Subgroups — C₃×#121 #961

Order 96.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	#121	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₃	C₂²	1	2	yes	—
8	C₂³×C₃	C₂²	1	1	yes	characteristic
9	C₃×D₄	—	2	4	no	—
10	C₃×D₄	—	2	2	no	—
11	C₂×C₃×C₄	—	2	2	no	—
12	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
15	C₂×D₄	C₂×C₃	1	2	yes	complemented
16	C₂×D₄	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
18	C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
20	C₂²×C₃	—	2	1	no	—
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	—	2	2	no	—
23	C₂²×C₃	—	2	2	no	—
24	C₂²×C₃	—	2	2	no	—
25	C₂²×C₃	D₄	1	2	yes	complemented
26	C₂²×C₃	C₂³	1	1	yes	characteristic
27	C₃×C₄	—	2	1	no	—
28	C₃×C₄	—	2	2	no	—
29	C₃×C₄	D₄	1	2	yes	complemented
30	C₂³	C₂²×C₃	1	2	yes	—
31	C₂³	C₂²×C₃	1	1	yes	characteristic
32	D₄	—	2	4	no	—
33	D₄	—	2	2	no	—
34	C₂×C₄	—	2	2	no	—
35	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₃	1	2	yes	—
37	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
38	C₂×C₃	—	2	2	no	—
39	C₂×C₃	—	4	2	no	—
40	C₂×C₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₃	#41	1	1	yes	characteristic
43	C₂²	—	2	1	no	—
44	C₂²	—	2	1	no	—
45	C₂²	—	2	2	no	—
46	C₂²	—	2	2	no	—
47	C₂²	—	2	2	no	—
48	C₂²	C₃×D₄	1	2	yes	complemented
49	C₂²	C₂³×C₃	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	2	no	—
52	C₄	C₃×D₄	1	2	yes	complemented
53	C₃	#121	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	—	2	2	no	—
55	C₂	—	4	2	no	—
56	C₂	C₂×C₃×D₄	1	1	yes	characteristic
57	C₂	C₂×C₃×D₄	1	1	yes	characteristic
58	C₂	C₃×#41	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃
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
1. C₂×C₃×D₄	C₂	semidirect
2. C₂×C₃×D₄	C₂	semidirect
3. C₂²×C₃×C₄	C₂	semidirect
4. C₃×C₄⋊C₄	C₂	semidirect
5. C₃×C₂²⋊C₄	C₂	semidirect
6. #121	C₃	direct (N × H)
15. C₂×D₄	C₂×C₃	semidirect
16. C₂×D₄	C₂×C₃	semidirect
17. C₂²×C₄	C₂×C₃	semidirect
18. C₄⋊C₄	C₂×C₃	semidirect
19. C₂²⋊C₄	C₂×C₃	semidirect
25. C₂²×C₃	D₄	semidirect
29. C₃×C₄	D₄	semidirect
48. C₂²	C₃×D₄	semidirect
52. C₄	C₃×D₄	semidirect
53. C₃	#121	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
#121	3

Subgroups — C3×#121 #961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#121 #961