Subgroups — C₃×#339 #4586

Order 192.

110 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	C₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
4	#339	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	—	2	1	no	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃×M₁₆	—	2	1	no	—
8	C₃×M₁₆	C₄	1	2	yes	complemented
9	C₂×C₃×C₈	—	2	1	no	—
10	C₃×C₄⋊C₄	C₄	1	2	yes	complemented
11	C₃×C₂²⋊C₄	—	2	1	no	—
12	C₃×C₄²	—	2	1	no	—
13	C₃×C₄²	—	2	1	no	—
14	C₃×C₄²	C₄	1	2	yes	complemented
15	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
16	#117	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
18	C₂³×C₃	D₄	1	1	yes	characteristic
19	C₂×C₃×C₄	—	2	4	no	—
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
28	C₃×C₈	—	2	2	no	—
29	C₂²×C₄	—	2	1	no	—
30	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
31	M₁₆	—	2	1	no	—
32	M₁₆	C₃×C₄	1	2	yes	complemented
33	C₂×C₈	—	2	1	no	—
34	C₄⋊C₄	C₃×C₄	1	2	yes	complemented
35	C₂²⋊C₄	—	2	1	no	—
36	C₄²	—	2	1	no	—
37	C₄²	—	2	1	no	—
38	C₄²	C₃×C₄	1	2	yes	complemented
39	C₂²×C₃	—	2	2	no	—
40	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
43	C₃×C₄	—	2	4	no	—
44	C₃×C₄	—	4	2	no	—
45	C₃×C₄	C₄²	1	1	yes	characteristic
46	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
47	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
48	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
49	C₂³	C₃×D₄	1	1	yes	characteristic
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
54	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
56	C₂×C₄	C₃×D₄	1	1	yes	characteristic
57	C₂×C₄	C₃×D₄	1	1	yes	characteristic
58	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	2	1	no	—
62	C₂×C₃	#95	1	1	yes	characteristic
63	C₂×C₃	#104	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
67	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	4	2	no	—
70	C₄	C₃×C₄²	1	1	yes	characteristic
71	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
72	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
73	C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
74	C₃	#339	1	1	yes	characteristic, direct product factor, Sylow
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	C₃×#95	1	1	yes	characteristic
78	C₂	C₃×#104	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂²×C₃
socle	C₂²×C₃	C₂²⋊C₄
prime radical	C₂³×C₃	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. #339	C₃	direct (N × H)
8. C₃×M₁₆	C₄	semidirect
10. C₃×C₄⋊C₄	C₄	semidirect
14. C₃×C₄²	C₄	semidirect
32. M₁₆	C₃×C₄	semidirect
34. C₄⋊C₄	C₃×C₄	semidirect
38. C₄²	C₃×C₄	semidirect
74. C₃	#339	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
C₃×#117	2
C₂×C₃×C₄²	2
#339	3

Subgroups — C3×#339 #4586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#339 #4586