C₂	1	3	yes	maximal
3	C₄²×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₄₅₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₄₅₇	C₂²	1	3	yes	—
6	C₂×C₄×C₄₅₇	C₂²	1	3	yes	—
7	C₂²×C₄₅₇	—	2	3	no	—
8	C₂²×C₄₅₇	C₂³	1	1	yes	characteristic
9	C₄×C₄₅₇	—	2	3	no	—
10	C₄×C₄₅₇	—	2	3	no	—
11	C₂×C₄₅₇	—	4	1	no	—
12	C₂×C₄₅₇	#41	1	3	yes	—
13	C₄₅₇	#126	1	1	yes	characteristic, direct product factor, Sylow
14	#126	C₄₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₄⋊C₄	C₂×C₄₅₇	1	3	yes	complemented
16	C₂²⋊C₄	C₂×C₄₅₇	1	3	yes	—
17	C₄²	C₂×C₄₅₇	1	1	yes	characteristic, complemented
18	C₂³	C₂²×C₄₅₇	1	1	yes	characteristic
19	C₂×C₄	C₂²×C₄₅₇	1	3	yes	—
20	C₂×C₄	C₂²×C₄₅₇	1	3	yes	—
21	C₂²	—	2	3	no	—
22	C₂²	C₂³×C₄₅₇	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	2	3	no	—
25	C₂	—	4	1	no	—
26	C₂	#41×C₄₅₇	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₅₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₄₅₇
prime radical	C₂³×C₄₅₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₅₇ ◁ G

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.