Subgroups — C₃×#123 #963

Order 96.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	#123	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₃	C₂²	1	1	yes	characteristic
8	C₂³×C₃	C₂²	1	1	yes	characteristic
9	C₃×D₄	—	2	2	no	—
10	C₂×C₃×C₄	—	2	2	no	—
11	C₂×C₃×C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₂×D₄	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
16	C₄⋊C₄	C₂×C₃	1	2	yes	complemented
17	C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
19	C₂²×C₃	—	2	2	no	—
20	C₂²×C₃	—	2	1	no	—
21	C₂²×C₃	—	2	2	no	—
22	C₂²×C₃	D₄	1	2	yes	—
23	C₂²×C₃	C₂³	1	1	yes	characteristic
24	C₃×C₄	—	2	2	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	—	2	2	no	—
27	C₂³	C₂²×C₃	1	1	yes	characteristic
28	C₂³	C₂²×C₃	1	1	yes	characteristic
29	D₄	—	2	2	no	—
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	C₂²×C₃	1	2	yes	—
32	C₂×C₄	C₂²×C₃	1	2	yes	—
33	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₃	—	2	2	no	—
35	C₂×C₃	—	4	1	no	—
36	C₂×C₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₃	#41	1	2	yes	—
38	C₂²	—	2	2	no	—
39	C₂²	—	2	1	no	—
40	C₂²	—	2	2	no	—
41	C₂²	C₃×D₄	1	2	yes	—
42	C₂²	C₂³×C₃	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	—	2	2	no	—
46	C₃	#123	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	—	2	2	no	—
48	C₂	—	4	1	no	—
49	C₂	C₂×C₃×D₄	1	1	yes	characteristic
50	C₂	C₃×#41	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄	C₂	semidirect
3. C₃×C₄⋊C₄	C₂	semidirect
4. C₃×C₂²⋊C₄	C₂	semidirect
5. C₃×C₂²⋊C₄	C₂	semidirect
6. #123	C₃	direct (N × H)
15. C₂²×C₄	C₂×C₃	semidirect
16. C₄⋊C₄	C₂×C₃	semidirect
17. C₂²⋊C₄	C₂×C₃	semidirect
18. C₂²⋊C₄	C₂×C₃	semidirect
46. C₃	#123	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄	2
C₂²×C₃×C₄	2
C₃×C₄⋊C₄	2
C₃×C₂²⋊C₄	2
#123	3

Subgroups — C3×#123 #963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#123 #963