Subgroups — C₃⋊#16838452 #26039655

Order 11466.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₉₁)	C₃	1	1	yes	maximal, characteristic, complemented
3	#16838452	—	3	1	no	maximal
4	C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊#3862	—	2	1	no	—
6	C₁₃⋊#3862	D₃	1	1	yes	characteristic, complemented
7	C₃⋊#10587722	—	7	1	no	maximal
8	C₃⋊#10587723	—	7	1	no	maximal
9	C₇⋊D₉₁	—	3	1	no	Hall
10	C₃⋊#64425	—	13	1	no	maximal, Hall
11	C₃×#63271	—	7	1	no	—
12	C₃×#63270	—	7	1	no	—
13	C₇²×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	D₂₇₃	—	7	1	no	—
15	D₂₇₃	—	7	1	no	—
16	D₂₇₃	—	21	2	no	—
17	#10587723	—	21	1	no	—
18	#10587722	—	21	1	no	—
19	C₃×#3862	—	13	1	no	Hall
20	C₃⋊(C₇⋊D₇)	—	13	1	no	—
21	#64425	—	39	1	no	—
22	C₃×C₇×C₁₃	—	3	2	no	—
23	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	#63271	—	7	1	no	—
26	#63271	—	14	1	no	—
27	#63270	—	7	1	no	—
28	#63270	—	14	1	no	—
29	C₃⋊(D₁₃⋊C₃)	—	49	1	no	Hall
30	D₉₁	—	21	1	no	—
31	D₉₁	—	21	1	no	—
32	D₉₁	—	63	2	no	—
33	C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
34	#3862	—	13	1	no	—
35	#3862	—	26	1	no	—
36	C₃⋊AGL(1,𝔽₇)	—	91	1	no	—
37	C₃⋊AGL(1,𝔽₇)	—	91	1	no	—
38	C₃×C₁₃⋊C₃	—	49	1	no	Hall
39	C₇⋊D₇	—	39	1	no	Hall
40	C₇×C₁₃	—	3	2	no	—
41	C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
43	D₃₉	—	49	1	no	—
44	D₁₃⋊C₃	—	147	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	91	1	no	—
46	C₃×ΓL(1,𝔽₈)	—	91	1	no	—
47	C₇²	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	D₂₁	—	273	2	no	—
49	D₂₁	—	91	1	no	—
50	D₂₁	—	91	1	no	—
51	AGL(1,𝔽₇)	—	273	1	no	—
52	AGL(1,𝔽₇)	—	273	1	no	—
53	C₃×C₁₃	#64425	1	1	yes	characteristic, complemented
54	C₁₃⋊C₃	—	49	1	no	—
55	C₁₃⋊C₃	—	98	1	no	—
56	D₁₃	—	147	1	no	Hall
57	C₃×C₇	—	3	2	no	—
58	C₃×C₇	#10587722	1	1	yes	characteristic, complemented
59	C₃×C₇	#10587723	1	1	yes	characteristic, complemented
60	ΓL(1,𝔽₈)	—	91	1	no	—
61	ΓL(1,𝔽₈)	—	91	1	no	—
62	ΓL(1,𝔽₈)	—	182	1	no	—
63	ΓL(1,𝔽₈)	—	182	1	no	—
64	C₃×D₃	—	637	1	no	Hall
65	D₇	—	273	1	no	—
66	D₇	—	273	1	no	—
67	D₇	—	819	2	no	—
68	C₁₃	C₃⋊#64425	1	1	yes	characteristic, complemented, Sylow
69	C₃²	—	637	1	no	Sylow
70	C₇	—	3	2	no	—
71	C₇	C₃⋊#10587723	1	1	yes	characteristic, complemented
72	C₇	C₃⋊#10587722	1	1	yes	characteristic, complemented
73	C₂×C₃	—	1911	1	no	—
74	D₃	—	637	1	no	—
75	C₃	—	637	1	no	—
76	C₃	—	1274	1	no	—
77	C₃	#16838452	1	1	yes	characteristic, complemented
78	C₂	—	1911	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₃	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
1. C₃×C₁₃⋊#3862	C₂	semidirect
2. C₃⋊(C₇⋊D₉₁)	C₃	semidirect
4. C₃×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃⋊#3862	D₃	semidirect
13. C₇²×C₁₃	C₃×D₃	semidirect
23. C₃×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
24. C₃×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
33. C₃×C₇²	D₁₃⋊C₃	semidirect
41. C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	semidirect
42. C₇×C₁₃	C₃⋊AGL(1,𝔽₇)	semidirect
47. C₇²	C₃⋊(D₁₃⋊C₃)	semidirect
53. C₃×C₁₃	#64425	semidirect
58. C₃×C₇	#10587722	semidirect
59. C₃×C₇	#10587723	semidirect
68. C₁₃	C₃⋊#64425	semidirect
71. C₇	C₃⋊#10587723	semidirect
72. C₇	C₃⋊#10587722	semidirect
77. C₃	#16838452	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃⋊#3862	2
C₃⋊(C₇⋊D₉₁)	3
#16838452	3
C₃⋊#10587722	7
C₃⋊#10587723	7
C₃⋊#64425	13

Subgroups — C3⋊#16838452 #26039655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#16838452 #26039655