Subgroups — C₄²×Dic₂₂₃ #28383422

Order 14272.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₂₂₃	C₂	1	6	yes	maximal
2	C₂×C₄²×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₂₂₃	C₂²	1	4	yes	—
4	C₄×Dic₂₂₃	C₄	1	24	yes	direct product factor
5	C₂²×C₄×C₂₂₃	C₂²	1	3	yes	—
6	C₄²×C₂₂₃	C₄	1	4	yes	complemented
7	C₂×Dic₂₂₃	C₂×C₄	1	24	yes	—
8	C₂³×C₂₂₃	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₂₂₃	C₂×C₄	1	12	yes	—
10	C₂×C₄×C₂₂₃	C₂×C₄	1	6	yes	—
11	C₂²×C₂₂₃	C₂²×C₄	1	6	yes	—
12	C₂²×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
13	C₄×C₂₂₃	C₄²	1	12	yes	complemented
14	Dic₂₂₃	C₄²	1	16	yes	direct product factor
15	C₂×C₂₂₃	C₂×C₄²	1	4	yes	—
16	C₂×C₂₂₃	C₂×C₄²	1	3	yes	—
17	C₂₂₃	C₄³	1	1	yes	characteristic, complemented, Sylow
18	C₄³	—	223	1	no	maximal, Sylow
19	C₂×C₄²	—	223	6	no	—
20	C₂×C₄²	D₂₂₃	1	1	yes	characteristic
21	C₂²×C₄	—	223	4	no	—
22	C₂²×C₄	C₂×D₂₂₃	1	3	yes	—
23	C₄²	—	223	24	no	—
24	C₄²	Dic₂₂₃	1	4	yes	direct product factor
25	C₂³	C₂²×D₂₂₃	1	1	yes	characteristic
26	C₂×C₄	—	223	24	no	—
27	C₂×C₄	C₄×D₂₂₃	1	12	yes	—
28	C₂×C₄	C₂×Dic₂₂₃	1	6	yes	—
29	C₂²	C₂×C₄×D₂₂₃	1	6	yes	—
30	C₂²	C₂²×Dic₂₂₃	1	1	yes	characteristic
31	C₄	—	223	16	no	—
32	C₄	C₄×Dic₂₂₃	1	12	yes	direct product factor
33	C₂	C₄²×D₂₂₃	1	4	yes	—
34	C₂	C₂×C₄×Dic₂₂₃	1	3	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.