Subgroups — #30657117

Order 16448.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₂₈	C₂	1	4	yes	maximal
2	#22551592	C₂	1	2	yes	maximal
3	C₄×C₈×C₂₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₁₄	C₂²	1	4	yes	—
5	Dic₁₀₂₈	—	2	8	no	—
6	C₄⋊Dic₂₅₇	—	2	4	no	—
7	C₂×C₈×C₂₅₇	C₂²	1	2	yes	—
8	C₄²×C₂₅₇	C₂²	1	1	yes	characteristic
9	Dic₅₁₄	—	2	8	no	—
10	C₂×Dic₂₅₇	—	2	4	no	—
11	C₂×C₄×C₂₅₇	D₄	1	2	yes	—
12	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
13	C₈×C₂₅₇	D₄	1	4	yes	—
14	C₂²×C₂₅₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₂₅₇	Q₁₆	1	4	yes	complemented
16	C₄×C₂₅₇	C₂×D₄	1	2	yes	—
17	Dic₂₅₇	—	4	4	no	—
18	C₂×C₂₅₇	#127	1	1	yes	characteristic
19	C₂×C₂₅₇	C₂×Q₁₆	1	2	yes	—
20	C₂₅₇	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	257	1	no	maximal, Sylow
22	C₂×Q₁₆	—	257	4	no	—
23	C₄⋊Q₈	—	257	2	no	—
24	C₄×C₈	D₂₅₇	1	1	yes	characteristic
25	C₂×Q₈	—	257	4	no	—
26	Q₁₆	—	514	8	no	—
27	C₂×C₈	C₂×D₂₅₇	1	2	yes	—
28	C₄⋊C₄	—	514	4	no	—
29	C₄²	C₂×D₂₅₇	1	1	yes	characteristic
30	Q₈	—	514	8	no	—
31	C₂×C₄	—	514	4	no	—
32	C₂×C₄	D₁₀₂₈	1	2	yes	—
33	C₂×C₄	C₂²×D₂₅₇	1	1	yes	characteristic
34	C₈	D₁₀₂₈	1	4	yes	—
35	C₂²	C₂×D₁₀₂₈	1	1	yes	characteristic
36	C₄	—	1028	4	no	—
37	C₄	Dic₁₀₂₈	1	4	yes	complemented
38	C₄	C₂×D₁₀₂₈	1	2	yes	—
39	C₂	#22551589	1	1	yes	characteristic
40	C₂	C₂×Dic₁₀₂₈	1	2	yes	—

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

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