Subgroups — C₂×ΓL(1,𝔽₈)⋊(D₄₃⋊C₃) #24925563

Order 10836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×ΓL(1,𝔽₈)×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×(C₄₃⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×ΓL(1,𝔽₈)⋊D₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#14268593	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×#14268594	C₃	1	1	yes	maximal, characteristic, complemented
7	ΓL(1,𝔽₈)×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744749	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×#11744748	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×ΓL(1,𝔽₈)×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₇×C₄₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
12	#14268594	C₂×C₃	1	2	yes	complemented
13	#14268593	C₂×C₃	1	2	yes	complemented
14	ΓL(1,𝔽₈)⋊D₄₃	C₂×C₃	1	2	yes	complemented
15	(C₄₃⋊C₃)⋊D₇	C₂×C₃	1	2	yes	complemented
16	C₂×C₃×D₄₃⋊C₃	—	7	1	no	maximal, Hall
17	C₂×D₃₀₁	C₃²	1	1	yes	characteristic, complemented, Hall
18	#11744749	C₂²×C₃	1	1	yes	characteristic, complemented
19	#11744748	C₂²×C₃	1	1	yes	characteristic, complemented
20	C₇×C₄₃⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₄₃⋊C₃	—	7	1	no	—
23	C₃×D₄₃⋊C₃	—	7	2	no	—
24	C₂×C₇×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented
25	D₃₀₁	C₂×C₃²	1	2	yes	complemented
26	C₂×C₃×D₄₃	—	7	1	no	—
27	C₂×D₄₃⋊C₃	—	7	1	no	—
28	C₂×D₄₃⋊C₃	—	7	1	no	—
29	C₂×D₄₃⋊C₃	—	7	1	no	—
30	C₃×C₄₃⋊C₃	—	7	1	no	Hall
31	C₇×C₄₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₄₃	—	7	1	no	—
33	C₃×D₄₃	—	7	2	no	—
34	C₂×C₄₃⋊C₃	—	7	1	no	—
35	C₂×C₄₃⋊C₃	—	7	1	no	—
36	C₂×C₄₃⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
37	D₄₃⋊C₃	—	7	2	no	—
38	D₄₃⋊C₃	—	7	2	no	—
39	D₄₃⋊C₃	—	7	2	no	—
40	C₂×C₃×AGL(1,𝔽₇)	—	43	1	no	maximal, Hall
41	C₂×D₄₃	—	7	1	no	Hall
42	C₃×C₄₃	—	7	1	no	—
43	C₄₃⋊C₃	—	7	1	no	—
44	C₄₃⋊C₃	—	7	1	no	—
45	C₄₃⋊C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
46	C₂×C₃×ΓL(1,𝔽₈)	—	43	1	no	—
47	C₃×AGL(1,𝔽₇)	—	43	2	no	—
48	C₂×C₄₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
49	D₄₃	—	7	2	no	—
50	C₂×C₃×D₇	—	43	1	no	—
51	C₂×AGL(1,𝔽₇)	—	43	1	no	—
52	C₂×AGL(1,𝔽₇)	—	43	1	no	—
53	C₂×AGL(1,𝔽₇)	—	43	1	no	—
54	C₃×ΓL(1,𝔽₈)	—	43	1	no	Hall
55	C₄₃	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	43	1	no	—
57	C₃×D₇	—	43	2	no	—
58	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
59	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
60	C₂×ΓL(1,𝔽₈)	D₄₃⋊C₃	1	1	yes	characteristic, complemented
