Subgroups — C₁₆×PSU(3,𝔽₂) #11798008

Order 1152.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×PSU(3,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#157	C₂	1	3	yes	maximal
3	#10590082	C₂	1	3	yes	maximal
4	C₄×PSU(3,𝔽₂)	C₄	1	1	yes	characteristic
5	C₈×#157	C₂²	1	3	yes	—
6	#63764	C₂²	1	3	yes	—
7	#63744	C₄	1	3	yes	—
8	C₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic
9	C₂×PSU(3,𝔽₂)	C₈	1	1	yes	characteristic
10	C₄×#157	C₂×C₄	1	3	yes	—
11	#3787	C₂×C₄	1	3	yes	—
12	#3777	C₈	1	3	yes	—
13	C₈×C₃⋊D₃	C₂³	1	1	yes	characteristic
14	#3708	—	2	3	no	—
15	C₃²×C₁₆	Q₈	1	1	yes	characteristic, complemented
16	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic, complemented
17	Q₈×C₁₆	—	9	1	no	maximal, Sylow
18	D₃×C₁₆	—	12	1	no	—
19	C₂×#157	C₂×C₈	1	3	yes	—
20	C₂×#157	C₂×C₈	1	3	yes	—
21	PSU(3,𝔽₂)	C₁₆	1	4	yes	direct product factor
22	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
23	#622	—	2	3	no	—
24	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
25	C₃⋊(C₃⋊C₈)	#41	1	1	yes	characteristic
26	C₈×Q₈	—	9	1	no	—
27	C₄⋊C₁₆	—	9	3	no	—
28	C₄×C₁₆	—	9	3	no	—
29	D₃×C₈	—	12	1	no	—
30	C₃×C₁₆	—	4	1	no	—
31	C₃⋊C₁₆	—	12	1	no	—
32	C₂×C₃⋊D₃	C₂²×C₈	1	1	yes	characteristic
33	#157	—	2	3	no	—
34	#157	C₂×C₁₆	1	6	yes	—
35	C₃²×C₄	C₄×Q₈	1	1	yes	characteristic
36	C₃⋊Dic₃	#131	1	1	yes	characteristic
37	C₄×Q₈	—	9	1	no	—
38	C₂×C₁₆	—	9	1	no	—
39	C₂×C₁₆	—	9	3	no	—
40	C₄⋊C₈	—	9	3	no	—
41	C₄×C₈	—	9	3	no	—
42	C₄×D₃	—	12	1	no	—
43	C₃×C₈	—	4	1	no	—
44	C₃⋊C₈	—	12	1	no	—
45	C₂×C₃²	C₈×Q₈	1	1	yes	characteristic
46	C₃⋊D₃	C₂²×C₁₆	1	1	yes	characteristic
47	C₃⋊D₃	#504	1	1	yes	characteristic
48	C₂×Q₈	—	9	1	no	—
49	C₂×C₈	—	9	1	no	—
50	C₂×C₈	—	9	3	no	—
51	C₄⋊C₄	—	9	3	no	—
52	C₄²	—	9	3	no	—
53	C₁₆	—	9	1	no	—
54	C₁₆	—	18	3	no	—
55	C₁₆	PSU(3,𝔽₂)	1	1	yes	characteristic, direct product factor
56	C₂×D₃	—	12	1	no	—
57	C₃×C₄	—	4	1	no	—
58	Dic₃	—	12	1	no	—
59	C₃²	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
60	Q₈	—	9	4	no	—
61	C₂×C₄	—	9	3	no	—
62	C₂×C₄	—	9	1	no	—
63	C₂×C₄	—	9	3	no	—
64	C₈	—	9	1	no	—
65	C₈	—	18	3	no	—
66	C₈	C₂×PSU(3,𝔽₂)	1	1	yes	characteristic
67	C₂×C₃	—	4	1	no	—
68	D₃	—	12	1	no	—
69	D₃	—	12	1	no	—
70	C₂²	—	9	1	no	—
71	C₄	—	9	6	no	—
72	C₄	—	9	1	no	—
73	C₄	—	18	3	no	—
74	C₄	C₄×PSU(3,𝔽₂)	1	1	yes	characteristic
75	C₃	—	4	1	no	—
76	C₂	—	9	1	no	—
77	C₂	—	9	1	no	—
78	C₂	C₈×PSU(3,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	PSU(3,𝔽₂)
commutator	C₃⋊D₃	C₂²×C₁₆
Frattini	C₈	C₂×PSU(3,𝔽₂)
Fitting	C₃²×C₁₆	Q₈
socle	C₂×C₃²	C₈×Q₈
prime radical	C₂×C₃⋊D₃	C₂²×C₈
cosocle	C₈×C₃⋊D₃	C₂³
hypocenter	C₃²	Q₈×C₁₆
LCS	G ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
15. C₃²×C₁₆	Q₈	semidirect
16. C₃⋊(C₃⋊C₁₆)	Q₈	semidirect
21. PSU(3,𝔽₂)	C₁₆	direct (N × H)
55. C₁₆	PSU(3,𝔽₂)	direct (N × H)
59. C₃²	Q₈×C₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈×PSU(3,𝔽₂)	2
C₁₆×#157	2
#10590082	2
Q₈×C₁₆	9

Subgroups — C16×PSU(3,𝔽2) #11798008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×PSU(3,𝔽₂) #11798008