Subgroups — #27212434

Order 13472.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13132997	C₂	1	2	yes	maximal
2	C₈×D₄₂₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#13132997	—	2	2	no	—
4	C₄×D₄₂₁	C₂²	1	1	yes	characteristic
5	#16809890	C₄	1	1	yes	characteristic, complemented
6	C₈×C₄₂₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₄₂₁	D₄	1	1	yes	characteristic
8	#13132997	—	4	2	no	—
9	C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
10	Dic₄₂₁	Q₈	1	1	yes	characteristic
11	C₂×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
12	D₄₂₁	SD₁₆	1	2	yes	—
13	C₄₂₁	#106	1	1	yes	characteristic, complemented, Sylow
14	#106	—	421	1	no	maximal, Sylow
15	C₂×C₈	—	421	1	no	—
16	C₄⋊C₄	—	421	2	no	—
17	C₂×C₄	—	842	2	no	—
18	C₂×C₄	—	421	1	no	—
19	C₈	—	421	1	no	—
20	C₈	#13132997	1	1	yes	characteristic, complemented
21	C₂²	—	421	1	no	—
22	C₄	—	1684	2	no	—
23	C₄	—	421	1	no	—
24	C₄	C₂×#13132997	1	1	yes	characteristic
25	C₂	—	421	2	no	—
26	C₂	C₄⋊#13132997	1	1	yes	characteristic

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.