Subgroups — #14581257

Order 2624.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620270	C₂	1	2	yes	maximal
2	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₄₁	C₄	1	1	yes	characteristic
4	C₄×Dic₄₁	C₄	1	1	yes	characteristic
5	C₂×#66491	C₂²	1	1	yes	characteristic
6	#10620270	—	2	2	no	—
7	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₄₁	C₈	1	1	yes	characteristic
9	C₂×Dic₄₁	C₈	1	1	yes	characteristic
10	C₈×C₄₁	—	2	1	no	—
11	#66491	D₄	1	1	yes	characteristic
12	#66491	Q₈	1	1	yes	characteristic
13	C₂²×C₄₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₁	M₁₆	1	1	yes	characteristic
16	Dic₄₁	—	2	1	no	—
17	Dic₄₁	C₁₆	1	2	yes	complemented
18	C₂×C₄₁	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₄₁	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄₁	M₃₂	1	1	yes	characteristic
21	C₄⋊C₁₆	—	41	1	no	maximal, Sylow
22	C₄₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	41	2	no	—
24	C₄×C₈	—	41	1	no	—
25	C₂×C₈	—	41	1	no	—
26	C₂×C₈	#4223	1	1	yes	characteristic
27	C₄²	—	41	1	no	—
28	C₁₆	—	82	2	no	—
29	C₂×C₄	—	41	1	no	—
30	C₂×C₄	—	41	1	no	—
31	C₂×C₄	C₂×#4223	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	41	1	no	—
34	C₈	—	41	1	no	—
35	C₂²	#10620296	1	1	yes	characteristic
36	C₄	—	41	2	no	—
37	C₄	—	82	1	no	—
38	C₄	C₄⋊#4223	1	1	yes	characteristic
39	C₄	#10620301	1	1	yes	characteristic
40	C₂	#13050231	1	1	yes	characteristic
41	C₂	#13050237	1	1	yes	characteristic
42	C₂	#13050239	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Dic₄₁	C₁₆	semidirect
22. C₄₁	C₄⋊C₁₆	semidirect

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