Subgroups — Dic₇₄₈₂ #72236601

Order 29928.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₄₉₄	—	3	1	no	maximal, Hall
2	Dic₃₇₄₁	C₂	1	2	yes	maximal
3	C₃×C₄×C₂₉×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₂₉×C₄₃	C₂²	1	1	yes	characteristic
5	Dic₁₂₄₇	—	3	2	no	—
6	C₄×C₂₉×C₄₃	D₃	1	1	yes	characteristic
7	C₃×C₂₉×C₄₃	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₂₉×C₄₃	C₂×D₃	1	1	yes	characteristic
9	C₂₉×C₄₃	Dic₆	1	1	yes	characteristic, complemented, Hall
10	Dic₂₅₈	—	29	1	no	maximal, Hall
11	Dic₁₇₄	—	43	1	no	maximal, Hall
12	C₃×C₄×C₄₃	D₂₉	1	1	yes	characteristic
13	Dic₁₂₉	—	29	2	no	—
14	C₃×C₄×C₂₉	D₄₃	1	1	yes	characteristic
15	Dic₈₇	—	43	2	no	—
16	Dic₈₆	—	87	1	no	Hall
17	C₂×C₃×C₄₃	C₂×D₂₉	1	1	yes	characteristic
18	Dic₅₈	—	129	1	no	Hall
19	C₂×C₃×C₂₉	C₂×D₄₃	1	1	yes	characteristic
20	C₄×C₄₃	D₈₇	1	1	yes	characteristic
21	Dic₄₃	—	87	2	no	—
22	C₃×C₄₃	Dic₅₈	1	1	yes	characteristic, complemented, Hall
23	C₄×C₂₉	D₁₂₉	1	1	yes	characteristic
24	Dic₂₉	—	129	2	no	—
25	C₃×C₂₉	Dic₈₆	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄₃	C₂×D₈₇	1	1	yes	characteristic
27	C₂×C₂₉	C₂×D₁₂₉	1	1	yes	characteristic
28	C₄₃	Dic₁₇₄	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	Dic₂₅₈	1	1	yes	characteristic, complemented, Sylow
30	Dic₆	—	1247	1	no	Hall
31	C₃×C₄	D₁₂₄₇	1	1	yes	characteristic
32	Dic₃	—	1247	2	no	—
33	Q₈	—	3741	1	no	Sylow
34	C₂×C₃	C₂×D₁₂₄₇	1	1	yes	characteristic
35	C₄	—	3741	2	no	—
36	C₄	D₃₇₄₁	1	1	yes	characteristic
37	C₃	Dic₂₄₉₄	1	1	yes	characteristic, complemented, Sylow
38	C₂	C₂×D₃₇₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃₇₄₁
commutator, socle, prime radical, cosocle	C₂×C₃×C₂₉×C₄₃	C₂²
Fitting	C₃×C₄×C₂₉×C₄₃	C₂
hypercenter	C₄	D₃₇₄₁
hypocenter	C₃×C₂₉×C₄₃	Q₈
LCS	G ▷ C₂×C₃×C₂₉×C₄₃ ▷ C₃×C₂₉×C₄₃
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
7. C₃×C₂₉×C₄₃	Q₈	semidirect
9. C₂₉×C₄₃	Dic₆	semidirect
22. C₃×C₄₃	Dic₅₈	semidirect
25. C₃×C₂₉	Dic₈₆	semidirect
28. C₄₃	Dic₁₇₄	semidirect
29. C₂₉	Dic₂₅₈	semidirect
37. C₃	Dic₂₄₉₄	semidirect

Maximal subgroups

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

subgroup	index
Dic₂₄₉₄	3
Dic₃₇₄₁	2
C₃×C₄×C₂₉×C₄₃	2
Dic₂₅₈	29
Dic₁₇₄	43

Subgroups — Dic7482 #72236601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇₄₈₂ #72236601