Subgroups — C₃×#454 #5328

Order 192.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	C₂	1	2	yes	maximal, complemented
5	C₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
6	#454	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	2	no	—
8	C₃×#41	—	2	2	no	—
9	C₃×#41	C₂²	1	2	yes	—
10	C₂×C₃×Q₈	—	2	2	no	—
11	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₃×SD₁₆	—	2	2	no	—
14	C₃×D₈	—	2	2	no	—
15	C₃×M₁₆	C₂²	1	2	yes	—
16	C₃×C₂²⋊C₄	—	2	2	no	—
17	C₃×C₄²	C₂²	1	1	yes	characteristic
18	2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
19	AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
20	#124	C₂×C₃	1	1	yes	characteristic, complemented
21	#104	C₂×C₃	1	2	yes	complemented
22	#101	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	1	no	—
24	C₃×Q₈	—	2	2	no	—
25	C₃×Q₈	—	2	2	no	—
26	C₃×Q₈	D₄	1	2	yes	—
27	C₃×D₄	—	2	2	no	—
28	C₃×D₄	—	2	2	no	—
29	C₃×D₄	—	2	2	no	—
30	C₃×D₄	D₄	1	2	yes	—
31	C₂×C₃×C₄	—	2	4	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	D₄	1	2	yes	—
35	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
36	C₃×C₈	—	2	2	no	—
37	#41	—	2	2	no	—
38	#41	—	2	2	no	—
39	#41	C₂²×C₃	1	2	yes	—
40	C₂×Q₈	—	2	2	no	—
41	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
42	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
43	SD₁₆	—	2	2	no	—
44	D₈	—	2	2	no	—
45	M₁₆	C₂²×C₃	1	2	yes	—
46	C₂²⋊C₄	—	2	2	no	—
47	C₄²	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃	—	2	2	no	—
49	C₂²×C₃	—	4	2	no	—
50	C₂²×C₃	—	4	1	no	—
51	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
52	C₃×C₄	—	2	2	no	—
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	C₂×D₄	1	2	yes	—
56	C₂³	—	2	1	no	—
57	Q₈	—	2	2	no	—
58	Q₈	—	2	2	no	—
59	Q₈	C₃×D₄	1	2	yes	—
60	D₄	—	2	2	no	—
61	D₄	—	2	2	no	—
62	D₄	—	2	2	no	—
63	D₄	C₃×D₄	1	2	yes	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	C₃×D₄	1	2	yes	—
68	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₈	—	2	2	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	4	2	no	—
72	C₂×C₃	—	8	1	no	—
73	C₂×C₃	#120	1	1	yes	characteristic
74	C₂²	—	2	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	—	4	1	no	—
77	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	2	no	—
80	C₄	—	4	1	no	—
81	C₄	C₂×C₃×D₄	1	2	yes	—
82	C₃	#454	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	2	1	no	—
84	C₂	—	4	2	no	—
85	C₂	—	8	1	no	—
86	C₂	C₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#120
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. C₃×2₋¹⁺⁴	C₂	semidirect
2. C₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₃×#124	C₂	semidirect
4. C₃×#104	C₂	semidirect
5. C₃×#101	C₂	semidirect
6. #454	C₃	direct (N × H)
18. 2₋¹⁺⁴	C₂×C₃	semidirect
19. AGL(1,ℤ/8)	C₂×C₃	semidirect
20. #124	C₂×C₃	semidirect
21. #104	C₂×C₃	semidirect
22. #101	C₂×C₃	semidirect
82. C₃	#454	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×2₋¹⁺⁴	2
C₃×AGL(1,ℤ/8)	2
C₃×#124	2
C₃×#104	2
C₃×#101	2
#454	3

Subgroups — C3×#454 #5328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#454 #5328