Subgroups — C₃₇⋊C₃×#64424 #45657458

Order 32634.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#24925950	C₃	1	1	yes	maximal, characteristic, complemented
4	#24925949	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#64424	C₃	1	1	yes	maximal, characteristic, complemented
6	#19129589	C₂×C₃	1	1	yes	characteristic, complemented
7	#19129588	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃₇×#3861	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	AGL(1,𝔽₇)×C₃₇⋊C₃	—	7	8	no	maximal
11	C₃₇×C₇⋊D₇	C₃²	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)×C₃₇⋊C₃	—	7	8	no	—
13	C₇²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	#13095536	—	7	8	no	—
15	#13095535	—	7	8	no	—
16	C₃₇×AGL(1,𝔽₇)	—	7	8	no	—
17	D₇×C₃₇⋊C₃	—	7	8	no	—
18	C₃×#64424	—	37	1	no	maximal, Hall
19	#11715913	—	7	8	no	—
20	#11715912	—	7	8	no	—
21	C₇×C₃₇⋊C₃	AGL(1,𝔽₇)	1	8	yes	complemented
22	ΓL(1,𝔽₈)×C₃₇	—	7	8	no	—
23	C₂×C₃×C₃₇⋊C₃	—	49	1	no	Hall
24	D₇×C₃₇	—	7	8	no	—
25	C₃×#3861	—	37	1	no	Hall
26	C₃×C₃₇⋊C₃	—	49	1	no	Hall
27	C₃×C₇⋊D₇	—	37	1	no	—
28	#64424	—	37	1	no	—
29	#64424	—	37	1	no	—
30	#64424	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₇×C₃₇	C₃×AGL(1,𝔽₇)	1	8	yes	complemented
32	C₂×C₃×C₃₇	—	49	1	no	—
33	C₂×C₃₇⋊C₃	—	49	1	no	—
34	C₂×C₃₇⋊C₃	—	49	1	no	—
35	C₂×C₃₇⋊C₃	—	49	1	no	—
36	C₃×C₇²	—	37	1	no	—
37	#3861	—	37	1	no	—
38	#3861	—	37	1	no	—
39	#3861	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
40	C₃×AGL(1,𝔽₇)	—	259	8	no	—
41	C₃×C₃₇	—	49	1	no	—
42	C₃₇⋊C₃	—	49	1	no	—
43	C₃₇⋊C₃	—	49	1	no	—
44	C₃₇⋊C₃	#64424	1	1	yes	characteristic, direct product factor
45	C₇⋊D₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃₇	—	49	1	no	Hall
47	C₃×ΓL(1,𝔽₈)	—	259	8	no	—
48	C₇²	C₂×C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
49	C₃×D₇	—	259	8	no	—
50	AGL(1,𝔽₇)	—	259	8	no	—
51	AGL(1,𝔽₇)	—	259	8	no	—
52	AGL(1,𝔽₇)	—	7	8	no	—
53	C₃₇	C₃×#64424	1	1	yes	characteristic, complemented, Sylow
54	C₃×C₇	—	37	8	no	—
55	ΓL(1,𝔽₈)	—	259	8	no	—
56	ΓL(1,𝔽₈)	—	259	8	no	—
57	ΓL(1,𝔽₈)	—	7	8	no	—
58	C₂×C₃²	—	1813	1	no	Hall
59	D₇	—	7	8	no	—
60	C₃²	—	1813	1	no	Sylow
61	C₇	AGL(1,𝔽₇)×C₃₇⋊C₃	1	8	yes	complemented
62	C₂×C₃	—	1813	1	no	—
63	C₂×C₃	—	1813	1	no	—
64	C₂×C₃	—	1813	1	no	—
65	C₂×C₃	—	49	1	no	—
66	C₃	—	1813	1	no	—
67	C₃	—	1813	1	no	—
68	C₃	—	37	1	no	—
69	C₃	—	49	1	no	—
70	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₃₇	C₂×C₃²
LCS	G ▷ C₇²×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃₇⋊C₃×#3861	C₂	semidirect
2. C₇⋊D₇×C₃₇⋊C₃	C₃	semidirect
3. #24925950	C₃	semidirect
4. #24925949	C₃	semidirect
5. C₃₇×#64424	C₃	semidirect
6. #19129589	C₂×C₃	semidirect
7. #19129588	C₂×C₃	semidirect
8. C₃₇×#3861	C₂×C₃	semidirect
9. C₇²×C₃₇⋊C₃	C₂×C₃	semidirect
11. C₃₇×C₇⋊D₇	C₃²	semidirect
13. C₇²×C₃₇	C₂×C₃²	semidirect
21. C₇×C₃₇⋊C₃	AGL(1,𝔽₇)	semidirect
30. #64424	C₃₇⋊C₃	direct (N × H)
31. C₇×C₃₇	C₃×AGL(1,𝔽₇)	semidirect
39. #3861	C₂×C₃₇⋊C₃	semidirect
44. C₃₇⋊C₃	#64424	direct (N × H)
45. C₇⋊D₇	C₃×C₃₇⋊C₃	semidirect
48. C₇²	C₂×C₃×C₃₇⋊C₃	semidirect
53. C₃₇	C₃×#64424	semidirect
61. C₇	AGL(1,𝔽₇)×C₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃₇⋊C₃×#3861	2
C₇⋊D₇×C₃₇⋊C₃	3
#24925950	3
#24925949	3
C₃₇×#64424	3
AGL(1,𝔽₇)×C₃₇⋊C₃	7
C₃×#64424	37

Subgroups — C37⋊C3×#64424 #45657458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇⋊C₃×#64424 #45657458