Subgroups — #29508801

Order 15424.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14515358	C₂	1	2	yes	maximal
2	C₈×#11757210	C₂	1	1	yes	maximal, characteristic
3	C₂×#14515358	C₄	1	4	yes	—
4	#16838778	C₄	1	1	yes	characteristic
5	C₄×#11757210	C₂²	1	1	yes	characteristic
6	C₈×D₂₄₁	C₄	1	1	yes	characteristic
7	#14515358	—	2	4	no	—
8	C₂×#11757210	C₂×C₄	1	2	yes	—
9	#14515356	C₈	1	2	yes	complemented
10	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
11	#14515349	C₈	1	1	yes	characteristic, complemented
12	C₈×C₂₄₁	C₈	1	1	yes	characteristic, complemented
13	C₂×D₂₄₁	C₄²	1	1	yes	characteristic
14	#11757210	M₁₆	1	4	yes	—
15	C₄×C₂₄₁	C₂×C₈	1	1	yes	characteristic
16	Dic₂₄₁	C₂×C₈	1	1	yes	characteristic
17	C₂×C₂₄₁	C₄×C₈	1	1	yes	characteristic
18	D₂₄₁	#97	1	2	yes	—
19	C₂₄₁	#322	1	1	yes	characteristic, complemented, Sylow
20	#322	—	241	1	no	maximal, Sylow
21	C₄×C₈	—	241	1	no	—
22	C₄×C₈	—	241	2	no	—
23	C₂×C₈	—	241	4	no	—
24	C₂×C₈	—	241	1	no	—
25	C₂×C₈	—	241	1	no	—
26	C₄²	—	241	1	no	—
27	C₂×C₄	—	241	2	no	—
28	C₂×C₄	—	241	1	no	—
29	C₈	—	482	4	no	—
30	C₈	—	241	2	no	—
31	C₈	—	241	1	no	—
32	C₈	#14515358	1	1	yes	characteristic, complemented
33	C₂²	—	241	1	no	—
34	C₄	—	241	4	no	—
35	C₄	—	241	1	no	—
36	C₄	C₂×#14515358	1	1	yes	characteristic
37	C₂	—	241	2	no	—
38	C₂	C₄×#14515358	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.