Subgroups — #30657831

Order 16448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861630	C₂	1	2	yes	maximal
2	C₄×#14523346	C₂	1	1	yes	maximal, characteristic
3	#16861630	C₄	1	4	yes	complemented
4	C₂×#14523346	C₄	1	1	yes	characteristic
5	C₂×#14523346	C₂²	1	1	yes	characteristic
6	C₄×Dic₂₅₇	C₄	1	1	yes	characteristic
7	#14523346	C₈	1	2	yes	—
8	#14523346	C₂×C₄	1	2	yes	—
9	C₂×Dic₂₅₇	C₈	1	1	yes	characteristic
10	C₂×Dic₂₅₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₂₅₇	C₈	1	1	yes	characteristic
12	C₂²×C₂₅₇	C₂×C₈	1	1	yes	characteristic
13	C₄×C₂₅₇	—	2	1	no	—
14	Dic₂₅₇	—	2	1	no	—
15	Dic₂₅₇	C₄²	1	1	yes	characteristic
16	Dic₂₅₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₂₅₇	C₄×C₈	1	1	yes	characteristic
18	C₂×C₂₅₇	M₃₂	1	1	yes	characteristic
19	C₂×C₂₅₇	M₃₂	1	1	yes	characteristic
20	C₂₅₇	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	257	1	no	maximal, Sylow
22	C₂×C₁₆	—	257	2	no	—
23	C₄×C₈	—	257	1	no	—
24	C₂×C₈	—	257	1	no	—
25	C₂×C₈	—	257	1	no	—
26	C₄²	—	257	1	no	—
27	C₁₆	—	257	4	no	—
28	C₂×C₄	—	257	1	no	—
29	C₂×C₄	—	257	1	no	—
30	C₂×C₄	#14523348	1	1	yes	characteristic
31	C₈	—	257	2	no	—
32	C₈	—	257	2	no	—
33	C₂²	C₂×#14523348	1	1	yes	characteristic
34	C₄	—	257	1	no	—
35	C₄	—	257	1	no	—
36	C₄	—	2	1	no	—
37	C₄	—	514	1	no	—
38	C₂	C₄×#14523348	1	1	yes	characteristic
39	C₂	#22551688	1	1	yes	characteristic
40	C₂	#22551689	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #16861630	C₄	semidirect
20. C₂₅₇	#346	semidirect

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