Subgroups — C₃×C₄×#41 #5847

Order 192.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×D₄	C₂	1	6	yes	maximal, complemented
4	C₃×#117	C₂	1	3	yes	maximal, complemented
5	C₂×C₃×C₄²	C₂	1	3	yes	maximal, complemented
6	C₄×#41	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	C₄	1	8	yes	direct product factor
8	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×D₄	C₂²	1	3	yes	—
10	C₂²×C₃×C₄	C₂²	1	6	yes	—
11	C₂²×C₃×C₄	C₂²	1	3	yes	—
12	C₃×C₄⋊C₄	C₂²	1	6	yes	—
13	C₃×C₂²⋊C₄	C₂²	1	6	yes	—
14	C₃×C₄²	C₂²	1	3	yes	—
15	C₃×C₄²	C₂²	1	6	yes	—
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×#41	C₂×C₃	1	1	yes	characteristic
18	C₄×Q₈	C₂×C₃	1	2	yes	complemented
19	C₄×D₄	C₂×C₃	1	6	yes	complemented
20	#117	C₂×C₃	1	3	yes	complemented
21	C₂×C₄²	C₂×C₃	1	3	yes	complemented
22	C₂³×C₃	C₂³	1	3	yes	—
23	C₃×Q₈	C₂×C₄	1	4	yes	complemented
24	C₃×D₄	C₂×C₄	1	12	yes	complemented
25	C₂×C₃×C₄	—	2	12	no	—
26	C₂×C₃×C₄	C₂×C₄	1	12	yes	complemented
27	C₂×C₃×C₄	C₂³	1	6	yes	—
28	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂³	1	3	yes	—
30	C₂×C₃×C₄	C₂³	1	2	yes	—
31	#41	C₃×C₄	1	8	yes	direct product factor
32	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
33	C₂×D₄	C₂²×C₃	1	3	yes	—
34	C₂²×C₄	C₂²×C₃	1	6	yes	—
35	C₂²×C₄	C₂²×C₃	1	3	yes	—
36	C₄⋊C₄	C₂²×C₃	1	6	yes	—
37	C₂²⋊C₄	C₂²×C₃	1	6	yes	—
38	C₄²	C₂²×C₃	1	1	yes	characteristic
39	C₄²	C₂²×C₃	1	3	yes	—
40	C₄²	C₂²×C₃	1	6	yes	—
41	C₂²×C₃	—	2	6	no	—
42	C₂²×C₃	C₂²×C₄	1	6	yes	—
43	C₂²×C₃	C₂⁴	1	1	yes	characteristic
44	C₃×C₄	—	2	6	no	—
45	C₃×C₄	C₂²×C₄	1	2	yes	—
46	C₃×C₄	C₂²×C₄	1	6	yes	—
47	C₃×C₄	#41	1	4	yes	direct product factor
48	C₂³	C₂³×C₃	1	3	yes	—
49	Q₈	C₂×C₃×C₄	1	4	yes	complemented
50	D₄	C₂×C₃×C₄	1	12	yes	complemented
51	C₂×C₄	—	2	12	no	—
52	C₂×C₄	C₂×C₃×C₄	1	12	yes	complemented
53	C₂×C₄	C₂³×C₃	1	6	yes	—
54	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
55	C₂×C₄	C₂³×C₃	1	3	yes	—
56	C₂×C₄	C₂³×C₃	1	2	yes	—
57	C₂×C₃	—	2	6	no	—
58	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
59	C₂×C₃	C₂×#41	1	2	yes	—
60	C₂²	—	2	6	no	—
61	C₂²	C₂²×C₃×C₄	1	6	yes	—
62	C₂²	C₂⁴×C₃	1	1	yes	characteristic
63	C₄	—	2	6	no	—
64	C₄	C₂²×C₃×C₄	1	2	yes	—
65	C₄	C₂²×C₃×C₄	1	6	yes	—
66	C₄	C₃×#41	1	4	yes	direct product factor
67	C₃	C₄×#41	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	2	6	no	—
69	C₂	C₂³×C₃×C₄	1	1	yes	characteristic
70	C₂	C₂×C₃×#41	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²
commutator	C₂	C₂³×C₃×C₄
Frattini, cosocle	C₂²	C₂⁴×C₃
socle	C₂²×C₃	C₂⁴
prime radical	C₂×C₃×#41	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×Q₈	C₂	semidirect
3. C₃×C₄×D₄	C₂	semidirect
4. C₃×#117	C₂	semidirect
5. C₂×C₃×C₄²	C₂	semidirect
6. C₄×#41	C₃	direct (N × H)
7. C₃×#41	C₄	direct (N × H)
18. C₄×Q₈	C₂×C₃	semidirect
19. C₄×D₄	C₂×C₃	semidirect
20. #117	C₂×C₃	semidirect
21. C₂×C₄²	C₂×C₃	semidirect
23. C₃×Q₈	C₂×C₄	semidirect
24. C₃×D₄	C₂×C₄	semidirect
26. C₂×C₃×C₄	C₂×C₄	semidirect
31. #41	C₃×C₄	direct (N × H)
47. C₃×C₄	#41	direct (N × H)
49. Q₈	C₂×C₃×C₄	semidirect
50. D₄	C₂×C₃×C₄	semidirect
52. C₂×C₄	C₂×C₃×C₄	semidirect
66. C₄	C₃×#41	direct (N × H)
67. C₃	C₄×#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
C₃×C₄×Q₈	2
C₃×C₄×D₄	2
C₃×#117	2
C₂×C₃×C₄²	2
C₄×#41	3

Subgroups — C3×C4×#41 #5847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#41 #5847