Subgroups — C₁₃⋊C₃×C₂²⋊#3862 #37525422

Order 22932.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₂²⋊#3862	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₁₃⋊#3862)	C₃	1	2	yes	maximal, complemented
4	C₁₃⋊C₃×#3862	—	4	1	no	maximal, Hall
5	C₂×C₇²×C₁₃⋊C₃	—	3	1	no	—
6	C₁₃⋊C₃×C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	maximal
7	C₂²×C₇²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₁₃⋊#3862	—	4	2	no	—
9	C₁₃×#3862	—	4	1	no	—
10	C₇²×C₁₃⋊C₃	A₄	1	1	yes	characteristic, complemented
11	C₃×C₂²⋊#3862	—	13	1	no	maximal, Hall
12	C₂×C₇²×C₁₃	—	3	1	no	—
13	C₂²⋊#63270	—	7	2	no	—
14	C₂²⋊#63271	—	7	2	no	—
15	C₁₃×C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	—
16	C₂²×C₇×C₁₃⋊C₃	—	3	2	no	—
17	C₂²×C₇×C₁₃⋊C₃	ΓL(1,𝔽₈)	1	2	yes	complemented
18	ΓL(1,𝔽₈)×C₁₃⋊C₃	—	28	2	no	—
19	C₇²×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₇²	—	13	1	no	—
21	C₂²⋊#3862	—	13	2	no	—
22	C₂²⋊#3862	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₂×C₇×C₁₃⋊C₃	—	3	6	no	—
24	C₂×C₇×C₁₃⋊C₃	—	3	2	no	—
25	A₄×C₁₃⋊C₃	—	49	1	no	Hall
26	C₃×#3862	—	52	1	no	Hall
27	C₂²×C₇×C₁₃	—	3	2	no	—
28	C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
29	C₂×C₃×C₇²	—	39	1	no	—
30	#63271	—	28	2	no	—
31	#63270	—	28	2	no	—
32	C₇×C₁₃⋊C₃	—	3	2	no	—
33	C₇×C₁₃⋊C₃	C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
34	C₁₃×ΓL(1,𝔽₈)	—	28	2	no	—
35	C₃×C₂²⋊ΓL(1,𝔽₈)	—	91	2	no	—
36	C₂²×C₇²	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	3	6	no	—
38	C₂×C₇×C₁₃	—	3	2	no	—
39	C₂²⋊(C₁₃⋊C₃)	—	49	2	no	—
40	A₄×C₁₃	—	49	1	no	—
41	C₂²×C₁₃⋊C₃	#3862	1	1	yes	characteristic, complemented
42	C₃×C₇²	—	13	1	no	—
43	#3862	—	4	1	no	—
44	#3862	—	52	2	no	—
45	C₃×C₁₃⋊C₃	—	196	1	no	Hall
46	C₂×C₇²	—	3	1	no	—
47	C₇×C₁₃	—	3	2	no	—
48	C₇×C₁₃	C₃×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
49	C₂²×C₃×C₇	—	13	2	no	—
50	C₂²×C₃×C₇	—	39	2	no	—
51	C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	—
52	C₂²⋊ΓL(1,𝔽₈)	—	91	2	no	—
53	C₂²⋊ΓL(1,𝔽₈)	—	91	2	no	—
54	C₂×C₁₃⋊C₃	—	3	1	no	—
55	C₃×ΓL(1,𝔽₈)	—	364	2	no	—
56	C₂²×C₁₃	C₃×#3862	1	1	yes	characteristic, complemented, Hall
57	C₇²	A₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	39	2	no	—
59	C₂×C₃×C₇	—	39	6	no	—
60	C₃×C₁₃	—	196	1	no	—
61	C₁₃⋊C₃	—	196	2	no	—
62	C₁₃⋊C₃	C₂²⋊#3862	1	1	yes	characteristic, direct product factor
63	C₃×A₄	—	637	1	no	Hall
64	C₂²×C₇	—	3	2	no	—
65	C₂²×C₇	ΓL(1,𝔽₈)×C₁₃⋊C₃	1	2	yes	complemented
66	C₂×C₁₃	—	3	1	no	—
67	C₃×C₇	—	13	2	no	—
68	C₃×C₇	—	39	2	no	—
69	ΓL(1,𝔽₈)	—	28	2	no	—
70	ΓL(1,𝔽₈)	—	364	2	no	—
71	ΓL(1,𝔽₈)	—	364	2	no	—
72	C₂×C₇	—	3	6	no	—
73	C₂×C₇	—	3	2	no	—
74	C₁₃	C₃×C₂²⋊#3862	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₃	—	13	1	no	—
76	A₄	—	49	1	no	—
77	A₄	—	637	2	no	—
78	C₃²	—	2548	1	no	Sylow
79	C₇	—	3	2	no	—
80	C₇	C₁₃⋊C₃×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
81	C₂×C₃	—	39	1	no	—
82	C₂²	C₁₃⋊C₃×#3862	1	1	yes	characteristic, complemented, Sylow
83	C₃	—	13	1	no	—
84	C₃	—	196	1	no	—
85	C₃	—	2548	2	no	—
86	C₂	—	3	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇²×C₁₃⋊C₃	C₃	semidirect
2. C₁₃×C₂²⋊#3862	C₃	semidirect
3. C₂²⋊(C₁₃⋊#3862)	C₃	semidirect
7. C₂²×C₇²×C₁₃	C₃²	semidirect
10. C₇²×C₁₃⋊C₃	A₄	semidirect
17. C₂²×C₇×C₁₃⋊C₃	ΓL(1,𝔽₈)	semidirect
19. C₇²×C₁₃	C₃×A₄	semidirect
22. C₂²⋊#3862	C₁₃⋊C₃	direct (N × H)
28. C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	semidirect
33. C₇×C₁₃⋊C₃	C₂²⋊ΓL(1,𝔽₈)	semidirect
36. C₂²×C₇²	C₃×C₁₃⋊C₃	semidirect
41. C₂²×C₁₃⋊C₃	#3862	semidirect
48. C₇×C₁₃	C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
56. C₂²×C₁₃	C₃×#3862	semidirect
57. C₇²	A₄×C₁₃⋊C₃	semidirect
62. C₁₃⋊C₃	C₂²⋊#3862	direct (N × H)
65. C₂²×C₇	ΓL(1,𝔽₈)×C₁₃⋊C₃	semidirect
74. C₁₃	C₃×C₂²⋊#3862	semidirect
80. C₇	C₁₃⋊C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
82. C₂²	C₁₃⋊C₃×#3862	semidirect

Maximal subgroups

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

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

Subgroups — C13⋊C3×C22⋊#3862 #37525422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×C₂²⋊#3862 #37525422