Subgroups — C₂×C₃×#131 #5897

Order 192.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#131	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂²×C₃×C₈	C₂	1	3	yes	maximal, complemented
5	C₂×#131	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃×#41	C₄	1	4	yes	—
7	C₃×#41	C₂²	1	4	yes	—
8	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
9	C₂×C₃×D₄	C₄	1	3	yes	—
10	C₂²×C₃×C₄	C₂²	1	3	yes	—
11	C₃×M₁₆	C₂²	1	12	yes	complemented
12	C₂×C₃×C₈	C₂²	1	3	yes	—
13	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂²	1	12	yes	complemented
15	C₂×#41	C₂×C₃	1	1	yes	characteristic
16	#131	C₂×C₃	1	8	yes	direct product factor
17	C₂×M₁₆	C₂×C₃	1	3	yes	complemented
18	C₂²×C₈	C₂×C₃	1	3	yes	complemented
19	C₂³×C₃	C₂×C₄	1	3	yes	—
20	C₃×Q₈	C₂×C₄	1	4	yes	—
21	C₃×D₄	C₂×C₄	1	12	yes	—
22	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
23	C₂×C₃×C₄	C₂×C₄	1	6	yes	—
24	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂³	1	6	yes	—
26	C₃×C₈	C₂³	1	6	yes	—
27	C₃×C₈	C₂³	1	2	yes	—
28	#41	C₃×C₄	1	4	yes	—
29	#41	C₂²×C₃	1	4	yes	—
30	C₂×Q₈	C₃×C₄	1	1	yes	characteristic
31	C₂×D₄	C₃×C₄	1	3	yes	—
32	C₂²×C₄	C₂²×C₃	1	3	yes	—
33	M₁₆	C₂²×C₃	1	12	yes	complemented
34	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
35	C₂×C₈	C₂²×C₃	1	3	yes	—
36	C₂×C₈	C₂²×C₃	1	12	yes	complemented
37	C₂²×C₃	—	2	6	no	—
38	C₂²×C₃	C₂²×C₄	1	6	yes	—
39	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
40	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₃×C₄	C₂²×C₄	1	6	yes	—
42	C₃×C₄	C₂⁴	1	1	yes	characteristic
43	C₂³	C₂×C₃×C₄	1	3	yes	—
44	Q₈	C₂×C₃×C₄	1	4	yes	—
45	D₄	C₂×C₃×C₄	1	12	yes	—
46	C₂×C₄	C₂×C₃×C₄	1	3	yes	—
47	C₂×C₄	C₂×C₃×C₄	1	6	yes	—
48	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
49	C₂×C₄	C₂³×C₃	1	6	yes	—
50	C₈	C₂³×C₃	1	2	yes	—
51	C₈	C₂³×C₃	1	6	yes	—
52	C₂×C₃	—	2	6	no	—
53	C₂×C₃	#131	1	2	yes	direct product factor
54	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
55	C₂²	—	2	6	no	—
56	C₂²	C₂²×C₃×C₄	1	6	yes	—
57	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
58	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
59	C₄	C₂²×C₃×C₄	1	6	yes	—
60	C₄	C₂⁴×C₃	1	1	yes	characteristic
61	C₃	C₂×#131	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	2	6	no	—
63	C₂	C₃×#131	1	2	yes	direct product factor
64	C₂	C₂³×C₃×C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²
commutator	C₂	C₂³×C₃×C₄
Frattini, cosocle	C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂×C₃×#41	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#131	C₂	direct (N × H)
3. C₂×C₃×M₁₆	C₂	semidirect
4. C₂²×C₃×C₈	C₂	semidirect
5. C₂×#131	C₃	direct (N × H)
11. C₃×M₁₆	C₂²	semidirect
14. C₂×C₃×C₈	C₂²	semidirect
16. #131	C₂×C₃	direct (N × H)
17. C₂×M₁₆	C₂×C₃	semidirect
18. C₂²×C₈	C₂×C₃	semidirect
33. M₁₆	C₂²×C₃	semidirect
36. C₂×C₈	C₂²×C₃	semidirect
53. C₂×C₃	#131	direct (N × H)
61. C₃	C₂×#131	direct (N × H)
63. C₂	C₃×#131	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×#41	2
C₃×#131	2
C₂×C₃×M₁₆	2
C₂²×C₃×C₈	2
C₂×#131	3

Subgroups — C2×C3×#131 #5897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#131 #5897