Subgroups — #11759817⋊D₁₇ #46828271

Order 34476.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇⋊#11759817	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#11759817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇⋊#11759815	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₂₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₇×#92788	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃⋊D₂₂₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₂₂₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×C₁₇×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇⋊(D₁₃⋊C₃)	—	13	1	no	maximal
11	D₁₇×D₁₃⋊C₃	—	13	1	no	maximal
12	#11759815⋊C₂	—	17	1	no	maximal, Hall
13	C₂×C₁₇×C₁₃⋊C₃	—	13	1	no	—
14	C₁₇⋊(D₁₃⋊C₃)	—	13	1	no	—
15	C₁₇⋊(D₁₃⋊C₃)	—	13	1	no	—
16	C₁₇⋊(D₁₃⋊C₃)	—	13	1	no	—
17	C₁₇⋊(D₁₃⋊C₃)	—	26	6	no	—
18	C₁₇×D₁₃⋊C₃	—	13	1	no	—
19	D₁₇×C₁₃⋊C₃	—	13	1	no	—
20	#11759817	—	17	1	no	—
21	#11759817	D₁₇	1	1	yes	characteristic, complemented
22	#11759815	—	17	1	no	—
23	C₂×D₂₂₁	—	13	1	no	—
24	D₁₃×D₁₇	—	13	1	no	—
25	D₁₃²	—	17	1	no	Hall
26	C₁₇×C₁₃⋊C₃	—	13	1	no	—
27	C₁₇×C₁₃⋊C₃	—	13	1	no	—
28	C₁₇×C₁₃⋊C₃	—	26	6	no	—
29	#92788	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×C₁₇	—	13	1	no	—
31	D₂₂₁	—	13	1	no	—
32	D₂₂₁	—	13	1	no	—
33	D₂₂₁	—	26	6	no	—
34	D₂₂₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
35	C₁₃×D₁₇	—	13	1	no	—
36	C₁₇×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
37	C₁₃⋊D₁₃	—	17	1	no	—
38	C₁₃×D₁₃	—	17	1	no	—
39	C₁₃×D₁₃	C₃×D₁₇	1	1	yes	characteristic, complemented
40	C₁₃×C₁₇	—	2	6	no	—
41	C₁₃×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
42	C₁₃×C₁₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×D₁₇	—	169	1	no	Hall
44	C₁₃²	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₁₃⋊C₃	—	221	1	no	—
46	C₂×D₁₃⋊C₃	—	221	1	no	—
47	C₂×C₃×C₁₇	—	169	1	no	—
48	C₃×D₁₇	—	169	1	no	—
49	C₃×D₁₇	—	169	1	no	—
50	C₂×C₁₃⋊C₃	—	13	1	no	—
51	C₂×C₁₃⋊C₃	—	221	1	no	—
52	D₁₃⋊C₃	—	13	1	no	—
53	D₁₃⋊C₃	—	442	6	no	—
54	D₁₃⋊C₃	—	221	1	no	—
55	D₁₃⋊C₃	—	221	1	no	—
56	D₁₃⋊C₃	—	221	1	no	—
57	C₂×D₁₇	—	169	1	no	Hall
58	C₂×D₁₃	—	221	1	no	—
59	C₂×D₁₃	—	221	1	no	—
60	C₃×C₁₇	—	169	1	no	Hall
61	C₁₃⋊C₃	—	13	1	no	—
62	C₁₃⋊C₃	—	13	1	no	—
63	C₁₃⋊C₃	—	26	6	no	—
64	C₂×C₁₇	—	13	1	no	—
65	D₁₇	—	13	1	no	—
66	D₁₇	—	169	1	no	—
67	C₂×C₁₃	—	13	1	no	—
68	C₂×C₁₃	—	221	1	no	—
69	D₁₃	—	17	1	no	—
70	D₁₃	—	442	6	no	—
71	D₁₃	—	221	1	no	—
72	D₁₃	—	221	1	no	—
73	D₁₃	C₁₇⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
74	C₁₇	#11759815⋊C₂	1	1	yes	characteristic, complemented, Sylow
75	C₁₃	—	2	6	no	—
76	C₁₃	D₁₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
77	C₁₃	C₂×C₁₇⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
78	C₂²×C₃	—	2873	1	no	Hall
79	C₂×C₃	—	2873	1	no	—
80	C₂×C₃	—	2873	1	no	—
81	C₂×C₃	—	169	1	no	—
82	C₂²	—	2873	1	no	Sylow
83	C₃	—	169	1	no	Sylow
84	C₂	—	13	1	no	—
85	C₂	—	2873	1	no	—
86	C₂	—	221	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₁₇	C₂²×C₃
LCS	G ▷ C₁₃²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇⋊#11759817	C₂	semidirect
2. C₁₇×#11759817	C₂	semidirect
3. C₁₇⋊#11759815	C₂	semidirect
4. D₁₃×D₂₂₁	C₃	semidirect
5. C₁₇×#92788	C₂²	semidirect
6. C₁₃⋊D₂₂₁	C₂×C₃	semidirect
7. C₁₃×D₂₂₁	C₂×C₃	semidirect
8. C₁₃×C₁₇×D₁₃	C₂×C₃	semidirect
9. C₁₃²×C₁₇	C₂²×C₃	semidirect
21. #11759817	D₁₇	semidirect
29. #92788	C₂×D₁₇	semidirect
34. D₂₂₁	D₁₃⋊C₃	semidirect
36. C₁₇×D₁₃	D₁₃⋊C₃	semidirect
39. C₁₃×D₁₃	C₃×D₁₇	semidirect
41. C₁₃×C₁₇	C₂×D₁₃⋊C₃	semidirect
42. C₁₃×C₁₇	C₂×D₁₃⋊C₃	semidirect
44. C₁₃²	C₂×C₃×D₁₇	semidirect
73. D₁₃	C₁₇⋊(D₁₃⋊C₃)	semidirect
74. C₁₇	#11759815⋊C₂	semidirect
76. C₁₃	D₁₇×D₁₃⋊C₃	semidirect
77. C₁₃	C₂×C₁₇⋊(D₁₃⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₁₇⋊#11759817	2
C₁₇×#11759817	2
C₁₇⋊#11759815	2
D₁₃×D₂₂₁	3
C₂×C₁₇⋊(D₁₃⋊C₃)	13
D₁₇×D₁₃⋊C₃	13
#11759815⋊C₂	17

Subgroups — #11759817⋊D17 #46828271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11759817⋊D₁₇ #46828271