Subgroups — #14580738

Order 2624.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	2	yes	maximal
2	#13050098	C₂	1	2	yes	maximal
3	#13050096	C₂	1	2	yes	maximal
4	C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₄²×C₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₁	C₂²	1	4	yes	—
9	#10620279	—	2	4	no	—
10	C₂×C₄×C₄₁	D₄	1	2	yes	—
11	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
12	C₂×Dic₄₁	—	2	4	no	—
13	C₈×C₄₁	Q₈	1	2	yes	—
14	C₈×C₄₁	Q₈	1	2	yes	—
15	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
16	C₄×C₄₁	—	2	2	no	—
17	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
19	Dic₄₁	—	4	4	no	—
20	C₂×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₄₁	#135	1	2	yes	—
22	#499	—	41	1	no	maximal, Sylow
23	C₄₁	#499	1	1	yes	characteristic, complemented, Sylow
24	#125	—	41	2	no	—
25	#107	—	41	2	no	—
26	#106	—	41	2	no	—
27	C₄×C₈	D₄₁	1	1	yes	characteristic
28	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
29	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
30	C₄⋊C₄	—	41	4	no	—
31	C₄⋊C₄	—	82	4	no	—
32	C₄²	C₂×D₄₁	1	1	yes	characteristic
33	C₂×C₄	—	82	4	no	—
34	C₂×C₄	D₁₆₄	1	2	yes	—
35	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
36	C₈	Dic₈₂	1	2	yes	—
37	C₈	Dic₈₂	1	2	yes	—
38	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	164	4	no	—
41	C₄	C₂×Dic₈₂	1	1	yes	characteristic
42	C₄	C₂×Dic₈₂	1	1	yes	characteristic
43	C₂	#13050164	1	1	yes	characteristic
44	C₂	#13050186	1	2	yes	—

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

N	H ≅ G/N	type
23. C₄₁	#499	semidirect

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