Subgroups — #30657598

Order 16448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14523346	C₂	1	2	yes	maximal
2	C₈×Dic₂₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#14523346	—	2	2	no	—
4	C₂×#14523339	C₄	1	1	yes	characteristic
5	C₄×Dic₂₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₅₇	C₄	1	1	yes	characteristic
7	#14523346	—	4	2	no	—
8	C₂×Dic₂₅₇	D₄	1	1	yes	characteristic
9	C₂×Dic₂₅₇	Q₈	1	1	yes	characteristic
10	#14523339	—	2	1	no	—
11	C₂×C₄×C₂₅₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₅₇	C₈	1	2	yes	complemented
13	C₂²×C₂₅₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₂₅₇	M₁₆	1	1	yes	characteristic
16	Dic₂₅₇	—	2	1	no	—
17	Dic₂₅₇	SD₁₆	1	2	yes	—
18	C₂×C₂₅₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₂₅₇	#106	1	1	yes	characteristic
20	C₂×C₂₅₇	#108	1	1	yes	characteristic
21	C₂₅₇	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	257	1	no	maximal, Sylow
23	C₄⋊C₈	—	257	2	no	—
24	C₄×C₈	—	257	1	no	—
25	C₂×C₈	—	257	1	no	—
26	C₂×C₈	—	514	2	no	—
27	C₂×C₈	#11759967	1	1	yes	characteristic
28	C₄²	—	257	1	no	—
29	C₂×C₄	—	257	1	no	—
30	C₂×C₄	—	257	1	no	—
31	C₂×C₄	C₂×#11759967	1	1	yes	characteristic
32	C₈	—	514	1	no	—
33	C₈	—	1028	2	no	—
34	C₈	#14523346	1	2	yes	complemented
35	C₂²	C₄⋊#11759967	1	1	yes	characteristic
36	C₄	—	257	2	no	—
37	C₄	—	514	1	no	—
38	C₄	C₂×#14523346	1	1	yes	characteristic
39	C₄	#16861628	1	1	yes	characteristic
40	C₂	C₄⋊#14523346	1	1	yes	characteristic
41	C₂	#22551660	1	1	yes	characteristic
42	C₂	#22551662	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.