Subgroups — #30659775

Order 16672.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861967	C₂	1	2	yes	maximal
2	C₄×Dic₅₂₁	C₂	1	1	yes	maximal, characteristic
3	#16861967	—	2	2	no	—
4	C₂×Dic₅₂₁	C₄	1	1	yes	characteristic
5	C₂×Dic₅₂₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅₂₁	C₄	1	1	yes	characteristic
7	C₂²×C₅₂₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₅₂₁	—	2	1	no	—
9	Dic₅₂₁	C₈	1	2	yes	complemented
10	Dic₅₂₁	D₄	1	1	yes	characteristic
11	Dic₅₂₁	Q₈	1	1	yes	characteristic
12	C₂×C₅₂₁	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₅₂₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₅₂₁	M₁₆	1	1	yes	characteristic
15	C₅₂₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	521	1	no	maximal, Sylow
17	C₂×C₈	—	521	2	no	—
18	C₄²	—	521	1	no	—
19	C₂×C₄	—	521	1	no	—
20	C₂×C₄	—	521	1	no	—
21	C₂×C₄	#14523438	1	1	yes	characteristic
22	C₈	—	1042	2	no	—
23	C₂²	C₂×#14523438	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	521	1	no	—
26	C₄	—	521	1	no	—
27	C₄	—	521	2	no	—
28	C₂	C₄⋊#14523438	1	1	yes	characteristic
29	C₂	#22552372	1	1	yes	characteristic
30	C₂	#22552373	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. Dic₅₂₁	C₈	semidirect
15. C₅₂₁	C₄⋊C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.