Subgroups — Q₈×C₃⋊C₁₆ #70948

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	C₄⋊(C₃⋊C₁₆)	C₂	1	3	yes	maximal
3	C₄×C₃⋊C₁₆	C₂	1	3	yes	maximal
4	Q₈×C₁₆	—	3	1	no	maximal, Sylow
5	C₃×C₄×Q₈	C₄	1	1	yes	characteristic
6	C₃×C₄⋊C₈	C₄	1	3	yes	—
7	C₃×C₄×C₈	C₂²	1	3	yes	—
8	C₂×C₃⋊C₁₆	C₂²	1	3	yes	—
9	C₂×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₈×Q₈	D₃	1	1	yes	characteristic
11	C₄⋊C₁₆	—	3	3	no	—
12	C₄×C₁₆	—	3	3	no	—
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	Dic₃	1	1	yes	characteristic
21	C₂×C₁₆	—	3	1	no	—
22	C₂×C₁₆	—	3	3	no	—
23	C₄⋊C₈	Dic₃	1	3	yes	—
24	C₄×C₈	C₂×D₃	1	3	yes	—
25	C₃×Q₈	C₁₆	1	4	yes	complemented
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×Dic₃	1	3	yes	—
34	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
35	C₄⋊C₄	C₃⋊C₈	1	3	yes	—
36	C₄²	C₂×Dic₃	1	3	yes	—
37	C₁₆	—	3	2	no	—
38	C₁₆	—	6	3	no	—
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×Dic₃	1	1	yes	characteristic
48	C₈	—	2	3	no	—
49	C₈	D₃×Q₈	1	1	yes	characteristic
50	C₈	#239	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	Q₈×Dic₃	1	1	yes	characteristic
58	C₄	#948	1	1	yes	characteristic
59	C₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
60	C₂	Q₈×C₃⋊C₈	1	1	yes	characteristic
61	C₂	C₂²×C₃⋊C₁₆	1	1	yes	characteristic
62	C₂	#5140	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₃
commutator	C₂×C₃	C₂²×C₁₆
Fitting	C₃×C₈×Q₈	C₂
socle, prime radical	C₂²×C₃	C₂²×C₈
cosocle	C₂×C₃×C₈	C₂³
hypercenter	C₈×Q₈	D₃
hypocenter	C₃	Q₈×C₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
19. C₃⋊C₁₆	Q₈	direct (N × H)
25. C₃×Q₈	C₁₆	semidirect
44. Q₈	C₃⋊C₁₆	direct (N × H)
59. C₃	Q₈×C₁₆	semidirect

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
C₄⋊(C₃⋊C₁₆)	2
C₄×C₃⋊C₁₆	2
Q₈×C₁₆	3

Subgroups — Q8×C3⋊C16 #70948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊C₁₆ #70948