Subgroups — C₇⋊C₉×C₇⋊#261 #37524477

Order 22932.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₃×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₇⋊#261	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₉×C₇⋊#261	—	7	1	no	maximal
6	#261×C₇⋊C₉	—	7	1	no	maximal
7	C₇×C₇⋊#261	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
9	Dic₇×C₇⋊C₉	—	13	1	no	maximal, Hall
10	C₇×C₉×D₁₃	—	7	1	no	—
11	D₁₃×C₇⋊C₉	D₇	1	1	yes	characteristic
12	C₇²×D₁₃	C₂×C₉	1	1	yes	characteristic
13	C₃×C₇⋊#261	ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₇×#261	—	7	1	no	—
15	C₂×C₇×C₇⋊C₉	—	13	1	no	—
16	C₇×C₉×C₁₃	—	7	1	no	—
17	C₁₃×C₇⋊C₉	Dic₇	1	1	yes	characteristic, complemented
18	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×Dic₇	—	13	1	no	—
20	C₃×C₇×D₁₃	—	6	1	no	—
21	C₃×C₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₃×C₇×D₁₃	C₃×D₇	1	1	yes	characteristic
23	C₉×#261	—	49	1	no	Hall
24	C₇×C₇⋊C₉	#261	1	1	yes	characteristic, complemented, Hall
25	C₇⋊#261	C₇⋊C₉	1	1	yes	characteristic, direct product factor
26	C₇×#261	—	7	1	no	—
27	C₂×C₃×C₇²	—	13	1	no	—
28	C₃×C₇×C₁₃	—	6	1	no	—
29	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₃×C₇×C₁₃	C₃×Dic₇	1	1	yes	characteristic
31	C₉×Dic₇	—	91	1	no	—
32	C₄×C₇⋊C₉	—	91	1	no	—
33	C₉×D₁₃	—	7	1	no	—
34	C₇×Dic₇	—	13	1	no	Hall
35	C₇×D₁₃	—	6	1	no	—
36	C₇×D₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic
37	C₇×D₁₃	C₉×D₇	1	1	yes	characteristic
38	C₃×#261	—	7	1	no	—
39	C₃×C₇²	C₃×#261	1	1	yes	characteristic
40	C₂×C₇×C₉	—	91	1	no	—
41	C₂×C₇⋊C₉	—	13	1	no	—
42	C₉×C₁₃	—	7	1	no	Hall
43	C₂×C₇²	—	13	1	no	—
44	C₇×C₁₃	—	6	1	no	—
45	C₇×C₁₃	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
46	C₇×C₁₃	C₉×Dic₇	1	1	yes	characteristic, complemented
47	C₃×C₄×C₇	—	91	1	no	—
48	C₃×Dic₇	—	13	1	no	—
49	C₃×D₁₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
50	C₇×C₉	—	7	1	no	—
51	C₇⋊C₉	C₇⋊#261	1	1	yes	characteristic, direct product factor
52	#261	—	7	1	no	Hall
53	C₇²	C₉×#261	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃×C₇	—	13	1	no	—
55	C₂×C₃×C₇	—	13	1	no	—
56	C₂×C₃×C₇	—	78	1	no	—
57	C₃×C₁₃	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic
58	C₄×C₉	—	637	1	no	Hall
59	C₄×C₇	—	91	1	no	—
60	Dic₇	—	13	1	no	—
61	D₁₃	D₇×C₇⋊C₉	1	1	yes	characteristic
62	C₃×C₇	—	6	1	no	—
63	C₃×C₇	ΓL(1,𝔽₈)×#261	1	1	yes	characteristic
64	C₃×C₇	C₃×C₇⋊#261	1	1	yes	characteristic
65	C₂×C₉	—	91	1	no	—
66	C₂×C₇	—	13	1	no	—
67	C₂×C₇	—	13	1	no	—
68	C₂×C₇	—	78	1	no	—
69	C₁₃	Dic₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
70	C₃×C₄	—	91	1	no	—
71	C₉	—	7	1	no	Sylow
72	C₇	—	6	1	no	—
73	C₇	#261×C₇⋊C₉	1	1	yes	characteristic, complemented
74	C₇	C₉×C₇⋊#261	1	1	yes	characteristic, complemented
75	C₂×C₃	—	13	1	no	—
76	C₄	—	91	1	no	Sylow
77	C₃	ΓL(1,𝔽₈)×C₇⋊#261	1	1	yes	characteristic
78	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×C₇⋊#261
commutator, hypocenter	C₇²×C₁₃	C₄×C₉
Fitting, socle	C₃×C₇²×C₁₃	C₃×C₄
prime radical, cosocle	C₃×C₇²×D₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₃×C₇⋊C₉	C₄	semidirect
7. C₇×C₇⋊#261	C₉	semidirect
17. C₁₃×C₇⋊C₉	Dic₇	semidirect
18. C₇²×C₁₃	C₄×C₉	semidirect
24. C₇×C₇⋊C₉	#261	semidirect
25. C₇⋊#261	C₇⋊C₉	direct (N × H)
45. C₇×C₁₃	C₄×C₇⋊C₉	semidirect
46. C₇×C₁₃	C₉×Dic₇	semidirect
51. C₇⋊C₉	C₇⋊#261	direct (N × H)
53. C₇²	C₉×#261	semidirect
69. C₁₃	Dic₇×C₇⋊C₉	semidirect
73. C₇	#261×C₇⋊C₉	semidirect
74. C₇	C₉×C₇⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₃×C₇⋊C₉	2
C₃×C₇×C₇⋊#261	3
C₉×C₇⋊#261	7
#261×C₇⋊C₉	7
Dic₇×C₇⋊C₉	13

Subgroups — C7⋊C9×C7⋊#261 #37524477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊C₉×C₇⋊#261 #37524477