Subgroups — #14581264

Order 2624.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050235	C₂	1	2	yes	maximal
2	C₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic
3	#10620297	—	2	2	no	—
4	C₈×D₄₁	C₂²	1	1	yes	characteristic
5	C₁₆×C₄₁	C₄	1	1	yes	characteristic
6	#10620268	C₄	1	1	yes	characteristic
7	C₄×D₄₁	D₄	1	1	yes	characteristic
8	#66493	—	4	2	no	—
9	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
10	#66491	Q₈	1	1	yes	characteristic
11	C₂×D₄₁	Q₁₆	1	1	yes	characteristic
12	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
13	Dic₄₁	D₈	1	1	yes	characteristic
14	C₂×C₄₁	#107	1	1	yes	characteristic
15	D₄₁	—	2	1	no	—
16	#368	—	41	1	no	maximal, Sylow
17	C₄₁	#368	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₆	—	41	1	no	—
19	#108	—	41	2	no	—
20	M₁₆	—	82	2	no	—
21	C₂×C₈	—	41	1	no	—
22	C₁₆	—	41	1	no	—
23	C₁₆	#4223	1	1	yes	characteristic
24	C₂×C₄	—	41	1	no	—
25	C₈	—	41	1	no	—
26	C₈	—	164	2	no	—
27	C₈	C₂×#4223	1	1	yes	characteristic
28	C₂²	—	41	1	no	—
29	C₄	—	41	1	no	—
30	C₄	C₄⋊#4223	1	1	yes	characteristic
31	C₂	—	82	1	no	—
32	C₂	#13050233	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₄₁	#368	semidirect

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