Subgroups — C₂×C₂²⋊(C₂²⋊A₄) #87589

Order 384.

9884 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₂²⋊A₄)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂⁷	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂×C₂²⋊A₄	—	4	21	no	maximal
4	C₂⁶	—	3	21	no	—
5	C₂⁶	—	3	21	no	—
6	C₂⁶	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²⋊A₄	—	4	21	no	—
8	C₂⁵	—	3	630	no	—
9	C₂⁵	—	3	210	no	—
10	C₂⁵	—	3	21	no	—
11	C₂⁵	—	3	21	no	—
12	C₂⁵	A₄	1	21	yes	complemented
13	C₂×A₄	—	16	21	no	—
14	C₂⁴	—	3	105	no	—
15	C₂⁴	—	3	2520	no	—
16	C₂⁴	—	3	360	no	—
17	C₂⁴	—	3	630	no	—
18	C₂⁴	—	3	210	no	—
19	C₂⁴	—	3	105	no	—
20	C₂⁴	C₂×A₄	1	21	yes	complemented
21	A₄	—	16	21	no	—
22	C₂³	—	3	630	no	—
23	C₂³	—	3	2520	no	—
24	C₂³	—	3	360	no	—
25	C₂³	—	3	210	no	—
26	C₂³	—	3	105	no	—
27	C₂³	—	3	105	no	—
28	C₂³	C₂²⋊A₄	1	21	yes	complemented
29	C₂×C₃	—	64	1	no	—
30	C₂²	—	3	21	no	—
31	C₂²	—	3	630	no	—
32	C₂²	—	3	210	no	—
33	C₂²	—	3	21	no	—
34	C₂²	C₂×C₂²⋊A₄	1	21	yes	complemented
35	C₃	—	64	1	no	Sylow
36	C₂	—	3	21	no	—
37	C₂	—	3	21	no	—
38	C₂	C₂²⋊(C₂²⋊A₄)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂²⋊(C₂²⋊A₄)
commutator, cosocle, hypocenter	C₂⁶	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂⁷	C₃
LCS	G ▷ C₂⁶
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.