Subgroups — C₁₇×D₉×C₇⋊D₇ #44472602

Order 29988.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₇⋊D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₁₇×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₇×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₇×C₇⋊D₇	—	3	1	no	maximal
5	C₇²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₃⋊(C₇⋊D₇)	—	3	1	no	—
7	D₃×C₇²×C₁₇	—	3	1	no	—
8	C₃×C₁₇×C₇⋊D₇	D₃	1	1	yes	characteristic
9	D₇×C₁₇×D₉	—	7	8	no	maximal
10	C₂×C₁₇×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₇	C₂×D₃	1	1	yes	characteristic
12	C₁₇×D₆₃	—	7	8	no	—
13	C₇×C₁₇×D₉	D₇	1	8	yes	complemented
14	C₉×D₇×C₁₇	—	7	8	no	—
15	D₉×C₇⋊D₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₇²×C₁₇	—	9	1	no	—
17	C₁₇×C₇⋊D₇	—	9	1	no	—
18	C₁₇×C₇⋊D₇	D₉	1	1	yes	characteristic, direct product factor
19	D₃×D₇×C₁₇	—	21	8	no	—
20	C₇×C₉×C₁₇	C₂×D₇	1	8	yes	complemented
21	C₇⋊D₆₃	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₇²×D₉	C₂×C₁₇	1	1	yes	characteristic, complemented
23	C₉×C₇⋊D₇	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₇²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
25	C₁₇×D₂₁	—	21	8	no	—
26	D₃×C₇×C₁₇	—	3	8	no	—
27	C₃×D₇×C₁₇	—	7	8	no	—
28	C₂×C₁₇×D₉	—	49	1	no	Hall
29	D₃×C₇⋊D₇	—	3	1	no	—
30	C₂×D₇×C₁₇	—	63	8	no	—
31	C₇²×C₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₇	D₃×D₇	1	8	yes	—
33	C₂×C₉×C₁₇	—	49	1	no	—
34	C₁₇×D₉	—	49	1	no	—
35	C₁₇×D₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor
36	C₃⋊(C₇⋊D₇)	—	3	1	no	—
37	D₃×C₇²	—	3	1	no	—
38	C₃×C₇⋊D₇	D₃×C₁₇	1	1	yes	characteristic
39	D₇×D₉	—	7	8	no	—
40	C₂×C₇×C₁₇	—	9	8	no	—
41	D₇×C₁₇	—	7	8	no	—
42	D₇×C₁₇	—	63	8	no	—
43	C₂×D₃×C₁₇	—	147	1	no	—
44	C₂×C₇⋊D₇	—	9	1	no	Hall
45	C₉×C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₇²	C₂×D₃×C₁₇	1	1	yes	characteristic
47	D₆₃	—	7	8	no	—
48	C₉×D₇	—	7	8	no	—
49	C₇×D₉	D₇×C₁₇	1	8	yes	complemented
50	C₇×C₁₇	D₇×D₉	1	8	yes	complemented
51	C₂×C₃×C₁₇	—	49	1	no	—
52	D₃×C₁₇	—	3	1	no	—
53	D₃×C₁₇	—	147	1	no	—
54	C₂×C₇²	—	9	1	no	—
55	C₇⋊D₇	—	9	1	no	—
56	C₇⋊D₇	C₁₇×D₉	1	1	yes	characteristic, direct product factor
57	D₃×D₇	—	21	8	no	—
58	C₂²×C₁₇	—	441	1	no	Hall
59	C₇×C₉	C₂×D₇×C₁₇	1	8	yes	complemented
60	C₃×C₁₇	D₃×C₇⋊D₇	1	1	yes	characteristic
61	C₇²	C₂×C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	21	8	no	—
63	C₃×D₇	—	7	8	no	—
64	D₃×C₇	—	3	8	no	—
65	C₂×D₉	—	49	1	no	Hall
66	C₂×C₁₇	—	9	1	no	—
67	C₂×C₁₇	—	49	1	no	—
68	C₂×C₁₇	—	441	1	no	—
69	C₂×D₇	—	63	8	no	—
70	C₃×C₇	D₃×D₇×C₁₇	1	8	yes	—
71	C₂×C₉	—	49	1	no	—
72	D₉	—	49	1	no	—
73	D₉	C₁₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor
74	C₁₇	D₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
75	C₂×C₇	—	9	8	no	—
76	D₇	—	7	8	no	—
77	D₇	—	63	8	no	—
78	C₂×D₃	—	147	1	no	—
79	C₉	C₂×C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₇×C₁₇×D₉	1	8	yes	complemented
81	C₂×C₃	—	49	1	no	—
82	D₃	—	3	1	no	—
83	D₃	—	147	1	no	—
84	C₂²	—	441	1	no	Sylow
85	C₃	D₃×C₁₇×C₇⋊D₇	1	1	yes	characteristic
86	C₂	—	9	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	441	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₉×C₇⋊D₇
commutator, cosocle, hypocenter	C₇²×C₉	C₂²×C₁₇
Frattini	C₃	D₃×C₁₇×C₇⋊D₇
Fitting	C₇²×C₉×C₁₇	C₂²
socle	C₃×C₇²×C₁₇	C₂×D₃
LCS	G ▷ C₇²×C₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₇⋊D₆₃	C₂	semidirect
2. C₇²×C₁₇×D₉	C₂	semidirect
3. C₉×C₁₇×C₇⋊D₇	C₂	semidirect
5. C₇²×C₉×C₁₇	C₂²	semidirect
13. C₇×C₁₇×D₉	D₇	semidirect
15. D₉×C₇⋊D₇	C₁₇	direct (N × H)
18. C₁₇×C₇⋊D₇	D₉	direct (N × H)
20. C₇×C₉×C₁₇	C₂×D₇	semidirect
21. C₇⋊D₆₃	C₂×C₁₇	semidirect
22. C₇²×D₉	C₂×C₁₇	semidirect
23. C₉×C₇⋊D₇	C₂×C₁₇	semidirect
24. C₇²×C₁₇	C₂×D₉	semidirect
31. C₇²×C₉	C₂²×C₁₇	semidirect
35. C₁₇×D₉	C₇⋊D₇	direct (N × H)
45. C₉×C₁₇	C₂×C₇⋊D₇	semidirect
49. C₇×D₉	D₇×C₁₇	semidirect
50. C₇×C₁₇	D₇×D₉	semidirect
56. C₇⋊D₇	C₁₇×D₉	direct (N × H)
59. C₇×C₉	C₂×D₇×C₁₇	semidirect
61. C₇²	C₂×C₁₇×D₉	semidirect
73. D₉	C₁₇×C₇⋊D₇	direct (N × H)
74. C₁₇	D₉×C₇⋊D₇	direct (N × H)
79. C₉	C₂×C₁₇×C₇⋊D₇	semidirect
80. C₇	D₇×C₁₇×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₇⋊D₆₃	2
C₇²×C₁₇×D₉	2
C₉×C₁₇×C₇⋊D₇	2
D₃×C₁₇×C₇⋊D₇	3
D₇×C₁₇×D₉	7
D₉×C₇⋊D₇	17

Subgroups — C17×D9×C7⋊D7 #44472602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₉×C₇⋊D₇ #44472602