Subgroups — C₃×Q₈×C₁₆ #72897

Order 384.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₁₆	C₂	1	3	yes	maximal
3	C₃×C₄×C₁₆	C₂	1	3	yes	maximal
4	Q₈×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄×Q₈	C₄	1	1	yes	characteristic
6	C₂×C₃×C₁₆	C₂²	1	3	yes	—
7	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊C₈	C₄	1	3	yes	—
9	C₃×C₄×C₈	C₂²	1	3	yes	—
10	C₈×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₄⋊C₁₆	C₂×C₃	1	3	yes	—
12	C₄×C₁₆	C₂×C₃	1	3	yes	—
13	C₂×C₃×Q₈	C₈	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂×C₄	1	3	yes	—
15	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
16	C₃×C₄⋊C₄	C₈	1	3	yes	—
17	C₃×C₄²	C₂×C₄	1	3	yes	—
18	C₃×C₁₆	—	2	3	no	—
19	C₃×C₁₆	Q₈	1	2	yes	direct product factor
20	C₄×Q₈	C₃×C₄	1	1	yes	characteristic
21	C₂×C₁₆	C₂²×C₃	1	3	yes	—
22	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
23	C₄⋊C₈	C₃×C₄	1	3	yes	—
24	C₄×C₈	C₂²×C₃	1	3	yes	—
25	C₃×Q₈	C₁₆	1	4	yes	direct product factor
26	C₂×C₃×C₄	C₂×C₈	1	3	yes	—
27	C₂×C₃×C₄	C₂×C₈	1	3	yes	—
28	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
29	C₃×C₈	—	2	3	no	—
30	C₃×C₈	C₂×Q₈	1	1	yes	characteristic
31	C₃×C₈	#41	1	1	yes	characteristic
32	C₂×Q₈	C₃×C₈	1	1	yes	characteristic
33	C₂×C₈	C₂×C₃×C₄	1	3	yes	—
34	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
35	C₄⋊C₄	C₃×C₈	1	3	yes	—
36	C₄²	C₂×C₃×C₄	1	3	yes	—
37	C₁₆	—	2	3	no	—
38	C₁₆	C₃×Q₈	1	2	yes	direct product factor
39	C₂²×C₃	C₂²×C₈	1	1	yes	characteristic
40	C₃×C₄	—	2	3	no	—
41	C₃×C₄	C₂×C₁₆	1	6	yes	—
42	C₃×C₄	C₄×Q₈	1	1	yes	characteristic
43	C₃×C₄	#131	1	1	yes	characteristic
44	Q₈	C₃×C₁₆	1	4	yes	direct product factor
45	C₂×C₄	C₂×C₃×C₈	1	3	yes	—
46	C₂×C₄	C₂×C₃×C₈	1	3	yes	—
47	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
48	C₈	—	2	3	no	—
49	C₈	C₂×C₃×Q₈	1	1	yes	characteristic
50	C₈	C₃×#41	1	1	yes	characteristic
51	C₂×C₃	C₈×Q₈	1	1	yes	characteristic
52	C₂×C₃	C₂²×C₁₆	1	1	yes	characteristic
53	C₂×C₃	#504	1	1	yes	characteristic
54	C₂²	C₂²×C₃×C₈	1	1	yes	characteristic
55	C₄	—	2	3	no	—
56	C₄	C₂×C₃×C₁₆	1	6	yes	—
57	C₄	C₃×C₄×Q₈	1	1	yes	characteristic
58	C₄	C₃×#131	1	1	yes	characteristic
59	C₃	Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	C₃×C₈×Q₈	1	1	yes	characteristic
61	C₂	C₂²×C₃×C₁₆	1	1	yes	characteristic
62	C₂	C₃×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₁₆	C₂²
commutator	C₂	C₂²×C₃×C₁₆
Frattini, cosocle	C₂×C₈	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. Q₈×C₁₆	C₃	direct (N × H)
19. C₃×C₁₆	Q₈	direct (N × H)
25. C₃×Q₈	C₁₆	direct (N × H)
38. C₁₆	C₃×Q₈	direct (N × H)
44. Q₈	C₃×C₁₆	direct (N × H)
59. C₃	Q₈×C₁₆	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×C₈×Q₈	2
C₃×C₄⋊C₁₆	2
C₃×C₄×C₁₆	2
Q₈×C₁₆	3

Subgroups — C3×Q8×C16 #72897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×C₁₆ #72897