Subgroups — #487×C₂₅₇ #30656356

Order 16448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Q₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#103×C₂₅₇	C₂	1	4	yes	maximal
4	C₄×C₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₅₇	—	2	1	no	—
6	C₂×Q₈×C₂₅₇	C₂²	1	2	yes	—
7	C₂×C₈×C₂₅₇	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₅₇	—	2	1	no	—
9	C₄⋊C₄×C₂₅₇	—	2	1	no	—
10	C₄⋊C₄×C₂₅₇	—	2	1	no	—
11	C₄⋊C₄×C₂₅₇	C₂²	1	2	yes	—
12	C₄²×C₂₅₇	C₂²	1	1	yes	characteristic
13	Q₈×C₂₅₇	—	2	4	no	—
14	Q₈×C₂₅₇	—	4	2	no	—
15	C₂×C₄×C₂₅₇	—	2	2	no	—
16	C₂×C₄×C₂₅₇	—	2	2	no	—
17	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
20	C₈×C₂₅₇	—	2	2	no	—
21	C₂²×C₂₅₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₂₅₇	—	4	2	no	—
23	C₄×C₂₅₇	—	4	2	no	—
24	C₄×C₂₅₇	SD₁₆	1	2	yes	—
25	C₄×C₂₅₇	Q₁₆	1	2	yes	—
26	C₄×C₂₅₇	#41	1	2	yes	—
27	C₂×C₂₅₇	#124	1	1	yes	characteristic
28	C₂×C₂₅₇	C₂×SD₁₆	1	1	yes	characteristic
29	C₂×C₂₅₇	C₂×Q₁₆	1	1	yes	characteristic
30	C₂₅₇	#487	1	1	yes	characteristic, direct product factor, Sylow
31	#487	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₄⋊Q₈	C₂×C₂₅₇	1	1	yes	characteristic
33	C₄⋊Q₈	C₂×C₂₅₇	1	1	yes	characteristic
34	#103	C₂×C₂₅₇	1	4	yes	—
35	C₄×C₈	C₂×C₂₅₇	1	1	yes	characteristic
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	C₂²×C₂₅₇	1	2	yes	—
38	C₂×C₈	C₂²×C₂₅₇	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	C₂²×C₂₅₇	1	2	yes	—
43	C₄²	C₂²×C₂₅₇	1	1	yes	characteristic
44	Q₈	—	2	4	no	—
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	D₄×C₂₅₇	1	1	yes	characteristic
49	C₂×C₄	D₄×C₂₅₇	1	1	yes	characteristic
50	C₂×C₄	C₂³×C₂₅₇	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₂²	C₂×D₄×C₂₅₇	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	4	2	no	—
55	C₄	SD₁₆×C₂₅₇	1	2	yes	—
56	C₄	Q₁₆×C₂₅₇	1	2	yes	—
57	C₄	#41×C₂₅₇	1	2	yes	—
58	C₂	#124×C₂₅₇	1	1	yes	characteristic
59	C₂	C₂×SD₁₆×C₂₅₇	1	1	yes	characteristic
60	C₂	C₂×Q₁₆×C₂₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₅₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₅₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₇ ◁ C₄²×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
30. C₂₅₇	#487	direct (N × H)
31. #487	C₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×C₂₅₇	2
#103×C₂₅₇	2
C₄×C₈×C₂₅₇	2
#487	257

Subgroups — #487×C257 #30656356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #487×C₂₅₇ #30656356