Subgroups — C₂×D₃×Q₁₆ #5763

Order 192.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈	C₂	1	2	yes	maximal
2	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#216	C₂	1	2	yes	maximal, complemented
4	D₃×Q₁₆	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₁₆	—	3	1	no	maximal, Sylow
8	C₂×C₃×Q₈	C₂²	1	2	yes	—
9	D₃×Q₈	—	2	4	no	—
10	D₃×Q₈	C₂²	1	8	yes	—
11	C₂×C₄×D₃	—	2	2	no	—
12	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₆	—	2	2	no	—
14	C₂×Dic₆	C₂²	1	2	yes	—
15	C₃×Q₁₆	C₂²	1	4	yes	complemented
16	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
17	#216	C₂²	1	8	yes	complemented
18	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	Dic₁₂	C₂²	1	4	yes	complemented
20	D₃×C₈	C₂²	1	4	yes	—
21	C₂²×Q₈	—	3	2	no	—
22	C₂×Q₁₆	—	3	2	no	—
23	C₂×Q₁₆	—	3	8	no	—
24	C₂×Q₁₆	—	3	1	no	—
25	C₂×Q₁₆	D₃	1	1	yes	characteristic, direct product factor
26	C₂²×C₈	—	3	1	no	—
27	C₂²×D₃	D₄	1	1	yes	characteristic
28	C₃×Q₈	—	2	2	no	—
29	C₃×Q₈	C₂³	1	4	yes	—
30	C₂×C₃×C₄	—	2	2	no	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₂×Dic₃	—	2	2	no	—
33	C₂×Dic₃	D₄	1	1	yes	characteristic
34	C₄×D₃	—	2	8	no	—
35	C₄×D₃	D₄	1	2	yes	—
36	C₄×D₃	C₂³	1	2	yes	—
37	Dic₆	—	2	2	no	—
38	Dic₆	—	2	8	no	—
39	Dic₆	C₂³	1	4	yes	—
40	C₃×C₈	C₂³	1	2	yes	—
41	C₃⋊C₈	C₂³	1	2	yes	—
42	C₂×Q₈	—	3	8	no	—
43	C₂×Q₈	—	3	2	no	—
44	C₂×Q₈	—	6	2	no	—
45	C₂×Q₈	—	6	4	no	—
46	C₂×Q₈	C₂×D₃	1	2	yes	—
47	C₂²×C₄	—	3	1	no	—
48	C₂²×C₄	—	6	2	no	—
49	Q₁₆	—	3	8	no	—
50	Q₁₆	—	3	4	no	—
51	Q₁₆	C₂×D₃	1	4	yes	direct product factor
52	C₂×C₈	—	3	1	no	—
53	C₂×C₈	—	3	4	no	—
54	C₂×C₈	C₂×D₃	1	1	yes	characteristic
55	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
56	C₂×D₃	Q₁₆	1	4	yes	direct product factor
57	C₂×D₃	C₂×D₄	1	2	yes	—
58	C₃×C₄	—	2	4	no	—
59	C₃×C₄	C₂×D₄	1	1	yes	characteristic
60	C₃×C₄	C₂⁴	1	1	yes	characteristic
61	Dic₃	—	2	4	no	—
62	Dic₃	C₂×D₄	1	2	yes	—
63	C₂³	—	3	1	no	—
64	Q₈	—	2	2	no	—
65	Q₈	—	3	4	no	—
66	Q₈	—	6	8	no	—
67	Q₈	—	6	2	no	—
68	Q₈	C₂²×D₃	1	4	yes	—
69	C₂×C₄	—	2	2	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	3	2	no	—
72	C₂×C₄	—	3	2	no	—
73	C₂×C₄	—	6	8	no	—
74	C₂×C₄	—	6	2	no	—
75	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₈	—	3	2	no	—
77	C₈	C₂²×D₃	1	2	yes	—
78	C₂×C₃	C₂×Q₁₆	1	2	yes	complemented
79	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
80	D₃	C₂×Q₁₆	1	4	yes	direct product factor
81	C₂²	—	3	4	no	—
82	C₂²	—	3	2	no	—
83	C₂²	D₃×D₄	1	1	yes	characteristic
84	C₄	—	2	4	no	—
85	C₄	—	3	2	no	—
86	C₄	—	6	4	no	—
87	C₄	D₃×D₄	1	1	yes	characteristic
88	C₄	C₂³×D₃	1	1	yes	characteristic
89	C₃	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
90	C₂	—	3	4	no	—
91	C₂	D₃×Q₁₆	1	2	yes	direct product factor
92	C₂	C₂×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴
Frattini	C₄	C₂³×D₃
Fitting	C₂×C₃×Q₁₆	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂²×D₃	D₄
hypercenter	C₂×Q₁₆	D₃
hypocenter	C₃	C₂²×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₁₆	C₂	semidirect
3. C₂×#216	C₂	semidirect
4. D₃×Q₁₆	C₂	direct (N × H)
5. C₂×Dic₁₂	C₂	semidirect
15. C₃×Q₁₆	C₂²	semidirect
17. #216	C₂²	semidirect
19. Dic₁₂	C₂²	semidirect
25. C₂×Q₁₆	D₃	direct (N × H)
51. Q₁₆	C₂×D₃	direct (N × H)
56. C₂×D₃	Q₁₆	direct (N × H)
78. C₂×C₃	C₂×Q₁₆	semidirect
80. D₃	C₂×Q₁₆	direct (N × H)
89. C₃	C₂²×Q₁₆	semidirect
91. C₂	D₃×Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈	2
C₂×C₃×Q₁₆	2
C₂×#216	2
D₃×Q₁₆	2
C₂×Dic₁₂	2
C₂×D₃×C₈	2
C₂²×Q₁₆	3

Subgroups — C2×D3×Q16 #5763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×Q₁₆ #5763