Subgroups — C₃×#405 #5279

Order 192.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×#97	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₈	C₂	1	2	yes	maximal, complemented
6	#405	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₃×M₁₆	C₄	1	4	yes	complemented
9	C₂×C₃×C₈	C₄	1	4	yes	complemented
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₄	1	2	yes	—
14	C₃×C₂²⋊C₄	C₄	1	2	yes	—
15	C₃×C₄²	C₂²	1	2	yes	—
16	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
17	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
18	#117	C₂×C₃	1	1	yes	characteristic
19	#97	C₂×C₃	1	2	yes	complemented
20	C₄×C₈	C₂×C₃	1	2	yes	complemented
21	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
23	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
25	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
27	C₃×C₈	C₂×C₄	1	2	yes	—
28	C₃×C₈	C₂×C₄	1	2	yes	—
29	C₃×C₈	C₂×C₄	1	4	yes	—
30	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
31	M₁₆	C₃×C₄	1	4	yes	complemented
32	C₂×C₈	C₃×C₄	1	4	yes	complemented
33	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₈	C₂²×C₃	1	2	yes	—
35	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
36	C₄⋊C₄	C₃×C₄	1	2	yes	—
37	C₂²⋊C₄	C₃×C₄	1	2	yes	—
38	C₄²	C₂²×C₃	1	2	yes	—
39	C₂²×C₃	—	2	2	no	—
40	C₂²×C₃	C₄²	1	2	yes	—
41	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
42	C₃×C₄	—	2	4	no	—
43	C₃×C₄	C₄²	1	2	yes	—
44	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
47	C₂×C₄	C₂×C₃×C₄	1	4	yes	—
48	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
50	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
51	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
52	C₈	C₂×C₃×C₄	1	2	yes	—
53	C₈	C₂×C₃×C₄	1	2	yes	—
54	C₈	C₂×C₃×C₄	1	4	yes	—
55	C₂×C₃	—	2	2	no	—
56	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
57	C₂×C₃	#131	1	2	yes	—
58	C₂²	—	2	2	no	—
59	C₂²	C₃×C₄²	1	2	yes	—
60	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
61	C₄	—	2	4	no	—
62	C₄	C₃×C₄²	1	2	yes	—
63	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
64	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
65	C₃	#405	1	1	yes	characteristic, direct product factor, Sylow
66	C₂	—	2	2	no	—
67	C₂	C₂×C₃×C₄²	1	1	yes	characteristic
68	C₂	C₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²
commutator	C₂	C₂×C₃×C₄²
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂³×C₃	C₂×C₄
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
4. C₃×#97	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. #405	C₃	direct (N × H)
8. C₃×M₁₆	C₄	semidirect
9. C₂×C₃×C₈	C₄	semidirect
19. #97	C₂×C₃	semidirect
20. C₄×C₈	C₂×C₃	semidirect
31. M₁₆	C₃×C₄	semidirect
32. C₂×C₈	C₃×C₄	semidirect
65. C₃	#405	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×M₁₆	2
C₂²×C₃×C₈	2
C₃×#117	2
C₃×#97	2
C₃×C₄×C₈	2
#405	3

Subgroups — C3×#405 #5279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#405 #5279