Subgroups — C₄×C₆₉₁⋊C₈ #36348708

Order 22112.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₉₁⋊C₈	C₂	1	2	yes	maximal
2	C₄²×C₆₉₁	C₂	1	1	yes	maximal, characteristic
3	C₆₉₁⋊C₈	C₄	1	4	yes	direct product factor
4	C₂×C₄×C₆₉₁	C₄	1	2	yes	—
5	C₂×C₄×C₆₉₁	C₂²	1	1	yes	characteristic
6	C₂²×C₆₉₁	C₂×C₄	1	1	yes	characteristic
7	C₄×C₆₉₁	C₈	1	4	yes	complemented
8	C₄×C₆₉₁	C₂×C₄	1	2	yes	—
9	C₂×C₆₉₁	C₄²	1	1	yes	characteristic
10	C₂×C₆₉₁	C₂×C₈	1	2	yes	—
11	C₆₉₁	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₈	—	691	1	no	maximal, Sylow
13	C₂×C₈	—	691	2	no	—
14	C₄²	D₆₉₁	1	1	yes	characteristic
15	C₂×C₄	Dic₆₉₁	1	2	yes	—
16	C₂×C₄	C₂×D₆₉₁	1	1	yes	characteristic
17	C₈	—	691	4	no	—
18	C₂²	C₂×Dic₆₉₁	1	1	yes	characteristic
19	C₄	C₆₉₁⋊C₈	1	4	yes	direct product factor
20	C₄	C₄×D₆₉₁	1	2	yes	—
21	C₂	C₄×Dic₆₉₁	1	1	yes	characteristic
22	C₂	C₂×C₆₉₁⋊C₈	1	2	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.