Subgroups — C₃×#21439683 #37525039

Order 22932.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16838448	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#5997	C₃	1	1	yes	maximal, characteristic, complemented
3	#21439683	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14274263	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	#16838448	C₂×C₃	1	3	yes	—
7	C₁₃×#5997	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
9	#14274263	C₃×C₄	1	3	yes	complemented
10	C₃×#5997⋊C₃	—	13	1	no	maximal, Hall
11	C₃×#10587720	—	14	1	no	—
12	C₃×#10587720	—	14	3	no	—
13	C₁₃×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
14	C₃×#64424	—	13	1	no	—
15	C₃×#63270	—	14	1	no	—
16	C₃×#63270	—	14	3	no	—
17	C₇²×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
18	C₃×#5997	C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	#5997⋊C₃	—	13	3	no	—
20	C₃×C₁₃×D₇	—	14	1	no	—
21	C₃×C₁₃×D₇	—	42	3	no	—
22	#10587720	—	14	3	no	—
23	#10587720	—	14	9	no	—
24	C₃×C₄×C₁₃⋊C₃	—	49	1	no	maximal, Hall
25	C₃×#3861	—	13	1	no	Hall
26	C₃×C₇⋊D₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
27	#64424	—	13	3	no	—
28	C₃×C₇×C₁₃	—	2	1	no	—
29	C₃×C₇×C₁₃	—	2	3	no	—
30	#63270	—	14	3	no	—
31	#63270	—	14	9	no	—
32	C₂×C₃×C₁₃⋊C₃	—	49	1	no	—
33	#5997	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₁₃×D₇	—	14	1	no	—
35	C₁₃×D₇	—	42	3	no	—
36	C₃×C₄×C₁₃	—	147	1	no	—
37	C₄×C₁₃⋊C₃	—	49	3	no	—
38	C₃×C₇²	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
39	#3861	—	13	3	no	—
40	C₃×AGL(1,𝔽₇)	—	182	1	no	—
41	C₃×AGL(1,𝔽₇)	—	182	3	no	—
42	C₃×C₁₃⋊C₃	—	49	1	no	Hall
43	C₇⋊D₇	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic
44	C₇×C₁₃	—	2	1	no	—
45	C₇×C₁₃	—	2	3	no	—
46	C₂×C₃×C₁₃	—	147	1	no	—
47	C₂×C₁₃⋊C₃	—	49	3	no	—
48	C₃×ΓL(1,𝔽₈)	—	182	1	no	—
49	C₃×ΓL(1,𝔽₈)	—	182	3	no	—
50	C₄×C₁₃	—	147	1	no	Hall
51	C₇²	C₃×C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
52	C₃×D₇	—	42	1	no	—
53	C₃×D₇	—	42	3	no	—
54	AGL(1,𝔽₇)	—	182	3	no	—
55	AGL(1,𝔽₇)	—	182	9	no	—
56	C₃×C₁₃	#5997⋊C₃	1	1	yes	characteristic, complemented
57	C₁₃⋊C₃	—	49	3	no	—
58	C₃²×C₄	—	637	1	no	Hall
59	C₂×C₁₃	—	147	1	no	—
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	—	2	3	no	—
62	ΓL(1,𝔽₈)	—	182	3	no	—
63	ΓL(1,𝔽₈)	—	182	9	no	—
64	C₂×C₃²	—	637	1	no	—
65	D₇	—	42	1	no	—
66	D₇	—	42	3	no	—
67	C₁₃	C₃×#5997⋊C₃	1	1	yes	characteristic, complemented, Sylow
68	C₃×C₄	—	637	3	no	—
69	C₃×C₄	—	147	1	no	—
70	C₃²	—	637	1	no	Sylow
71	C₇	—	2	1	no	—
72	C₇	—	2	3	no	—
73	C₂×C₃	—	49	1	no	—
74	C₂×C₃	—	637	3	no	—
75	C₄	—	147	1	no	Sylow
76	C₃	—	637	3	no	—
77	C₃	#21439683	1	1	yes	characteristic, direct product factor
78	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#21439683
commutator, hypocenter	C₇²×C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₃×C₄
prime radical	C₃×#16838448	C₂
cosocle	C₁₃×C₇⋊D₇	C₂×C₃²
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×#5997	C₃	semidirect
3. #21439683	C₃	direct (N × H)
4. C₃×#14274263	C₄	semidirect
7. C₁₃×#5997	C₃²	semidirect
8. C₃×C₇²×C₁₃	C₃×C₄	semidirect
9. #14274263	C₃×C₄	semidirect
17. C₇²×C₁₃	C₃²×C₄	semidirect
18. C₃×#5997	C₁₃⋊C₃	semidirect
33. #5997	C₃×C₁₃⋊C₃	semidirect
38. C₃×C₇²	C₄×C₁₃⋊C₃	semidirect
51. C₇²	C₃×C₄×C₁₃⋊C₃	semidirect
56. C₃×C₁₃	#5997⋊C₃	semidirect
67. C₁₃	C₃×#5997⋊C₃	semidirect
77. C₃	#21439683	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16838448	2
C₃×C₁₃×#5997	3
#21439683	3
C₃×#5997⋊C₃	13
C₃×C₄×C₁₃⋊C₃	49

Subgroups — C3×#21439683 #37525039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21439683 #37525039