Subgroups — C₃×#137 #977

Order 96.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₁₆	C₂	1	2	yes	maximal, complemented
4	C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#137	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×Q₈	—	2	1	no	—
8	C₃×Q₈	C₂²	1	2	yes	—
9	C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₃×D₄	—	2	1	no	—
11	C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄	—	2	1	no	—
13	C₂×C₃×C₄	—	2	1	no	—
14	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
15	C₃×C₈	C₂²	1	2	yes	—
16	#41	C₂×C₃	1	1	yes	characteristic
17	C₂×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
18	Q₁₆	C₂×C₃	1	2	yes	complemented
19	SD₁₆	C₂×C₃	1	2	yes	complemented
20	M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	D₄	1	1	yes	characteristic
23	C₃×C₄	—	2	1	no	—
24	C₃×C₄	—	2	2	no	—
25	C₃×C₄	D₄	1	1	yes	characteristic
26	C₃×C₄	C₂³	1	1	yes	characteristic
27	Q₈	—	2	1	no	—
28	Q₈	C₂²×C₃	1	2	yes	—
29	Q₈	C₂²×C₃	1	1	yes	characteristic
30	D₄	—	2	1	no	—
31	D₄	C₂²×C₃	1	1	yes	characteristic
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
35	C₈	C₂²×C₃	1	2	yes	—
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	—	4	1	no	—
38	C₂×C₃	C₂×D₄	1	1	yes	characteristic
39	C₂²	—	2	1	no	—
40	C₂²	C₃×D₄	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	—	2	2	no	—
43	C₄	C₃×D₄	1	1	yes	characteristic
44	C₄	C₂³×C₃	1	1	yes	characteristic
45	C₃	#137	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
prime radical	C₃×#41	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₈	C₂	semidirect
3. C₃×Q₁₆	C₂	semidirect
4. C₃×SD₁₆	C₂	semidirect
5. C₃×M₁₆	C₂	semidirect
6. #137	C₃	direct (N × H)
17. C₂×Q₈	C₂×C₃	semidirect
18. Q₁₆	C₂×C₃	semidirect
19. SD₁₆	C₂×C₃	semidirect
20. M₁₆	C₂×C₃	semidirect
45. C₃	#137	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×#41	2
C₂×C₃×Q₈	2
C₃×Q₁₆	2
C₃×SD₁₆	2
C₃×M₁₆	2
#137	3

Subgroups — C3×#137 #977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#137 #977