61	AGL(1,𝔽₇)	—	43	2	no	—
62	AGL(1,𝔽₇)	—	43	2	no	—
63	AGL(1,𝔽₇)	—	43	2	no	—
64	C₂²×C₃²	—	301	1	no	Hall
65	C₂×D₇	—	43	1	no	Hall
66	C₃×C₇	—	43	1	no	—
67	ΓL(1,𝔽₈)	—	43	1	no	—
68	ΓL(1,𝔽₈)	—	43	1	no	—
69	ΓL(1,𝔽₈)	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented
70	C₂×C₃²	—	301	1	no	—
71	C₂×C₃²	—	301	2	no	—
72	C₂×C₇	C₃×D₄₃⋊C₃	1	1	yes	characteristic, complemented
73	D₇	—	43	2	no	—
74	C₂²×C₃	—	301	1	no	—
75	C₂²×C₃	—	301	1	no	—
76	C₂²×C₃	—	301	1	no	—
77	C₂²×C₃	—	301	1	no	—
78	C₃²	—	301	1	no	Sylow
79	C₇	C₂×C₃×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	7	1	no	—
81	C₂×C₃	—	43	1	no	—
82	C₂×C₃	—	301	2	no	—
83	C₂×C₃	—	301	2	no	—
84	C₂×C₃	—	301	2	no	—
85	C₂×C₃	—	301	2	no	—
86	C₂×C₃	—	301	1	no	—
87	C₂×C₃	—	301	1	no	—
88	C₂²	—	301	1	no	Sylow
89	C₃	—	7	1	no	—
90	C₃	—	43	1	no	—
91	C₃	—	301	1	no	—
92	C₃	—	301	1	no	—
93	C₂	—	301	2	no	—
94	C₂	ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₄₃	C₂×C₃²
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×ΓL(1,𝔽₈)×C₄₃⋊C₃	C₂	semidirect
2. ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)	C₂	direct (N × H)
3. C₂×(C₄₃⋊C₃)⋊D₇	C₃	semidirect
4. C₂×ΓL(1,𝔽₈)⋊D₄₃	C₃	semidirect
5. C₂×#14268593	C₃	semidirect
6. C₂×#14268594	C₃	semidirect
7. ΓL(1,𝔽₈)×C₄₃⋊C₃	C₂²	semidirect
8. C₂×#11744749	C₂×C₃	semidirect
9. C₂×#11744748	C₂×C₃	semidirect
10. C₂×ΓL(1,𝔽₈)×C₄₃	C₂×C₃	semidirect
11. C₂×C₇×C₄₃⋊C₃	C₂×C₃	semidirect
12. #14268594	C₂×C₃	semidirect
13. #14268593	C₂×C₃	semidirect
14. ΓL(1,𝔽₈)⋊D₄₃	C₂×C₃	semidirect
15. (C₄₃⋊C₃)⋊D₇	C₂×C₃	semidirect
17. C₂×D₃₀₁	C₃²	semidirect
18. #11744749	C₂²×C₃	semidirect
19. #11744748	C₂²×C₃	semidirect
20. C₇×C₄₃⋊C₃	C₂²×C₃	semidirect
21. ΓL(1,𝔽₈)×C₄₃	C₂²×C₃	semidirect
24. C₂×C₇×C₄₃	C₂×C₃²	semidirect
25. D₃₀₁	C₂×C₃²	semidirect
31. C₇×C₄₃	C₂²×C₃²	semidirect
36. C₂×C₄₃⋊C₃	AGL(1,𝔽₇)	semidirect
45. C₄₃⋊C₃	C₂×AGL(1,𝔽₇)	semidirect
48. C₂×C₄₃	C₃×AGL(1,𝔽₇)	semidirect
55. C₄₃	C₂×C₃×AGL(1,𝔽₇)	semidirect
60. C₂×ΓL(1,𝔽₈)	D₄₃⋊C₃	semidirect
69. ΓL(1,𝔽₈)	C₂×D₄₃⋊C₃	semidirect
72. C₂×C₇	C₃×D₄₃⋊C₃	semidirect
79. C₇	C₂×C₃×D₄₃⋊C₃	semidirect
94. C₂	ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)	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×ΓL(1,𝔽₈)×C₄₃⋊C₃	2
ΓL(1,𝔽₈)⋊(D₄₃⋊C₃)	2
C₂×(C₄₃⋊C₃)⋊D₇	3
C₂×ΓL(1,𝔽₈)⋊D₄₃	3
C₂×#14268593	3
C₂×#14268594	3
C₂×C₃×D₄₃⋊C₃	7
C₂×C₃×AGL(1,𝔽₇)	43

Subgroups — C2×ΓL(1,𝔽8)⋊(D43⋊C3) #24925563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×ΓL(1,𝔽₈)⋊(D₄₃⋊C₃) #24925563