Subgroups — #14581224

Order 2624.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620270	C₂	1	2	yes	maximal
2	C₄×#66491	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₄₁	C₄	1	1	yes	characteristic
4	C₂×#66491	C₄	1	1	yes	characteristic
5	C₂×#66491	C₂²	1	1	yes	characteristic
6	#10620270	C₄	1	4	yes	complemented
7	C₂×C₄×C₄₁	C₈	1	2	yes	—
8	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
9	#66491	C₈	1	2	yes	—
10	#66491	C₂×C₄	1	2	yes	—
11	C₂²×C₄₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₄₁	—	2	2	no	—
13	C₄×C₄₁	C₄²	1	1	yes	characteristic
14	C₄×C₄₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₄₁	C₄×C₈	1	1	yes	characteristic
16	C₂×C₄₁	M₃₂	1	2	yes	—
17	#346	—	41	1	no	maximal, Sylow
18	C₄₁	#346	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₆	—	41	2	no	—
20	C₄×C₈	—	41	1	no	—
21	C₂×C₈	—	41	1	no	—
22	C₂×C₈	—	41	1	no	—
23	C₄²	#4223	1	1	yes	characteristic
24	C₁₆	—	41	4	no	—
25	C₂×C₄	#66493	1	2	yes	—
26	C₂×C₄	C₂×#4223	1	1	yes	characteristic
27	C₈	—	41	2	no	—
28	C₈	—	41	2	no	—
29	C₂²	C₂×#66493	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	#10620296	1	1	yes	characteristic
32	C₄	C₄×#4223	1	1	yes	characteristic
33	C₂	C₄×#66493	1	1	yes	characteristic
34	C₂	#13050238	1	2	yes	—

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

N	H ≅ G/N	type
6. #10620270	C₄	semidirect
18. C₄₁	#346	semidirect

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