Subgroups — C₂×C₄⋊#14523339 #30656758

Order 16448.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523339	C₂	1	2	yes	maximal
2	C₄⋊#14523339	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₂₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#14523339	—	2	4	no	—
5	C₂×#14523339	C₂²	1	4	yes	—
6	C₂²×C₄×C₂₅₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₂₅₇	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₂₅₇	C₂²	1	1	yes	characteristic
9	C₄²×C₂₅₇	C₄	1	2	yes	—
10	C₄²×C₂₅₇	C₂²	1	2	yes	—
11	#14523339	—	2	4	no	—
12	C₂³×C₂₅₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₅₇	—	2	2	no	—
14	C₂×C₄×C₂₅₇	C₈	1	4	yes	complemented
15	C₂×C₄×C₂₅₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₅₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₅₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₅₇	D₄	1	2	yes	—
19	C₂×C₄×C₂₅₇	Q₈	1	2	yes	—
20	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
21	C₂²×C₂₅₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₂₅₇	C₂×C₈	1	2	yes	—
23	C₂²×C₂₅₇	M₁₆	1	2	yes	—
24	C₂²×C₂₅₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₅₇	—	2	2	no	—
26	C₄×C₂₅₇	C₄⋊C₄	1	2	yes	—
27	C₄×C₂₅₇	C₂×C₈	1	4	yes	complemented
28	C₄×C₂₅₇	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₅₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₂₅₇	C₄⋊C₈	1	4	yes	complemented
31	C₂×C₂₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₂₅₇	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₂₅₇	C₂×M₁₆	1	1	yes	characteristic
34	C₂₅₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₄⋊C₈	—	257	1	no	maximal, Sylow
36	C₂²×C₈	—	257	2	no	—
37	C₂×C₄²	D₂₅₇	1	1	yes	characteristic
38	C₄⋊C₈	—	257	4	no	—
39	C₂²×C₄	Dic₂₅₇	1	1	yes	characteristic
40	C₂²×C₄	Dic₂₅₇	1	1	yes	characteristic
41	C₂²×C₄	C₂×D₂₅₇	1	1	yes	characteristic
42	C₂×C₈	—	257	4	no	—
43	C₂×C₈	—	514	4	no	—
44	C₄²	Dic₂₅₇	1	2	yes	—
45	C₄²	C₂×D₂₅₇	1	2	yes	—
46	C₂³	C₂×Dic₂₅₇	1	1	yes	characteristic
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	#14523339	1	4	yes	complemented
49	C₂×C₄	C₂×Dic₂₅₇	1	2	yes	—
50	C₂×C₄	C₂×Dic₂₅₇	1	1	yes	characteristic
51	C₂×C₄	C₂×Dic₂₅₇	1	2	yes	—
52	C₂×C₄	D₁₀₂₈	1	2	yes	—
53	C₂×C₄	Dic₅₁₄	1	2	yes	—
54	C₂×C₄	C₂²×D₂₅₇	1	1	yes	characteristic
55	C₈	—	514	4	no	—
56	C₂²	C₄⋊Dic₂₅₇	1	2	yes	—
57	C₂²	C₂×#14523339	1	2	yes	—
58	C₂²	#16861602	1	2	yes	—
59	C₂²	C₂²×Dic₂₅₇	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	C₄⋊Dic₂₅₇	1	2	yes	—
62	C₄	C₂×#14523339	1	4	yes	complemented
63	C₄	C₂×D₁₀₂₈	1	1	yes	characteristic
64	C₄	C₂×Dic₅₁₄	1	1	yes	characteristic
65	C₂	C₄⋊#14523339	1	4	yes	direct product factor
66	C₂	C₂×C₄⋊Dic₂₅₇	1	1	yes	characteristic
67	C₂	C₂²×#14523339	1	1	yes	characteristic
68	C₂	C₂×#16861602	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₅₇
commutator	C₂×C₂₅₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₂₅₇
Fitting	C₂×C₄²×C₂₅₇	C₂
socle, prime radical	C₂³×C₂₅₇	C₂×C₄
cosocle	C₂×C₄×C₂₅₇	C₂³
hypercenter	C₂×C₄²	D₂₅₇
hypocenter	C₂₅₇	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#14523339	C₂	direct (N × H)
14. C₂×C₄×C₂₅₇	C₈	semidirect
27. C₄×C₂₅₇	C₂×C₈	semidirect
30. C₂×C₂₅₇	C₄⋊C₈	semidirect
34. C₂₅₇	C₂×C₄⋊C₈	semidirect
48. C₂×C₄	#14523339	semidirect
62. C₄	C₂×#14523339	semidirect
65. C₂	C₄⋊#14523339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523339	2
C₄⋊#14523339	2
C₂×C₄²×C₂₅₇	2
C₂×C₄⋊C₈	257

Subgroups — C2×C4⋊#14523339 #30656758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊#14523339 #30656758