Subgroups — C₂⁴×A₄ #5980

Order 192.

1165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×A₄	C₂	1	15	yes	maximal, direct product factor
2	C₂⁶	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂⁴×C₃	—	4	1	no	maximal
4	C₂²×A₄	C₂²	1	35	yes	direct product factor
5	C₂⁵	—	3	15	no	—
6	C₂⁵	—	3	1	no	—
7	C₂⁵	C₂×C₃	1	15	yes	complemented
8	C₂³×C₃	—	4	15	no	—
9	C₂×A₄	C₂³	1	15	yes	direct product factor
10	C₂⁴	—	3	105	no	—
11	C₂⁴	—	3	70	no	—
12	C₂⁴	—	3	15	no	—
13	C₂⁴	—	3	15	no	—
14	C₂⁴	A₄	1	1	yes	characteristic, direct product factor
15	C₂⁴	C₂²×C₃	1	35	yes	complemented
16	C₂²×C₃	—	4	35	no	—
17	A₄	C₂⁴	1	1	yes	characteristic, direct product factor
18	C₂³	—	3	105	no	—
19	C₂³	—	3	210	no	—
20	C₂³	—	3	105	no	—
21	C₂³	—	3	35	no	—
22	C₂³	C₂×A₄	1	15	yes	direct product factor
23	C₂³	C₂³×C₃	1	15	yes	complemented
24	C₂×C₃	—	4	15	no	—
25	C₂²	—	3	15	no	—
26	C₂²	—	3	70	no	—
27	C₂²	—	3	105	no	—
28	C₂²	—	3	15	no	—
29	C₂²	C₂²×A₄	1	35	yes	direct product factor
30	C₂²	C₂⁴×C₃	1	1	yes	characteristic, complemented
31	C₃	—	4	1	no	Sylow
32	C₂	—	3	15	no	—
33	C₂	—	3	1	no	—
34	C₂	C₂³×A₄	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	A₄
commutator, cosocle, hypocenter	C₂²	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂⁶	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂⁴

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.