Subgroups — C₃×#442 #5316

Order 192.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#102	C₂	1	2	yes	maximal, complemented
5	C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	#442	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	—	2	2	no	—
9	C₃×D₈	C₄	1	4	yes	complemented
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₂²⋊C₄	—	2	2	no	—
14	C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂×D₈	C₂×C₃	1	1	yes	characteristic
16	C₄×D₄	C₂×C₃	1	2	yes	complemented
17	#106	C₂×C₃	1	1	yes	characteristic, complemented
18	#102	C₂×C₃	1	2	yes	complemented
19	#97	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂³×C₃	—	2	2	no	—
21	C₃×D₄	—	2	2	no	—
22	C₃×D₄	C₂×C₄	1	4	yes	complemented
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	4	4	no	—
25	C₂×C₃×C₄	D₄	1	2	yes	—
26	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
27	C₃×C₈	—	2	1	no	—
28	C₃×C₈	C₂×C₄	1	2	yes	complemented
29	C₂×D₄	C₂²×C₃	1	2	yes	—
30	C₂²×C₄	—	2	2	no	—
31	D₈	C₃×C₄	1	4	yes	complemented
32	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₄⋊C₄	C₂²×C₃	1	2	yes	—
35	C₂²⋊C₄	—	2	2	no	—
36	C₄²	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₃	—	2	4	no	—
38	C₂²×C₃	—	4	2	no	—
39	C₂²×C₃	—	4	2	no	—
40	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
41	C₃×C₄	—	2	2	no	—
42	C₃×C₄	—	4	2	no	—
43	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
44	C₃×C₄	#41	1	1	yes	characteristic
45	C₂³	—	2	2	no	—
46	D₄	—	2	2	no	—
47	D₄	C₂×C₃×C₄	1	4	yes	complemented
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	4	4	no	—
50	C₂×C₄	C₃×D₄	1	2	yes	—
51	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
52	C₈	—	2	1	no	—
53	C₈	C₂×C₃×C₄	1	2	yes	complemented
54	C₂×C₃	—	4	4	no	—
55	C₂×C₃	C₄×D₄	1	1	yes	characteristic
56	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
57	C₂²	—	2	4	no	—
58	C₂²	—	4	2	no	—
59	C₂²	—	4	2	no	—
60	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
61	C₄	—	2	2	no	—
62	C₄	—	4	2	no	—
63	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
64	C₄	C₃×#41	1	1	yes	characteristic
65	C₃	#442	1	1	yes	characteristic, direct product factor, Sylow
66	C₂	—	4	4	no	—
67	C₂	C₃×C₄×D₄	1	1	yes	characteristic
68	C₂	C₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₄	C₂	semidirect
3. C₃×#106	C₂	semidirect
4. C₃×#102	C₂	semidirect
5. C₃×#97	C₂	semidirect
6. #442	C₃	direct (N × H)
9. C₃×D₈	C₄	semidirect
16. C₄×D₄	C₂×C₃	semidirect
17. #106	C₂×C₃	semidirect
18. #102	C₂×C₃	semidirect
19. #97	C₂×C₃	semidirect
22. C₃×D₄	C₂×C₄	semidirect
28. C₃×C₈	C₂×C₄	semidirect
31. D₈	C₃×C₄	semidirect
47. D₄	C₂×C₃×C₄	semidirect
53. C₈	C₂×C₃×C₄	semidirect
65. C₃	#442	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×D₈	2
C₃×C₄×D₄	2
C₃×#106	2
C₃×#102	2
C₃×#97	2
#442	3

Subgroups — C3×#442 #5316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#442 #5316