Subgroups — #14580204

Order 2624.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050071	C₂	1	6	yes	maximal
2	C₂×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₁	C₂²	1	3	yes	—
4	C₂²×Dic₄₁	C₂²	1	4	yes	—
5	C₄²×C₄₁	C₄	1	4	yes	complemented
6	C₂³×C₄₁	C₂³	1	1	yes	characteristic
7	C₂×C₄×C₄₁	—	2	6	no	—
8	C₂×C₄×C₄₁	C₂×C₄	1	6	yes	—
9	C₂×Dic₄₁	—	2	12	no	—
10	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₄₁	#41	1	6	yes	—
12	C₄×C₄₁	—	2	6	no	—
13	Dic₄₁	—	4	4	no	—
14	C₂×C₄₁	#117	1	3	yes	—
15	C₂×C₄₁	#126	1	4	yes	—
16	#383	—	41	1	no	maximal, Sylow
17	C₄₁	#383	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄²	D₄₁	1	1	yes	characteristic
19	#95	—	41	6	no	—
20	C₂²×C₄	—	41	4	no	—
21	C₂²×C₄	C₂×D₄₁	1	3	yes	—
22	C₄²	Dic₄₁	1	4	yes	complemented
23	C₂³	C₂²×D₄₁	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	82	12	no	—
26	C₂×C₄	C₂×Dic₄₁	1	6	yes	—
27	C₂²	#10620306	1	6	yes	—
28	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
29	C₄	—	2	6	no	—
30	C₄	—	164	4	no	—
31	C₂	#13050123	1	3	yes	—
32	C₂	#13050158	1	4	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.