Subgroups — #29508603

Order 15424.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838773	C₂	1	2	yes	maximal
2	C₈×Dic₂₄₁	C₂	1	1	yes	maximal, characteristic
3	#16838773	C₄	1	4	yes	complemented
4	C₂×#14515349	C₂²	1	1	yes	characteristic
5	C₄×Dic₂₄₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₂₄₁	C₄	1	1	yes	characteristic
7	C₂×Dic₂₄₁	C₈	1	2	yes	—
8	#14515349	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
10	C₈×C₂₄₁	C₈	1	2	yes	—
11	C₂²×C₂₄₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₄₁	C₄²	1	1	yes	characteristic
13	C₄×C₂₄₁	C₂×C₈	1	1	yes	characteristic
14	Dic₂₄₁	C₁₆	1	4	yes	complemented
15	C₂×C₂₄₁	C₄×C₈	1	1	yes	characteristic
16	C₂×C₂₄₁	C₂×C₁₆	1	2	yes	—
17	C₂₄₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	241	1	no	maximal, Sylow
19	C₂×C₁₆	—	241	2	no	—
20	C₄×C₈	—	241	1	no	—
21	C₂×C₈	—	241	1	no	—
22	C₂×C₈	#11757210	1	1	yes	characteristic
23	C₄²	—	241	1	no	—
24	C₁₆	—	241	4	no	—
25	C₂×C₄	—	241	2	no	—
26	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
27	C₈	—	241	2	no	—
28	C₈	#14515356	1	2	yes	—
29	C₂²	#16838778	1	1	yes	characteristic
30	C₄	—	241	4	no	—
31	C₄	C₄×#11757210	1	1	yes	characteristic
32	C₄	C₂×#14515356	1	1	yes	characteristic
33	C₂	C₄×#14515356	1	1	yes	characteristic
34	C₂	#21440715	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.