Subgroups — #13050239

Order 1312.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄₁	C₂	1	1	yes	maximal, characteristic
2	#10620270	C₂	1	2	yes	maximal, complemented
3	C₄×D₄₁	C₄	1	1	yes	characteristic
4	C₈×C₄₁	C₄	1	1	yes	characteristic
5	#66491	C₂²	1	1	yes	characteristic
6	C₂×D₄₁	C₈	1	1	yes	characteristic
7	C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
8	Dic₄₁	C₈	1	1	yes	characteristic
9	C₂×C₄₁	C₂×C₈	1	1	yes	characteristic
10	D₄₁	—	2	1	no	—
11	C₄₁	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	41	1	no	maximal, Sylow
13	C₂×C₈	—	41	1	no	—
14	C₁₆	—	41	2	no	—
15	C₂×C₄	—	41	1	no	—
16	C₈	—	41	1	no	—
17	C₈	#4223	1	1	yes	characteristic
18	C₂²	—	41	1	no	—
19	C₄	—	41	1	no	—
20	C₄	C₂×#4223	1	1	yes	characteristic
21	C₂	—	82	1	no	—
22	C₂	#10620296	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #10620270	C₂	semidirect
11. C₄₁	M₃₂	semidirect

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