Subgroups — C₃×#472 #5346

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#100	C₂	1	2	yes	maximal, complemented
6	#472	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₄	C₂²	1	2	yes	—
9	C₃×SD₁₆	—	2	2	no	—
10	C₃×D₈	—	2	2	no	—
11	C₃×D₈	—	2	1	no	—
12	C₃×D₈	—	2	1	no	—
13	C₃×M₁₆	—	2	1	no	—
14	C₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₃×M₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₈	—	2	1	no	—
17	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
18	AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
19	C₂×D₈	C₂×C₃	1	1	yes	characteristic, complemented
20	#131	C₂×C₃	1	1	yes	characteristic, complemented
21	#108	C₂×C₃	1	1	yes	characteristic, complemented
22	#100	C₂×C₃	1	2	yes	complemented
23	C₂³×C₃	—	2	2	no	—
24	C₃×Q₈	D₄	1	1	yes	characteristic
25	C₃×D₄	—	2	1	no	—
26	C₃×D₄	—	2	2	no	—
27	C₃×D₄	—	2	2	no	—
28	C₃×D₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	—	2	1	no	—
32	C₃×C₈	—	2	2	no	—
33	C₃×C₈	D₄	1	1	yes	characteristic
34	C₃×C₈	D₄	1	1	yes	characteristic
35	#41	C₂²×C₃	1	1	yes	characteristic
36	C₂×D₄	C₂²×C₃	1	2	yes	—
37	SD₁₆	—	2	2	no	—
38	D₈	—	2	2	no	—
39	D₈	—	2	1	no	—
40	D₈	—	2	1	no	—
41	M₁₆	—	2	1	no	—
42	M₁₆	C₂²×C₃	1	1	yes	characteristic
43	M₁₆	C₂²×C₃	1	2	yes	—
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₃	—	2	1	no	—
47	C₂²×C₃	—	4	2	no	—
48	C₂²×C₃	—	8	2	no	—
49	C₂²×C₃	#41	1	1	yes	characteristic
50	C₃×C₄	—	2	1	no	—
51	C₃×C₄	C₂×D₄	1	1	yes	characteristic
52	C₃×C₄	C₂×D₄	1	1	yes	characteristic
53	C₂³	—	2	2	no	—
54	Q₈	C₃×D₄	1	1	yes	characteristic
55	D₄	—	2	1	no	—
56	D₄	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	C₃×D₄	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	2	2	no	—
63	C₈	C₃×D₄	1	1	yes	characteristic
64	C₈	C₃×D₄	1	1	yes	characteristic
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	—	4	1	no	—
67	C₂×C₃	—	8	2	no	—
68	C₂×C₃	#121	1	1	yes	characteristic
69	C₂²	—	2	1	no	—
70	C₂²	—	4	2	no	—
71	C₂²	—	8	2	no	—
72	C₂²	C₃×#41	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	C₂×C₃×D₄	1	1	yes	characteristic
75	C₄	C₂×C₃×D₄	1	1	yes	characteristic
76	C₃	#472	1	1	yes	characteristic, direct product factor, Sylow
77	C₂	—	2	1	no	—
78	C₂	—	4	1	no	—
79	C₂	—	8	2	no	—
80	C₂	C₃×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#121
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×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
1. C₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×D₈	C₂	semidirect
3. C₃×#131	C₂	semidirect
4. C₃×#108	C₂	semidirect
5. C₃×#100	C₂	semidirect
6. #472	C₃	direct (N × H)
18. AGL(1,ℤ/8)	C₂×C₃	semidirect
19. C₂×D₈	C₂×C₃	semidirect
20. #131	C₂×C₃	semidirect
21. #108	C₂×C₃	semidirect
22. #100	C₂×C₃	semidirect
76. C₃	#472	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×AGL(1,ℤ/8)	2
C₂×C₃×D₈	2
C₃×#131	2
C₃×#108	2
C₃×#100	2
#472	3

Subgroups — C3×#472 #5346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#472 #5346