Subgroups — C₃⋊#21439685 #37525152

Order 22932.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#64424	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#14579331	C₃	1	1	yes	maximal, characteristic, complemented
3	#21439685	—	3	1	no	maximal
4	C₃×C₁₃×#3861	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₁₃×#64424	—	2	1	no	—
7	C₁₃×#64424	D₃	1	1	yes	characteristic
8	#14579331	—	3	1	no	Hall
9	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₃×#3861	—	2	1	no	—
11	C₁₃×#3861	Dic₃	1	1	yes	characteristic, complemented
12	C₃⋊(#5997⋊C₃)	—	13	1	no	maximal, Hall
13	C₃×C₁₃×AGL(1,𝔽₇)	—	14	1	no	—
14	C₃×C₁₃×AGL(1,𝔽₇)	—	14	3	no	—
15	C₁₃×C₇⋊D₇	C₃×D₃	1	1	yes	characteristic
16	C₃×#64424	D₁₃	1	1	yes	characteristic
17	C₃×C₁₃×ΓL(1,𝔽₈)	—	28	1	no	—
18	C₃×C₁₃×ΓL(1,𝔽₈)	—	28	3	no	—
19	C₇²×C₁₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃⋊#5997	—	13	1	no	—
21	#5997⋊C₃	—	39	1	no	—
22	C₃×C₁₃×D₇	—	14	1	no	—
23	C₃×C₁₃×D₇	—	14	3	no	—
24	C₁₃×AGL(1,𝔽₇)	—	14	1	no	—
25	C₁₃×AGL(1,𝔽₇)	—	14	3	no	—
26	C₁₃×AGL(1,𝔽₇)	—	14	2	no	—
27	C₁₃×AGL(1,𝔽₇)	—	14	6	no	—
28	C₃×Dic₃₉	—	49	1	no	maximal, Hall
29	C₃×#3861	Dic₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇⋊D₇	C₃×D₁₃	1	1	yes	characteristic
31	#64424	—	2	1	no	—
32	#64424	D₃₉	1	1	yes	characteristic
33	C₃×C₇×C₁₃	—	2	1	no	—
34	C₃×C₇×C₁₃	—	2	3	no	—
35	C₁₃×ΓL(1,𝔽₈)	—	28	2	no	—
36	C₁₃×ΓL(1,𝔽₈)	—	28	6	no	—
37	C₁₃×ΓL(1,𝔽₈)	—	28	1	no	—
38	C₁₃×ΓL(1,𝔽₈)	—	28	3	no	—
39	C₂×C₃²×C₁₃	—	49	1	no	—
40	#5997	—	39	1	no	Hall
41	C₁₃×D₇	—	14	1	no	—
42	C₁₃×D₇	—	14	3	no	—
43	Dic₃₉	—	49	1	no	—
44	C₃×Dic₁₃	—	147	1	no	—
45	C₃×C₇²	C₃×Dic₁₃	1	1	yes	characteristic, complemented
46	#3861	—	2	1	no	—
47	#3861	Dic₃₉	1	1	yes	characteristic, complemented
48	C₃×AGL(1,𝔽₇)	—	14	1	no	—
49	C₃×AGL(1,𝔽₇)	—	14	3	no	—
50	C₃²×C₁₃	—	196	1	no	Hall
51	C₇⋊D₇	C₃×D₃₉	1	1	yes	characteristic
52	C₇×C₁₃	—	2	1	no	—
53	C₇×C₁₃	—	2	3	no	—
54	C₂×C₃×C₁₃	—	49	1	no	—
55	C₂×C₃×C₁₃	—	49	1	no	—
56	C₂×C₃×C₁₃	—	98	1	no	—
57	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
58	C₃×ΓL(1,𝔽₈)	—	28	3	no	—
59	Dic₁₃	—	147	1	no	Hall
60	C₇²	C₃×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
61	C₃×D₇	—	14	1	no	—
62	C₃×D₇	—	14	3	no	—
63	AGL(1,𝔽₇)	—	14	1	no	—
64	AGL(1,𝔽₇)	—	14	3	no	—
65	AGL(1,𝔽₇)	—	14	2	no	—
66	AGL(1,𝔽₇)	—	14	6	no	—
67	C₃×C₁₃	—	196	1	no	—
68	C₃×C₁₃	—	196	1	no	—
69	C₃×C₁₃	#5997⋊C₃	1	1	yes	characteristic, complemented
70	C₃×Dic₃	—	637	1	no	Hall
71	C₂×C₁₃	—	49	1	no	—
72	C₃×C₇	—	2	1	no	—
73	C₃×C₇	—	2	3	no	—
74	ΓL(1,𝔽₈)	—	14	2	no	—
75	ΓL(1,𝔽₈)	—	28	6	no	—
76	ΓL(1,𝔽₈)	—	28	1	no	—
77	ΓL(1,𝔽₈)	—	28	3	no	—
78	C₂×C₃²	—	49	1	no	—
79	D₇	—	14	1	no	—
80	D₇	—	14	3	no	—
81	C₁₃	C₃⋊(#5997⋊C₃)	1	1	yes	characteristic, complemented, Sylow
82	C₃×C₄	—	1911	1	no	—
83	Dic₃	—	637	1	no	—
84	C₃²	—	196	1	no	Sylow
85	C₇	—	2	1	no	—
86	C₇	—	2	3	no	—
87	C₂×C₃	—	49	1	no	—
88	C₂×C₃	—	49	1	no	—
89	C₂×C₃	—	98	1	no	—
90	C₄	—	1911	1	no	Sylow
91	C₃	—	196	1	no	—
92	C₃	—	196	1	no	—
93	C₃	#21439685	1	1	yes	characteristic, complemented
94	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₁₃	C₃×C₄
prime radical	C₃×C₁₃×#64424	C₂
cosocle	C₃×C₁₃×C₇⋊D₇	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⋊#14579331	C₃	semidirect
4. C₃×C₁₃×#3861	C₄	semidirect
9. C₃×C₇²×C₁₃	C₃×C₄	semidirect
11. C₁₃×#3861	Dic₃	semidirect
19. C₇²×C₁₃	C₃×Dic₃	semidirect
29. C₃×#3861	Dic₁₃	semidirect
45. C₃×C₇²	C₃×Dic₁₃	semidirect
47. #3861	Dic₃₉	semidirect
60. C₇²	C₃×Dic₃₉	semidirect
69. C₃×C₁₃	#5997⋊C₃	semidirect
81. C₁₃	C₃⋊(#5997⋊C₃)	semidirect
93. C₃	#21439685	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×#64424	2
C₃⋊#14579331	3
#21439685	3
C₃⋊(#5997⋊C₃)	13
C₃×Dic₃₉	49

Subgroups — C3⋊#21439685 #37525152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#21439685 #37525152