Subgroups — C₂²×C₃×C₄² #5841

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	3	yes	maximal
2	C₂×C₃×C₄²	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄²	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	C₂²	1	1	yes	characteristic
5	C₂²×C₃×C₄	C₄	1	24	yes	direct product factor
6	C₂²×C₃×C₄	C₂²	1	18	yes	—
7	C₃×C₄²	C₂²	1	16	yes	direct product factor
8	C₂³×C₄	C₂×C₃	1	3	yes	—
9	C₂×C₄²	C₂×C₃	1	12	yes	direct product factor
10	C₂³×C₃	C₂×C₄	1	12	yes	—
11	C₂³×C₃	C₂³	1	3	yes	—
12	C₂×C₃×C₄	C₂×C₄	1	72	yes	direct product factor
13	C₂×C₃×C₄	C₂³	1	12	yes	—
14	C₂⁴	C₂²×C₃	1	1	yes	characteristic
15	C₂²×C₄	C₃×C₄	1	24	yes	direct product factor
16	C₂²×C₄	C₂²×C₃	1	18	yes	—
17	C₄²	C₂²×C₃	1	16	yes	direct product factor
18	C₂²×C₃	C₄²	1	16	yes	direct product factor
19	C₂²×C₃	C₂²×C₄	1	18	yes	—
20	C₂²×C₃	C₂⁴	1	1	yes	characteristic
21	C₃×C₄	C₂²×C₄	1	24	yes	direct product factor
22	C₂³	C₂×C₃×C₄	1	12	yes	—
23	C₂³	C₂³×C₃	1	3	yes	—
24	C₂×C₄	C₂×C₃×C₄	1	72	yes	direct product factor
25	C₂×C₄	C₂³×C₃	1	12	yes	—
26	C₂×C₃	C₂×C₄²	1	12	yes	direct product factor
27	C₂×C₃	C₂³×C₄	1	3	yes	—
28	C₂²	C₃×C₄²	1	16	yes	direct product factor
29	C₂²	C₂²×C₃×C₄	1	18	yes	—
30	C₂²	C₂⁴×C₃	1	1	yes	characteristic
31	C₄	C₂²×C₃×C₄	1	24	yes	direct product factor
32	C₃	C₂²×C₄²	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₂×C₃×C₄²	1	12	yes	direct product factor
34	C₂	C₂³×C₃×C₄	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₄²	C₂	direct (N × H)
3. C₂²×C₄²	C₃	direct (N × H)
5. C₂²×C₃×C₄	C₄	direct (N × H)
7. C₃×C₄²	C₂²	direct (N × H)
9. C₂×C₄²	C₂×C₃	direct (N × H)
12. C₂×C₃×C₄	C₂×C₄	direct (N × H)
15. C₂²×C₄	C₃×C₄	direct (N × H)
17. C₄²	C₂²×C₃	direct (N × H)
18. C₂²×C₃	C₄²	direct (N × H)
21. C₃×C₄	C₂²×C₄	direct (N × H)
24. C₂×C₄	C₂×C₃×C₄	direct (N × H)
26. C₂×C₃	C₂×C₄²	direct (N × H)
28. C₂²	C₃×C₄²	direct (N × H)
31. C₄	C₂²×C₃×C₄	direct (N × H)
32. C₃	C₂²×C₄²	direct (N × H)
33. C₂	C₂×C₃×C₄²	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₄	2
C₂×C₃×C₄²	2
C₂²×C₄²	3

Subgroups — C22×C3×C42 #5841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄² #5841