Subgroups — C₃²×#87639 #72277785

Order 3528.

282 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×Dic₇	C₂	1	2	yes	maximal, complemented
3	C₃×#87639	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₇²	C₂²	1	1	yes	characteristic
5	C₃²×C₇⋊D₇	C₄	1	2	yes	complemented
6	C₂×C₃×C₇⋊D₇	C₂×C₃	1	4	yes	—
7	C₃×C₇×Dic₇	C₂×C₃	1	8	yes	complemented
8	C₃²×C₄×D₇	—	7	2	no	maximal
9	C₃²×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	#87639	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇²	C₂²×C₃	1	4	yes	—
12	C₃×C₇⋊D₇	C₃×C₄	1	8	yes	complemented
13	C₂×C₃²×D₇	—	7	2	no	—
14	C₂×C₃²×D₇	—	14	3	no	—
15	C₃²×C₄×C₇	—	7	2	no	—
16	C₃²×Dic₇	D₇	1	2	yes	complemented
17	C₂×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
18	C₇×Dic₇	C₂×C₃²	1	2	yes	complemented
19	C₃×C₄×D₇	—	7	8	no	—
20	C₃×C₇²	C₂×C₃×C₄	1	4	yes	complemented
21	C₂×C₃²×C₇	—	2	3	no	—
22	C₂×C₃²×C₇	C₂×D₇	1	2	yes	—
23	C₃²×D₇	—	7	4	no	—
24	C₃²×D₇	—	14	6	no	—
25	C₂×C₇²	C₂²×C₃²	1	1	yes	characteristic
26	C₇⋊D₇	C₃²×C₄	1	2	yes	complemented
27	C₂×C₃×D₇	—	7	8	no	—
28	C₂×C₃×D₇	—	14	12	no	—
29	C₃×C₄×C₇	—	7	8	no	—
30	C₃×Dic₇	C₃×D₇	1	8	yes	complemented
31	C₂×C₃²×C₄	—	49	1	no	Hall
32	C₃²×C₇	—	2	3	no	—
33	C₃²×C₇	C₄×D₇	1	2	yes	complemented
34	C₄×D₇	—	7	2	no	—
35	C₇²	C₂×C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	2	12	no	—
37	C₂×C₃×C₇	C₂×C₃×D₇	1	8	yes	—
38	C₃×D₇	—	7	16	no	—
39	C₃×D₇	—	14	24	no	—
40	C₂²×C₃²	—	49	1	no	—
41	C₃²×C₄	—	7	2	no	—
42	C₂×D₇	—	7	2	no	—
43	C₂×D₇	—	14	3	no	—
44	C₄×C₇	—	7	2	no	—
45	Dic₇	C₃²×D₇	1	2	yes	complemented
46	C₂×C₃×C₄	—	49	4	no	—
47	C₃×C₇	—	2	12	no	—
48	C₃×C₇	C₃×C₄×D₇	1	8	yes	complemented
49	C₂×C₃²	—	49	2	no	—
50	C₂×C₃²	D₇²	1	1	yes	characteristic
51	C₂×C₇	—	2	3	no	—
52	C₂×C₇	C₂×C₃²×D₇	1	2	yes	—
53	D₇	—	7	4	no	—
54	D₇	—	14	6	no	—
55	C₂²×C₃	—	49	4	no	—
56	C₃×C₄	—	7	8	no	—
57	C₃²	#87639	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₄	—	49	1	no	Sylow
59	C₇	—	2	3	no	—
60	C₇	C₃²×C₄×D₇	1	2	yes	complemented
61	C₂×C₃	—	49	8	no	—
62	C₂×C₃	C₃×D₇²	1	4	yes	—
63	C₂²	—	49	1	no	—
64	C₄	—	7	2	no	—
65	C₃	C₃×#87639	1	4	yes	direct product factor
66	C₂	—	49	2	no	—
67	C₂	C₃²×D₇²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₇²
commutator, hypocenter	C₇²	C₂×C₃²×C₄
Frattini	C₂	C₃²×D₇²
Fitting, socle	C₂×C₃²×C₇²	C₂²
prime radical	C₂×C₃²×C₇⋊D₇	C₂
cosocle	C₂×C₇²	C₂²×C₃²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×Dic₇	C₂	semidirect
3. C₃×#87639	C₃	direct (N × H)
5. C₃²×C₇⋊D₇	C₄	semidirect
7. C₃×C₇×Dic₇	C₂×C₃	semidirect
9. C₃²×C₇²	C₂×C₄	semidirect
10. #87639	C₃²	direct (N × H)
12. C₃×C₇⋊D₇	C₃×C₄	semidirect
16. C₃²×Dic₇	D₇	semidirect
18. C₇×Dic₇	C₂×C₃²	semidirect
20. C₃×C₇²	C₂×C₃×C₄	semidirect
26. C₇⋊D₇	C₃²×C₄	semidirect
30. C₃×Dic₇	C₃×D₇	semidirect
33. C₃²×C₇	C₄×D₇	semidirect
35. C₇²	C₂×C₃²×C₄	semidirect
45. Dic₇	C₃²×D₇	semidirect
48. C₃×C₇	C₃×C₄×D₇	semidirect
57. C₃²	#87639	direct (N × H)
60. C₇	C₃²×C₄×D₇	semidirect
65. C₃	C₃×#87639	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×C₃²×C₇⋊D₇	2
C₃²×C₇×Dic₇	2
C₃×#87639	3
C₃²×C₄×D₇	7

Subgroups — C32×#87639 #72277785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#87639 #72277785