Subgroups — C₂×Dic₂₄₃ #14515613

Order 1944.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₄₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₄₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×Dic₈₁	—	3	1	no	maximal
4	C₂×C₂₄₃	C₄	1	2	yes	complemented
5	C₂×C₂₄₃	C₂²	1	1	yes	characteristic
6	C₂²×C₈₁	D₃	1	1	yes	characteristic
7	Dic₈₁	—	3	2	no	—
8	C₂₄₃	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂×Dic₂₇	—	9	1	no	—
10	C₂×C₈₁	Dic₃	1	2	yes	—
11	C₂×C₈₁	C₂×D₃	1	1	yes	characteristic
12	C₂²×C₂₇	D₉	1	1	yes	characteristic
13	Dic₂₇	—	9	2	no	—
14	C₈₁	C₂×Dic₃	1	1	yes	characteristic
15	C₂×Dic₉	—	27	1	no	—
16	C₂×C₂₇	Dic₉	1	2	yes	—
17	C₂×C₂₇	C₂×D₉	1	1	yes	characteristic
18	C₂²×C₉	D₂₇	1	1	yes	characteristic
19	Dic₉	—	27	2	no	—
20	C₂₇	C₂×Dic₉	1	1	yes	characteristic
21	C₂×Dic₃	—	81	1	no	—
22	C₂×C₉	Dic₂₇	1	2	yes	—
23	C₂×C₉	C₂×D₂₇	1	1	yes	characteristic
24	C₂²×C₃	D₈₁	1	1	yes	characteristic
25	Dic₃	—	81	2	no	—
26	C₉	C₂×Dic₂₇	1	1	yes	characteristic
27	C₂×C₄	—	243	1	no	Sylow
28	C₂×C₃	Dic₈₁	1	2	yes	—
29	C₂×C₃	C₂×D₈₁	1	1	yes	characteristic
30	C₂²	D₂₄₃	1	1	yes	characteristic
31	C₄	—	243	2	no	—
32	C₃	C₂×Dic₈₁	1	1	yes	characteristic
33	C₂	Dic₂₄₃	1	2	yes	direct product factor
34	C₂	C₂×D₂₄₃	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.