Subgroups — Dic₄₃₃₂ #72215771

Order 17328.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₁₆₆	C₂	1	2	yes	maximal
2	Dic₁₄₄₄	—	3	1	no	maximal, Hall
3	Dic₇₂₂	—	3	2	no	—
4	C₃×C₈×C₃₆₁	C₂	1	1	yes	maximal, characteristic
5	C₈×C₃₆₁	D₃	1	1	yes	characteristic
6	Dic₁₀₈₃	—	2	2	no	—
7	C₃×C₄×C₃₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₃₆₁	D₄	1	1	yes	characteristic
9	C₄×C₃₆₁	C₂×D₃	1	1	yes	characteristic
10	Dic₃₆₁	—	6	2	no	—
11	C₃×C₃₆₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
12	Dic₂₂₈	—	19	1	no	maximal
13	C₂×C₃₆₁	D₁₂	1	1	yes	characteristic
14	Dic₁₁₄	—	19	2	no	—
15	C₃×C₈×C₁₉	D₁₉	1	1	yes	characteristic
16	C₃₆₁	Dic₁₂	1	1	yes	characteristic, complemented, Sylow
17	Dic₇₆	—	57	1	no	—
18	C₃×C₄×C₁₉	C₂×D₁₉	1	1	yes	characteristic
19	Dic₅₇	—	38	2	no	—
20	Dic₃₈	—	57	2	no	—
21	C₈×C₁₉	D₅₇	1	1	yes	characteristic
22	C₂×C₃×C₁₉	D₇₆	1	1	yes	characteristic
23	C₄×C₁₉	C₂×D₅₇	1	1	yes	characteristic
24	Dic₁₉	—	114	2	no	—
25	C₃×C₁₉	Dic₇₆	1	1	yes	characteristic
26	Dic₁₂	—	361	1	no	Hall
27	C₂×C₁₉	D₂₂₈	1	1	yes	characteristic
28	Dic₆	—	361	2	no	—
29	C₃×C₈	D₃₆₁	1	1	yes	characteristic
30	C₁₉	Dic₂₂₈	1	1	yes	characteristic
31	Q₁₆	—	1083	1	no	Sylow
32	C₃×C₄	C₂×D₃₆₁	1	1	yes	characteristic
33	Dic₃	—	722	2	no	—
34	Q₈	—	1083	2	no	—
35	C₈	D₁₀₈₃	1	1	yes	characteristic
36	C₂×C₃	D₁₄₄₄	1	1	yes	characteristic
37	C₄	—	2166	2	no	—
38	C₄	C₂×D₁₀₈₃	1	1	yes	characteristic
39	C₃	Dic₁₄₄₄	1	1	yes	characteristic, complemented, Sylow
40	C₂	D₄₃₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄₃₃₂
commutator, cosocle	C₃×C₄×C₃₆₁	C₂²
Frattini	C₄×C₁₉	C₂×D₅₇
Fitting	C₃×C₈×C₃₆₁	C₂
socle, prime radical	C₂×C₃×C₁₉	D₇₆
hypercenter	C₈	D₁₀₈₃
hypocenter	C₃×C₃₆₁	Q₁₆
LCS	G ▷ C₃×C₄×C₃₆₁ ▷ C₂×C₃×C₃₆₁ ▷ C₃×C₃₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
11. C₃×C₃₆₁	Q₁₆	semidirect
16. C₃₆₁	Dic₁₂	semidirect
39. C₃	Dic₁₄₄₄	semidirect

Maximal subgroups

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

subgroup	index
Dic₂₁₆₆	2
Dic₁₄₄₄	3
C₃×C₈×C₃₆₁	2
Dic₂₂₈	19

Subgroups — Dic4332 #72215771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₃₃₂ #72215771