Subgroups — #27193361

Order 13184.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₆₄₈	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	Dic₈₂₄	—	2	1	no	—
5	Q₃₂×C₁₀₃	—	2	1	no	—
6	C₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
7	Dic₄₁₂	—	4	1	no	—
8	Q₁₆×C₁₀₃	—	4	1	no	—
9	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
10	Q₈×C₁₀₃	—	8	1	no	—
11	Dic₂₀₆	—	8	1	no	—
12	C₈×C₁₀₃	D₈	1	1	yes	characteristic
13	C₄×C₁₀₃	—	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	Q₁₂₈	—	103	1	no	maximal, Sylow
18	C₁₀₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	103	1	no	—
20	Q₆₄	D₁₀₃	1	1	yes	characteristic
21	C₆₄	—	103	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	206	1	no	—
24	C₃₂	C₂×D₁₀₃	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	412	1	no	—
27	C₁₆	C₂²⋊D₁₀₃	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	824	1	no	—
30	C₈	#13110090	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1648	1	no	—
33	C₄	#15692962	1	1	yes	characteristic
34	C₂	#20267626	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
18. C₁₀₃	Q₁₂₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.