Subgroups — C₂²×D₂₄ #5740

Order 192.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₈	—	3	1	no	maximal, Sylow
5	C₂³×D₃	—	2	2	no	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×D₁₂	—	2	6	no	—
8	C₂×D₁₂	C₂²	1	12	yes	complemented
9	C₂×C₃×C₈	C₂²	1	6	yes	complemented
10	D₂₄	C₂²	1	16	yes	direct product factor
11	C₂²×D₄	—	3	2	no	—
12	C₂×D₈	—	3	12	no	—
13	C₂²×C₈	D₃	1	1	yes	characteristic, complemented
14	C₂³×C₃	D₄	1	1	yes	characteristic
15	C₂²×D₃	—	2	12	no	—
16	C₂²×D₃	—	4	8	no	—
17	C₂×C₃×C₄	D₄	1	3	yes	—
18	C₂×C₃×C₄	C₂³	1	3	yes	—
19	D₁₂	—	2	12	no	—
20	D₁₂	C₂³	1	8	yes	complemented
21	C₃×C₈	C₂³	1	4	yes	complemented
22	C₂⁴	—	6	2	no	—
23	C₂×D₄	—	3	12	no	—
24	C₂×D₄	—	6	6	no	—
25	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
26	D₈	—	3	16	no	—
27	C₂×C₈	C₂×D₃	1	6	yes	complemented
28	C₂²×C₃	D₈	1	4	yes	complemented
29	C₂²×C₃	C₂×D₄	1	3	yes	—
30	C₂×D₃	—	2	8	no	—
31	C₂×D₃	—	4	24	no	—
32	C₃×C₄	C₂×D₄	1	3	yes	—
33	C₃×C₄	C₂⁴	1	1	yes	characteristic
34	C₂³	—	6	12	no	—
35	C₂³	—	12	8	no	—
36	C₂³	D₁₂	1	1	yes	characteristic
37	D₄	—	3	8	no	—
38	D₄	—	6	12	no	—
39	C₂×C₄	D₁₂	1	3	yes	—
40	C₂×C₄	C₂²×D₃	1	3	yes	—
41	C₈	C₂²×D₃	1	4	yes	complemented
42	C₂×C₃	C₂×D₈	1	6	yes	complemented
43	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
44	D₃	—	4	8	no	—
45	C₂²	—	6	8	no	—
46	C₂²	—	12	24	no	—
47	C₂²	D₂₄	1	4	yes	direct product factor
48	C₂²	C₂×D₁₂	1	3	yes	—
49	C₄	C₂×D₁₂	1	3	yes	—
50	C₄	C₂³×D₃	1	1	yes	characteristic
51	C₃	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	12	8	no	—
53	C₂	C₂×D₂₄	1	6	yes	direct product factor
54	C₂	C₂²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂
commutator, cosocle	C₃×C₄	C₂⁴
Frattini	C₄	C₂³×D₃
Fitting	C₂²×C₃×C₈	C₂
socle	C₂³×C₃	D₄
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂²×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₂	C₂	semidirect
2. C₂²×C₃×C₈	C₂	semidirect
3. C₂×D₂₄	C₂	direct (N × H)
8. C₂×D₁₂	C₂²	semidirect
9. C₂×C₃×C₈	C₂²	semidirect
10. D₂₄	C₂²	direct (N × H)
13. C₂²×C₈	D₃	semidirect
20. D₁₂	C₂³	semidirect
21. C₃×C₈	C₂³	semidirect
27. C₂×C₈	C₂×D₃	semidirect
28. C₂²×C₃	D₈	semidirect
41. C₈	C₂²×D₃	semidirect
42. C₂×C₃	C₂×D₈	semidirect
47. C₂²	D₂₄	direct (N × H)
51. C₃	C₂²×D₈	semidirect
53. C₂	C₂×D₂₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₂	2
C₂²×C₃×C₈	2
C₂×D₂₄	2
C₂²×D₈	3

Subgroups — C22×D24 #5740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₂₄ #5740