Subgroups — C₃×#469 #5343

Order 192.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#121	C₂	1	2	yes	maximal, complemented
4	C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#102	C₂	1	2	yes	maximal, complemented
6	#469	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	—	2	2	no	—
8	C₂×C₃×D₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₃×D₈	—	2	2	no	—
11	C₃×M₁₆	—	2	2	no	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₃×C₂²⋊C₄	—	2	2	no	—
16	C₂×D₈	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
18	#121	C₂×C₃	1	2	yes	complemented
19	#106	C₂×C₃	1	1	yes	characteristic, complemented
20	#102	C₂×C₃	1	2	yes	complemented
21	C₂³×C₃	—	2	2	no	—
22	C₂³×C₃	D₄	1	1	yes	characteristic
23	C₃×D₄	—	2	2	no	—
24	C₃×D₄	—	2	2	no	—
25	C₃×D₄	—	4	4	no	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	2	no	—
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	—	2	1	no	—
32	C₃×C₈	D₄	1	2	yes	complemented
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂²×C₃	1	2	yes	—
35	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
36	D₈	—	2	2	no	—
37	M₁₆	—	2	2	no	—
38	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
39	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₄⋊C₄	C₂²×C₃	1	2	yes	—
41	C₂²⋊C₄	—	2	2	no	—
42	C₂²×C₃	—	2	1	no	—
43	C₂²×C₃	—	2	2	no	—
44	C₂²×C₃	—	4	2	no	—
45	C₂²×C₃	—	4	2	no	—
46	C₂²×C₃	—	4	2	no	—
47	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	4	2	no	—
50	C₃×C₄	C₂×D₄	1	1	yes	characteristic
51	C₃×C₄	#41	1	1	yes	characteristic
52	C₂³	—	2	2	no	—
53	C₂³	C₃×D₄	1	1	yes	characteristic
54	D₄	—	2	2	no	—
55	D₄	—	2	2	no	—
56	D₄	—	4	4	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	C₃×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	C₃×D₄	1	2	yes	complemented
64	C₂×C₃	—	4	1	no	—
65	C₂×C₃	—	8	2	no	—
66	C₂×C₃	#121	1	1	yes	characteristic
67	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
68	C₂²	—	2	1	no	—
69	C₂²	—	2	2	no	—
70	C₂²	—	4	2	no	—
71	C₂²	—	4	2	no	—
72	C₂²	—	4	2	no	—
73	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	4	2	no	—
76	C₄	C₂×C₃×D₄	1	1	yes	characteristic
77	C₄	C₃×#41	1	1	yes	characteristic
78	C₃	#469	1	1	yes	characteristic, direct product factor, Sylow
79	C₂	—	4	1	no	—
80	C₂	—	8	2	no	—
81	C₂	C₃×#121	1	1	yes	characteristic
82	C₂	C₃×AGL(1,ℤ/8)	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₈	C₂	semidirect
2. C₂×C₃×M₁₆	C₂	semidirect
3. C₃×#121	C₂	semidirect
4. C₃×#106	C₂	semidirect
5. C₃×#102	C₂	semidirect
6. #469	C₃	direct (N × H)
16. C₂×D₈	C₂×C₃	semidirect
17. C₂×M₁₆	C₂×C₃	semidirect
18. #121	C₂×C₃	semidirect
19. #106	C₂×C₃	semidirect
20. #102	C₂×C₃	semidirect
32. C₃×C₈	D₄	semidirect
63. C₈	C₃×D₄	semidirect
78. C₃	#469	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×D₈	2
C₂×C₃×M₁₆	2
C₃×#121	2
C₃×#106	2
C₃×#102	2
#469	3

Subgroups — C3×#469 #5343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#469 #5343