Subgroups — C₂²×Dic₁₀₄₆ #30660413

Order 16736.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₄₆	C₂	1	12	yes	maximal, direct product factor
2	C₂²×Dic₅₂₃	C₂	1	2	yes	maximal
3	C₂²×C₄×C₅₂₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₀₄₆	C₂²	1	16	yes	direct product factor
5	C₂×Dic₅₂₃	C₂²	1	12	yes	—
6	C₂³×C₅₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅₂₃	C₂²	1	6	yes	—
8	C₂²×C₅₂₃	Q₈	1	4	yes	complemented
9	C₂²×C₅₂₃	C₂³	1	3	yes	—
10	C₄×C₅₂₃	C₂³	1	4	yes	—
11	Dic₅₂₃	C₂³	1	8	yes	—
12	C₂×C₅₂₃	C₂×Q₈	1	6	yes	complemented
13	C₂×C₅₂₃	C₂⁴	1	1	yes	characteristic
14	C₅₂₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×Q₈	—	523	1	no	maximal, Sylow
16	C₂×Q₈	—	523	12	no	—
17	C₂²×C₄	—	523	2	no	—
18	C₂²×C₄	D₅₂₃	1	1	yes	characteristic
19	C₂³	C₂×D₅₂₃	1	1	yes	characteristic
20	Q₈	—	523	16	no	—
21	C₂×C₄	—	523	12	no	—
22	C₂×C₄	C₂×D₅₂₃	1	6	yes	—
23	C₂²	Dic₁₀₄₆	1	4	yes	direct product factor
24	C₂²	C₂²×D₅₂₃	1	3	yes	—
25	C₄	—	523	8	no	—
26	C₄	C₂²×D₅₂₃	1	4	yes	—
27	C₂	C₂×Dic₁₀₄₆	1	6	yes	direct product factor
28	C₂	C₂³×D₅₂₃	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.