Subgroups — C₃×#428 #5302

Order 192.

118 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×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#107	C₂	1	2	yes	maximal, complemented
5	C₃×#106	C₂	1	2	yes	maximal, complemented
6	#428	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×C₄	—	2	1	no	—
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₃×M₁₆	C₄	1	4	yes	complemented
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²	—	2	1	no	—
17	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
18	#117	C₂×C₃	1	1	yes	characteristic
19	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
20	#107	C₂×C₃	1	2	yes	complemented
21	#106	C₂×C₃	1	2	yes	complemented
22	C₂³×C₃	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	—	2	1	no	—
24	C₂×C₃×C₄	—	2	1	no	—
25	C₂×C₃×C₄	—	2	2	no	—
26	C₂×C₃×C₄	—	4	2	no	—
27	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	Q₈	1	2	yes	—
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	C₂×C₄	1	4	yes	complemented
32	C₂²×C₄	—	2	1	no	—
33	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
34	M₁₆	C₃×C₄	1	4	yes	complemented
35	C₂×C₈	C₂²×C₃	1	2	yes	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
38	C₄⋊C₄	C₂²×C₃	1	2	yes	—
39	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂²⋊C₄	—	2	1	no	—
41	C₄²	—	2	1	no	—
42	C₂²×C₃	—	2	1	no	—
43	C₂²×C₃	—	2	1	no	—
44	C₂²×C₃	C₄⋊C₄	1	2	yes	—
45	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
46	C₃×C₄	—	4	1	no	—
47	C₃×C₄	—	4	2	no	—
48	C₃×C₄	—	4	1	no	—
49	C₃×C₄	C₄⋊C₄	1	2	yes	—
50	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
51	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
52	C₂³	C₃×D₄	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	4	2	no	—
57	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
58	C₂×C₄	C₃×D₄	1	1	yes	characteristic
59	C₂×C₄	C₃×Q₈	1	2	yes	—
60	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₈	C₂×C₃×C₄	1	4	yes	complemented
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×C₃	#137	1	1	yes	characteristic
66	C₂²	—	2	1	no	—
67	C₂²	—	2	1	no	—
68	C₂²	C₃×C₄⋊C₄	1	2	yes	—
69	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	C₃×C₄⋊C₄	1	2	yes	—
74	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
75	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
76	C₃	#428	1	1	yes	characteristic, direct product factor, Sylow
77	C₂	—	2	2	no	—
78	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
79	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
80	C₂	C₃×#137	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃×#107	C₂	semidirect
5. C₃×#106	C₂	semidirect
6. #428	C₃	direct (N × H)
9. C₃×M₁₆	C₄	semidirect
20. #107	C₂×C₃	semidirect
21. #106	C₂×C₃	semidirect
31. C₃×C₈	C₂×C₄	semidirect
34. M₁₆	C₃×C₄	semidirect
61. C₈	C₂×C₃×C₄	semidirect
76. C₃	#428	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×C₄⋊C₄	2
C₃×#107	2
C₃×#106	2
#428	3

Subgroups — C3×#428 #5302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#428 #5302