Subgroups — C₃×#6390 #10620573

Order 672.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	#6390	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×Dic₇	—	2	1	no	—
7	C₂×C₃×Dic₇	—	2	1	no	—
8	C₃×Dic₁₄	—	2	1	no	—
9	C₃×Dic₁₄	C₄	1	2	yes	complemented
10	C₃×C₇×C₈	—	2	1	no	—
11	C₂×Dic₁₄	C₂×C₃	1	1	yes	characteristic
12	C₂×C₇×C₈	C₂×C₃	1	1	yes	characteristic
13	C₄⋊Dic₇	C₂×C₃	1	1	yes	characteristic
14	C₃×#103	—	7	1	no	maximal, Hall
15	C₂²×C₃×C₇	D₄	1	1	yes	characteristic
16	C₃×C₄×C₇	C₂×C₄	1	1	yes	characteristic
17	C₃×C₄×C₇	D₄	1	1	yes	characteristic
18	C₃×Dic₇	—	2	2	no	—
19	C₃×Dic₇	—	4	1	no	—
20	C₂×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
21	C₂×Dic₇	—	2	1	no	—
22	C₂×Dic₇	—	2	1	no	—
23	Dic₁₄	—	2	1	no	—
24	Dic₁₄	C₃×C₄	1	2	yes	complemented
25	C₇×C₈	—	2	1	no	—
26	C₂×C₃×Q₈	—	7	1	no	—
27	C₂×C₃×C₈	D₇	1	1	yes	characteristic
28	C₃×C₄⋊C₄	—	7	1	no	—
29	C₂×C₃×C₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₃×C₇	SD₁₆	1	1	yes	characteristic
31	C₂×C₃×C₇	Q₁₆	1	1	yes	characteristic
32	#103	—	7	1	no	Sylow
33	C₂²×C₇	C₃×D₄	1	1	yes	characteristic
34	C₄×C₇	C₂×C₃×C₄	1	1	yes	characteristic
35	C₄×C₇	C₃×D₄	1	1	yes	characteristic
36	Dic₇	—	2	2	no	—
37	Dic₇	—	4	1	no	—
38	C₃×Q₈	—	7	2	no	—
39	C₃×Q₈	—	14	1	no	—
40	C₂×C₃×C₄	—	14	1	no	—
41	C₂×C₃×C₄	—	14	1	no	—
42	C₂×C₃×C₄	C₂×D₇	1	1	yes	characteristic
43	C₃×C₈	—	2	1	no	—
44	C₃×C₇	#103	1	1	yes	characteristic, complemented, Hall
45	C₂×Q₈	—	7	1	no	—
46	C₂×C₈	C₃×D₇	1	1	yes	characteristic
47	C₄⋊C₄	—	7	1	no	—
48	C₂×C₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₇	C₃×SD₁₆	1	1	yes	characteristic
50	C₂×C₇	C₃×Q₁₆	1	1	yes	characteristic
51	C₂²×C₃	D₂₈	1	1	yes	characteristic
52	C₃×C₄	—	14	2	no	—
53	C₃×C₄	—	28	1	no	—
54	C₃×C₄	C₄×D₇	1	1	yes	characteristic
55	C₃×C₄	C₂²⋊D₇	1	1	yes	characteristic
56	Q₈	—	7	2	no	—
57	Q₈	—	14	1	no	—
58	C₂×C₄	—	14	1	no	—
59	C₂×C₄	—	14	1	no	—
60	C₂×C₄	C₂×C₃×D₇	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₇	C₃×#103	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₃	#1132	1	1	yes	characteristic
64	C₂×C₃	Dic₂₈	1	1	yes	characteristic
65	C₂×C₃	(C₂×D₇)⋊C₄	1	1	yes	characteristic
66	C₂²	C₃×D₂₈	1	1	yes	characteristic
67	C₄	—	14	2	no	—
68	C₄	—	28	1	no	—
69	C₄	C₃×C₄×D₇	1	1	yes	characteristic
70	C₄	C₃×C₂²⋊D₇	1	1	yes	characteristic
71	C₃	#6390	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	C₃×#1132	1	1	yes	characteristic
73	C₂	C₃×Dic₂₈	1	1	yes	characteristic
74	C₂	C₃×(C₂×D₇)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₂₈
commutator	C₄×C₇	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₇
Fitting	C₂×C₃×C₇×C₈	C₂
socle, prime radical	C₂²×C₃×C₇	D₄
cosocle	C₂×C₄×C₇	C₂²×C₃
hypercenter	C₂×C₃×C₈	D₇
hypocenter	C₇	C₃×#103
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. #6390	C₃	direct (N × H)
9. C₃×Dic₁₄	C₄	semidirect
24. Dic₁₄	C₃×C₄	semidirect
44. C₃×C₇	#103	semidirect
62. C₇	C₃×#103	semidirect
71. C₃	#6390	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×Dic₁₄	2
C₂×C₃×C₇×C₈	2
C₃×C₄⋊Dic₇	2
#6390	3
C₃×#103	7

Subgroups — C3×#6390 #10620573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#6390 #10620573