Subgroups — C₈×#13097544 #27163148

Order 12704.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×#13097544	C₂	1	1	yes	maximal, characteristic
3	C₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#13097544	C₄	1	2	yes	—
5	#15691794	C₄	1	2	yes	complemented
6	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
7	#15691787	C₄	1	1	yes	characteristic, complemented
8	C₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
9	C₂×D₃₉₇	C₂×C₄	1	1	yes	characteristic
10	#13097544	C₈	1	4	yes	direct product factor
11	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
12	Dic₃₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃₉₇	C₄²	1	1	yes	characteristic
14	D₃₉₇	C₂×C₈	1	2	yes	—
15	C₃₉₇	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₈	—	397	1	no	maximal, Sylow
17	C₂×C₈	—	397	1	no	—
18	C₂×C₈	—	397	1	no	—
19	C₄²	—	397	1	no	—
20	C₂×C₄	—	397	2	no	—
21	C₂×C₄	—	397	1	no	—
22	C₈	—	397	2	no	—
23	C₈	—	397	1	no	—
24	C₈	#13097544	1	1	yes	characteristic, direct product factor
25	C₂²	—	397	1	no	—
26	C₄	—	397	4	no	—
27	C₄	—	397	1	no	—
28	C₄	C₂×#13097544	1	1	yes	characteristic
29	C₂	—	397	2	no	—
30	C₂	C₄×#13097544	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.