Subgroups — Q₈×#13097544 #27163177

Order 12704.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13097544	C₂	1	3	yes	maximal
2	C₄×#13097544	C₂	1	3	yes	maximal
3	Q₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#13097544	C₂²	1	3	yes	—
5	C₂×#13097544	C₂²	1	1	yes	characteristic
6	Dic₇₉₄	C₄	1	3	yes	complemented
7	C₄×D₃₉₇	C₂²	1	3	yes	—
8	Q₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
9	C₂×D₃₉₇	C₂³	1	1	yes	characteristic
10	#13097544	—	2	3	no	—
11	#13097544	Q₈	1	2	yes	direct product factor
12	C₄×C₃₉₇	C₂×C₄	1	3	yes	—
13	Dic₃₉₇	C₂×C₄	1	3	yes	—
14	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
15	D₃₉₇	C₂×Q₈	1	1	yes	characteristic
16	D₃₉₇	#41	1	1	yes	characteristic
17	C₃₉₇	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	397	1	no	maximal, Sylow
19	C₂×Q₈	—	397	1	no	—
20	C₄⋊C₄	—	397	3	no	—
21	C₄²	—	397	3	no	—
22	Q₈	—	397	3	no	—
23	Q₈	#13097544	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	397	3	no	—
25	C₂×C₄	—	397	1	no	—
26	C₂×C₄	—	397	3	no	—
27	C₂²	—	397	1	no	—
28	C₄	—	794	3	no	—
29	C₄	—	397	2	no	—
30	C₄	—	397	3	no	—
31	C₄	C₂×#13097544	1	3	yes	—
32	C₂	—	397	1	no	—
33	C₂	—	397	1	no	—
34	C₂	C₂²×#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.