Subgroups — #367×C₂₅₇ #30656236

Order 16448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	#107×C₂₅₇	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₅₇	C₂²	1	1	yes	characteristic
4	C₄⋊C₄×C₂₅₇	—	2	2	no	—
5	C₁₆×C₂₅₇	C₄	1	2	yes	complemented
6	C₂×C₄×C₂₅₇	—	4	2	no	—
7	C₂×C₄×C₂₅₇	D₄	1	1	yes	characteristic
8	C₈×C₂₅₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₅₇	Q₈	1	1	yes	characteristic
10	C₂²×C₂₅₇	D₈	1	1	yes	characteristic
11	C₄×C₂₅₇	—	8	2	no	—
12	C₄×C₂₅₇	C₄⋊C₄	1	1	yes	characteristic
13	C₄×C₂₅₇	Q₁₆	1	1	yes	characteristic
14	C₂×C₂₅₇	#107	1	1	yes	characteristic
15	C₂×C₂₅₇	SD₃₂	1	2	yes	—
16	C₂₅₇	#367	1	1	yes	characteristic, direct product factor, Sylow
17	#367	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₁₆	C₂×C₂₅₇	1	1	yes	characteristic
19	#107	C₂×C₂₅₇	1	2	yes	—
20	C₂×C₈	C₂²×C₂₅₇	1	1	yes	characteristic
21	C₄⋊C₄	—	2	2	no	—
22	C₁₆	C₄×C₂₅₇	1	2	yes	complemented
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	D₄×C₂₅₇	1	1	yes	characteristic
25	C₈	C₂×C₄×C₂₅₇	1	1	yes	characteristic
26	C₈	Q₈×C₂₅₇	1	1	yes	characteristic
27	C₂²	D₈×C₂₅₇	1	1	yes	characteristic
28	C₄	—	8	2	no	—
29	C₄	C₄⋊C₄×C₂₅₇	1	1	yes	characteristic
30	C₄	Q₁₆×C₂₅₇	1	1	yes	characteristic
31	C₂	#107×C₂₅₇	1	1	yes	characteristic
32	C₂	SD₃₂×C₂₅₇	1	2	yes	—

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.