Subgroups — (C₂×D₃)⋊C₁₆ #4507

Order 192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₁₆	—	3	1	no	maximal, Sylow
5	C₂×C₄×D₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₈	C₄	1	1	yes	characteristic
8	D₃×C₈	—	2	1	no	—
9	D₃×C₈	—	2	1	no	—
10	C₃×C₁₆	—	2	1	no	—
11	C₃⋊C₁₆	—	2	1	no	—
12	C₂²×C₈	—	3	1	no	—
13	C₂×C₁₆	—	3	1	no	—
14	C₂×C₁₆	D₃	1	1	yes	characteristic, complemented
15	C₂²×D₃	C₈	1	1	yes	characteristic
16	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₃	C₈	1	1	yes	characteristic
18	C₄×D₃	—	2	1	no	—
19	C₄×D₃	—	2	1	no	—
20	C₃×C₈	D₄	1	1	yes	characteristic
21	C₃×C₈	D₄	1	1	yes	characteristic
22	C₃⋊C₈	—	2	1	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₂×C₈	—	3	1	no	—
25	C₂×C₈	—	6	1	no	—
26	C₂×C₈	—	6	1	no	—
27	C₂×C₈	C₂×D₃	1	1	yes	characteristic
28	C₁₆	—	2	1	no	—
29	C₁₆	—	6	1	no	—
30	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
31	C₂×D₃	—	2	1	no	—
32	C₂×D₃	—	2	1	no	—
33	C₂×D₃	C₁₆	1	2	yes	complemented
34	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₃×C₄	M₁₆	1	1	yes	characteristic
36	Dic₃	—	2	1	no	—
37	C₂³	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	6	1	no	—
40	C₂×C₄	—	6	1	no	—
41	C₂×C₄	C₄×D₃	1	1	yes	characteristic
42	C₈	—	6	1	no	—
43	C₈	D₁₂	1	1	yes	characteristic
44	C₈	#67	1	1	yes	characteristic
45	C₂×C₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₃	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₃	M₃₂	1	1	yes	characteristic
48	D₃	—	2	2	no	—
49	C₂²	—	3	2	no	—
50	C₂²	—	6	1	no	—
51	C₂²	—	6	1	no	—
52	C₂²	D₃×C₈	1	1	yes	characteristic
53	C₄	—	6	1	no	—
54	C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
55	C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
56	C₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	6	2	no	—
58	C₂	D₃×C₁₆	1	1	yes	characteristic
59	C₂	#798	1	1	yes	characteristic
60	C₂	(C₂×D₃)⋊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	C₂²×C₃	C₂×C₈
prime radical	C₂²×D₃	C₈
cosocle	C₂×C₃×C₈	C₂²
hypercenter	C₂×C₁₆	D₃
hypocenter	C₃	C₂²⋊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
2. C₂×C₃×C₁₆	C₂	semidirect
3. C₂×C₃⋊C₁₆	C₂	semidirect
14. C₂×C₁₆	D₃	semidirect
33. C₂×D₃	C₁₆	semidirect
56. C₃	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈	2
C₂×C₃×C₁₆	2
C₂×C₃⋊C₁₆	2
C₂²⋊C₁₆	3

Subgroups — (C2×D3)⋊C16 #4507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₃)⋊C₁₆ #4507