Subgroups — C₂³×C₃×D₄ #5972

Order 192.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×D₄	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁴×C₃	—	2	16	no	—
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂⁴×C₃	C₂²	1	28	yes	complemented
8	C₂×C₃×D₄	C₂²	1	112	yes	direct product factor
9	C₂²×C₃×C₄	C₂²	1	14	yes	complemented
10	C₂⁵	C₂×C₃	1	2	yes	complemented
11	C₂²×D₄	C₂×C₃	1	28	yes	direct product factor
12	C₂³×C₄	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	—	2	112	no	—
14	C₂³×C₃	D₄	1	8	yes	direct product factor
15	C₂³×C₃	C₂³	1	7	yes	—
16	C₂³×C₃	C₂³	1	56	yes	complemented
17	C₃×D₄	C₂³	1	64	yes	direct product factor
18	C₂×C₃×C₄	C₂³	1	28	yes	complemented
19	C₂⁴	—	2	16	no	—
20	C₂⁴	C₂²×C₃	1	1	yes	characteristic
21	C₂⁴	C₂²×C₃	1	28	yes	complemented
22	C₂×D₄	C₂²×C₃	1	112	yes	direct product factor
23	C₂²×C₄	C₂²×C₃	1	14	yes	complemented
24	C₂²×C₃	—	2	112	no	—
25	C₂²×C₃	C₂×D₄	1	28	yes	direct product factor
26	C₂²×C₃	C₂⁴	1	7	yes	—
27	C₂²×C₃	C₂⁴	1	16	yes	complemented
28	C₃×C₄	C₂⁴	1	8	yes	complemented
29	C₂³	—	2	112	no	—
30	C₂³	C₃×D₄	1	8	yes	direct product factor
31	C₂³	C₂³×C₃	1	7	yes	—
32	C₂³	C₂³×C₃	1	56	yes	complemented
33	D₄	C₂³×C₃	1	64	yes	direct product factor
34	C₂×C₄	C₂³×C₃	1	28	yes	complemented
35	C₂×C₃	—	2	16	no	—
36	C₂×C₃	C₂²×D₄	1	14	yes	direct product factor
37	C₂×C₃	C₂⁵	1	1	yes	characteristic
38	C₂²	—	2	112	no	—
39	C₂²	C₂×C₃×D₄	1	28	yes	direct product factor
40	C₂²	C₂⁴×C₃	1	7	yes	—
41	C₂²	C₂⁴×C₃	1	16	yes	complemented
42	C₄	C₂⁴×C₃	1	8	yes	complemented
43	C₃	C₂³×D₄	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	2	16	no	—
45	C₂	C₂²×C₃×D₄	1	14	yes	direct product factor
46	C₂	C₂⁵×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁵×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₃	C₂	semidirect
2. C₂²×C₃×D₄	C₂	direct (N × H)
3. C₂³×C₃×C₄	C₂	semidirect
4. C₂³×D₄	C₃	direct (N × H)
7. C₂⁴×C₃	C₂²	semidirect
8. C₂×C₃×D₄	C₂²	direct (N × H)
9. C₂²×C₃×C₄	C₂²	semidirect
10. C₂⁵	C₂×C₃	semidirect
11. C₂²×D₄	C₂×C₃	direct (N × H)
12. C₂³×C₄	C₂×C₃	semidirect
14. C₂³×C₃	D₄	direct (N × H)
16. C₂³×C₃	C₂³	semidirect
17. C₃×D₄	C₂³	direct (N × H)
18. C₂×C₃×C₄	C₂³	semidirect
21. C₂⁴	C₂²×C₃	semidirect
22. C₂×D₄	C₂²×C₃	direct (N × H)
23. C₂²×C₄	C₂²×C₃	semidirect
25. C₂²×C₃	C₂×D₄	direct (N × H)
27. C₂²×C₃	C₂⁴	semidirect
28. C₃×C₄	C₂⁴	semidirect
30. C₂³	C₃×D₄	direct (N × H)
32. C₂³	C₂³×C₃	semidirect
33. D₄	C₂³×C₃	direct (N × H)
34. C₂×C₄	C₂³×C₃	semidirect
36. C₂×C₃	C₂²×D₄	direct (N × H)
39. C₂²	C₂×C₃×D₄	direct (N × H)
41. C₂²	C₂⁴×C₃	semidirect
42. C₄	C₂⁴×C₃	semidirect
43. C₃	C₂³×D₄	direct (N × H)
45. C₂	C₂²×C₃×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃	2
C₂²×C₃×D₄	2
C₂³×C₃×C₄	2
C₂³×D₄	3

Subgroups — C23×C3×D4 #5972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×D₄ #5972