Subgroups — C₂²×C₄²⋊C₃ #5433

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₄²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²×A₄	—	4	1	no	maximal
4	C₄²⋊C₃	C₂²	1	1	yes	characteristic, direct product factor
5	C₂³×C₄	—	3	1	no	—
6	C₂×C₄²	—	3	3	no	—
7	C₂×C₄²	C₂×C₃	1	3	yes	complemented
8	C₂×A₄	—	4	3	no	—
9	C₂⁴	A₄	1	1	yes	characteristic
10	C₂²×C₄	—	3	6	no	—
11	C₂²×C₄	—	3	2	no	—
12	C₂²×C₄	—	3	3	no	—
13	C₂²×C₄	—	3	3	no	—
14	C₄²	—	3	3	no	—
15	C₄²	—	3	2	no	—
16	C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₂²×C₃	—	16	1	no	—
18	A₄	—	4	1	no	—
19	C₂³	—	3	3	no	—
20	C₂³	—	3	1	no	—
21	C₂³	C₂×A₄	1	3	yes	—
22	C₂×C₄	—	3	6	no	—
23	C₂×C₄	—	3	6	no	—
24	C₂×C₄	—	3	6	no	—
25	C₂×C₄	—	3	6	no	—
26	C₂×C₄	—	3	1	no	—
27	C₂×C₄	—	3	3	no	—
28	C₂×C₃	—	16	3	no	—
29	C₂²	—	3	3	no	—
30	C₂²	—	3	2	no	—
31	C₂²	—	3	3	no	—
32	C₂²	—	3	3	no	—
33	C₂²	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
34	C₂²	C₂²×A₄	1	1	yes	characteristic
35	C₄	—	3	2	no	—
36	C₄	—	3	6	no	—
37	C₃	—	16	1	no	Sylow
38	C₂	—	3	1	no	—
39	C₂	—	3	3	no	—
40	C₂	C₂×C₄²⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂²×C₃
Frattini	C₂²	C₂²×A₄
Fitting	C₂²×C₄²	C₃
socle	C₂⁴	A₄
LCS	G ▷ C₄²
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.