Subgroups — SD₁₆×C₃⋊D₃ #64122

Order 288.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#3755	C₂	1	1	yes	maximal, characteristic, complemented
5	#3754	C₂	1	1	yes	maximal, characteristic, complemented
6	#3744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×SD₁₆	—	3	4	no	maximal
9	C₂²×C₃⋊D₃	—	2	1	no	—
10	C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₃²×D₄	C₂²	1	1	yes	characteristic
12	#638	—	2	1	no	—
13	C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₄×C₃⋊D₃	—	2	1	no	—
15	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	#634	—	2	1	no	—
17	#634	C₂²	1	1	yes	characteristic, complemented
18	C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
19	C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
20	D₃×Q₈	—	3	4	no	—
21	D₃×D₄	—	3	4	no	—
22	C₃×SD₁₆	D₃	1	4	yes	complemented
23	#215	—	3	4	no	—
24	#214	—	3	4	no	—
25	#204	—	3	4	no	—
26	D₃×C₈	—	3	4	no	—
27	C₂²×C₃²	—	2	1	no	—
28	C₂×C₃⋊D₃	—	2	1	no	—
29	C₂×C₃⋊D₃	—	4	2	no	—
30	C₂×C₃⋊D₃	D₄	1	1	yes	characteristic
31	C₃²×C₄	—	2	1	no	—
32	C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₃⋊Dic₃	—	2	1	no	—
34	C₃⋊Dic₃	D₄	1	1	yes	characteristic
35	C₂×SD₁₆	—	9	1	no	Sylow
36	C₂²×D₃	—	6	4	no	—
37	C₃×Q₈	C₂×D₃	1	4	yes	complemented
38	C₃×D₄	C₂×D₃	1	4	yes	—
39	#67	—	6	4	no	—
40	D₁₂	—	3	4	no	—
41	C₄×D₃	—	3	4	no	—
42	C₄×D₃	—	6	4	no	—
43	Dic₆	—	3	4	no	—
44	Dic₆	—	6	4	no	—
45	C₃×C₈	C₂×D₃	1	4	yes	complemented
46	C₃⋊C₈	—	3	4	no	—
47	C₂×C₃²	—	4	1	no	—
48	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
49	C₃⋊D₃	—	4	1	no	—
50	C₃⋊D₃	SD₁₆	1	2	yes	direct product factor
51	C₂×Q₈	—	9	1	no	—
52	C₂×D₄	—	9	1	no	—
53	SD₁₆	—	9	1	no	—
54	SD₁₆	—	9	1	no	—
55	SD₁₆	—	9	1	no	—
56	SD₁₆	C₃⋊D₃	1	1	yes	characteristic, direct product factor
57	C₂×C₈	—	9	1	no	—
58	C₂²×C₃	—	2	4	no	—
59	C₂×D₃	—	3	4	no	—
60	C₂×D₃	—	6	4	no	—
61	C₂×D₃	—	12	8	no	—
62	C₃×C₄	—	2	4	no	—
63	C₃×C₄	C₂²×D₃	1	4	yes	—
64	Dic₃	—	3	4	no	—
65	Dic₃	—	6	4	no	—
66	C₃²	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	18	1	no	—
68	Q₈	—	9	1	no	—
69	Q₈	—	18	1	no	—
70	Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
71	D₄	—	9	1	no	—
72	D₄	—	18	1	no	—
73	D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	—	18	1	no	—
76	C₈	—	9	1	no	—
77	C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
78	C₂×C₃	—	4	4	no	—
79	C₂×C₃	D₃×D₄	1	4	yes	—
80	D₃	—	3	8	no	—
81	D₃	—	12	4	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	9	1	no	—
84	C₂²	—	18	1	no	—
85	C₂²	—	36	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	9	1	no	—
88	C₄	—	18	1	no	—
89	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
90	C₃	D₃×SD₁₆	1	4	yes	complemented
91	C₂	—	4	1	no	—
92	C₂	—	9	2	no	—
93	C₂	—	36	1	no	—
94	C₂	D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂²×C₃⋊D₃
Fitting	C₃²×SD₁₆	C₂
socle	C₂×C₃²	C₂×D₄
prime radical	D₄×C₃⋊D₃	C₂
hypercenter	SD₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×SD₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×C₃⋊D₃	C₂	semidirect
3. C₃²×SD₁₆	C₂	semidirect
4. #3755	C₂	semidirect
5. #3754	C₂	semidirect
6. #3744	C₂	semidirect
7. C₈×C₃⋊D₃	C₂	semidirect
10. C₃²×Q₈	C₂²	semidirect
17. #634	C₂²	semidirect
18. C₃²×C₈	C₂²	semidirect
19. C₃⋊(C₃⋊C₈)	C₂²	semidirect
22. C₃×SD₁₆	D₃	semidirect
37. C₃×Q₈	C₂×D₃	semidirect
45. C₃×C₈	C₂×D₃	semidirect
50. C₃⋊D₃	SD₁₆	direct (N × H)
56. SD₁₆	C₃⋊D₃	direct (N × H)
66. C₃²	C₂×SD₁₆	semidirect
70. Q₈	C₂×C₃⋊D₃	semidirect
77. C₈	C₂×C₃⋊D₃	semidirect
90. C₃	D₃×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₃⋊D₃	2
D₄×C₃⋊D₃	2
C₃²×SD₁₆	2
#3755	2
#3754	2
#3744	2
C₈×C₃⋊D₃	2
D₃×SD₁₆	3

Subgroups — SD16×C3⋊D3 #64122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₃⋊D₃ #64122