Subgroups — C₂⁵×Dic₉₇ #27156526

Order 12416.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₉₇	C₂	1	62	yes	maximal, direct product factor
2	C₂⁶×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₉₇	C₂²	1	620	yes	direct product factor
4	C₂⁵×C₉₇	C₄	1	32	yes	complemented
5	C₂⁵×C₉₇	C₂²	1	31	yes	—
6	C₂²×Dic₉₇	C₂³	1	1240	yes	direct product factor
7	C₂⁴×C₉₇	C₂×C₄	1	496	yes	complemented
8	C₂⁴×C₉₇	C₂³	1	155	yes	—
9	C₂³×C₉₇	C₂²×C₄	1	1240	yes	complemented
10	C₂³×C₉₇	C₂⁴	1	155	yes	—
11	C₂×Dic₉₇	C₂⁴	1	496	yes	direct product factor
12	C₂²×C₉₇	C₂³×C₄	1	620	yes	complemented
13	C₂²×C₉₇	C₂⁵	1	31	yes	—
14	Dic₉₇	C₂⁵	1	32	yes	direct product factor
15	C₂×C₉₇	C₂⁴×C₄	1	62	yes	complemented
16	C₂×C₉₇	C₂⁶	1	1	yes	characteristic
17	C₂⁵×C₄	—	97	1	no	maximal, Sylow
18	C₉₇	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂⁶	D₉₇	1	1	yes	characteristic
20	C₂⁴×C₄	—	97	62	no	—
21	C₂⁵	Dic₉₇	1	32	yes	direct product factor
22	C₂⁵	C₂×D₉₇	1	31	yes	—
23	C₂³×C₄	—	97	620	no	—
24	C₂⁴	C₂×Dic₉₇	1	496	yes	direct product factor
25	C₂⁴	C₂²×D₉₇	1	155	yes	—
26	C₂²×C₄	—	97	1240	no	—
27	C₂³	C₂²×Dic₉₇	1	1240	yes	direct product factor
28	C₂³	C₂³×D₉₇	1	155	yes	—
29	C₂×C₄	—	97	496	no	—
30	C₂²	C₂³×Dic₉₇	1	620	yes	direct product factor
31	C₂²	C₂⁴×D₉₇	1	31	yes	—
32	C₄	—	97	32	no	—
33	C₂	C₂⁴×Dic₉₇	1	62	yes	direct product factor
34	C₂	C₂⁵×D₉₇	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.