Subgroups — C₂×Dic₄₈ #69370

Order 384.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₄	C₂	1	2	yes	maximal
2	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Dic₄₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₆₄	—	3	1	no	maximal, Sylow
5	C₂×Dic₁₂	—	2	2	no	—
6	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
7	Dic₂₄	—	2	2	no	—
8	Dic₂₄	C₂²	1	4	yes	—
9	C₃×C₃₂	C₂²	1	2	yes	—
10	C₂×Q₃₂	—	3	2	no	—
11	Q₆₄	—	3	4	no	—
12	C₂×C₃₂	D₃	1	1	yes	characteristic
13	C₂×Dic₆	—	4	2	no	—
14	C₂×C₃×C₈	D₄	1	1	yes	characteristic
15	Dic₁₂	—	2	4	no	—
16	Dic₁₂	—	4	2	no	—
17	C₃×C₁₆	D₄	1	1	yes	characteristic
18	C₃×C₁₆	C₂³	1	1	yes	characteristic
19	C₂×Q₁₆	—	6	2	no	—
20	Q₃₂	—	3	4	no	—
21	Q₃₂	—	6	2	no	—
22	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
23	C₃₂	C₂×D₃	1	2	yes	—
24	C₂×C₃×C₄	D₈	1	1	yes	characteristic
25	C₂×Dic₃	—	8	2	no	—
26	Dic₆	—	4	4	no	—
27	Dic₆	—	8	2	no	—
28	C₃×C₈	D₈	1	1	yes	characteristic
29	C₃×C₈	C₂×D₄	1	1	yes	characteristic
30	C₂×Q₈	—	12	2	no	—
31	Q₁₆	—	6	4	no	—
32	Q₁₆	—	12	2	no	—
33	C₂×C₈	D₁₂	1	1	yes	characteristic
34	C₁₆	D₁₂	1	1	yes	characteristic
35	C₁₆	C₂²×D₃	1	1	yes	characteristic
36	C₂²×C₃	D₁₆	1	1	yes	characteristic
37	C₃×C₄	D₁₆	1	1	yes	characteristic
38	C₃×C₄	C₂×D₈	1	1	yes	characteristic
39	Dic₃	—	8	4	no	—
40	Q₈	—	12	4	no	—
41	Q₈	—	24	2	no	—
42	C₂×C₄	—	24	2	no	—
43	C₂×C₄	D₂₄	1	1	yes	characteristic
44	C₈	D₂₄	1	1	yes	characteristic
45	C₈	C₂×D₁₂	1	1	yes	characteristic
46	C₂×C₃	Q₆₄	1	2	yes	complemented
47	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
48	C₂²	D₄₈	1	1	yes	characteristic
49	C₄	—	24	4	no	—
50	C₄	D₄₈	1	1	yes	characteristic
51	C₄	C₂×D₂₄	1	1	yes	characteristic
52	C₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
53	C₂	Dic₄₈	1	2	yes	direct product factor
54	C₂	C₂×D₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₈
commutator, cosocle	C₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₃
Fitting	C₂×C₃×C₃₂	C₂
socle, prime radical	C₂²×C₃	D₁₆
hypercenter	C₂×C₃₂	D₃
hypocenter	C₃	C₂×Q₆₄
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
3. Dic₄₈	C₂	direct (N × H)
46. C₂×C₃	Q₆₄	semidirect
52. C₃	C₂×Q₆₄	semidirect
53. C₂	Dic₄₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₂₄	2
C₂×C₃×C₃₂	2
Dic₄₈	2
C₂×Q₆₄	3

Subgroups — C2×Dic48 #69370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₈ #69370