Subgroups — #14580704

Order 2624.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	1	yes	maximal, characteristic
2	#13050088	C₂	1	4	yes	maximal
3	#13050075	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₄₁	C₂²	1	2	yes	—
6	C₄⋊C₄×C₄₁	—	2	2	no	—
7	C₄²×C₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₁	C₂²	1	2	yes	—
9	#10620279	—	2	2	no	—
10	C₂×#66491	C₂²	1	2	yes	—
11	Q₈×C₄₁	—	2	4	no	—
12	C₂×C₄×C₄₁	—	2	2	no	—
13	C₂×C₄×C₄₁	D₄	1	2	yes	—
14	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₄₁	—	2	2	no	—
16	#66491	—	2	2	no	—
17	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
18	C₄×C₄₁	—	2	2	no	—
19	C₄×C₄₁	—	4	2	no	—
20	C₄×C₄₁	#41	1	2	yes	—
21	Dic₄₁	—	4	2	no	—
22	C₂×C₄₁	#124	1	1	yes	characteristic
23	C₂×C₄₁	#137	1	2	yes	—
24	#491	—	41	1	no	maximal, Sylow
25	C₄₁	#491	1	1	yes	characteristic, complemented, Sylow
26	C₄⋊Q₈	D₄₁	1	1	yes	characteristic
27	#125	—	41	1	no	—
28	#103	—	41	4	no	—
29	#97	—	41	1	no	—
30	C₂×Q₈	C₂×D₄₁	1	2	yes	—
31	C₂×C₈	—	41	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	41	2	no	—
34	C₄⋊C₄	—	82	2	no	—
35	C₄²	C₂×D₄₁	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	82	2	no	—
39	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
40	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
41	C₈	—	82	2	no	—
42	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	164	2	no	—
46	C₄	#10620308	1	2	yes	—
47	C₂	#13050151	1	1	yes	characteristic
48	C₂	#13050195	1	2	yes	—

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

N	H ≅ G/N	type
25. C₄₁	#491	semidirect

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