Subgroups — #2244×C₂₅₇ #45660786

Order 32896.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#499×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#493×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#357×C₂₅₇	C₂	1	4	yes	maximal, complemented
4	#346×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₂₅₇	—	2	1	no	—
6	C₂×D₈×C₂₅₇	C₂²	1	2	yes	—
7	#127×C₂₅₇	—	2	1	no	—
8	#125×C₂₅₇	—	2	1	no	—
9	C₂×C₁₆×C₂₅₇	C₂²	1	2	yes	—
10	#107×C₂₅₇	C₂²	1	2	yes	—
11	#106×C₂₅₇	—	2	1	no	—
12	C₄×C₈×C₂₅₇	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₂₅₇	—	2	2	no	—
14	C₂×D₄×C₂₅₇	—	4	2	no	—
15	D₈×C₂₅₇	—	2	4	no	—
16	D₈×C₂₅₇	—	4	2	no	—
17	C₂×C₈×C₂₅₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₅₇	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₂₅₇	—	2	2	no	—
20	C₄⋊C₄×C₂₅₇	—	4	2	no	—
21	C₄²×C₂₅₇	D₄	1	1	yes	characteristic
22	C₁₆×C₂₅₇	—	2	2	no	—
23	C₂³×C₂₅₇	—	4	2	no	—
24	D₄×C₂₅₇	—	4	2	no	—
25	D₄×C₂₅₇	—	4	2	no	—
26	D₄×C₂₅₇	—	8	4	no	—
27	C₂×C₄×C₂₅₇	—	4	2	no	—
28	C₂×C₄×C₂₅₇	D₈	1	2	yes	—
29	C₂×C₄×C₂₅₇	C₂×D₄	1	1	yes	characteristic
30	C₈×C₂₅₇	SD₁₆	1	2	yes	—
31	C₈×C₂₅₇	#41	1	2	yes	—
32	C₂²×C₂₅₇	—	8	2	no	—
33	C₂²×C₂₅₇	—	8	4	no	—
34	C₂²×C₂₅₇	C₂×D₈	1	1	yes	characteristic
35	C₄×C₂₅₇	—	2	2	no	—
36	C₄×C₂₅₇	—	8	2	no	—
37	C₄×C₂₅₇	#124	1	1	yes	characteristic
38	C₄×C₂₅₇	C₂×SD₁₆	1	1	yes	characteristic
39	C₂×C₂₅₇	—	16	2	no	—
40	C₂×C₂₅₇	#486	1	1	yes	characteristic
41	C₂×C₂₅₇	#509	1	2	yes	—
42	C₂₅₇	#2244	1	1	yes	characteristic, direct product factor, Sylow
43	#2244	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	#499	C₂×C₂₅₇	1	1	yes	characteristic, complemented
45	#493	C₂×C₂₅₇	1	1	yes	characteristic
46	#357	C₂×C₂₅₇	1	4	yes	complemented
47	#346	C₂×C₂₅₇	1	1	yes	characteristic, complemented
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	C₂²×C₂₅₇	1	2	yes	—
50	#127	—	2	1	no	—
51	#125	—	2	1	no	—
52	C₂×C₁₆	C₂²×C₂₅₇	1	2	yes	—
53	#107	C₂²×C₂₅₇	1	2	yes	—
54	#106	—	2	1	no	—
55	C₄×C₈	C₂²×C₂₅₇	1	1	yes	characteristic
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	D₄×C₂₅₇	1	1	yes	characteristic
61	C₂×C₈	C₂³×C₂₅₇	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	4	2	no	—
64	C₄²	D₄×C₂₅₇	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	D₈×C₂₅₇	1	2	yes	—
72	C₂×C₄	C₂×D₄×C₂₅₇	1	1	yes	characteristic
73	C₈	SD₁₆×C₂₅₇	1	2	yes	—
74	C₈	#41×C₂₅₇	1	2	yes	—
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×D₈×C₂₅₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	#124×C₂₅₇	1	1	yes	characteristic
81	C₄	C₂×SD₁₆×C₂₅₇	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#486×C₂₅₇	1	1	yes	characteristic
84	C₂	#509×C₂₅₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₅₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₅₇
prime radical	#493×C₂₅₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₇ ◁ C₄²×C₂₅₇ ◁ C₄×C₈×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #499×C₂₅₇	C₂	semidirect
3. #357×C₂₅₇	C₂	semidirect
4. #346×C₂₅₇	C₂	semidirect
42. C₂₅₇	#2244	direct (N × H)
43. #2244	C₂₅₇	direct (N × H)
44. #499	C₂×C₂₅₇	semidirect
46. #357	C₂×C₂₅₇	semidirect
47. #346	C₂×C₂₅₇	semidirect

Maximal subgroups

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

subgroup	index
#499×C₂₅₇	2
#493×C₂₅₇	2
#357×C₂₅₇	2
#346×C₂₅₇	2
#2244	257

Subgroups — #2244×C257 #45660786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2244×C₂₅₇ #45660786