Subgroups — #21440696

Order 7712.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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