Subgroups — #14581281

Order 2624.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂×#4223)⋊C₄	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	C₄²×C₄₁	C₄	1	1	yes	characteristic, complemented
6	C₄×Dic₄₁	C₄	1	3	yes	complemented
7	C₂²×D₄₁	C₂³	1	1	yes	characteristic
8	C₂×#4223	—	2	12	no	—
9	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
10	C₂×Dic₄₁	C₂×C₄	1	3	yes	—
11	C₄×D₄₁	—	2	6	no	—
12	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
13	C₂×D₄₁	#41	1	6	yes	—
14	#4223	—	4	4	no	—
15	C₄×C₄₁	—	2	3	no	—
16	Dic₄₁	—	2	3	no	—
17	C₂×C₄₁	#117	1	3	yes	—
18	D₄₁	#126	1	4	yes	—
19	#383	—	41	1	no	maximal, Sylow
20	C₄₁	#383	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₄²	—	41	1	no	—
22	#95	—	41	6	no	—
23	C₂²×C₄	—	41	3	no	—
24	C₂²×C₄	—	41	4	no	—
25	C₄²	—	41	3	no	—
26	C₄²	#4223	1	1	yes	characteristic, complemented
27	C₂³	—	41	1	no	—
28	C₂×C₄	—	41	3	no	—
29	C₂×C₄	—	82	6	no	—
30	C₂×C₄	—	82	12	no	—
31	C₂×C₄	C₂×#4223	1	3	yes	—
32	C₂²	—	41	6	no	—
33	C₂²	C₂²×#4223	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	82	3	no	—
36	C₄	—	164	4	no	—
37	C₂	—	41	4	no	—
38	C₂	#13050243	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.