Subgroups — Dic₇₄₄₈ #72236621

Order 29792.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₇₂₄	C₂	1	2	yes	maximal
2	Dic₁₈₆₂	—	2	2	no	—
3	Dic₁₀₆₄	—	7	1	no	maximal
4	Dic₅₃₂	—	7	2	no	—
5	C₁₆×C₁₉×C₄₉	C₂	1	1	yes	maximal, characteristic
6	C₈×C₁₉×C₄₉	C₂²	1	1	yes	characteristic
7	C₇×C₁₆×C₁₉	D₇	1	1	yes	characteristic
8	Dic₉₃₁	—	4	2	no	—
9	C₄×C₁₉×C₄₉	D₄	1	1	yes	characteristic
10	C₂×C₁₉×C₄₉	D₈	1	1	yes	characteristic
11	Dic₃₉₂	—	19	1	no	maximal, Hall
12	Dic₂₆₆	—	14	2	no	—
13	C₇×C₈×C₁₉	C₂×D₇	1	1	yes	characteristic
14	C₁₉×C₄₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
15	Dic₁₉₆	—	19	2	no	—
16	C₁₆×C₄₉	D₁₉	1	1	yes	characteristic
17	Dic₁₅₂	—	49	1	no	Hall
18	C₄×C₇×C₁₉	D₂₈	1	1	yes	characteristic
19	Dic₁₃₃	—	28	2	no	—
20	Dic₉₈	—	38	2	no	—
21	C₈×C₄₉	C₂×D₁₉	1	1	yes	characteristic
22	Dic₇₆	—	49	2	no	—
23	C₁₆×C₁₉	D₄₉	1	1	yes	characteristic
24	C₂×C₇×C₁₉	D₅₆	1	1	yes	characteristic
25	Dic₅₆	—	133	1	no	—
26	C₄×C₄₉	D₇₆	1	1	yes	characteristic
27	Dic₄₉	—	76	2	no	—
28	Dic₃₈	—	98	2	no	—
29	C₈×C₁₉	C₂×D₄₉	1	1	yes	characteristic
30	C₇×C₁₉	Dic₅₆	1	1	yes	characteristic
31	Dic₂₈	—	133	2	no	—
32	C₇×C₁₆	D₁₃₃	1	1	yes	characteristic
33	C₂×C₄₉	D₁₅₂	1	1	yes	characteristic
34	C₄×C₁₉	D₁₉₆	1	1	yes	characteristic
35	Dic₁₉	—	196	2	no	—
36	Dic₁₄	—	266	2	no	—
37	C₇×C₈	C₂×D₁₃₃	1	1	yes	characteristic
38	C₄₉	Dic₁₅₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₁₉	D₃₉₂	1	1	yes	characteristic
40	Q₃₂	—	931	1	no	Sylow
41	C₄×C₇	D₅₃₂	1	1	yes	characteristic
42	Dic₇	—	532	2	no	—
43	C₁₉	Dic₃₉₂	1	1	yes	characteristic, complemented, Sylow
44	Q₁₆	—	931	2	no	—
45	C₁₆	D₉₃₁	1	1	yes	characteristic
46	C₂×C₇	D₁₀₆₄	1	1	yes	characteristic
47	Q₈	—	1862	2	no	—
48	C₈	C₂×D₉₃₁	1	1	yes	characteristic
49	C₇	Dic₁₀₆₄	1	1	yes	characteristic
50	C₄	—	3724	2	no	—
51	C₄	D₃₇₂₄	1	1	yes	characteristic
52	C₂	D₇₄₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₇₄₄₈
commutator, cosocle	C₈×C₁₉×C₄₉	C₂²
Frattini	C₇×C₈	C₂×D₁₃₃
Fitting	C₁₆×C₁₉×C₄₉	C₂
socle, prime radical	C₂×C₇×C₁₉	D₅₆
hypercenter	C₁₆	D₉₃₁
hypocenter	C₁₉×C₄₉	Q₃₂
LCS	G ▷ C₈×C₁₉×C₄₉ ▷ C₄×C₁₉×C₄₉ ▷ C₂×C₁₉×C₄₉ ▷ C₁₉×C₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
14. C₁₉×C₄₉	Q₃₂	semidirect
38. C₄₉	Dic₁₅₂	semidirect
43. C₁₉	Dic₃₉₂	semidirect

Maximal subgroups

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

subgroup	index
Dic₃₇₂₄	2
Dic₁₀₆₄	7
C₁₆×C₁₉×C₄₉	2
Dic₃₉₂	19

Subgroups — Dic7448 #72236621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇₄₄₈ #72236621