Subgroups — #30657826

Order 16448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14523348	C₂	1	2	yes	maximal
2	C₈×#11759967	C₂	1	1	yes	maximal, characteristic
3	C₂×#14523348	—	2	2	no	—
4	#16861626	C₄	1	1	yes	characteristic
5	C₄×#11759967	C₂²	1	1	yes	characteristic
6	C₈×D₂₅₇	C₄	1	1	yes	characteristic
7	#14523348	—	4	2	no	—
8	C₂×#11759967	D₄	1	1	yes	characteristic
9	C₂×#11759967	Q₈	1	1	yes	characteristic
10	#14523346	—	2	1	no	—
11	C₄×D₂₅₇	C₂×C₄	1	1	yes	characteristic
12	#14523339	C₈	1	1	yes	characteristic, complemented
13	C₈×C₂₅₇	C₈	1	1	yes	characteristic, complemented
14	C₂×D₂₅₇	C₄⋊C₄	1	1	yes	characteristic
15	#11759967	—	2	1	no	—
16	#11759967	SD₁₆	1	2	yes	—
17	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
18	Dic₂₅₇	M₁₆	1	1	yes	characteristic
19	C₂×C₂₅₇	C₄⋊C₈	1	1	yes	characteristic
20	D₂₅₇	#106	1	1	yes	characteristic
21	D₂₅₇	#108	1	1	yes	characteristic
22	C₂₅₇	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	257	1	no	maximal, Sylow
24	C₄⋊C₈	—	257	2	no	—
25	C₄×C₈	—	257	1	no	—
26	C₂×C₈	—	257	1	no	—
27	C₂×C₈	—	257	1	no	—
28	C₂×C₈	—	514	2	no	—
29	C₄²	—	257	1	no	—
30	C₂×C₄	—	257	1	no	—
31	C₂×C₄	—	257	1	no	—
32	C₂×C₄	—	257	1	no	—
33	C₈	—	257	1	no	—
34	C₈	—	514	1	no	—
35	C₈	—	1028	2	no	—
36	C₈	#14523348	1	1	yes	characteristic, complemented
37	C₂²	—	257	1	no	—
38	C₄	—	257	2	no	—
39	C₄	—	257	1	no	—
40	C₄	—	514	1	no	—
41	C₄	C₂×#14523348	1	1	yes	characteristic
42	C₂	—	257	1	no	—
43	C₂	—	257	1	no	—
44	C₂	C₄⋊#14523348	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.