Subgroups — #3861×C₃⋊#261 #37525261

Order 22932.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×#3861	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₃⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	#261×#3861	—	3	1	no	maximal
4	C₃×C₁₃×#3861	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×D₁₃	C₂×C₃	1	1	yes	characteristic
6	D₁₃×#3861	—	2	1	no	—
7	D₁₃×#3861	D₃	1	1	yes	characteristic
8	ΓL(1,𝔽₈)×C₃⋊#261	—	7	8	no	maximal
9	C₇²×#261	—	3	1	no	Hall
10	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
11	C₁₃×#3861	—	2	1	no	—
12	C₁₃×#3861	Dic₃	1	1	yes	characteristic, complemented
13	Dic₃×#3861	—	13	1	no	maximal, Hall
14	C₃×ΓL(1,𝔽₈)×D₁₃	—	7	8	no	—
15	C₇²×D₁₃	C₃×D₃	1	1	yes	characteristic
16	C₇×C₃⋊#261	ΓL(1,𝔽₈)	1	8	yes	complemented
17	ΓL(1,𝔽₈)×#261	—	21	8	no	—
18	C₂×C₃×#3861	—	13	1	no	—
19	C₃×C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
20	C₇²×C₁₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
21	C₇²×Dic₃	—	13	1	no	—
22	C₄×#3861	—	39	1	no	—
23	C₃×C₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
24	ΓL(1,𝔽₈)×D₁₃	—	7	8	no	—
25	ΓL(1,𝔽₈)×D₁₃	—	14	8	no	—
26	C₃×C₃⋊#261	—	49	1	no	Hall
27	C₃×#3861	#261	1	1	yes	characteristic, complemented, Hall
28	C₇×#261	—	3	8	no	—
29	C₂×C₃×C₇²	—	13	1	no	—
30	C₂×#3861	—	13	1	no	—
31	C₂×#3861	—	26	1	no	—
32	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
33	C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
34	C₁₃×ΓL(1,𝔽₈)	—	14	8	no	—
35	Dic₃×ΓL(1,𝔽₈)	—	91	8	no	—
36	C₃²×D₁₃	—	49	1	no	—
37	C₄×C₇²	—	39	1	no	Hall
38	C₇×D₁₃	D₃×ΓL(1,𝔽₈)	1	8	yes	—
39	C₃⋊#261	#3861	1	1	yes	characteristic, direct product factor
40	C₃×#261	—	147	1	no	—
41	C₃×C₇²	C₃×#261	1	1	yes	characteristic, complemented
42	#3861	—	2	1	no	—
43	#3861	C₃⋊#261	1	1	yes	characteristic, direct product factor
44	C₂×C₃×ΓL(1,𝔽₈)	—	91	8	no	—
45	C₃²×C₁₃	—	49	1	no	Hall
46	C₂×C₇²	—	13	1	no	—
47	C₇×C₁₃	Dic₃×ΓL(1,𝔽₈)	1	8	yes	complemented
48	C₇×Dic₃	—	13	8	no	—
49	C₄×ΓL(1,𝔽₈)	—	273	8	no	—
50	C₃×D₁₃	—	49	1	no	—
51	C₃×D₁₃	—	98	1	no	—
52	C₃×D₁₃	C₂×#3861	1	1	yes	characteristic
53	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
54	#261	—	3	1	no	Hall
55	C₇²	C₃×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃×C₇	—	13	8	no	—
57	C₂×ΓL(1,𝔽₈)	—	91	8	no	—
58	C₂×ΓL(1,𝔽₈)	—	182	8	no	—
59	C₃×C₁₃	—	49	1	no	—
60	C₃×C₁₃	—	98	1	no	—
61	C₃×C₁₃	C₄×#3861	1	1	yes	characteristic, complemented
62	C₃×Dic₃	—	637	1	no	Hall
63	C₄×C₇	—	39	8	no	—
64	D₁₃	D₃×#3861	1	1	yes	characteristic
65	C₃×C₇	ΓL(1,𝔽₈)×#261	1	8	yes	complemented
66	ΓL(1,𝔽₈)	—	7	8	no	—
67	ΓL(1,𝔽₈)	—	14	8	no	—
68	C₂×C₃²	—	637	1	no	—
69	C₂×C₇	—	13	8	no	—
70	C₁₃	Dic₃×#3861	1	1	yes	characteristic, complemented, Sylow
71	C₃×C₄	—	1911	1	no	—
72	Dic₃	—	13	1	no	—
73	C₃²	—	49	1	no	Sylow
74	C₇	ΓL(1,𝔽₈)×C₃⋊#261	1	8	yes	complemented
75	C₂×C₃	—	13	1	no	—
76	C₂×C₃	—	637	1	no	—
77	C₂×C₃	—	1274	1	no	—
78	C₄	—	39	1	no	Sylow
79	C₃	—	49	1	no	—
80	C₃	—	98	1	no	—
81	C₃	#261×#3861	1	1	yes	characteristic, complemented
82	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₁₃	C₃×C₄
prime radical	C₃×D₁₃×#3861	C₂
cosocle	C₃×C₇²×D₁₃	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₇²×C₃⋊#261	C₃	semidirect
4. C₃×C₁₃×#3861	C₄	semidirect
10. C₃×C₇²×C₁₃	C₃×C₄	semidirect
12. C₁₃×#3861	Dic₃	semidirect
16. C₇×C₃⋊#261	ΓL(1,𝔽₈)	semidirect
20. C₇²×C₁₃	C₃×Dic₃	semidirect
27. C₃×#3861	#261	semidirect
32. C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	semidirect
39. C₃⋊#261	#3861	direct (N × H)
41. C₃×C₇²	C₃×#261	semidirect
43. #3861	C₃⋊#261	direct (N × H)
47. C₇×C₁₃	Dic₃×ΓL(1,𝔽₈)	semidirect
55. C₇²	C₃×C₃⋊#261	semidirect
61. C₃×C₁₃	C₄×#3861	semidirect
65. C₃×C₇	ΓL(1,𝔽₈)×#261	semidirect
70. C₁₃	Dic₃×#3861	semidirect
74. C₇	ΓL(1,𝔽₈)×C₃⋊#261	semidirect
81. C₃	#261×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₃×#3861	2
C₇²×C₃⋊#261	3
#261×#3861	3
ΓL(1,𝔽₈)×C₃⋊#261	7
Dic₃×#3861	13

Subgroups — #3861×C3⋊#261 #37525261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3861×C₃⋊#261 #37525261