Subgroups — C₄²×#4223 #14581270

Order 2624.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#4223	C₂	1	6	yes	maximal
2	C₄²×D₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#4223	C₂²	1	4	yes	—
4	C₂×C₄×D₄₁	C₂²	1	3	yes	—
5	C₄×#4223	C₄	1	24	yes	direct product factor
6	C₄²×C₄₁	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₄₁	C₄	1	3	yes	complemented
8	C₂²×D₄₁	C₂³	1	1	yes	characteristic
9	C₂×#4223	C₂×C₄	1	24	yes	—
10	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
11	C₂×Dic₄₁	C₂×C₄	1	3	yes	—
12	C₄×D₄₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₄₁	C₂²×C₄	1	6	yes	—
15	#4223	C₄²	1	16	yes	direct product factor
16	C₄×C₄₁	C₄²	1	6	yes	complemented
17	Dic₄₁	C₄²	1	6	yes	complemented
18	C₂×C₄₁	C₂×C₄²	1	3	yes	—
19	D₄₁	C₂×C₄²	1	4	yes	—
20	C₄³	—	41	1	no	maximal, Sylow
21	C₄₁	C₄³	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄²	—	41	6	no	—
23	C₂×C₄²	—	41	1	no	—
24	C₂²×C₄	—	41	4	no	—
25	C₂²×C₄	—	41	3	no	—
26	C₄²	—	41	24	no	—
27	C₄²	—	41	3	no	—
28	C₄²	#4223	1	1	yes	characteristic, direct product factor
29	C₂³	—	41	1	no	—
30	C₂×C₄	—	41	24	no	—
31	C₂×C₄	—	41	3	no	—
32	C₂×C₄	—	41	12	no	—
33	C₂×C₄	C₂×#4223	1	3	yes	—
34	C₂²	—	41	6	no	—
35	C₂²	C₂²×#4223	1	1	yes	characteristic
36	C₄	—	41	16	no	—
37	C₄	—	41	6	no	—
38	C₄	C₄×#4223	1	6	yes	direct product factor
39	C₂	—	41	4	no	—
40	C₂	C₂×C₄×#4223	1	3	yes	—

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

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