Subgroups — C₃×#340 #4587

Order 192.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊C₄	C₂	1	2	yes	maximal
3	#340	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	—	2	2	no	—
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₈	—	2	2	no	—
7	C₂×C₃×C₈	C₄	1	2	yes	complemented
8	C₃×C₄⋊C₄	—	2	2	no	—
9	C₃×C₄⋊C₄	C₄	1	4	yes	complemented
10	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
11	C₂×C₄⋊C₄	C₂×C₃	1	2	yes	—
12	C₂³×C₃	D₄	1	1	yes	characteristic
13	C₂×C₃×C₄	—	2	4	no	—
14	C₂×C₃×C₄	—	4	2	no	—
15	C₂×C₃×C₄	—	4	2	no	—
16	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₄	D₄	1	2	yes	—
19	C₂×C₃×C₄	Q₈	1	1	yes	characteristic
20	C₃×C₈	—	2	2	no	—
21	C₂²×C₄	—	2	2	no	—
22	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	C₃×C₄	1	2	yes	complemented
25	C₄⋊C₄	—	2	2	no	—
26	C₄⋊C₄	C₃×C₄	1	4	yes	complemented
27	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
28	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₃	D₈	1	1	yes	characteristic
30	C₂²×C₃	SD₁₆	1	2	yes	—
31	C₂²×C₃	Q₁₆	1	1	yes	characteristic
32	C₃×C₄	—	4	4	no	—
33	C₃×C₄	C₄²	1	1	yes	characteristic
34	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₃×C₄	C₄⋊C₄	1	2	yes	—
36	C₂³	C₃×D₄	1	1	yes	characteristic
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	—	4	2	no	—
39	C₂×C₄	—	4	2	no	—
40	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
41	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₄	C₃×D₄	1	2	yes	—
43	C₂×C₄	C₃×Q₈	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₂×C₃	#95	1	1	yes	characteristic
46	C₂×C₃	#102	1	2	yes	—
47	C₂×C₃	#103	1	2	yes	—
48	C₂×C₃	#106	1	1	yes	characteristic
49	C₂×C₃	#107	1	1	yes	characteristic
50	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
51	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
52	C₂²	C₃×D₈	1	1	yes	characteristic
53	C₂²	C₃×SD₁₆	1	2	yes	—
54	C₂²	C₃×Q₁₆	1	1	yes	characteristic
55	C₄	—	4	4	no	—
56	C₄	C₃×C₄²	1	1	yes	characteristic
57	C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
58	C₄	C₃×C₄⋊C₄	1	2	yes	—
59	C₃	#340	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	C₃×#95	1	1	yes	characteristic
61	C₂	C₃×#102	1	2	yes	—
62	C₂	C₃×#103	1	2	yes	—
63	C₂	C₃×#106	1	1	yes	characteristic
64	C₂	C₃×#107	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #340	C₃	direct (N × H)
7. C₂×C₃×C₈	C₄	semidirect
9. C₃×C₄⋊C₄	C₄	semidirect
24. C₂×C₈	C₃×C₄	semidirect
26. C₄⋊C₄	C₃×C₄	semidirect
59. C₃	#340	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈	2
C₂×C₃×C₄⋊C₄	2
#340	3

Subgroups — C3×#340 #4587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#340 #4587