Subgroups — C₂²×C₂²⋊A₄ #5981

Order 192.

1000 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊A₄	C₂	1	3	yes	maximal, direct product factor
2	C₂⁶	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²⋊A₄	C₂²	1	1	yes	characteristic, direct product factor
4	C₂²×A₄	—	4	5	no	maximal
5	C₂⁵	—	3	15	no	—
6	C₂⁵	—	3	5	no	—
7	C₂⁵	C₂×C₃	1	3	yes	complemented
8	C₂×A₄	—	4	15	no	—
9	C₂⁴	—	3	15	no	—
10	C₂⁴	—	3	90	no	—
11	C₂⁴	—	3	60	no	—
12	C₂⁴	—	3	10	no	—
13	C₂⁴	—	3	10	no	—
14	C₂⁴	—	3	15	no	—
15	C₂⁴	—	3	15	no	—
16	C₂⁴	A₄	1	5	yes	complemented
17	C₂⁴	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃	—	16	1	no	—
19	A₄	—	4	5	no	—
20	C₂³	—	3	15	no	—
21	C₂³	—	3	90	no	—
22	C₂³	—	3	90	no	—
23	C₂³	—	3	120	no	—
24	C₂³	—	3	90	no	—
25	C₂³	—	3	30	no	—
26	C₂³	—	3	15	no	—
27	C₂³	—	3	5	no	—
28	C₂³	—	3	5	no	—
29	C₂³	C₂×A₄	1	15	yes	complemented
30	C₂×C₃	—	16	3	no	—
31	C₂²	—	3	15	no	—
32	C₂²	—	3	10	no	—
33	C₂²	—	3	60	no	—
34	C₂²	—	3	90	no	—
35	C₂²	—	3	10	no	—
36	C₂²	—	3	15	no	—
37	C₂²	—	3	15	no	—
38	C₂²	C₂²×A₄	1	5	yes	complemented
39	C₂²	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
40	C₃	—	16	1	no	Sylow
41	C₂	—	3	15	no	—
42	C₂	—	3	5	no	—
43	C₂	C₂×C₂²⋊A₄	1	3	yes	direct product factor

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