Subgroups — C₂×C₄×D₁₄₂₃ #36384705

Order 22768.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₄₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₄₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₁₄₂₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₄₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₄₂₃	C₂²	1	1	yes	characteristic
6	C₂×D₁₄₂₃	C₄	1	4	yes	direct product factor
7	C₂×D₁₄₂₃	C₂²	1	2	yes	—
8	C₄×C₁₄₂₃	C₂²	1	2	yes	complemented
9	Dic₁₄₂₃	C₂²	1	2	yes	complemented
10	C₂×C₁₄₂₃	C₂×C₄	1	2	yes	complemented
11	C₂×C₁₄₂₃	C₂³	1	1	yes	characteristic
12	D₁₄₂₃	C₂×C₄	1	4	yes	direct product factor
13	C₁₄₂₃	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₄	—	1423	1	no	maximal, Sylow
15	C₂³	—	1423	1	no	—
16	C₂×C₄	—	1423	1	no	—
17	C₂×C₄	—	1423	4	no	—
18	C₂×C₄	D₁₄₂₃	1	1	yes	characteristic, direct product factor
19	C₂²	—	1423	4	no	—
20	C₂²	—	1423	2	no	—
21	C₂²	C₂×D₁₄₂₃	1	1	yes	characteristic
22	C₄	—	1423	2	no	—
23	C₄	C₂×D₁₄₂₃	1	2	yes	direct product factor
24	C₂	—	1423	4	no	—
25	C₂	C₄×D₁₄₂₃	1	2	yes	direct product factor
26	C₂	C₂²×D₁₄₂₃	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.