Subgroups — #44417208

Order 29248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28410575	C₂	1	1	yes	maximal, characteristic, complemented
2	#28410571	C₂	1	1	yes	maximal, characteristic, complemented
3	#28410498	C₂	1	1	yes	maximal, characteristic, complemented
4	#28410497	C₂	1	1	yes	maximal, characteristic, complemented
5	#28410493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×D₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₄₅₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#20300742	—	2	1	no	—
9	#20300740	—	2	1	no	—
10	Dic₁₈₂₈	C₂²	1	1	yes	characteristic
11	#20300729	—	2	1	no	—
12	#20300728	—	2	1	no	—
13	D₃₆₅₆	C₂²	1	1	yes	characteristic
14	C₈×D₄₅₇	C₂²	1	1	yes	characteristic
15	#20300716	C₂²	1	1	yes	characteristic
16	Q₁₆×C₄₅₇	C₂²	1	1	yes	characteristic
17	D₈×C₄₅₇	C₂²	1	1	yes	characteristic
18	C₁₆×C₄₅₇	C₂²	1	1	yes	characteristic
19	Dic₉₁₄	—	2	1	no	—
20	D₁₈₂₈	—	2	1	no	—
21	D₁₈₂₈	—	4	1	no	—
22	C₂²⋊D₄₅₇	—	4	1	no	—
23	C₂×Dic₄₅₇	—	4	1	no	—
24	C₄×D₄₅₇	—	4	1	no	—
25	C₄×D₄₅₇	D₄	1	1	yes	characteristic
26	#16814532	D₄	1	1	yes	characteristic
27	Q₈×C₄₅₇	—	2	1	no	—
28	D₄×C₄₅₇	—	2	1	no	—
29	C₈×C₄₅₇	C₂³	1	1	yes	characteristic
30	C₂²×C₄₅₇	—	4	1	no	—
31	C₂×D₄₅₇	—	4	1	no	—
32	C₂×D₄₅₇	D₈	1	1	yes	characteristic
33	C₄×C₄₅₇	—	4	1	no	—
34	C₄×C₄₅₇	C₂×D₄	1	1	yes	characteristic
35	Dic₄₅₇	—	4	1	no	—
36	Dic₄₅₇	D₈	1	1	yes	characteristic
37	C₂×C₄₅₇	—	8	1	no	—
38	C₂×C₄₅₇	C₂×D₈	1	1	yes	characteristic
39	D₄₅₇	—	2	1	no	—
40	D₄₅₇	—	8	1	no	—
41	C₄₅₇	#508	1	1	yes	characteristic, complemented, Sylow
42	#508	—	457	1	no	maximal, Sylow
43	#135	—	457	1	no	—
44	#135	—	457	1	no	—
45	Q₃₂	—	457	1	no	—
46	SD₃₂	—	457	1	no	—
47	SD₃₂	D₄₅₇	1	1	yes	characteristic, complemented
48	D₁₆	—	457	1	no	—
49	C₂×C₁₆	—	457	1	no	—
50	#41	—	914	1	no	—
51	#41	—	914	1	no	—
52	Q₁₆	—	457	1	no	—
53	Q₁₆	C₂×D₄₅₇	1	1	yes	characteristic
54	SD₁₆	—	914	1	no	—
55	SD₁₆	—	914	1	no	—
56	D₈	—	457	1	no	—
57	D₈	C₂×D₄₅₇	1	1	yes	characteristic
58	C₂×C₈	—	457	1	no	—
59	C₁₆	—	457	1	no	—
60	C₁₆	C₂×D₄₅₇	1	1	yes	characteristic
61	Q₈	—	2	1	no	—
62	Q₈	—	914	1	no	—
63	D₄	—	2	1	no	—
64	D₄	—	1828	1	no	—
65	D₄	—	1828	1	no	—
66	D₄	—	914	1	no	—
67	C₂×C₄	—	1828	1	no	—
68	C₂×C₄	—	1828	1	no	—
69	C₂×C₄	—	457	1	no	—
70	C₈	—	457	1	no	—
71	C₈	C₂²×D₄₅₇	1	1	yes	characteristic
72	C₂²	—	4	1	no	—
73	C₂²	—	1828	1	no	—
74	C₂²	—	457	1	no	—
75	C₄	—	4	1	no	—
76	C₄	—	1828	1	no	—
77	C₄	—	457	1	no	—
78	C₄	D₄×D₄₅₇	1	1	yes	characteristic
79	C₂	—	8	1	no	—
80	C₂	—	3656	1	no	—
81	C₂	—	914	1	no	—
82	C₂	D₈×D₄₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₅₇
commutator, cosocle	C₈×C₄₅₇	C₂³
Frattini	C₈	C₂²×D₄₅₇
Fitting	SD₃₂×C₄₅₇	C₂
socle	C₂×C₄₅₇	C₂×D₈
hypercenter	SD₃₂	D₄₅₇
hypocenter	C₄₅₇	#508
LCS	G ▷ C₈×C₄₅₇ ▷ C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #28410575	C₂	semidirect
2. #28410571	C₂	semidirect
3. #28410498	C₂	semidirect
4. #28410497	C₂	semidirect
5. #28410493	C₂	semidirect
6. C₁₆×D₄₅₇	C₂	semidirect
7. SD₃₂×C₄₅₇	C₂	semidirect
41. C₄₅₇	#508	semidirect
47. SD₃₂	D₄₅₇	semidirect

Maximal subgroups

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

subgroup	index
#28410575	2
#28410571	2
#28410498	2
#28410497	2
#28410493	2
C₁₆×D₄₅₇	2
SD₃₂×C₄₅₇	2
#508	457