Subgroups — C₂²×C₃×SD₁₆ #5900

Order 192.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×SD₁₆	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁴×C₃	—	2	1	no	—
7	C₂×C₃×Q₈	—	2	3	no	—
8	C₂×C₃×Q₈	C₂²	1	6	yes	complemented
9	C₂×C₃×D₄	—	2	3	no	—
10	C₂×C₃×D₄	C₂²	1	6	yes	—
11	C₂²×C₃×C₄	—	2	1	no	—
12	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₃×SD₁₆	C₂²	1	16	yes	direct product factor
14	C₂×C₃×C₈	C₂²	1	6	yes	complemented
15	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂²×D₄	C₂×C₃	1	1	yes	characteristic
17	C₂×SD₁₆	C₂×C₃	1	12	yes	direct product factor
18	C₂²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂³×C₃	—	2	6	no	—
20	C₂³×C₃	—	4	4	no	—
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₃×Q₈	—	2	6	no	—
23	C₃×Q₈	C₂³	1	4	yes	complemented
24	C₃×D₄	—	2	6	no	—
25	C₃×D₄	C₂³	1	4	yes	—
26	C₂×C₃×C₄	—	2	6	no	—
27	C₂×C₃×C₄	D₄	1	3	yes	—
28	C₂×C₃×C₄	C₂³	1	3	yes	—
29	C₃×C₈	C₂³	1	4	yes	complemented
30	C₂⁴	—	2	1	no	—
31	C₂×Q₈	—	2	3	no	—
32	C₂×Q₈	C₂²×C₃	1	6	yes	complemented
33	C₂×D₄	—	2	3	no	—
34	C₂×D₄	C₂²×C₃	1	6	yes	—
35	C₂²×C₄	—	2	1	no	—
36	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
37	SD₁₆	C₂²×C₃	1	16	yes	direct product factor
38	C₂×C₈	C₂²×C₃	1	6	yes	complemented
39	C₂²×C₃	—	2	4	no	—
40	C₂²×C₃	—	4	12	no	—
41	C₂²×C₃	SD₁₆	1	4	yes	direct product factor
42	C₂²×C₃	C₂×D₄	1	3	yes	—
43	C₃×C₄	—	2	4	no	—
44	C₃×C₄	C₂×D₄	1	3	yes	—
45	C₃×C₄	C₂⁴	1	1	yes	characteristic
46	C₂³	—	2	6	no	—
47	C₂³	—	4	4	no	—
48	C₂³	C₃×D₄	1	1	yes	characteristic
49	Q₈	—	2	6	no	—
50	Q₈	C₂³×C₃	1	4	yes	complemented
51	D₄	—	2	6	no	—
52	D₄	C₂³×C₃	1	4	yes	—
53	C₂×C₄	—	2	6	no	—
54	C₂×C₄	C₃×D₄	1	3	yes	—
55	C₂×C₄	C₂³×C₃	1	3	yes	—
56	C₈	C₂³×C₃	1	4	yes	complemented
57	C₂×C₃	—	4	4	no	—
58	C₂×C₃	C₂×SD₁₆	1	6	yes	direct product factor
59	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
60	C₂²	—	2	4	no	—
61	C₂²	—	4	12	no	—
62	C₂²	C₃×SD₁₆	1	4	yes	direct product factor
63	C₂²	C₂×C₃×D₄	1	3	yes	—
64	C₄	—	2	4	no	—
65	C₄	C₂×C₃×D₄	1	3	yes	—
66	C₄	C₂⁴×C₃	1	1	yes	characteristic
67	C₃	C₂²×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	4	4	no	—
69	C₂	C₂×C₃×SD₁₆	1	6	yes	direct product factor
70	C₂	C₂²×C₃×D₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈	C₂	semidirect
3. C₂×C₃×SD₁₆	C₂	direct (N × H)
4. C₂²×C₃×C₈	C₂	semidirect
5. C₂²×SD₁₆	C₃	direct (N × H)
8. C₂×C₃×Q₈	C₂²	semidirect
13. C₃×SD₁₆	C₂²	direct (N × H)
14. C₂×C₃×C₈	C₂²	semidirect
15. C₂²×Q₈	C₂×C₃	semidirect
17. C₂×SD₁₆	C₂×C₃	direct (N × H)
18. C₂²×C₈	C₂×C₃	semidirect
23. C₃×Q₈	C₂³	semidirect
29. C₃×C₈	C₂³	semidirect
32. C₂×Q₈	C₂²×C₃	semidirect
37. SD₁₆	C₂²×C₃	direct (N × H)
38. C₂×C₈	C₂²×C₃	semidirect
41. C₂²×C₃	SD₁₆	direct (N × H)
50. Q₈	C₂³×C₃	semidirect
56. C₈	C₂³×C₃	semidirect
58. C₂×C₃	C₂×SD₁₆	direct (N × H)
62. C₂²	C₃×SD₁₆	direct (N × H)
67. C₃	C₂²×SD₁₆	direct (N × H)
69. C₂	C₂×C₃×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈	2
C₂²×C₃×D₄	2
C₂×C₃×SD₁₆	2
C₂²×C₃×C₈	2
C₂²×SD₁₆	3

Subgroups — C22×C3×SD16 #5900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×SD₁₆ #5900