Subgroups — C₃×#334 #4581

Order 192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#334	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	—	2	2	no	—
5	C₂×C₃×C₈	C₄	1	1	yes	characteristic
6	C₂×C₃×C₈	C₄	1	1	yes	characteristic
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₄⋊C₈	C₂×C₃	1	2	yes	—
9	C₄×C₈	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₄	D₄	1	1	yes	characteristic
12	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
13	C₃×C₈	—	2	1	no	—
14	C₃×C₈	—	4	2	no	—
15	C₃×C₈	C₈	1	2	yes	complemented
16	C₂×C₈	—	2	2	no	—
17	C₂×C₈	C₃×C₄	1	1	yes	characteristic
18	C₂×C₈	C₃×C₄	1	1	yes	characteristic
19	C₄²	C₂²×C₃	1	1	yes	characteristic
20	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
21	C₃×C₄	—	2	1	no	—
22	C₃×C₄	C₂×C₈	1	1	yes	characteristic
23	C₃×C₄	M₁₆	1	1	yes	characteristic
24	C₃×C₄	SD₁₆	1	2	yes	—
25	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
26	C₂×C₄	C₃×D₄	1	1	yes	characteristic
27	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₈	—	4	2	no	—
30	C₈	C₃×C₈	1	2	yes	complemented
31	C₂×C₃	C₄⋊C₈	1	1	yes	characteristic
32	C₂×C₃	#106	1	1	yes	characteristic
33	C₂×C₃	#108	1	1	yes	characteristic
34	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	C₂×C₃×C₈	1	1	yes	characteristic
37	C₄	C₃×M₁₆	1	1	yes	characteristic
38	C₄	C₃×SD₁₆	1	2	yes	—
39	C₃	#334	1	1	yes	characteristic, direct product factor, Sylow
40	C₂	C₃×C₄⋊C₈	1	1	yes	characteristic
41	C₂	C₃×#106	1	1	yes	characteristic
42	C₂	C₃×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂×C₃×C₈
Frattini, cosocle	C₄²	C₂²×C₃
socle, prime radical	C₂²×C₃	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
3. #334	C₃	direct (N × H)
15. C₃×C₈	C₈	semidirect
30. C₈	C₃×C₈	semidirect
39. C₃	#334	direct (N × H)

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
C₃×C₄×C₈	2
#334	3

Subgroups — C3×#334 #4581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#334 #4581