Subgroups — C₂⁶×D₉₇ #27156550

Order 12416.

58424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₉₇	C₂	1	126	yes	maximal, direct product factor
2	C₂⁶×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×D₉₇	C₂²	1	2604	yes	direct product factor
4	C₂⁵×C₉₇	C₂²	1	63	yes	complemented
5	C₂³×D₉₇	C₂³	1	11160	yes	direct product factor
6	C₂⁴×C₉₇	C₂³	1	651	yes	complemented
7	C₂³×C₉₇	C₂⁴	1	1395	yes	complemented
8	C₂²×D₉₇	C₂⁴	1	10416	yes	direct product factor
9	C₂²×C₉₇	C₂⁵	1	651	yes	complemented
10	C₂×D₉₇	C₂⁵	1	2016	yes	direct product factor
11	C₂×C₉₇	C₂⁶	1	63	yes	complemented
12	D₉₇	C₂⁶	1	64	yes	direct product factor
13	C₂⁷	—	97	1	no	maximal, Sylow
14	C₉₇	C₂⁷	1	1	yes	characteristic, complemented, Sylow
15	C₂⁶	—	97	126	no	—
16	C₂⁶	D₉₇	1	1	yes	characteristic, direct product factor
17	C₂⁵	—	97	2604	no	—
18	C₂⁵	C₂×D₉₇	1	63	yes	direct product factor
19	C₂⁴	—	97	11160	no	—
20	C₂⁴	C₂²×D₉₇	1	651	yes	direct product factor
21	C₂³	—	97	10416	no	—
22	C₂³	C₂³×D₉₇	1	1395	yes	direct product factor
23	C₂²	—	97	2016	no	—
24	C₂²	C₂⁴×D₉₇	1	651	yes	direct product factor
25	C₂	—	97	64	no	—
26	C₂	C₂⁵×D₉₇	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	D₉₇
commutator, cosocle, hypocenter	C₉₇	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₉₇	C₂
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂⁶

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.