Subgroups — C₃⋊#21439686 #37525141

Order 22932.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₃⋊C₃)⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#14579330	C₃	1	1	yes	maximal, characteristic, complemented
3	#21439686	—	3	1	no	maximal
4	C₃×C₇²×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇⋊D₉₁	C₂×C₃	1	1	yes	characteristic
6	(C₁₃⋊C₃)⋊(C₇⋊D₇)	—	2	1	no	—
7	(C₁₃⋊C₃)⋊(C₇⋊D₇)	D₃	1	1	yes	characteristic
8	#14579330	—	3	1	no	Hall
9	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
10	C₇²×C₁₃⋊C₃	—	2	1	no	—
11	C₇²×C₁₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₃⋊#5997	—	13	1	no	maximal, Hall
13	C₃×(C₁₃⋊C₃)⋊D₇	—	14	4	no	—
14	C₇⋊D₉₁	C₃×D₃	1	1	yes	characteristic
15	C₃²×C₇⋊D₇	—	13	1	no	—
16	C₃×C₇×C₁₃⋊C₃	—	2	4	no	—
17	C₇²×C₁₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₃⋊#5997	—	13	1	no	—
19	C₃×#5997	—	39	1	no	—
20	C₃×D₉₁	—	14	4	no	—
21	(C₁₃⋊C₃)⋊D₇	—	14	4	no	—
22	(C₁₃⋊C₃)⋊D₇	—	14	8	no	—
23	C₃⋊AGL(1,𝔽₁₃)	—	49	1	no	maximal, Hall
24	C₃²×C₇²	—	52	1	no	Hall
25	C₃×C₇⋊D₇	—	13	1	no	—
26	C₃×C₇⋊D₇	—	13	1	no	—
27	C₃×C₇⋊D₇	—	26	1	no	—
28	C₃×C₇×C₁₃	—	2	4	no	—
29	C₇×C₁₃⋊C₃	—	2	8	no	—
30	C₇×C₁₃⋊C₃	—	2	4	no	—
31	C₃×D₁₃⋊C₃	—	49	1	no	—
32	#5997	—	39	1	no	Hall
33	D₉₁	—	14	4	no	—
34	C₃⋊#261	—	49	1	no	—
35	AGL(1,𝔽₁₃)	—	147	1	no	—
36	C₃×C₇²	—	52	1	no	—
37	C₃×C₇²	—	52	1	no	—
38	C₃×C₇²	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
39	C₃²×D₇	—	182	4	no	—
40	C₃×C₁₃⋊C₃	#5997	1	1	yes	characteristic, complemented, Hall
41	C₇⋊D₇	—	13	1	no	—
42	C₇×C₁₃	—	2	4	no	—
43	C₃×D₁₃	—	49	1	no	—
44	D₁₃⋊C₃	—	49	1	no	—
45	D₁₃⋊C₃	—	98	1	no	—
46	C₃²×C₇	—	52	4	no	—
47	#261	—	147	1	no	Hall
48	C₇²	C₃⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
49	C₃×D₇	—	182	4	no	—
50	C₃×D₇	—	182	4	no	—
51	C₃×D₇	—	182	8	no	—
52	C₃×C₁₃	C₃×#5997	1	1	yes	characteristic, complemented
53	C₁₃⋊C₃	—	2	1	no	—
54	C₁₃⋊C₃	C₃⋊#5997	1	1	yes	characteristic, complemented
55	C₃×Dic₃	—	637	1	no	Hall
56	D₁₃	—	49	1	no	—
57	C₃×C₇	—	2	4	no	—
58	C₃×C₇	—	52	4	no	—
59	C₃×C₇	—	52	8	no	—
60	C₂×C₃²	—	637	1	no	—
61	D₇	—	182	4	no	—
62	C₁₃	C₃×C₃⋊#5997	1	1	yes	characteristic, complemented, Sylow
63	C₃×C₄	—	1911	1	no	—
64	Dic₃	—	637	1	no	—
65	C₃²	—	52	1	no	Sylow
66	C₇	—	2	4	no	—
67	C₂×C₃	—	637	1	no	—
68	C₂×C₃	—	637	1	no	—
69	C₂×C₃	—	1274	1	no	—
70	C₄	—	1911	1	no	Sylow
71	C₃	—	52	1	no	—
72	C₃	—	52	1	no	—
73	C₃	#21439686	1	1	yes	characteristic, complemented
74	C₂	—	637	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₁₃	C₃×C₄
prime radical	C₃×(C₁₃⋊C₃)⋊(C₇⋊D₇)	C₂
cosocle	C₃×C₇⋊D₉₁	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. C₃⋊#14579330	C₃	semidirect
4. C₃×C₇²×C₁₃⋊C₃	C₄	semidirect
9. C₃×C₇²×C₁₃	C₃×C₄	semidirect
11. C₇²×C₁₃⋊C₃	Dic₃	semidirect
17. C₇²×C₁₃	C₃×Dic₃	semidirect
38. C₃×C₇²	AGL(1,𝔽₁₃)	semidirect
40. C₃×C₁₃⋊C₃	#5997	semidirect
48. C₇²	C₃⋊AGL(1,𝔽₁₃)	semidirect
52. C₃×C₁₃	C₃×#5997	semidirect
54. C₁₃⋊C₃	C₃⋊#5997	semidirect
62. C₁₃	C₃×C₃⋊#5997	semidirect
73. C₃	#21439686	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₁₃⋊C₃)⋊(C₇⋊D₇)	2
C₃⋊#14579330	3
#21439686	3
C₃×C₃⋊#5997	13
C₃⋊AGL(1,𝔽₁₃)	49

Subgroups — C3⋊#21439686 #37525141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#21439686 #37525141