Subgroups — A₄×C₁₃×#3862 #37525423

Order 22932.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#3862	C₃	1	1	yes	maximal, characteristic, complemented
2	C₇²×A₄×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₂²⋊#3862	C₃	1	2	yes	maximal, complemented
4	C₃×C₁₃×#3862	—	4	1	no	maximal, Hall
5	C₂×C₁₃×#3862	—	3	1	no	—
6	A₄×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	maximal
7	C₂²×C₇²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	—	4	1	no	—
9	C₁₃×#3862	—	4	2	no	—
10	C₁₃×#3862	A₄	1	1	yes	characteristic, direct product factor
11	A₄×#3862	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₇²×C₁₃	—	3	1	no	—
13	C₁₃×C₂²⋊ΓL(1,𝔽₈)	—	7	4	no	—
14	C₇×A₄×C₁₃	—	3	2	no	—
15	C₇×A₄×C₁₃	ΓL(1,𝔽₈)	1	2	yes	complemented
16	C₂²×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
17	C₃×C₁₃×ΓL(1,𝔽₈)	—	28	2	no	—
18	C₇²×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
19	C₂²⋊#3862	C₃×C₁₃	1	2	yes	complemented
20	C₇²×A₄	C₃×C₁₃	1	1	yes	characteristic, complemented
21	C₂²×#3862	C₃×C₁₃	1	1	yes	characteristic, complemented
22	C₂×C₁₃×ΓL(1,𝔽₈)	—	21	2	no	—
23	C₃×A₄×C₁₃	—	49	1	no	Hall
24	C₃×#3862	—	4	1	no	Hall
25	C₂²×C₇×C₁₃	—	3	2	no	—
26	C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
27	C₂×#3862	—	3	1	no	—
28	C₃×C₇×C₁₃	—	4	2	no	—
29	C₃×C₇×C₁₃	—	12	2	no	—
30	C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
31	C₁₃×ΓL(1,𝔽₈)	—	28	4	no	—
32	A₄×ΓL(1,𝔽₈)	—	7	2	no	—
33	C₂²×C₇²	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₇×C₁₃	—	3	2	no	—
35	C₂×C₇×C₁₃	—	9	2	no	—
36	C₂²×C₃×C₁₃	—	49	1	no	—
37	A₄×C₁₃	—	49	2	no	—
38	A₄×C₁₃	#3862	1	1	yes	characteristic, direct product factor
39	C₃×C₇²	—	4	1	no	—
40	#3862	—	4	2	no	—
41	#3862	A₄×C₁₃	1	1	yes	characteristic, direct product factor
42	C₃²×C₁₃	—	196	1	no	Hall
43	C₂×C₇²	—	3	1	no	—
44	C₇×C₁₃	—	3	2	no	—
45	C₇×C₁₃	A₄×ΓL(1,𝔽₈)	1	2	yes	complemented
46	C₂²⋊ΓL(1,𝔽₈)	—	7	4	no	—
47	C₇×A₄	—	3	2	no	—
48	C₇×A₄	C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
49	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
50	C₂×C₃×C₁₃	—	147	1	no	—
51	C₃×ΓL(1,𝔽₈)	—	28	2	no	—
52	C₂²×C₁₃	C₃×#3862	1	1	yes	characteristic, complemented, Hall
53	C₇²	C₃×A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×ΓL(1,𝔽₈)	—	21	2	no	—
55	C₃×C₁₃	—	4	1	no	—
56	C₃×C₁₃	—	49	1	no	—
57	C₃×C₁₃	—	196	2	no	—
58	C₃×A₄	—	49	1	no	Hall
59	C₂²×C₇	—	3	2	no	—
60	C₂²×C₇	C₃×C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
61	C₂×C₁₃	—	3	1	no	—
62	C₃×C₇	—	4	2	no	—
63	C₃×C₇	—	12	2	no	—
64	ΓL(1,𝔽₈)	—	7	2	no	—
65	ΓL(1,𝔽₈)	—	28	4	no	—
66	C₂×C₇	—	3	2	no	—
67	C₂×C₇	—	9	2	no	—
68	C₁₃	A₄×#3862	1	1	yes	characteristic, direct product factor, Sylow
69	C₂²×C₃	—	49	1	no	—
70	A₄	—	49	2	no	—
71	A₄	C₁₃×#3862	1	1	yes	characteristic, direct product factor
72	C₃²	—	196	1	no	Sylow
73	C₇	—	3	2	no	—
74	C₇	A₄×C₁₃×ΓL(1,𝔽₈)	1	2	yes	complemented
75	C₂×C₃	—	147	1	no	—
76	C₂²	C₃×C₁₃×#3862	1	1	yes	characteristic, complemented, Sylow
77	C₃	—	4	1	no	—
78	C₃	—	49	1	no	—
79	C₃	—	196	2	no	—
80	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	A₄×#3862
commutator, cosocle, hypocenter	C₂²×C₇²	C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₃	C₃²
LCS	G ▷ C₂²×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#3862	C₃	semidirect
2. C₇²×A₄×C₁₃	C₃	semidirect
3. C₁₃×C₂²⋊#3862	C₃	semidirect
7. C₂²×C₇²×C₁₃	C₃²	semidirect
10. C₁₃×#3862	A₄	direct (N × H)
11. A₄×#3862	C₁₃	direct (N × H)
15. C₇×A₄×C₁₃	ΓL(1,𝔽₈)	semidirect
18. C₇²×C₁₃	C₃×A₄	semidirect
19. C₂²⋊#3862	C₃×C₁₃	semidirect
20. C₇²×A₄	C₃×C₁₃	semidirect
21. C₂²×#3862	C₃×C₁₃	semidirect
26. C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	semidirect
33. C₂²×C₇²	C₃²×C₁₃	semidirect
38. A₄×C₁₃	#3862	direct (N × H)
41. #3862	A₄×C₁₃	direct (N × H)
45. C₇×C₁₃	A₄×ΓL(1,𝔽₈)	semidirect
48. C₇×A₄	C₁₃×ΓL(1,𝔽₈)	semidirect
52. C₂²×C₁₃	C₃×#3862	semidirect
53. C₇²	C₃×A₄×C₁₃	semidirect
60. C₂²×C₇	C₃×C₁₃×ΓL(1,𝔽₈)	semidirect
68. C₁₃	A₄×#3862	direct (N × H)
71. A₄	C₁₃×#3862	direct (N × H)
74. C₇	A₄×C₁₃×ΓL(1,𝔽₈)	semidirect
76. C₂²	C₃×C₁₃×#3862	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#3862	3
C₇²×A₄×C₁₃	3
C₁₃×C₂²⋊#3862	3
C₃×C₁₃×#3862	4
A₄×C₁₃×ΓL(1,𝔽₈)	7
A₄×#3862	13

Subgroups — A4×C13×#3862 #37525423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×C₁₃×#3862 #37525423