Subgroups — Dic₇×#11924776 #45691511

Order 33516.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#11924776	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₁₉×Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₇×#11924776	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×#11924776	—	7	1	no	maximal
6	Dic₇×#4294	—	7	1	no	maximal
7	C₇×C₁₉×Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₂×#11924776	D₇	1	1	yes	characteristic
10	C₂×C₇×#4294	—	7	1	no	—
11	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
12	Dic₇×C₇⋊C₉	—	19	1	no	maximal, Hall
13	C₃×C₄×C₇×C₁₉	—	7	1	no	—
14	C₃×C₁₉×Dic₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	#11924776	Dic₇	1	1	yes	characteristic, direct product factor
16	C₇×#4294	—	7	1	no	—
17	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₇⋊C₉	—	19	1	no	—
19	C₂×C₃×C₇×C₁₉	—	6	1	no	—
20	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
22	C₄×#4294	—	49	1	no	Hall
23	C₃×C₇×Dic₇	C₁₉⋊C₃	1	1	yes	characteristic
24	C₄×C₇×C₁₉	—	7	1	no	—
25	C₁₉×Dic₇	C₇⋊C₉	1	1	yes	characteristic, complemented
26	C₇×C₇⋊C₉	—	19	1	no	Hall
27	C₃×C₇×C₁₉	—	6	1	no	—
28	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic
30	C₂×#4294	—	7	1	no	—
31	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
32	C₂×C₇×C₁₉	—	6	1	no	—
33	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic
34	C₂×C₇×C₁₉	C₉×D₇	1	1	yes	characteristic
35	C₉×Dic₇	—	133	1	no	—
36	C₄×C₇⋊C₉	—	133	1	no	—
37	C₃×C₄×C₁₉	—	7	1	no	—
38	C₇×Dic₇	#4294	1	1	yes	characteristic, complemented, Hall
39	#4294	—	7	1	no	Hall
40	C₃×C₇²	C₄×C₁₉⋊C₃	1	1	yes	characteristic
41	C₇×C₁₉	—	6	1	no	—
42	C₇×C₁₉	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
43	C₇×C₁₉	C₉×Dic₇	1	1	yes	characteristic, complemented
44	C₂×C₇×C₉	—	133	1	no	—
45	C₂×C₇⋊C₉	—	19	1	no	—
46	C₂×C₃×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
47	C₂×C₇²	C₂×#4294	1	1	yes	characteristic
48	C₃×C₄×C₇	—	7	1	no	—
49	C₃×Dic₇	#87704	1	1	yes	characteristic
50	C₄×C₁₉	—	7	1	no	Hall
51	C₇×C₉	—	133	1	no	—
52	C₇⋊C₉	—	19	1	no	—
53	C₃×C₁₉	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic
54	C₇²	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₇	—	6	1	no	—
56	C₂×C₃×C₇	D₇×C₁₉⋊C₃	1	1	yes	characteristic
57	C₂×C₃×C₇	C₂×#87704	1	1	yes	characteristic
58	C₂×C₁₉	D₇×C₇⋊C₉	1	1	yes	characteristic
59	C₄×C₉	—	931	1	no	Hall
60	C₄×C₇	—	7	1	no	—
61	Dic₇	#11924776	1	1	yes	characteristic, direct product factor
62	C₃×C₇	—	6	1	no	—
63	C₃×C₇	Dic₇×C₁₉⋊C₃	1	1	yes	characteristic
64	C₃×C₇	C₄×#87704	1	1	yes	characteristic
65	C₁₉	Dic₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₉	—	133	1	no	—
67	C₂×C₇	—	6	1	no	—
68	C₂×C₇	D₇×#4294	1	1	yes	characteristic
69	C₂×C₇	C₂×#11924776	1	1	yes	characteristic
70	C₃×C₄	—	7	1	no	—
71	C₉	—	133	1	no	Sylow
72	C₇	—	6	1	no	—
73	C₇	Dic₇×#4294	1	1	yes	characteristic, complemented
74	C₇	C₄×#11924776	1	1	yes	characteristic, complemented
75	C₂×C₃	D₇×#87704	1	1	yes	characteristic
76	C₄	—	7	1	no	Sylow
77	C₃	Dic₇×#87704	1	1	yes	characteristic
78	C₂	D₇×#11924776	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₇×#87704
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₇×#11924776	C₄	semidirect
7. C₇×C₁₉×Dic₇	C₉	semidirect
15. #11924776	Dic₇	direct (N × H)
17. C₇²×C₁₉	C₄×C₉	semidirect
25. C₁₉×Dic₇	C₇⋊C₉	semidirect
38. C₇×Dic₇	#4294	semidirect
42. C₇×C₁₉	C₄×C₇⋊C₉	semidirect
43. C₇×C₁₉	C₉×Dic₇	semidirect
54. C₇²	C₄×#4294	semidirect
61. Dic₇	#11924776	direct (N × H)
65. C₁₉	Dic₇×C₇⋊C₉	semidirect
73. C₇	Dic₇×#4294	semidirect
74. C₇	C₄×#11924776	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#11924776	2
C₃×C₇×C₁₉×Dic₇	3
C₄×#11924776	7
Dic₇×#4294	7
Dic₇×C₇⋊C₉	19

Subgroups — Dic7×#11924776 #45691511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇×#11924776 #45691511