Subgroups — C₄⋊#16812367 #28357313

Order 13856.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812367	C₂	1	2	yes	maximal
2	C₄×#13181884	C₂	1	1	yes	maximal, characteristic
3	#16812367	—	2	2	no	—
4	C₂×#13181884	C₄	1	1	yes	characteristic
5	C₂×#13181884	C₂²	1	1	yes	characteristic
6	C₄×D₄₃₃	C₄	1	1	yes	characteristic
7	C₂×D₄₃₃	C₂×C₄	1	1	yes	characteristic
8	#13181884	—	2	1	no	—
9	#13181884	D₄	1	1	yes	characteristic
10	#13181884	Q₈	1	1	yes	characteristic
11	C₄×C₄₃₃	C₈	1	1	yes	characteristic, complemented
12	Dic₄₃₃	C₈	1	1	yes	characteristic, complemented
13	C₂×C₄₃₃	C₂×C₈	1	1	yes	characteristic
14	D₄₃₃	C₄⋊C₄	1	1	yes	characteristic
15	D₄₃₃	M₁₆	1	1	yes	characteristic
16	C₄₃₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
17	C₄⋊C₈	—	433	1	no	maximal, Sylow
18	C₂×C₈	—	433	2	no	—
19	C₄²	—	433	1	no	—
20	C₂×C₄	—	433	1	no	—
21	C₂×C₄	—	433	1	no	—
22	C₂×C₄	—	433	1	no	—
23	C₈	—	866	2	no	—
24	C₂²	—	433	1	no	—
25	C₄	—	866	1	no	—
26	C₄	—	433	1	no	—
27	C₄	—	433	1	no	—
28	C₄	—	433	1	no	—
29	C₄	#16812367	1	1	yes	characteristic, complemented
30	C₂	—	433	1	no	—
31	C₂	—	433	1	no	—
32	C₂	C₂×#16812367	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.