Subgroups — #14581269

Order 2624.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050214	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄₁	C₄	1	1	yes	characteristic
4	C₁₆×C₄₁	C₄	1	1	yes	characteristic
5	#10620268	C₂²	1	1	yes	characteristic
6	C₄×D₄₁	C₈	1	1	yes	characteristic
7	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
8	#66491	C₈	1	1	yes	characteristic
9	C₂×D₄₁	C₁₆	1	1	yes	characteristic
10	C₄×C₄₁	C₂×C₈	1	1	yes	characteristic
11	Dic₄₁	C₁₆	1	1	yes	characteristic
12	C₂×C₄₁	C₂×C₁₆	1	1	yes	characteristic
13	D₄₁	—	2	1	no	—
14	M₆₄	—	41	1	no	maximal, Sylow
15	C₄₁	M₆₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₆	—	41	1	no	—
17	C₃₂	—	41	2	no	—
18	C₂×C₈	—	41	1	no	—
19	C₁₆	—	41	1	no	—
20	C₁₆	#4223	1	1	yes	characteristic
21	C₂×C₄	—	41	1	no	—
22	C₈	—	41	1	no	—
23	C₈	C₂×#4223	1	1	yes	characteristic
24	C₂²	—	41	1	no	—
25	C₄	—	41	1	no	—
26	C₄	#10620296	1	1	yes	characteristic
27	C₂	—	82	1	no	—
28	C₂	#13050237	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #13050214	C₂	semidirect
15. C₄₁	M₆₄	semidirect

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