Subgroups — C₄×Dic₁₂₃ #14520149

Order 1968.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₂₃	C₂	1	2	yes	maximal
3	C₄×Dic₄₁	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄₁	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₄₁	C₄	1	2	yes	complemented
6	Dic₁₂₃	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₄₁	D₃	1	1	yes	characteristic
8	C₂×Dic₄₁	—	3	2	no	—
9	C₂×C₃×C₄₁	C₂×C₄	1	2	yes	—
10	C₂×C₃×C₄₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄₁	C₂×D₃	1	1	yes	characteristic
12	C₄×C₄₁	Dic₃	1	2	yes	complemented
13	Dic₄₁	—	3	4	no	—
14	C₃×C₄₁	C₄²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₄₁	C₄×D₃	1	2	yes	—
16	C₂×C₄₁	C₂×Dic₃	1	1	yes	characteristic
17	C₄×Dic₃	—	41	1	no	maximal, Hall
18	C₄₁	C₄×Dic₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₄	D₄₁	1	1	yes	characteristic
20	C₂×Dic₃	—	41	2	no	—
21	C₄²	—	123	1	no	Sylow
22	C₂²×C₃	C₂×D₄₁	1	1	yes	characteristic
23	C₃×C₄	Dic₄₁	1	2	yes	complemented
24	Dic₃	—	41	4	no	—
25	C₂×C₄	—	123	2	no	—
26	C₂×C₄	D₁₂₃	1	1	yes	characteristic
27	C₂×C₃	C₄×D₄₁	1	2	yes	—
28	C₂×C₃	C₂×Dic₄₁	1	1	yes	characteristic
29	C₂²	C₂×D₁₂₃	1	1	yes	characteristic
30	C₄	—	123	4	no	—
31	C₄	Dic₁₂₃	1	2	yes	direct product factor
32	C₃	C₄×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₄×D₁₂₃	1	2	yes	—
34	C₂	C₂×Dic₁₂₃	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.