Subgroups — C₃×#418 #5292

Order 192.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#102	C₂	1	4	yes	maximal, complemented
5	#418	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁴×C₃	—	2	1	no	—
7	C₂×C₃×D₄	—	2	1	no	—
8	C₂×C₃×D₄	—	2	2	no	—
9	C₂×C₃×D₄	C₄	1	4	yes	complemented
10	C₂×C₃×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₃×M₁₆	—	2	2	no	—
13	C₂×C₃×C₈	C₂²	1	2	yes	complemented
14	C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²	—	2	1	no	—
17	C₂²×D₄	C₂×C₃	1	1	yes	characteristic
18	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
19	#117	C₂×C₃	1	1	yes	characteristic, complemented
20	#102	C₂×C₃	1	4	yes	complemented
21	C₂³×C₃	—	2	4	no	—
22	C₂³×C₃	—	2	2	no	—
23	C₂³×C₃	—	4	4	no	—
24	C₂³×C₃	D₄	1	1	yes	characteristic
25	C₃×D₄	—	2	4	no	—
26	C₃×D₄	—	2	2	no	—
27	C₃×D₄	C₂×C₄	1	4	yes	—
28	C₂×C₃×C₄	—	2	2	no	—
29	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
30	C₂×C₃×C₄	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄	D₄	1	2	yes	—
32	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
33	C₃×C₈	—	2	2	no	—
34	C₂⁴	—	2	1	no	—
35	C₂×D₄	—	2	1	no	—
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	C₃×C₄	1	4	yes	complemented
38	C₂×D₄	C₂²×C₃	1	2	yes	—
39	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
40	M₁₆	—	2	2	no	—
41	C₂×C₈	C₂²×C₃	1	2	yes	complemented
42	C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
43	C₂²⋊C₄	—	2	1	no	—
44	C₄²	—	2	1	no	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	—	2	4	no	—
47	C₂²×C₃	—	4	8	no	—
48	C₂²×C₃	—	4	4	no	—
49	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
51	C₃×C₄	—	4	2	no	—
52	C₃×C₄	C₂²⋊C₄	1	2	yes	—
53	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
54	C₃×C₄	C₂×D₄	1	1	yes	characteristic
55	C₂³	—	2	4	no	—
56	C₂³	—	2	2	no	—
57	C₂³	—	4	4	no	—
58	C₂³	C₃×D₄	1	1	yes	characteristic
59	D₄	—	2	4	no	—
60	D₄	—	2	2	no	—
61	D₄	C₂×C₃×C₄	1	4	yes	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
64	C₂×C₄	C₃×D₄	1	1	yes	characteristic
65	C₂×C₄	C₃×D₄	1	2	yes	—
66	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₂×C₃	—	2	2	no	—
69	C₂×C₃	—	4	4	no	—
70	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
72	C₂²	—	2	2	no	—
73	C₂²	—	2	4	no	—
74	C₂²	—	4	8	no	—
75	C₂²	—	4	4	no	—
76	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
77	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	C₃×C₂²⋊C₄	1	2	yes	—
80	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
81	C₄	C₂×C₃×D₄	1	1	yes	characteristic
82	C₃	#418	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	2	2	no	—
84	C₂	—	4	4	no	—
85	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
86	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	C₂²×C₃×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×M₁₆	C₂	semidirect
3. C₃×#117	C₂	semidirect
4. C₃×#102	C₂	semidirect
5. #418	C₃	direct (N × H)
9. C₂×C₃×D₄	C₄	semidirect
13. C₂×C₃×C₈	C₂²	semidirect
14. C₃×C₄⋊C₄	C₂²	semidirect
18. C₂×M₁₆	C₂×C₃	semidirect
19. #117	C₂×C₃	semidirect
20. #102	C₂×C₃	semidirect
37. C₂×D₄	C₃×C₄	semidirect
41. C₂×C₈	C₂²×C₃	semidirect
42. C₄⋊C₄	C₂²×C₃	semidirect
82. C₃	#418	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×D₄	2
C₂×C₃×M₁₆	2
C₃×#117	2
C₃×#102	2
#418	3

Subgroups — C3×#418 #5292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#418 #5292