Subgroups — C₃×#462 #5336

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	2	yes	maximal
2	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×#103	C₂	1	2	yes	maximal
6	#462	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
9	C₃×Q₁₆	—	2	4	no	—
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	—	2	1	no	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₄²	—	2	1	no	—
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆	C₂×C₃	1	2	yes	—
18	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
19	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
20	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
21	#103	C₂×C₃	1	2	yes	—
22	C₃×Q₈	—	2	1	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₃×Q₈	—	2	2	no	—
25	C₃×Q₈	D₄	1	2	yes	—
26	C₂×C₃×C₄	—	2	1	no	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	2	no	—
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₃×C₈	—	2	2	no	—
33	C₂×Q₈	C₂²×C₃	1	2	yes	—
34	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
35	Q₁₆	—	2	4	no	—
36	C₂×C₈	C₂²×C₃	1	2	yes	—
37	C₄⋊C₄	—	2	1	no	—
38	C₄⋊C₄	—	2	1	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
41	C₄²	—	2	1	no	—
42	C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₃×C₄	—	2	2	no	—
45	C₃×C₄	—	2	1	no	—
46	C₃×C₄	—	4	2	no	—
47	C₃×C₄	—	4	1	no	—
48	C₃×C₄	Q₁₆	1	2	yes	complemented
49	C₃×C₄	C₂×D₄	1	1	yes	characteristic
50	C₃×C₄	#41	1	1	yes	characteristic
51	Q₈	—	2	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	2	2	no	—
54	Q₈	C₃×D₄	1	2	yes	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	C₃×D₄	1	1	yes	characteristic
59	C₂×C₄	C₃×D₄	1	1	yes	characteristic
60	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₂×C₃	#121	1	1	yes	characteristic
63	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
64	C₂×C₃	#137	1	1	yes	characteristic
65	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	2	1	no	—
68	C₄	—	4	2	no	—
69	C₄	—	4	1	no	—
70	C₄	C₃×Q₁₆	1	2	yes	complemented
71	C₄	C₂×C₃×D₄	1	1	yes	characteristic
72	C₄	C₃×#41	1	1	yes	characteristic
73	C₃	#462	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	C₃×#121	1	1	yes	characteristic
75	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic
76	C₂	C₃×#137	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
6. #462	C₃	direct (N × H)
48. C₃×C₄	Q₁₆	semidirect
70. C₄	C₃×Q₁₆	semidirect
73. C₃	#462	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×C₄×Q₈	2
C₃×C₄⋊C₈	2
C₃×#103	2
#462	3

Subgroups — C3×#462 #5336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#462 #5336