Subgroups — C₃×#446 #5320

Order 192.

94 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⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₈	C₂	1	2	yes	maximal
4	C₃×#97	C₂	1	2	yes	maximal
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
6	#446	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₈	C₂²	1	2	yes	—
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₄	C₄	1	2	yes	—
12	C₃×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₃×C₄²	C₂²	1	1	yes	characteristic
14	C₃×C₄²	C₂²	1	2	yes	—
15	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
16	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
17	C₄⋊C₈	C₂×C₃	1	2	yes	—
18	#97	C₂×C₃	1	2	yes	—
19	C₄×C₈	C₂×C₃	1	1	yes	characteristic
20	C₃×Q₈	—	2	2	no	—
21	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
26	C₃×C₈	—	2	1	no	—
27	C₃×C₈	—	2	2	no	—
28	C₃×C₈	Q₈	1	2	yes	complemented
29	C₂×Q₈	C₃×C₄	1	1	yes	characteristic
30	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₈	C₂²×C₃	1	2	yes	—
32	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₄⋊C₄	C₃×C₄	1	2	yes	—
34	C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
35	C₄²	C₂²×C₃	1	1	yes	characteristic
36	C₄²	C₂²×C₃	1	2	yes	—
37	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
38	C₃×C₄	—	2	2	no	—
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	M₁₆	1	2	yes	—
42	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
43	C₃×C₄	#41	1	1	yes	characteristic
44	Q₈	—	2	2	no	—
45	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
46	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
47	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
48	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
49	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	—	2	2	no	—
52	C₈	C₃×Q₈	1	2	yes	complemented
53	C₂×C₃	C₄×Q₈	1	1	yes	characteristic
54	C₂×C₃	C₂×M₁₆	1	1	yes	characteristic
55	C₂×C₃	#131	1	1	yes	characteristic
56	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	2	no	—
60	C₄	C₃×M₁₆	1	2	yes	—
61	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
62	C₄	C₃×#41	1	1	yes	characteristic
63	C₃	#446	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×C₄×Q₈	1	1	yes	characteristic
65	C₂	C₂×C₃×M₁₆	1	1	yes	characteristic
66	C₂	C₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³
commutator	C₂²	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂²×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
6. #446	C₃	direct (N × H)
28. C₃×C₈	Q₈	semidirect
52. C₈	C₃×Q₈	semidirect
63. C₃	#446	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×C₄⋊C₈	2
C₃×#97	2
C₃×C₄×C₈	2
#446	3

Subgroups — C3×#446 #5320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#446 #5320