Subgroups — #27193360

Order 13184.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₂₉₆	C₂	1	1	yes	maximal, characteristic
3	C₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₈₂₄	—	2	1	no	—
5	D₁₆₄₈	—	2	1	no	—
6	C₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
7	Dic₄₁₂	—	4	1	no	—
8	D₈₂₄	—	4	1	no	—
9	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
10	D₄₁₂	—	8	1	no	—
11	Dic₂₀₆	—	8	1	no	—
12	C₈×C₁₀₃	D₈	1	1	yes	characteristic
13	C₂×D₁₀₃	—	16	1	no	—
14	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
15	Dic₁₀₃	—	16	1	no	—
16	C₂×C₁₀₃	D₃₂	1	1	yes	characteristic
17	D₁₀₃	—	32	1	no	—
18	SD₁₂₈	—	103	1	no	maximal, Sylow
19	C₁₀₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	—	103	1	no	—
21	D₃₂	—	103	1	no	—
22	C₆₄	D₁₀₃	1	1	yes	characteristic, complemented
23	Q₃₂	—	206	1	no	—
24	D₁₆	—	206	1	no	—
25	C₃₂	C₂×D₁₀₃	1	1	yes	characteristic
26	Q₁₆	—	412	1	no	—
27	D₈	—	412	1	no	—
28	C₁₆	D₄₁₂	1	1	yes	characteristic
29	Q₈	—	824	1	no	—
30	D₄	—	824	1	no	—
31	C₈	D₈₂₄	1	1	yes	characteristic
32	C₂²	—	1648	1	no	—
33	C₄	—	1648	1	no	—
34	C₄	D₁₆₄₈	1	1	yes	characteristic
35	C₂	—	3296	1	no	—
36	C₂	D₃₂₉₆	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.