Subgroups — C₃×#501 #5375

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#125	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	2	yes	maximal
4	C₃×#106	C₂	1	2	yes	maximal
5	C₃×#97	C₂	1	1	yes	maximal, characteristic
6	#501	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	—	2	1	no	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄⋊C₄	—	2	1	no	—
10	C₃×C₄⋊C₄	—	2	1	no	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
17	#125	C₂×C₃	1	1	yes	characteristic
18	#107	C₂×C₃	1	2	yes	—
19	#106	C₂×C₃	1	2	yes	—
20	#97	C₂×C₃	1	1	yes	characteristic
21	C₃×Q₈	—	4	2	no	—
22	C₂×C₃×C₄	—	2	1	no	—
23	C₂×C₃×C₄	—	2	1	no	—
24	C₂×C₃×C₄	—	2	2	no	—
25	C₂×C₃×C₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₃×C₈	Q₈	1	4	yes	complemented
29	C₂×Q₈	—	2	1	no	—
30	C₂×C₈	C₂²×C₃	1	2	yes	—
31	C₄⋊C₄	—	2	1	no	—
32	C₄⋊C₄	—	2	1	no	—
33	C₄⋊C₄	—	2	1	no	—
34	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
35	C₄⋊C₄	C₂²×C₃	1	2	yes	—
36	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
37	C₄²	C₂²×C₃	1	1	yes	characteristic
38	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	—	4	1	no	—
42	C₃×C₄	—	4	2	no	—
43	C₃×C₄	—	4	1	no	—
44	C₃×C₄	C₂×Q₈	1	2	yes	—
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	2	1	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	C₃×D₄	1	1	yes	characteristic
50	C₂×C₄	C₃×D₄	1	1	yes	characteristic
51	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
52	C₈	C₃×Q₈	1	4	yes	complemented
53	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₂×C₃	#137	1	1	yes	characteristic
56	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	2	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	C₂×C₃×Q₈	1	2	yes	—
63	C₃	#501	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×C₄⋊Q₈	1	1	yes	characteristic
65	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₂	C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
6. #501	C₃	direct (N × H)
28. C₃×C₈	Q₈	semidirect
52. C₈	C₃×Q₈	semidirect
63. C₃	#501	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⋊Q₈	2
C₃×#125	2
C₃×#107	2
C₃×#106	2
C₃×#97	2
#501	3

Subgroups — C3×#501 #5375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#501 #5375