Subgroups — D₈×#14523266 #45656274

Order 32576.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#14523266	C₂	1	2	yes	maximal, complemented
2	#30654284	C₂	1	1	yes	maximal, characteristic, complemented
3	#30654277	C₂	1	2	yes	maximal, complemented
4	C₈×#14523266	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₅₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14523266	—	2	2	no	—
7	D₅₀₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊#14523266	C₂²	1	2	yes	—
9	C₂²⋊#14523266	—	2	2	no	—
10	C₄×#14523266	C₂²	1	1	yes	characteristic
11	D₄×D₅₀₉	C₂²	1	2	yes	—
12	D₄₀₇₂	C₄	1	1	yes	characteristic, complemented
13	#22550846	C₄	1	2	yes	complemented
14	C₈×D₅₀₉	C₂²	1	1	yes	characteristic
15	D₈×C₅₀₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#14523266	—	2	2	no	—
17	C₂×#14523266	—	4	4	no	—
18	C₂×#14523266	D₄	1	1	yes	characteristic
19	C₂×#14523266	D₄	1	1	yes	characteristic
20	#16861332	—	2	1	no	—
21	C₂²×D₅₀₉	—	2	2	no	—
22	D₂₀₃₆	C₂×C₄	1	2	yes	complemented
23	C₂²⋊D₅₀₉	—	2	2	no	—
24	C₄×D₅₀₉	C₂³	1	1	yes	characteristic
25	#16861325	C₂×C₄	1	1	yes	characteristic, complemented
26	D₄×C₅₀₉	C₂×C₄	1	2	yes	complemented
27	C₈×C₅₀₉	C₂×C₄	1	1	yes	characteristic, complemented
28	C₂²×C₅₀₉	—	2	2	no	—
29	C₂×D₅₀₉	—	2	2	no	—
30	C₂×D₅₀₉	—	4	2	no	—
31	C₂×D₅₀₉	—	4	2	no	—
32	C₂×D₅₀₉	C₂×D₄	1	1	yes	characteristic
33	#14523266	—	2	1	no	—
34	#14523266	—	4	2	no	—
35	#14523266	D₈	1	2	yes	direct product factor
36	C₄×C₅₀₉	C₂²×C₄	1	1	yes	characteristic
37	Dic₅₀₉	#41	1	1	yes	characteristic
38	C₂×C₅₀₉	—	4	2	no	—
39	C₂×C₅₀₉	C₄×D₄	1	1	yes	characteristic
40	D₅₀₉	—	4	2	no	—
41	D₅₀₉	C₂×D₈	1	1	yes	characteristic
42	D₅₀₉	#135	1	1	yes	characteristic
43	C₅₀₉	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₄×D₈	—	509	1	no	maximal, Sylow
45	C₂×D₈	—	509	1	no	—
46	C₄×D₄	—	509	2	no	—
47	#107	—	509	1	no	—
48	#102	—	509	2	no	—
49	C₄×C₈	—	509	1	no	—
50	C₂×D₄	—	509	2	no	—
51	C₂²×C₄	—	1018	2	no	—
52	D₈	—	509	2	no	—
53	D₈	—	509	1	no	—
54	D₈	#14523266	1	1	yes	characteristic, direct product factor
55	C₂×C₈	—	509	1	no	—
56	C₂×C₈	—	509	1	no	—
57	C₄⋊C₄	—	509	2	no	—
58	C₂²⋊C₄	—	1018	2	no	—
59	C₄²	—	509	1	no	—
60	C₂³	—	1018	2	no	—
61	D₄	—	1018	2	no	—
62	D₄	—	509	2	no	—
63	D₄	C₂×#14523266	1	2	yes	complemented
64	C₂×C₄	—	2036	4	no	—
65	C₂×C₄	—	1018	2	no	—
66	C₂×C₄	—	509	1	no	—
67	C₂×C₄	—	509	1	no	—
68	C₂×C₄	—	509	1	no	—
69	C₈	—	1018	1	no	—
70	C₈	—	509	1	no	—
71	C₈	C₂×#14523266	1	1	yes	characteristic, complemented
72	C₂²	—	2	2	no	—
73	C₂²	—	2036	2	no	—
74	C₂²	—	2036	2	no	—
75	C₂²	—	1018	2	no	—
76	C₂²	—	509	1	no	—
77	C₄	—	2036	2	no	—
78	C₄	—	1018	1	no	—
79	C₄	—	509	2	no	—
80	C₄	—	509	1	no	—
81	C₄	C₂²×#14523266	1	1	yes	characteristic
82	C₂	—	4	2	no	—
83	C₂	—	2036	2	no	—
84	C₂	—	509	1	no	—
85	C₂	—	509	1	no	—
86	C₂	D₄×#14523266	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14523266
commutator	C₄×C₅₀₉	C₂²×C₄
Frattini	C₄	C₂²×#14523266
Fitting	D₈×C₅₀₉	C₄
socle	C₂×C₅₀₉	C₄×D₄
prime radical	D₈×D₅₀₉	C₂
cosocle	C₄×D₅₀₉	C₂³
hypercenter	D₈	#14523266
hypocenter	C₅₀₉	C₄×D₈
LCS	G ▷ C₄×C₅₀₉ ▷ C₂×C₅₀₉ ▷ C₅₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#14523266	C₂	semidirect
2. #30654284	C₂	semidirect
3. #30654277	C₂	semidirect
4. C₈×#14523266	C₂	semidirect
12. D₄₀₇₂	C₄	semidirect
13. #22550846	C₄	semidirect
15. D₈×C₅₀₉	C₄	semidirect
22. D₂₀₃₆	C₂×C₄	semidirect
25. #16861325	C₂×C₄	semidirect
26. D₄×C₅₀₉	C₂×C₄	semidirect
27. C₈×C₅₀₉	C₂×C₄	semidirect
35. #14523266	D₈	direct (N × H)
43. C₅₀₉	C₄×D₈	semidirect
54. D₈	#14523266	direct (N × H)
63. D₄	C₂×#14523266	semidirect
71. C₈	C₂×#14523266	semidirect

Maximal subgroups

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

subgroup	index
D₄×#14523266	2
#30654284	2
#30654277	2
C₈×#14523266	2
D₈×D₅₀₉	2
C₄×D₈	509

Subgroups — D8×#14523266 #45656274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#14523266 #45656274