Subgroups — C₂²×C₃×#41 #5974

Order 192.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×D₄	C₂	1	3	yes	maximal, complemented
4	C₂³×C₃×C₄	C₂	1	3	yes	maximal, complemented
5	C₂²×#41	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁴×C₃	C₂²	1	3	yes	—
7	C₃×#41	C₂²	1	64	yes	direct product factor
8	C₂×C₃×Q₈	C₂²	1	12	yes	complemented
9	C₂×C₃×D₄	C₂²	1	36	yes	complemented
10	C₂²×C₃×C₄	C₂²	1	3	yes	—
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₂²	1	36	yes	complemented
13	C₂×#41	C₂×C₃	1	24	yes	direct product factor
14	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×D₄	C₂×C₃	1	3	yes	complemented
16	C₂³×C₄	C₂×C₃	1	3	yes	complemented
17	C₂³×C₃	—	2	12	no	—
18	C₂³×C₃	C₂³	1	18	yes	—
19	C₂³×C₃	C₂³	1	1	yes	characteristic
20	C₃×Q₈	C₂³	1	16	yes	complemented
21	C₃×D₄	C₂³	1	48	yes	complemented
22	C₂×C₃×C₄	C₂³	1	18	yes	—
23	C₂×C₃×C₄	C₂³	1	6	yes	—
24	C₂×C₃×C₄	C₂³	1	48	yes	complemented
25	C₂⁴	C₂²×C₃	1	3	yes	—
26	#41	C₂²×C₃	1	64	yes	direct product factor
27	C₂×Q₈	C₂²×C₃	1	12	yes	complemented
28	C₂×D₄	C₂²×C₃	1	36	yes	complemented
29	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
30	C₂²×C₄	C₂²×C₃	1	3	yes	—
31	C₂²×C₄	C₂²×C₃	1	36	yes	complemented
32	C₂²×C₃	—	2	36	no	—
33	C₂²×C₃	#41	1	4	yes	direct product factor
34	C₂²×C₃	C₂⁴	1	12	yes	—
35	C₂²×C₃	C₂⁴	1	3	yes	—
36	C₃×C₄	C₂⁴	1	4	yes	—
37	C₃×C₄	C₂⁴	1	12	yes	—
38	C₂³	—	2	12	no	—
39	C₂³	C₂³×C₃	1	18	yes	—
40	C₂³	C₂³×C₃	1	1	yes	characteristic
41	Q₈	C₂³×C₃	1	16	yes	complemented
42	D₄	C₂³×C₃	1	48	yes	complemented
43	C₂×C₄	C₂³×C₃	1	6	yes	—
44	C₂×C₄	C₂³×C₃	1	18	yes	—
45	C₂×C₄	C₂³×C₃	1	48	yes	complemented
46	C₂×C₃	—	2	12	no	—
47	C₂×C₃	C₂×#41	1	6	yes	direct product factor
48	C₂×C₃	C₂⁵	1	1	yes	characteristic
49	C₂²	—	2	36	no	—
50	C₂²	C₃×#41	1	4	yes	direct product factor
51	C₂²	C₂⁴×C₃	1	12	yes	—
52	C₂²	C₂⁴×C₃	1	3	yes	—
53	C₄	C₂⁴×C₃	1	4	yes	—
54	C₄	C₂⁴×C₃	1	12	yes	—
55	C₃	C₂²×#41	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	12	no	—
57	C₂	C₂×C₃×#41	1	6	yes	direct product factor
58	C₂	C₂⁵×C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²
commutator, Frattini, cosocle	C₂	C₂⁵×C₃
socle	C₂³×C₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#41	C₂	direct (N × H)
2. C₂²×C₃×Q₈	C₂	semidirect
3. C₂²×C₃×D₄	C₂	semidirect
4. C₂³×C₃×C₄	C₂	semidirect
5. C₂²×#41	C₃	direct (N × H)
7. C₃×#41	C₂²	direct (N × H)
8. C₂×C₃×Q₈	C₂²	semidirect
9. C₂×C₃×D₄	C₂²	semidirect
12. C₂²×C₃×C₄	C₂²	semidirect
13. C₂×#41	C₂×C₃	direct (N × H)
14. C₂²×Q₈	C₂×C₃	semidirect
15. C₂²×D₄	C₂×C₃	semidirect
16. C₂³×C₄	C₂×C₃	semidirect
20. C₃×Q₈	C₂³	semidirect
21. C₃×D₄	C₂³	semidirect
24. C₂×C₃×C₄	C₂³	semidirect
26. #41	C₂²×C₃	direct (N × H)
27. C₂×Q₈	C₂²×C₃	semidirect
28. C₂×D₄	C₂²×C₃	semidirect
31. C₂²×C₄	C₂²×C₃	semidirect
33. C₂²×C₃	#41	direct (N × H)
41. Q₈	C₂³×C₃	semidirect
42. D₄	C₂³×C₃	semidirect
45. C₂×C₄	C₂³×C₃	semidirect
47. C₂×C₃	C₂×#41	direct (N × H)
50. C₂²	C₃×#41	direct (N × H)
55. C₃	C₂²×#41	direct (N × H)
57. C₂	C₂×C₃×#41	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×C₃×#41	2
C₂²×C₃×Q₈	2
C₂²×C₃×D₄	2
C₂³×C₃×C₄	2
C₂²×#41	3

Subgroups — C22×C3×#41 #5974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#41 #5974