Subgroups — C₃×#423 #5297

Order 192.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
4	#423	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	C₄	1	2	yes	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃×M₁₆	—	2	4	no	—
8	C₂×C₃×C₈	C₂²	1	4	yes	—
9	C₃×C₄²	C₄	1	1	yes	characteristic
10	C₃×C₄²	C₄	1	1	yes	characteristic
11	C₃×C₄²	C₂²	1	2	yes	—
12	C₂×M₁₆	C₂×C₃	1	2	yes	—
13	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
14	C₄⋊C₈	C₂×C₃	1	4	yes	complemented
15	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄	—	2	4	no	—
17	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
18	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
20	C₂×C₃×C₄	D₄	1	2	yes	—
21	C₂×C₃×C₄	Q₈	1	2	yes	—
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	C₃×C₈	—	2	4	no	—
24	C₂²×C₄	C₃×C₄	1	2	yes	—
25	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
26	M₁₆	—	2	4	no	—
27	C₂×C₈	C₂²×C₃	1	4	yes	—
28	C₄²	C₃×C₄	1	1	yes	characteristic
29	C₄²	C₃×C₄	1	1	yes	characteristic
30	C₄²	C₂²×C₃	1	2	yes	—
31	C₂²×C₃	—	2	2	no	—
32	C₂²×C₃	C₄⋊C₄	1	2	yes	—
33	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
34	C₃×C₄	—	2	2	no	—
35	C₃×C₄	C₄⋊C₄	1	2	yes	—
36	C₃×C₄	M₁₆	1	4	yes	complemented
37	C₃×C₄	C₂×D₄	1	1	yes	characteristic
38	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
39	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
42	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
43	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
44	C₂×C₄	C₃×D₄	1	2	yes	—
45	C₂×C₄	C₃×Q₈	1	2	yes	—
46	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
47	C₈	—	2	4	no	—
48	C₂×C₃	—	2	2	no	—
49	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₃	C₂×M₁₆	1	2	yes	—
51	C₂²	—	2	2	no	—
52	C₂²	C₃×C₄⋊C₄	1	2	yes	—
53	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₃×C₄⋊C₄	1	2	yes	—
56	C₄	C₃×M₁₆	1	4	yes	complemented
57	C₄	C₂×C₃×D₄	1	1	yes	characteristic
58	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
59	C₃	#423	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	—	2	2	no	—
61	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
62	C₂	C₂×C₃×M₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊C₈	C₂	semidirect
4. #423	C₃	direct (N × H)
14. C₄⋊C₈	C₂×C₃	semidirect
36. C₃×C₄	M₁₆	semidirect
56. C₄	C₃×M₁₆	semidirect
59. C₃	#423	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
C₂×C₃×C₄²	2
C₃×C₄⋊C₈	2
#423	3

Subgroups — C3×#423 #5297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#423 #5297