Subgroups — C₈×#16861960 #45687152

Order 33344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16861960	C₂	1	2	yes	maximal
2	C₄×C₈×C₅₂₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#16861960	C₄	1	4	yes	—
4	C₂×C₈×C₅₂₁	C₄	1	2	yes	—
5	C₄²×C₅₂₁	C₂²	1	1	yes	characteristic
6	#16861960	C₈	1	8	yes	direct product factor
7	C₂×C₄×C₅₂₁	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₅₂₁	C₈	1	4	yes	complemented
10	C₂²×C₅₂₁	C₄²	1	1	yes	characteristic
11	C₄×C₅₂₁	C₂×C₈	1	4	yes	—
12	C₄×C₅₂₁	C₂×C₈	1	2	yes	—
13	C₂×C₅₂₁	C₄×C₈	1	2	yes	—
14	C₂×C₅₂₁	C₄×C₈	1	1	yes	characteristic
15	C₅₂₁	C₈²	1	1	yes	characteristic, complemented, Sylow
16	C₈²	—	521	1	no	maximal, Sylow
17	C₄×C₈	—	521	2	no	—
18	C₄×C₈	D₅₂₁	1	1	yes	characteristic
19	C₂×C₈	—	521	4	no	—
20	C₂×C₈	Dic₅₂₁	1	2	yes	—
21	C₄²	C₂×D₅₂₁	1	1	yes	characteristic
22	C₂×C₄	C₄×D₅₂₁	1	2	yes	—
23	C₂×C₄	C₂×Dic₅₂₁	1	1	yes	characteristic
24	C₈	—	521	8	no	—
25	C₈	#16861960	1	4	yes	direct product factor
26	C₂²	C₄×Dic₅₂₁	1	1	yes	characteristic
27	C₄	C₈×D₅₂₁	1	4	yes	—
28	C₄	C₂×#16861960	1	2	yes	—
29	C₂	C₈×Dic₅₂₁	1	2	yes	—
30	C₂	C₄×#16861960	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.