Subgroups — #30656560

Order 16448.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22551528	C₂	1	1	yes	maximal, characteristic
2	#22551524	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₂₅₇	C₂	1	1	yes	maximal, characteristic
4	#16861602	—	2	1	no	—
5	C₄⋊Dic₂₅₇	—	2	1	no	—
6	C₂×C₈×C₂₅₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₂₅₇	C₄	1	2	yes	complemented
8	C₂×Dic₂₅₇	—	4	1	no	—
9	#14523339	—	4	1	no	—
10	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
11	C₈×C₂₅₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₅₇	Q₈	1	1	yes	characteristic
13	C₂²×C₂₅₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₅₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₅₇	SD₁₆	1	1	yes	characteristic
16	Dic₂₅₇	—	8	1	no	—
17	C₂×C₂₅₇	—	2	1	no	—
18	C₂×C₂₅₇	#106	1	1	yes	characteristic
19	C₂₅₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	257	1	no	maximal, Sylow
21	M₃₂	D₂₅₇	1	1	yes	characteristic
22	#108	—	257	1	no	—
23	#106	—	257	1	no	—
24	M₁₆	—	514	1	no	—
25	C₂×C₈	C₂×D₂₅₇	1	1	yes	characteristic
26	C₄⋊C₄	—	514	1	no	—
27	C₁₆	Dic₂₅₇	1	2	yes	complemented
28	C₂×C₄	—	1028	1	no	—
29	C₂×C₄	D₁₀₂₈	1	1	yes	characteristic
30	C₈	—	1028	1	no	—
31	C₈	C₂×Dic₂₅₇	1	1	yes	characteristic
32	C₈	Dic₅₁₄	1	1	yes	characteristic
33	C₂²	#16861607	1	1	yes	characteristic
34	C₄	—	2056	1	no	—
35	C₄	C₄⋊Dic₂₅₇	1	1	yes	characteristic
36	C₄	#16861607	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#22551524	1	1	yes	characteristic

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.