Subgroups — C₂²×D₄₈ #82001

Order 384.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₄	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₈	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₁₆	—	3	1	no	maximal, Sylow
5	C₂²×D₁₂	—	2	2	no	—
6	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₂×D₂₄	—	2	6	no	—
8	C₂×D₂₄	C₂²	1	12	yes	complemented
9	C₂×C₃×C₁₆	C₂²	1	6	yes	complemented
10	D₄₈	C₂²	1	16	yes	direct product factor
11	C₂²×D₈	—	3	2	no	—
12	C₂×D₁₆	—	3	12	no	—
13	C₂²×C₁₆	D₃	1	1	yes	characteristic, complemented
14	C₂³×D₃	—	4	2	no	—
15	C₂²×C₃×C₄	D₄	1	1	yes	characteristic
16	C₂×D₁₂	—	2	12	no	—
17	C₂×D₁₂	—	4	6	no	—
18	C₂×C₃×C₈	D₄	1	3	yes	—
19	C₂×C₃×C₈	C₂³	1	3	yes	—
20	D₂₄	—	2	12	no	—
21	D₂₄	C₂³	1	8	yes	complemented
22	C₃×C₁₆	C₂³	1	4	yes	complemented
23	C₂²×D₄	—	6	2	no	—
24	C₂×D₈	—	3	12	no	—
25	C₂×D₈	—	6	6	no	—
26	C₂²×C₈	C₂×D₃	1	1	yes	characteristic
27	D₁₆	—	3	16	no	—
28	C₂×C₁₆	C₂×D₃	1	6	yes	complemented
29	C₂³×C₃	D₈	1	1	yes	characteristic
30	C₂²×D₃	—	4	12	no	—
31	C₂²×D₃	—	8	8	no	—
32	C₂×C₃×C₄	D₈	1	3	yes	—
33	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
34	D₁₂	—	2	8	no	—
35	D₁₂	—	4	12	no	—
36	C₃×C₈	C₂×D₄	1	3	yes	—
37	C₃×C₈	C₂⁴	1	1	yes	characteristic
38	C₂⁴	—	12	2	no	—
39	C₂×D₄	—	6	12	no	—
40	C₂×D₄	—	12	6	no	—
41	C₂²×C₄	D₁₂	1	1	yes	characteristic
42	D₈	—	3	8	no	—
43	D₈	—	6	12	no	—
44	C₂×C₈	D₁₂	1	3	yes	—
45	C₂×C₈	C₂²×D₃	1	3	yes	—
46	C₁₆	C₂²×D₃	1	4	yes	complemented
47	C₂²×C₃	D₁₆	1	4	yes	complemented
48	C₂²×C₃	C₂×D₈	1	3	yes	—
49	C₂×D₃	—	4	8	no	—
50	C₂×D₃	—	8	24	no	—
51	C₃×C₄	C₂×D₈	1	3	yes	—
52	C₃×C₄	C₂²×D₄	1	1	yes	characteristic
53	C₂³	—	12	12	no	—
54	C₂³	—	24	8	no	—
55	C₂³	D₂₄	1	1	yes	characteristic
56	D₄	—	6	8	no	—
57	D₄	—	12	12	no	—
58	C₂×C₄	D₂₄	1	3	yes	—
59	C₂×C₄	C₂×D₁₂	1	3	yes	—
60	C₈	C₂×D₁₂	1	3	yes	—
61	C₈	C₂³×D₃	1	1	yes	characteristic
62	C₂×C₃	C₂×D₁₆	1	6	yes	complemented
63	C₂×C₃	C₂²×D₈	1	1	yes	characteristic
64	D₃	—	8	8	no	—
65	C₂²	—	12	8	no	—
66	C₂²	—	24	24	no	—
67	C₂²	D₄₈	1	4	yes	direct product factor
68	C₂²	C₂×D₂₄	1	3	yes	—
69	C₄	C₂×D₂₄	1	3	yes	—
70	C₄	C₂²×D₁₂	1	1	yes	characteristic
71	C₃	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	24	8	no	—
73	C₂	C₂×D₄₈	1	6	yes	direct product factor
74	C₂	C₂²×D₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₄
commutator, cosocle	C₃×C₈	C₂⁴
Frattini	C₈	C₂³×D₃
Fitting	C₂²×C₃×C₁₆	C₂
socle	C₂³×C₃	D₈
hypercenter	C₂²×C₁₆	D₃
hypocenter	C₃	C₂²×D₁₆
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₄	C₂	semidirect
2. C₂²×C₃×C₁₆	C₂	semidirect
3. C₂×D₄₈	C₂	direct (N × H)
8. C₂×D₂₄	C₂²	semidirect
9. C₂×C₃×C₁₆	C₂²	semidirect
10. D₄₈	C₂²	direct (N × H)
13. C₂²×C₁₆	D₃	semidirect
21. D₂₄	C₂³	semidirect
22. C₃×C₁₆	C₂³	semidirect
28. C₂×C₁₆	C₂×D₃	semidirect
46. C₁₆	C₂²×D₃	semidirect
47. C₂²×C₃	D₁₆	semidirect
62. C₂×C₃	C₂×D₁₆	semidirect
67. C₂²	D₄₈	direct (N × H)
71. C₃	C₂²×D₁₆	semidirect
73. C₂	C₂×D₄₈	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×D₂₄	2
C₂²×C₃×C₁₆	2
C₂×D₄₈	2
C₂²×D₁₆	3

Subgroups — C22×D48 #82001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄₈ #82001