Subgroups — C₃×#473 #5347

Order 192.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#137	C₂	1	2	yes	maximal
2	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#131	C₂	1	1	yes	maximal, characteristic
4	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#101	C₂	1	2	yes	maximal, complemented
6	#473	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	C₂²	1	1	yes	characteristic
8	C₂×C₃×Q₈	C₂²	1	2	yes	—
9	C₃×Q₁₆	—	2	2	no	—
10	C₃×Q₁₆	—	2	1	no	—
11	C₃×Q₁₆	—	2	1	no	—
12	C₃×SD₁₆	—	2	2	no	—
13	C₃×M₁₆	—	2	1	no	—
14	C₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₃×M₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₈	—	2	1	no	—
17	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
18	#137	C₂×C₃	1	2	yes	—
19	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
20	#131	C₂×C₃	1	1	yes	characteristic
21	#108	C₂×C₃	1	1	yes	characteristic, complemented
22	#101	C₂×C₃	1	2	yes	complemented
23	C₃×Q₈	—	2	2	no	—
24	C₃×Q₈	—	2	2	no	—
25	C₃×Q₈	D₄	1	1	yes	characteristic
26	C₃×D₄	—	2	1	no	—
27	C₃×D₄	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	—	2	1	no	—
32	C₃×C₈	—	2	2	no	—
33	C₃×C₈	D₄	1	1	yes	characteristic
34	C₃×C₈	D₄	1	1	yes	characteristic
35	#41	C₂²×C₃	1	1	yes	characteristic
36	C₂×Q₈	C₂²×C₃	1	2	yes	—
37	Q₁₆	—	2	2	no	—
38	Q₁₆	—	2	1	no	—
39	Q₁₆	—	2	1	no	—
40	SD₁₆	—	2	2	no	—
41	M₁₆	—	2	1	no	—
42	M₁₆	C₂²×C₃	1	1	yes	characteristic
43	M₁₆	C₂²×C₃	1	2	yes	—
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₃	—	2	1	no	—
47	C₂²×C₃	#41	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	4	2	no	—
50	C₃×C₄	C₂×D₄	1	1	yes	characteristic
51	C₃×C₄	C₂×D₄	1	1	yes	characteristic
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	C₃×D₄	1	1	yes	characteristic
55	D₄	—	2	1	no	—
56	D₄	C₃×D₄	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	—	2	2	no	—
62	C₈	C₃×D₄	1	1	yes	characteristic
63	C₈	C₃×D₄	1	1	yes	characteristic
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	—	4	1	no	—
66	C₂×C₃	#121	1	1	yes	characteristic
67	C₂²	—	2	1	no	—
68	C₂²	C₃×#41	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	4	2	no	—
71	C₄	C₂×C₃×D₄	1	1	yes	characteristic
72	C₄	C₂×C₃×D₄	1	1	yes	characteristic
73	C₃	#473	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	C₃×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#121
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₁₆	C₂	semidirect
4. C₃×#108	C₂	semidirect
5. C₃×#101	C₂	semidirect
6. #473	C₃	direct (N × H)
19. C₂×Q₁₆	C₂×C₃	semidirect
21. #108	C₂×C₃	semidirect
22. #101	C₂×C₃	semidirect
73. C₃	#473	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×#137	2
C₂×C₃×Q₁₆	2
C₃×#131	2
C₃×#108	2
C₃×#101	2
#473	3

Subgroups — C3×#473 #5347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#473 #5347