Subgroups — #14581282

Order 2624.

186 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	—	2	12	no	—
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	—	2	12	no	—
10	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
11	C₂×Dic₄₁	C₂×C₄	1	3	yes	—
12	C₄×D₄₁	D₄	1	6	yes	—
13	C₄×D₄₁	Q₈	1	6	yes	—
14	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
15	C₂×D₄₁	C₂×D₄	1	3	yes	—
16	C₂×D₄₁	C₂×Q₈	1	3	yes	—
17	#4223	—	4	4	no	—
18	C₄×C₄₁	C₄⋊C₄	1	6	yes	complemented
19	Dic₄₁	C₄⋊C₄	1	6	yes	complemented
20	C₂×C₄₁	C₂×C₄⋊C₄	1	3	yes	—
21	D₄₁	#127	1	1	yes	characteristic
22	D₄₁	C₄⋊Q₈	1	3	yes	—
23	#384	—	41	1	no	maximal, Sylow
24	C₄₁	#384	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₄⋊C₄	—	41	6	no	—
26	C₂×C₄²	—	41	1	no	—
27	C₂²×C₄	—	41	3	no	—
28	C₂²×C₄	—	41	4	no	—
29	C₄⋊C₄	—	82	12	no	—
30	C₄²	—	41	3	no	—
31	C₄²	#4223	1	1	yes	characteristic, complemented
32	C₂³	—	41	1	no	—
33	C₂×C₄	—	41	3	no	—
34	C₂×C₄	—	41	6	no	—
35	C₂×C₄	—	41	6	no	—
36	C₂×C₄	—	82	12	no	—
37	C₂×C₄	C₂×#4223	1	3	yes	—
38	C₂²	—	41	3	no	—
39	C₂²	—	41	3	no	—
40	C₂²	C₂²×#4223	1	1	yes	characteristic
41	C₄	—	41	6	no	—
42	C₄	—	164	4	no	—
43	C₄	C₄⋊#4223	1	6	yes	complemented
44	C₂	—	41	1	no	—
45	C₂	—	41	3	no	—
46	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.