Subgroups — D₁₇₁⋊(C₇⋊D₇) #45691678

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₇⋊D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₇⋊D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₇⋊(C₇⋊D₇)	—	3	1	no	maximal
5	C₇²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₃⋊(C₇⋊D₇)	—	3	1	no	—
7	C₇²×D₅₇	—	3	1	no	—
8	C₃×C₇⋊D₁₃₃	D₃	1	1	yes	characteristic
9	D₆₃⋊D₁₉	—	7	8	no	maximal
10	D₁₉×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic
12	C₁₉×D₆₃	—	7	8	no	—
13	C₇×D₁₇₁	D₇	1	8	yes	complemented
14	C₉×D₁₃₃	—	7	8	no	—
15	C₇⋊D₁₃₃	D₉	1	1	yes	characteristic, complemented
16	C₁₉×C₇⋊D₇	—	9	1	no	—
17	C₇²×D₁₉	—	9	1	no	—
18	D₉×C₇⋊D₇	—	19	1	no	maximal, Hall
19	D₂₁⋊D₁₉	—	21	8	no	—
20	C₇×C₉×C₁₉	C₂×D₇	1	8	yes	complemented
21	C₇²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
22	C₇⋊D₆₃	D₁₉	1	1	yes	characteristic, complemented
23	C₇²×D₉	—	19	1	no	—
24	C₉×C₇⋊D₇	—	19	1	no	—
25	C₁₉×D₂₁	—	21	8	no	—
26	C₇×D₅₇	—	3	8	no	—
27	C₃×D₁₃₃	—	7	8	no	—
28	D₉×D₁₉	—	49	1	no	Hall
29	D₃×C₇⋊D₇	—	57	1	no	—
30	D₇×D₁₉	—	63	8	no	—
31	C₇²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₉	D₃×D₇	1	8	yes	—
33	D₁₇₁	C₇⋊D₇	1	1	yes	characteristic, complemented
34	C₉×D₁₉	—	49	1	no	—
35	D₉×C₁₉	—	49	1	no	—
36	C₃⋊(C₇⋊D₇)	—	3	1	no	—
37	D₃×C₇²	—	57	1	no	—
38	C₃×C₇⋊D₇	—	19	1	no	—
39	D₁₃₃	—	7	8	no	—
40	C₇×D₁₉	—	9	8	no	—
41	D₇×C₁₉	—	63	8	no	—
42	D₇×D₉	—	133	8	no	—
43	D₃×D₁₉	—	147	1	no	—
44	C₂×C₇⋊D₇	—	171	1	no	Hall
45	C₉×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
46	C₃×C₇²	D₃×D₁₉	1	1	yes	characteristic
47	C₇×C₁₉	D₇×D₉	1	8	yes	complemented
48	D₆₃	—	7	8	no	—
49	C₉×D₇	—	133	8	no	—
50	C₇×D₉	—	19	8	no	—
51	D₅₇	—	3	1	no	—
52	C₃×D₁₉	—	49	1	no	—
53	D₃×C₁₉	—	147	1	no	—
54	C₂×C₇²	—	171	1	no	—
55	C₇⋊D₇	—	9	1	no	—
56	C₇⋊D₇	—	19	1	no	—
57	D₃×D₇	—	399	8	no	—
58	C₂×D₁₉	—	441	1	no	Hall
59	C₇×C₉	D₇×D₁₉	1	8	yes	complemented
60	C₃×C₁₉	D₃×C₇⋊D₇	1	1	yes	characteristic
61	C₇²	D₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
62	D₂₁	—	21	8	no	—
63	C₃×D₇	—	133	8	no	—
64	D₃×C₇	—	57	8	no	—
65	C₂×C₁₉	—	441	1	no	—
66	D₁₉	—	9	1	no	—
67	D₁₉	—	49	1	no	—
68	C₂×D₉	—	931	1	no	Hall
69	C₂×D₇	—	1197	8	no	—
70	C₃×C₇	D₂₁⋊D₁₉	1	8	yes	—
71	C₁₉	D₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₉	—	931	1	no	—
73	D₉	—	19	1	no	—
74	D₉	—	49	1	no	—
75	C₂×C₇	—	171	8	no	—
76	D₇	—	63	8	no	—
77	D₇	—	133	8	no	—
78	C₂×D₃	—	2793	1	no	—
79	C₉	D₁₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₆₃⋊D₁₉	1	8	yes	complemented
81	C₂×C₃	—	931	1	no	—
82	D₃	—	57	1	no	—
83	D₃	—	147	1	no	—
84	C₂²	—	8379	1	no	Sylow
85	C₃	D₅₇⋊(C₇⋊D₇)	1	1	yes	characteristic
86	C₂	—	931	1	no	—
87	C₂	—	171	1	no	—
88	C₂	—	441	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇²×C₉×C₁₉	C₂²
Frattini	C₃	D₅₇⋊(C₇⋊D₇)
socle	C₃×C₇²×C₁₉	C₂×D₃
LCS	G ▷ C₇²×C₉×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₇⋊D₆₃	C₂	semidirect
2. C₇²×D₁₇₁	C₂	semidirect
3. C₉×C₇⋊D₁₃₃	C₂	semidirect
5. C₇²×C₉×C₁₉	C₂²	semidirect
13. C₇×D₁₇₁	D₇	semidirect
15. C₇⋊D₁₃₃	D₉	semidirect
20. C₇×C₉×C₁₉	C₂×D₇	semidirect
21. C₇²×C₁₉	C₂×D₉	semidirect
22. C₇⋊D₆₃	D₁₉	semidirect
31. C₇²×C₉	C₂×D₁₉	semidirect
33. D₁₇₁	C₇⋊D₇	semidirect
45. C₉×C₁₉	C₂×C₇⋊D₇	semidirect
47. C₇×C₁₉	D₇×D₉	semidirect
59. C₇×C₉	D₇×D₁₉	semidirect
61. C₇²	D₉×D₁₉	semidirect
71. C₁₉	D₉×C₇⋊D₇	semidirect
79. C₉	D₁₉×C₇⋊D₇	semidirect
80. C₇	D₆₃⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₇⋊D₆₃	2
C₇²×D₁₇₁	2
C₉×C₇⋊D₁₃₃	2
D₅₇⋊(C₇⋊D₇)	3
D₆₃⋊D₁₉	7
D₉×C₇⋊D₇	19

Subgroups — D171⋊(C7⋊D7) #45691678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇₁⋊(C₇⋊D₇) #45691678