Subgroups — C₃×#487 #5361

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	4	yes	maximal
4	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
5	#487	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	1	no	—
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄⋊C₄	—	2	1	no	—
10	C₃×C₄⋊C₄	—	2	1	no	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
15	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
16	#103	C₂×C₃	1	4	yes	—
17	C₄×C₈	C₂×C₃	1	1	yes	characteristic
18	C₃×Q₈	—	2	4	no	—
19	C₃×Q₈	—	4	2	no	—
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	D₄	1	1	yes	characteristic
24	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
25	C₃×C₈	—	2	2	no	—
26	C₂×Q₈	—	2	1	no	—
27	C₂×Q₈	C₂²×C₃	1	2	yes	—
28	C₂×C₈	C₂²×C₃	1	2	yes	—
29	C₄⋊C₄	—	2	1	no	—
30	C₄⋊C₄	—	2	1	no	—
31	C₄⋊C₄	—	2	1	no	—
32	C₄⋊C₄	C₂²×C₃	1	2	yes	—
33	C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄	—	4	2	no	—
36	C₃×C₄	—	4	2	no	—
37	C₃×C₄	SD₁₆	1	2	yes	—
38	C₃×C₄	Q₁₆	1	2	yes	—
39	C₃×C₄	#41	1	2	yes	—
40	Q₈	—	2	4	no	—
41	Q₈	—	4	2	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	C₃×D₄	1	1	yes	characteristic
45	C₂×C₄	C₃×D₄	1	1	yes	characteristic
46	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₂×C₃	#124	1	1	yes	characteristic
49	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
51	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	4	2	no	—
54	C₄	C₃×SD₁₆	1	2	yes	—
55	C₄	C₃×Q₁₆	1	2	yes	—
56	C₄	C₃×#41	1	2	yes	—
57	C₃	#487	1	1	yes	characteristic, direct product factor, Sylow
58	C₂	C₃×#124	1	1	yes	characteristic
59	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic
60	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×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
5. #487	C₃	direct (N × H)
57. C₃	#487	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×C₄⋊Q₈	2
C₃×#103	2
C₃×C₄×C₈	2
#487	3

Subgroups — C3×#487 #5361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#487 #5361