Subgroups — D₃₉₇⋊C₁₆ #27163169

Order 12704.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263734	C₂	1	2	yes	maximal, complemented
2	C₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₄×D₃₉₇	C₄	1	1	yes	characteristic
4	#15691787	C₂²	1	1	yes	characteristic
5	C₈×C₃₉₇	C₄	1	1	yes	characteristic
6	C₂×D₃₉₇	C₈	1	1	yes	characteristic
7	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
8	Dic₃₉₇	C₈	1	1	yes	characteristic
9	C₂×C₃₉₇	C₂×C₈	1	1	yes	characteristic
10	D₃₉₇	C₁₆	1	2	yes	complemented
11	C₃₉₇	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₆	—	397	1	no	maximal, Sylow
13	C₂×C₈	—	397	1	no	—
14	C₁₆	—	397	2	no	—
15	C₂×C₄	—	397	1	no	—
16	C₈	—	397	1	no	—
17	C₈	#13097544	1	1	yes	characteristic
18	C₂²	—	397	1	no	—
19	C₄	—	397	1	no	—
20	C₄	C₂×#13097544	1	1	yes	characteristic
21	C₂	—	397	2	no	—
22	C₂	D₃₉₇⋊C₈	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.