Subgroups — C₃×#496 #5370

Order 192.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₈	C₂	1	2	yes	maximal, complemented
3	C₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	#496	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₄	—	2	2	no	—
9	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄	C₂²	1	2	yes	—
11	C₃×SD₁₆	—	2	4	no	—
12	C₃×D₈	—	2	4	no	—
13	C₂×C₃×C₈	C₂²	1	2	yes	—
14	C₃×C₂²⋊C₄	—	2	2	no	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂×SD₁₆	C₂×C₃	1	2	yes	complemented
17	C₂×D₈	C₂×C₃	1	2	yes	complemented
18	#127	C₂×C₃	1	1	yes	characteristic, complemented
19	#124	C₂×C₃	1	1	yes	characteristic, complemented
20	#97	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂³×C₃	—	2	1	no	—
22	C₂³×C₃	—	2	2	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₃×D₄	—	2	2	no	—
25	C₃×D₄	—	2	2	no	—
26	C₃×D₄	—	2	2	no	—
27	C₃×D₄	—	4	4	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	D₄	1	2	yes	—
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	D₄	1	4	yes	complemented
32	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
35	C₂×D₄	C₂²×C₃	1	2	yes	—
36	SD₁₆	—	2	4	no	—
37	D₈	—	2	4	no	—
38	C₂×C₈	C₂²×C₃	1	2	yes	—
39	C₂²⋊C₄	—	2	2	no	—
40	C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃	—	4	1	no	—
42	C₂²×C₃	—	4	2	no	—
43	C₂²×C₃	—	4	4	no	—
44	C₂²×C₃	—	4	2	no	—
45	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
46	C₃×C₄	—	2	2	no	—
47	C₃×C₄	—	4	1	no	—
48	C₃×C₄	C₂×D₄	1	2	yes	—
49	C₂³	—	2	1	no	—
50	C₂³	—	2	2	no	—
51	Q₈	—	2	2	no	—
52	D₄	—	2	2	no	—
53	D₄	—	2	2	no	—
54	D₄	—	2	2	no	—
55	D₄	—	4	4	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	C₃×D₄	1	2	yes	—
58	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
59	C₈	C₃×D₄	1	4	yes	complemented
60	C₂×C₃	—	8	2	no	—
61	C₂×C₃	—	8	1	no	—
62	C₂×C₃	#127	1	1	yes	characteristic
63	C₂×C₃	AGL(1,ℤ/8)	1	2	yes	—
64	C₂²	—	4	1	no	—
65	C₂²	—	4	2	no	—
66	C₂²	—	4	4	no	—
67	C₂²	—	4	2	no	—
68	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	4	1	no	—
71	C₄	C₂×C₃×D₄	1	2	yes	—
72	C₃	#496	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	—	8	2	no	—
74	C₂	—	8	1	no	—
75	C₂	C₃×#127	1	1	yes	characteristic
76	C₂	C₃×AGL(1,ℤ/8)	1	2	yes	—

	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×SD₁₆	C₂	semidirect
2. C₂×C₃×D₈	C₂	semidirect
3. C₃×#127	C₂	semidirect
4. C₃×#124	C₂	semidirect
5. C₃×#97	C₂	semidirect
6. #496	C₃	direct (N × H)
16. C₂×SD₁₆	C₂×C₃	semidirect
17. C₂×D₈	C₂×C₃	semidirect
18. #127	C₂×C₃	semidirect
19. #124	C₂×C₃	semidirect
20. #97	C₂×C₃	semidirect
31. C₃×C₈	D₄	semidirect
59. C₈	C₃×D₄	semidirect
72. C₃	#496	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×SD₁₆	2
C₂×C₃×D₈	2
C₃×#127	2
C₃×#124	2
C₃×#97	2
#496	3

Subgroups — C3×#496 #5370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#496 #5370