Subgroups — C₄⁴×C₈₉ #36391592

Order 22784.

3966 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₈₉	C₂	1	15	yes	maximal
2	C₂²×C₄²×C₈₉	C₂²	1	35	yes	—
3	C₄³×C₈₉	C₄	1	120	yes	direct product factor
4	C₂³×C₄×C₈₉	C₂³	1	15	yes	—
5	C₂×C₄²×C₈₉	C₂×C₄	1	420	yes	—
6	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
7	C₂²×C₄×C₈₉	C₂²×C₄	1	210	yes	—
8	C₄²×C₈₉	C₄²	1	560	yes	direct product factor
9	C₂³×C₈₉	C₂³×C₄	1	15	yes	—
10	C₂×C₄×C₈₉	C₂×C₄²	1	420	yes	—
11	C₂²×C₈₉	C₂²×C₄²	1	35	yes	—
12	C₄×C₈₉	C₄³	1	120	yes	direct product factor
13	C₄⁴	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₈₉	C₂×C₄³	1	15	yes	—
15	C₂×C₄³	C₂×C₈₉	1	15	yes	—
16	C₈₉	C₄⁴	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₄²	C₂²×C₈₉	1	35	yes	—
18	C₄³	C₄×C₈₉	1	120	yes	direct product factor
19	C₂³×C₄	C₂³×C₈₉	1	15	yes	—
20	C₂×C₄²	C₂×C₄×C₈₉	1	420	yes	—
21	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
22	C₂²×C₄	C₂²×C₄×C₈₉	1	210	yes	—
23	C₄²	C₄²×C₈₉	1	560	yes	direct product factor
24	C₂³	C₂³×C₄×C₈₉	1	15	yes	—
25	C₂×C₄	C₂×C₄²×C₈₉	1	420	yes	—
26	C₂²	C₂²×C₄²×C₈₉	1	35	yes	—
27	C₄	C₄³×C₈₉	1	120	yes	direct product factor
28	C₂	C₂×C₄³×C₈₉	1	15	yes	—

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.

subgroup	index
C₂×C₄³×C₈₉	2
C₄⁴	89