Subgroups — C₃×#427 #5301

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	C₃×#117	C₂	1	2	yes	maximal
3	C₃×#107	C₂	1	2	yes	maximal, complemented
4	C₃×#106	C₂	1	2	yes	maximal, complemented
5	#427	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	C₄	1	4	yes	complemented
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₃×C₂²⋊C₄	—	2	2	no	—
12	C₃×C₄²	—	2	2	no	—
13	C₂²×C₈	C₂×C₃	1	1	yes	characteristic
14	#117	C₂×C₃	1	2	yes	—
15	#107	C₂×C₃	1	2	yes	complemented
16	#106	C₂×C₃	1	2	yes	complemented
17	C₂³×C₃	D₄	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	4	no	—
19	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
20	C₂×C₃×C₄	D₄	1	1	yes	characteristic
21	C₂×C₃×C₄	Q₈	1	2	yes	—
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	C₃×C₈	C₂×C₄	1	2	yes	—
24	C₃×C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₈	C₃×C₄	1	4	yes	complemented
27	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
29	C₄⋊C₄	C₂²×C₃	1	4	yes	—
30	C₂²⋊C₄	—	2	2	no	—
31	C₄²	—	2	2	no	—
32	C₂²×C₃	—	2	2	no	—
33	C₂²×C₃	C₄⋊C₄	1	2	yes	—
34	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄	—	4	4	no	—
36	C₃×C₄	C₄⋊C₄	1	2	yes	—
37	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
38	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
39	C₂³	C₃×D₄	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₄	C₃×D₄	1	1	yes	characteristic
43	C₂×C₄	C₃×Q₈	1	2	yes	—
44	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
45	C₈	C₂×C₃×C₄	1	2	yes	—
46	C₈	C₂×C₃×C₄	1	2	yes	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₃	#135	1	2	yes	—
50	C₂²	—	2	2	no	—
51	C₂²	C₃×C₄⋊C₄	1	2	yes	—
52	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
53	C₄	—	4	4	no	—
54	C₄	C₃×C₄⋊C₄	1	2	yes	—
55	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
56	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
57	C₃	#427	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	—	2	2	no	—
59	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
60	C₂	C₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×D₄
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
3. C₃×#107	C₂	semidirect
4. C₃×#106	C₂	semidirect
5. #427	C₃	direct (N × H)
7. C₂×C₃×C₈	C₄	semidirect
15. #107	C₂×C₃	semidirect
16. #106	C₂×C₃	semidirect
26. C₂×C₈	C₃×C₄	semidirect
57. C₃	#427	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
C₃×#117	2
C₃×#107	2
C₃×#106	2
#427	3

Subgroups — C3×#427 #5301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#427 #5301