Subgroups — C₂²×#16861632 #30657869

Order 16448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861632	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#14523348	C₂	1	1	yes	maximal, characteristic
3	#16861632	C₂²	1	4	yes	direct product factor
4	C₂×#14523348	C₄	1	3	yes	—
5	C₂×#14523348	C₂²	1	3	yes	—
6	C₂²×#11759967	C₄	1	1	yes	characteristic
7	#14523348	C₂×C₄	1	3	yes	—
8	#14523348	C₂³	1	1	yes	characteristic
9	C₂×#11759967	C₈	1	3	yes	—
10	C₂×#11759967	C₂×C₄	1	3	yes	—
11	C₂²×D₂₅₇	C₈	1	1	yes	characteristic
12	C₂²×C₂₅₇	C₁₆	1	1	yes	characteristic, complemented
13	C₂×D₂₅₇	C₁₆	1	3	yes	complemented
14	C₂×D₂₅₇	C₂×C₈	1	3	yes	—
15	#11759967	C₂×C₈	1	3	yes	—
16	#11759967	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₂₅₇	C₂×C₁₆	1	3	yes	complemented
18	D₂₅₇	C₂×C₁₆	1	3	yes	complemented
19	D₂₅₇	C₂²×C₈	1	1	yes	characteristic
20	C₂₅₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₁₆	—	257	1	no	maximal, Sylow
22	C₂²×C₈	—	257	1	no	—
23	C₂×C₁₆	—	257	6	no	—
24	C₂²×C₄	—	257	1	no	—
25	C₂×C₈	—	257	3	no	—
26	C₂×C₈	—	257	3	no	—
27	C₁₆	—	257	4	no	—
28	C₂³	—	257	1	no	—
29	C₂×C₄	—	257	3	no	—
30	C₂×C₄	—	257	3	no	—
31	C₈	—	257	1	no	—
32	C₈	—	257	3	no	—
33	C₂²	—	257	3	no	—
34	C₂²	—	257	3	no	—
35	C₂²	#16861632	1	1	yes	characteristic, direct product factor
36	C₄	—	257	1	no	—
37	C₄	—	257	3	no	—
38	C₂	—	257	1	no	—
39	C₂	—	257	3	no	—
40	C₂	C₂×#16861632	1	3	yes	direct product factor

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.