Subgroups — C₃×#460 #5334

Order 192.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#102	C₂	1	2	yes	maximal, complemented
6	#460	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₄	—	2	1	no	—
9	C₂×C₃×D₄	—	2	1	no	—
10	C₂×C₃×D₄	C₂²	1	2	yes	—
11	C₃×SD₁₆	—	2	4	no	—
12	C₂×C₃×C₈	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₄²	—	2	1	no	—
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×SD₁₆	C₂×C₃	1	2	yes	complemented
18	#127	C₂×C₃	1	1	yes	characteristic
19	C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
20	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	#102	C₂×C₃	1	2	yes	complemented
22	C₂³×C₃	—	2	2	no	—
23	C₃×Q₈	—	2	1	no	—
24	C₃×Q₈	D₄	1	2	yes	complemented
25	C₃×D₄	—	2	2	no	—
26	C₃×D₄	—	2	2	no	—
27	C₃×D₄	—	4	2	no	—
28	C₃×D₄	—	4	2	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	D₄	1	1	yes	characteristic
32	C₂×C₃×C₄	D₄	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₃×C₈	—	2	2	no	—
35	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
36	C₂×D₄	—	2	1	no	—
37	C₂×D₄	—	2	1	no	—
38	C₂×D₄	C₂²×C₃	1	2	yes	—
39	SD₁₆	—	2	4	no	—
40	C₂×C₈	C₂²×C₃	1	2	yes	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
43	C₄²	—	2	1	no	—
44	C₄²	C₂²×C₃	1	1	yes	characteristic
45	C₂²×C₃	—	4	2	no	—
46	C₂²×C₃	—	4	2	no	—
47	C₂²×C₃	—	4	2	no	—
48	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	—	2	1	no	—
51	C₃×C₄	—	4	1	no	—
52	C₃×C₄	SD₁₆	1	2	yes	complemented
53	C₃×C₄	C₂×D₄	1	1	yes	characteristic
54	C₃×C₄	#41	1	1	yes	characteristic
55	C₂³	—	2	2	no	—
56	Q₈	—	2	1	no	—
57	Q₈	C₃×D₄	1	2	yes	complemented
58	D₄	—	2	2	no	—
59	D₄	—	2	2	no	—
60	D₄	—	4	2	no	—
61	D₄	—	4	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	C₃×D₄	1	1	yes	characteristic
65	C₂×C₄	C₃×D₄	1	1	yes	characteristic
66	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₂×C₃	—	8	2	no	—
69	C₂×C₃	#121	1	1	yes	characteristic
70	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
71	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
72	C₂²	—	4	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	2	1	no	—
78	C₄	—	4	1	no	—
79	C₄	C₃×SD₁₆	1	2	yes	complemented
80	C₄	C₂×C₃×D₄	1	1	yes	characteristic
81	C₄	C₃×#41	1	1	yes	characteristic
82	C₃	#460	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	8	2	no	—
84	C₂	C₃×#121	1	1	yes	characteristic
85	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic
86	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₃×#127	C₂
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
1. C₂×C₃×SD₁₆	C₂	semidirect
3. C₃×C₄×Q₈	C₂	semidirect
4. C₃×C₄⋊C₈	C₂	semidirect
5. C₃×#102	C₂	semidirect
6. #460	C₃	direct (N × H)
17. C₂×SD₁₆	C₂×C₃	semidirect
19. C₄×Q₈	C₂×C₃	semidirect
20. C₄⋊C₈	C₂×C₃	semidirect
21. #102	C₂×C₃	semidirect
24. C₃×Q₈	D₄	semidirect
52. C₃×C₄	SD₁₆	semidirect
57. Q₈	C₃×D₄	semidirect
79. C₄	C₃×SD₁₆	semidirect
82. C₃	#460	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×SD₁₆	2
C₃×#127	2
C₃×C₄×Q₈	2
C₃×C₄⋊C₈	2
C₃×#102	2
#460	3

Subgroups — C3×#460 #5334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#460 #5334