Subgroups — C₂³×Dic₇₆ #14578358

Order 2432.

1464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₃₈	C₂	1	2	yes	maximal
2	C₂²×Dic₇₆	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₂³×Dic₁₉	—	2	2	no	—
6	C₂²×Dic₃₈	—	2	14	no	—
7	C₂²×Dic₃₈	C₂²	1	28	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	14	yes	—
9	C₂×Dic₇₆	C₂²	1	112	yes	direct product factor
10	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₉	D₄	1	7	yes	—
12	C₂²×C₄×C₁₉	C₂³	1	7	yes	—
13	C₂²×Dic₁₉	—	2	28	no	—
14	C₂×Dic₃₈	—	2	84	no	—
15	C₂×Dic₃₈	C₂³	1	56	yes	—
16	C₂×C₈×C₁₉	C₂³	1	28	yes	—
17	Dic₇₆	C₂³	1	64	yes	direct product factor
18	C₂³×C₁₉	Q₁₆	1	8	yes	complemented
19	C₂³×C₁₉	C₂×D₄	1	7	yes	—
20	C₂×C₄×C₁₉	C₂×D₄	1	21	yes	—
21	C₂×C₄×C₁₉	C₂⁴	1	7	yes	—
22	C₂×Dic₁₉	—	2	56	no	—
23	Dic₃₈	—	2	56	no	—
24	Dic₃₈	C₂⁴	1	16	yes	—
25	C₈×C₁₉	C₂⁴	1	8	yes	—
26	C₂³×Q₁₆	—	19	1	no	maximal, Sylow
27	C₂²×C₁₉	C₂×Q₁₆	1	28	yes	complemented
28	C₂²×C₁₉	C₂²×D₄	1	7	yes	—
29	C₄×C₁₉	C₂²×D₄	1	7	yes	—
30	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
31	Dic₁₉	—	2	16	no	—
32	C₂³×Q₈	—	19	2	no	—
33	C₂²×Q₁₆	—	19	28	no	—
34	C₂³×C₈	D₁₉	1	1	yes	characteristic
35	C₂×C₁₉	C₂²×Q₁₆	1	14	yes	complemented
36	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
37	C₂²×Q₈	—	19	28	no	—
38	C₂²×Q₈	—	38	14	no	—
39	C₂³×C₄	—	38	2	no	—
40	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
41	C₂×Q₁₆	—	19	112	no	—
42	C₂²×C₈	C₂×D₁₉	1	14	yes	—
43	C₁₉	C₂³×Q₁₆	1	1	yes	characteristic, complemented, Sylow
44	C₂⁴	D₇₆	1	1	yes	characteristic
45	C₂×Q₈	—	19	56	no	—
46	C₂×Q₈	—	38	84	no	—
47	C₂²×C₄	—	38	28	no	—
48	C₂²×C₄	D₇₆	1	7	yes	—
49	C₂²×C₄	C₂²×D₁₉	1	7	yes	—
50	Q₁₆	—	19	64	no	—
51	C₂×C₈	C₂²×D₁₉	1	28	yes	—
52	C₂³	Dic₇₆	1	8	yes	direct product factor
53	C₂³	C₂×D₇₆	1	7	yes	—
54	Q₈	—	19	16	no	—
55	Q₈	—	38	56	no	—
56	C₂×C₄	—	38	56	no	—
57	C₂×C₄	C₂×D₇₆	1	21	yes	—
58	C₂×C₄	C₂³×D₁₉	1	7	yes	—
59	C₈	C₂³×D₁₉	1	8	yes	—
60	C₂²	C₂×Dic₇₆	1	28	yes	direct product factor
61	C₂²	C₂²×D₇₆	1	7	yes	—
62	C₄	—	38	16	no	—
63	C₄	C₂²×D₇₆	1	7	yes	—
64	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
65	C₂	C₂²×Dic₇₆	1	14	yes	direct product factor
66	C₂	C₂³×D₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₇₆
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂³×C₈×C₁₉	C₂
socle, prime radical	C₂⁴×C₁₉	D₄
hypercenter	C₂³×C₈	D₁₉
hypocenter	C₁₉	C₂³×Q₁₆
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₇₆	C₂	direct (N × H)
9. C₂×Dic₇₆	C₂²	direct (N × H)
17. Dic₇₆	C₂³	direct (N × H)
18. C₂³×C₁₉	Q₁₆	semidirect
27. C₂²×C₁₉	C₂×Q₁₆	semidirect
35. C₂×C₁₉	C₂²×Q₁₆	semidirect
43. C₁₉	C₂³×Q₁₆	semidirect
52. C₂³	Dic₇₆	direct (N × H)
60. C₂²	C₂×Dic₇₆	direct (N × H)
65. C₂	C₂²×Dic₇₆	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×Dic₃₈	2
C₂²×Dic₇₆	2
C₂³×C₈×C₁₉	2
C₂³×Q₁₆	19

Subgroups — C23×Dic76 #14578358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₇₆ #14578358