Subgroups — C₂³×Dic₃₉₇ #27163131

Order 12704.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₉₇	C₂	1	14	yes	maximal, direct product factor
2	C₂⁴×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃₉₇	C₂²	1	28	yes	direct product factor
4	C₂³×C₃₉₇	C₄	1	8	yes	complemented
5	C₂³×C₃₉₇	C₂²	1	7	yes	—
6	C₂²×C₃₉₇	C₂×C₄	1	28	yes	complemented
7	C₂²×C₃₉₇	C₂³	1	7	yes	—
8	Dic₃₉₇	C₂³	1	8	yes	direct product factor
9	C₂×C₃₉₇	C₂²×C₄	1	14	yes	complemented
10	C₂×C₃₉₇	C₂⁴	1	1	yes	characteristic
11	C₃₉₇	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₂³×C₄	—	397	1	no	maximal, Sylow
13	C₂⁴	D₃₉₇	1	1	yes	characteristic
14	C₂²×C₄	—	397	14	no	—
15	C₂³	Dic₃₉₇	1	8	yes	direct product factor
16	C₂³	C₂×D₃₉₇	1	7	yes	—
17	C₂×C₄	—	397	28	no	—
18	C₂²	C₂×Dic₃₉₇	1	28	yes	direct product factor
19	C₂²	C₂²×D₃₉₇	1	7	yes	—
20	C₄	—	397	8	no	—
21	C₂	C₂²×Dic₃₉₇	1	14	yes	direct product factor
22	C₂	C₂³×D₃₉₇	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.