Subgroups — C₃×#441 #5315

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈	C₂	1	2	yes	maximal
3	C₃×#106	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₂	1	2	yes	maximal
5	C₃×#97	C₂	1	1	yes	maximal, characteristic
6	#441	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₃×Q₁₆	C₄	1	4	yes	complemented
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₄	—	2	2	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄²	—	2	2	no	—
14	C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic
16	C₄×Q₈	C₂×C₃	1	2	yes	—
17	#106	C₂×C₃	1	1	yes	characteristic
18	#103	C₂×C₃	1	2	yes	—
19	#97	C₂×C₃	1	1	yes	characteristic
20	C₃×Q₈	—	2	2	no	—
21	C₃×Q₈	C₂×C₄	1	4	yes	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	D₄	1	2	yes	—
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₃×C₈	—	2	1	no	—
27	C₃×C₈	C₂×C₄	1	2	yes	—
28	C₂×Q₈	C₂²×C₃	1	2	yes	—
29	Q₁₆	C₃×C₄	1	4	yes	complemented
30	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	C₂²×C₃	1	2	yes	—
34	C₄²	—	2	2	no	—
35	C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
37	C₃×C₄	—	2	4	no	—
38	C₃×C₄	—	2	2	no	—
39	C₃×C₄	—	4	2	no	—
40	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₃×C₄	#41	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	Q₈	C₂×C₃×C₄	1	4	yes	—
44	C₂×C₄	—	2	2	no	—
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	C₃×D₄	1	2	yes	—
47	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
48	C₈	—	2	1	no	—
49	C₈	C₂×C₃×C₄	1	2	yes	—
50	C₂×C₃	C₄×D₄	1	1	yes	characteristic
51	C₂×C₃	#137	1	2	yes	—
52	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
53	C₄	—	2	4	no	—
54	C₄	—	2	2	no	—
55	C₄	—	4	2	no	—
56	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
57	C₄	C₃×#41	1	1	yes	characteristic
58	C₃	#441	1	1	yes	characteristic, direct product factor, Sylow
59	C₂	C₃×C₄×D₄	1	1	yes	characteristic
60	C₂	C₃×#137	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ 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
6. #441	C₃	direct (N × H)
8. C₃×Q₁₆	C₄	semidirect
29. Q₁₆	C₃×C₄	semidirect
58. C₃	#441	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×Q₁₆	2
C₃×C₄×Q₈	2
C₃×#106	2
C₃×#103	2
C₃×#97	2
#441	3

Subgroups — C3×#441 #5315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#441 #5315