Subgroups — C₃×#490 #5364

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#102	C₂	1	4	yes	maximal, complemented
4	C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	#490	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×D₄	—	2	2	no	—
7	C₂×C₃×D₄	C₂²	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄⋊C₄	—	2	2	no	—
10	C₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₃×C₄²	C₂²	1	1	yes	characteristic
12	#127	C₂×C₃	1	1	yes	characteristic
13	#125	C₂×C₃	1	1	yes	characteristic, complemented
14	#102	C₂×C₃	1	4	yes	complemented
15	#97	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂³×C₃	—	2	2	no	—
17	C₃×D₄	—	2	4	no	—
18	C₃×D₄	—	4	4	no	—
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×C₃×C₄	D₄	1	2	yes	—
21	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
22	C₃×C₈	—	2	2	no	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	C₂²×C₃	1	2	yes	—
25	C₂×C₈	C₂²×C₃	1	2	yes	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄⋊C₄	C₂²×C₃	1	2	yes	—
28	C₄²	C₂²×C₃	1	1	yes	characteristic
29	C₂²×C₃	—	4	2	no	—
30	C₂²×C₃	—	4	4	no	—
31	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
32	C₃×C₄	—	2	2	no	—
33	C₃×C₄	—	4	2	no	—
34	C₃×C₄	#41	1	2	yes	—
35	C₂³	—	2	2	no	—
36	D₄	—	2	4	no	—
37	D₄	—	4	4	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	C₃×D₄	1	2	yes	—
40	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂×C₃	—	8	2	no	—
43	C₂×C₃	#124	1	1	yes	characteristic
44	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
45	C₂²	—	4	2	no	—
46	C₂²	—	4	4	no	—
47	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	4	2	no	—
50	C₄	C₃×#41	1	2	yes	—
51	C₃	#490	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	—	8	2	no	—
53	C₂	C₃×#124	1	1	yes	characteristic
54	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
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
2. C₃×#125	C₂	semidirect
3. C₃×#102	C₂	semidirect
4. C₃×#97	C₂	semidirect
5. #490	C₃	direct (N × H)
13. #125	C₂×C₃	semidirect
14. #102	C₂×C₃	semidirect
15. #97	C₂×C₃	semidirect
51. C₃	#490	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#127	2
C₃×#125	2
C₃×#102	2
C₃×#97	2
#490	3

Subgroups — C3×#490 #5364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#490 #5364