Subgroups — C₃×#459 #5333

Order 192.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#102	C₂	1	2	yes	maximal, complemented
6	#459	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	—	2	1	no	—
8	C₂×C₃×D₄	—	2	1	no	—
9	C₂×C₃×D₄	C₂²	1	2	yes	—
10	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄	—	2	1	no	—
12	C₃×D₈	—	2	4	no	—
13	C₂×C₃×C₈	C₂²	1	2	yes	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×D₈	C₂×C₃	1	2	yes	complemented
18	#127	C₂×C₃	1	1	yes	characteristic, complemented
19	C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
20	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	#102	C₂×C₃	1	2	yes	complemented
22	C₂³×C₃	—	2	1	no	—
23	C₂³×C₃	—	2	2	no	—
24	C₃×D₄	—	2	2	no	—
25	C₃×D₄	—	2	1	no	—
26	C₃×D₄	—	2	2	no	—
27	C₃×D₄	—	4	2	no	—
28	C₃×D₄	—	4	2	no	—
29	C₃×D₄	D₄	1	2	yes	complemented
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	4	2	no	—
32	C₂×C₃×C₄	D₄	1	1	yes	characteristic
33	C₂×C₃×C₄	D₄	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₃×C₈	—	2	2	no	—
36	C₂×D₄	—	2	1	no	—
37	C₂×D₄	—	2	1	no	—
38	C₂×D₄	C₂²×C₃	1	2	yes	—
39	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
40	C₂²×C₄	—	2	1	no	—
41	D₈	—	2	4	no	—
42	C₂×C₈	C₂²×C₃	1	2	yes	—
43	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
44	C₂²⋊C₄	—	2	1	no	—
45	C₄²	C₂²×C₃	1	1	yes	characteristic
46	C₂²×C₃	—	2	2	no	—
47	C₂²×C₃	—	4	1	no	—
48	C₂²×C₃	—	4	1	no	—
49	C₂²×C₃	—	4	2	no	—
50	C₂²×C₃	—	4	2	no	—
51	C₂²×C₃	—	4	2	no	—
52	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	D₈	1	2	yes	complemented
56	C₃×C₄	C₂×D₄	1	1	yes	characteristic
57	C₃×C₄	#41	1	1	yes	characteristic
58	C₂³	—	2	1	no	—
59	C₂³	—	2	2	no	—
60	D₄	—	2	2	no	—
61	D₄	—	2	1	no	—
62	D₄	—	2	2	no	—
63	D₄	—	4	2	no	—
64	D₄	—	4	2	no	—
65	D₄	C₃×D₄	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	4	2	no	—
68	C₂×C₄	C₃×D₄	1	1	yes	characteristic
69	C₂×C₄	C₃×D₄	1	1	yes	characteristic
70	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂×C₃	—	4	2	no	—
73	C₂×C₃	—	8	2	no	—
74	C₂×C₃	#121	1	1	yes	characteristic
75	C₂×C₃	C₂×D₈	1	1	yes	characteristic
76	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
77	C₂²	—	2	2	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	1	no	—
80	C₂²	—	4	2	no	—
81	C₂²	—	4	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	C₃×D₈	1	2	yes	complemented
87	C₄	C₂×C₃×D₄	1	1	yes	characteristic
88	C₄	C₃×#41	1	1	yes	characteristic
89	C₃	#459	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	4	2	no	—
91	C₂	—	8	2	no	—
92	C₂	C₃×#121	1	1	yes	characteristic
93	C₂	C₂×C₃×D₈	1	1	yes	characteristic
94	C₂	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
LCS	G ▷ C₂×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
1. C₂×C₃×D₈	C₂	semidirect
2. C₃×#127	C₂	semidirect
3. C₃×C₄×D₄	C₂	semidirect
4. C₃×C₄⋊C₈	C₂	semidirect
5. C₃×#102	C₂	semidirect
6. #459	C₃	direct (N × H)
17. C₂×D₈	C₂×C₃	semidirect
18. #127	C₂×C₃	semidirect
19. C₄×D₄	C₂×C₃	semidirect
20. C₄⋊C₈	C₂×C₃	semidirect
21. #102	C₂×C₃	semidirect
29. C₃×D₄	D₄	semidirect
55. C₃×C₄	D₈	semidirect
65. D₄	C₃×D₄	semidirect
86. C₄	C₃×D₈	semidirect
89. C₃	#459	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×#127	2
C₃×C₄×D₄	2
C₃×C₄⋊C₈	2
C₃×#102	2
#459	3

Subgroups — C3×#459 #5333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#459 #5333