Subgroups — C₃×#6482 #10621230

Order 672.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#1161	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#1143	C₂	1	2	yes	maximal, complemented
4	C₃×D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#6482	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×Q₈	C₂²	1	2	yes	—
8	C₃×D₂₈	—	2	2	no	—
9	C₃×D₂₈	C₂²	1	2	yes	—
10	C₃×C₄×D₇	—	2	2	no	—
11	C₃×C₄×D₇	C₂²	1	1	yes	characteristic
12	C₃×C₇×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₇⋊C₈	C₂²	1	1	yes	characteristic
14	#1161	C₂×C₃	1	2	yes	complemented
15	C₇×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
16	#1143	C₂×C₃	1	2	yes	complemented
17	D₅₆	C₂×C₃	1	1	yes	characteristic, complemented
18	C₈×D₇	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×#135	—	7	1	no	maximal, Hall
20	C₂×C₃×D₇	—	2	2	no	—
21	C₂×C₃×D₇	D₄	1	1	yes	characteristic
22	C₃×C₄×C₇	—	2	2	no	—
23	C₃×C₄×C₇	C₂³	1	1	yes	characteristic
24	C₃×Dic₇	D₄	1	1	yes	characteristic
25	C₇×Q₈	C₂²×C₃	1	2	yes	—
26	D₂₈	—	2	2	no	—
27	D₂₈	C₂²×C₃	1	2	yes	—
28	C₄×D₇	—	2	2	no	—
29	C₄×D₇	C₂²×C₃	1	1	yes	characteristic
30	C₇×C₈	C₂²×C₃	1	1	yes	characteristic
31	C₇⋊C₈	C₂²×C₃	1	1	yes	characteristic
32	C₃×#41	—	7	2	no	—
33	C₃×Q₁₆	D₇	1	1	yes	characteristic, complemented
34	C₃×SD₁₆	—	7	2	no	—
35	C₃×D₈	—	7	1	no	—
36	C₂×C₃×C₈	—	7	1	no	—
37	C₂×C₃×C₇	C₂×D₄	1	1	yes	characteristic
38	C₃×D₇	—	2	1	no	—
39	C₃×D₇	—	4	2	no	—
40	#135	—	7	1	no	Sylow
41	C₂×D₇	—	2	2	no	—
42	C₂×D₇	C₃×D₄	1	1	yes	characteristic
43	C₄×C₇	—	2	2	no	—
44	C₄×C₇	C₂³×C₃	1	1	yes	characteristic
45	Dic₇	C₃×D₄	1	1	yes	characteristic
46	C₃×Q₈	C₂×D₇	1	2	yes	—
47	C₃×D₄	—	7	2	no	—
48	C₃×D₄	—	14	2	no	—
49	C₂×C₃×C₄	—	7	1	no	—
50	C₂×C₃×C₄	—	14	2	no	—
51	C₃×C₈	—	7	1	no	—
52	C₃×C₈	C₂×D₇	1	1	yes	characteristic
53	C₃×C₇	#135	1	1	yes	characteristic, complemented, Hall
54	#41	—	7	2	no	—
55	Q₁₆	C₃×D₇	1	1	yes	characteristic, complemented
56	SD₁₆	—	7	2	no	—
57	D₈	—	7	1	no	—
58	C₂×C₈	—	7	1	no	—
59	C₂×C₇	C₂×C₃×D₄	1	1	yes	characteristic
60	D₇	—	2	1	no	—
61	D₇	—	4	2	no	—
62	C₂²×C₃	—	7	1	no	—
63	C₂²×C₃	—	14	2	no	—
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	—	7	1	no	—
66	C₃×C₄	C₂²×D₇	1	1	yes	characteristic
67	Q₈	C₂×C₃×D₇	1	2	yes	—
68	D₄	—	7	2	no	—
69	D₄	—	14	2	no	—
70	C₂×C₄	—	7	1	no	—
71	C₂×C₄	—	14	2	no	—
72	C₈	—	7	1	no	—
73	C₈	C₂×C₃×D₇	1	1	yes	characteristic
74	C₇	C₃×#135	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₃	—	14	1	no	—
76	C₂×C₃	—	28	2	no	—
77	C₂×C₃	D₄×D₇	1	1	yes	characteristic
78	C₂²	—	7	1	no	—
79	C₂²	—	14	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	7	1	no	—
82	C₄	C₂²×C₃×D₇	1	1	yes	characteristic
83	C₃	#6482	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	14	1	no	—
85	C₂	—	28	2	no	—
86	C₂	C₃×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₇
commutator, cosocle	C₄×C₇	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₇
Fitting	C₃×C₇×Q₁₆	C₂
socle	C₂×C₃×C₇	C₂×D₄
hypercenter	C₃×Q₁₆	D₇
hypocenter	C₇	C₃×#135
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#1161	C₂	semidirect
2. C₃×C₇×Q₁₆	C₂	semidirect
3. C₃×#1143	C₂	semidirect
4. C₃×D₅₆	C₂	semidirect
5. C₃×C₈×D₇	C₂	semidirect
6. #6482	C₃	direct (N × H)
14. #1161	C₂×C₃	semidirect
15. C₇×Q₁₆	C₂×C₃	semidirect
16. #1143	C₂×C₃	semidirect
17. D₅₆	C₂×C₃	semidirect
18. C₈×D₇	C₂×C₃	semidirect
33. C₃×Q₁₆	D₇	semidirect
53. C₃×C₇	#135	semidirect
55. Q₁₆	C₃×D₇	semidirect
74. C₇	C₃×#135	semidirect
83. C₃	#6482	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#1161	2
C₃×C₇×Q₁₆	2
C₃×#1143	2
C₃×D₅₆	2
C₃×C₈×D₇	2
#6482	3
C₃×#135	7

Subgroups — C3×#6482 #10621230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#6482 #10621230