Subgroups — C₄⋊(C₃⋊C₁₆) #4462

Order 192.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊C₁₆	C₂	1	2	yes	maximal
3	C₄⋊C₁₆	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄²	C₄	1	1	yes	characteristic
7	C₃⋊C₁₆	—	2	2	no	—
8	C₂×C₁₆	—	3	2	no	—
9	C₄×C₈	D₃	1	1	yes	characteristic
10	C₂×C₃×C₄	C₈	1	1	yes	characteristic
11	C₂×C₃×C₄	C₈	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
13	C₃×C₈	—	2	1	no	—
14	C₃×C₈	D₄	1	1	yes	characteristic
15	C₃×C₈	Q₈	1	1	yes	characteristic
16	C₂×C₈	Dic₃	1	1	yes	characteristic
17	C₂×C₈	C₂×D₃	1	1	yes	characteristic
18	C₄²	Dic₃	1	1	yes	characteristic
19	C₁₆	—	6	2	no	—
20	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₁₆	1	2	yes	complemented
23	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₃×C₄	M₁₆	1	1	yes	characteristic
25	C₂×C₄	C₃⋊C₈	1	1	yes	characteristic
26	C₂×C₄	C₃⋊C₈	1	1	yes	characteristic
27	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₈	Dic₆	1	1	yes	characteristic
30	C₈	D₁₂	1	1	yes	characteristic
31	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
32	C₂×C₃	C₂×C₁₆	1	1	yes	characteristic
33	C₂×C₃	M₃₂	1	1	yes	characteristic
34	C₂²	C₂×C₃⋊C₈	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	C₃⋊C₁₆	1	2	yes	complemented
37	C₄	#208	1	1	yes	characteristic
38	C₄	C₄⋊Dic₃	1	1	yes	characteristic
39	C₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
41	C₂	C₂×C₃⋊C₁₆	1	1	yes	characteristic
42	C₂	#812	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
22. C₃×C₄	C₁₆	semidirect
36. C₄	C₃⋊C₁₆	semidirect
39. 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
C₃×C₄×C₈	2
C₂×C₃⋊C₁₆	2
C₄⋊C₁₆	3

Subgroups — C4⋊(C3⋊C16) #4462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊C₁₆) #4462