Subgroups — C₂³×#67 #5970

Order 192.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#67	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₄	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	—	2	8	no	—
7	C₂⁴×C₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₃	C₂²	1	14	yes	complemented
9	C₂³×D₃	—	2	8	no	—
10	C₂³×D₃	C₂²	1	14	yes	complemented
11	C₂×#67	C₂²	1	112	yes	direct product factor
12	C₂²×Dic₃	C₂²	1	14	yes	complemented
13	C₂⁵	—	3	1	no	—
14	C₂⁵	D₃	1	1	yes	characteristic, complemented
15	C₂²×D₄	—	3	28	no	—
16	C₂³×C₄	—	3	1	no	—
17	C₂³×C₃	—	2	56	no	—
18	C₂³×C₃	D₄	1	8	yes	complemented
19	C₂³×C₃	C₂³	1	7	yes	—
20	C₂³×C₃	C₂³	1	28	yes	complemented
21	C₂²×D₃	—	2	56	no	—
22	C₂²×D₃	C₂³	1	28	yes	complemented
23	#67	C₂³	1	64	yes	direct product factor
24	C₂×Dic₃	C₂³	1	28	yes	complemented
25	C₂⁴	—	2	8	no	—
26	C₂⁴	—	3	14	no	—
27	C₂⁴	—	6	8	no	—
28	C₂⁴	C₂×D₃	1	1	yes	characteristic
29	C₂⁴	C₂×D₃	1	14	yes	complemented
30	C₂×D₄	—	3	112	no	—
31	C₂²×C₄	—	3	14	no	—
32	C₂²×C₃	—	2	56	no	—
33	C₂²×C₃	C₂×D₄	1	28	yes	complemented
34	C₂²×C₃	C₂⁴	1	7	yes	—
35	C₂²×C₃	C₂⁴	1	8	yes	complemented
36	C₂×D₃	—	2	56	no	—
37	C₂×D₃	C₂⁴	1	8	yes	complemented
38	Dic₃	C₂⁴	1	8	yes	complemented
39	C₂³	—	2	56	no	—
40	C₂³	—	3	28	no	—
41	C₂³	—	6	56	no	—
42	C₂³	#67	1	8	yes	direct product factor
43	C₂³	C₂²×D₃	1	7	yes	—
44	C₂³	C₂²×D₃	1	28	yes	complemented
45	D₄	—	3	64	no	—
46	C₂×C₄	—	3	28	no	—
47	C₂×C₃	—	2	8	no	—
48	C₂×C₃	C₂²×D₄	1	14	yes	complemented
49	C₂×C₃	C₂⁵	1	1	yes	characteristic
50	D₃	—	2	8	no	—
51	C₂²	—	2	56	no	—
52	C₂²	—	3	8	no	—
53	C₂²	—	6	56	no	—
54	C₂²	C₂×#67	1	28	yes	direct product factor
55	C₂²	C₂³×D₃	1	7	yes	—
56	C₂²	C₂³×D₃	1	8	yes	complemented
57	C₄	—	3	8	no	—
58	C₃	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	2	8	no	—
60	C₂	—	6	8	no	—
61	C₂	C₂²×#67	1	14	yes	direct product factor
62	C₂	C₂⁴×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁵
Frattini	C₂	C₂⁴×D₃
Fitting	C₂⁵×C₃	C₂
socle	C₂⁴×C₃	C₂²
hypercenter	C₂⁵	D₃
hypocenter	C₃	C₂³×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₃	C₂	semidirect
2. C₂⁴×D₃	C₂	semidirect
3. C₂²×#67	C₂	direct (N × H)
4. C₂³×Dic₃	C₂	semidirect
8. C₂⁴×C₃	C₂²	semidirect
10. C₂³×D₃	C₂²	semidirect
11. C₂×#67	C₂²	direct (N × H)
12. C₂²×Dic₃	C₂²	semidirect
14. C₂⁵	D₃	semidirect
18. C₂³×C₃	D₄	semidirect
20. C₂³×C₃	C₂³	semidirect
22. C₂²×D₃	C₂³	semidirect
23. #67	C₂³	direct (N × H)
24. C₂×Dic₃	C₂³	semidirect
29. C₂⁴	C₂×D₃	semidirect
33. C₂²×C₃	C₂×D₄	semidirect
35. C₂²×C₃	C₂⁴	semidirect
37. C₂×D₃	C₂⁴	semidirect
38. Dic₃	C₂⁴	semidirect
42. C₂³	#67	direct (N × H)
44. C₂³	C₂²×D₃	semidirect
48. C₂×C₃	C₂²×D₄	semidirect
54. C₂²	C₂×#67	direct (N × H)
56. C₂²	C₂³×D₃	semidirect
58. C₃	C₂³×D₄	semidirect
61. C₂	C₂²×#67	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃	2
C₂⁴×D₃	2
C₂²×#67	2
C₂³×Dic₃	2
C₂³×D₄	3

Subgroups — C23×#67 #5970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#67 #5970