Subgroups — Dic₃⋊C₁₆ #4501

Order 192.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₁₆	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₄×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₃⋊C₈	C₄	1	1	yes	characteristic
8	C₃×C₁₆	—	2	1	no	—
9	C₃⋊C₁₆	—	2	1	no	—
10	C₂×C₁₆	—	3	1	no	—
11	C₂×C₁₆	D₃	1	1	yes	characteristic
12	C₄×C₈	—	3	1	no	—
13	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃	C₈	1	1	yes	characteristic
15	C₂×Dic₃	C₈	1	1	yes	characteristic
16	C₃×C₈	D₄	1	1	yes	characteristic
17	C₃×C₈	Q₈	1	1	yes	characteristic
18	C₃⋊C₈	—	2	1	no	—
19	C₂×C₈	—	3	1	no	—
20	C₂×C₈	C₂×D₃	1	1	yes	characteristic
21	C₄²	—	3	1	no	—
22	C₁₆	—	2	1	no	—
23	C₁₆	—	6	1	no	—
24	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
25	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
26	C₃×C₄	M₁₆	1	1	yes	characteristic
27	Dic₃	—	2	1	no	—
28	Dic₃	C₁₆	1	2	yes	complemented
29	C₂×C₄	—	3	1	no	—
30	C₂×C₄	—	3	1	no	—
31	C₂×C₄	C₄×D₃	1	1	yes	characteristic
32	C₈	—	6	1	no	—
33	C₈	Dic₆	1	1	yes	characteristic
34	C₈	#67	1	1	yes	characteristic
35	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
36	C₂×C₃	C₂×C₁₆	1	1	yes	characteristic
37	C₂×C₃	M₃₂	1	1	yes	characteristic
38	C₂²	D₃×C₈	1	1	yes	characteristic
39	C₄	—	3	2	no	—
40	C₄	—	6	1	no	—
41	C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
42	C₄	Dic₃⋊C₄	1	1	yes	characteristic
43	C₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
44	C₂	D₃×C₁₆	1	1	yes	characteristic
45	C₂	#798	1	1	yes	characteristic
46	C₂	Dic₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃
commutator	C₂×C₃	C₂×C₁₆
Fitting	C₂×C₃×C₁₆	C₂
socle, prime radical	C₂²×C₃	C₂×C₈
cosocle	C₂×C₃×C₈	C₂²
hypercenter	C₂×C₁₆	D₃
hypocenter	C₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
28. Dic₃	C₁₆	semidirect
43. C₃	C₄⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₆	2
C₈×Dic₃	2
C₂×C₃⋊C₁₆	2
C₄⋊C₁₆	3

Subgroups — Dic3⋊C16 #4501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃⋊C₁₆ #4501