Subgroups — #28361246

Order 13952.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₈₈	C₂	1	1	yes	maximal, characteristic
2	#20294745	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₆₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇₄₄	—	2	1	no	—
5	Q₃₂×C₁₀₉	—	2	1	no	—
6	C₃₂×C₁₀₉	C₂²	1	1	yes	characteristic
7	D₈₇₂	—	4	1	no	—
8	Q₁₆×C₁₀₉	—	4	1	no	—
9	C₁₆×C₁₀₉	D₄	1	1	yes	characteristic
10	Q₈×C₁₀₉	—	8	1	no	—
11	D₄₃₆	—	8	1	no	—
12	C₈×C₁₀₉	D₈	1	1	yes	characteristic
13	C₂×D₁₀₉	—	16	1	no	—
14	C₄×C₁₀₉	—	16	1	no	—
15	C₄×C₁₀₉	D₁₆	1	1	yes	characteristic
16	C₂×C₁₀₉	D₃₂	1	1	yes	characteristic
17	D₁₀₉	—	32	1	no	—
18	SD₁₂₈	—	109	1	no	maximal, Sylow
19	C₁₀₉	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	D₁₀₉	1	1	yes	characteristic, complemented
21	D₃₂	—	109	1	no	—
22	C₆₄	—	109	1	no	—
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	218	1	no	—
25	C₃₂	C₂×D₁₀₉	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	436	1	no	—
28	C₁₆	C₂²⋊D₁₀₉	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	872	1	no	—
31	C₈	#13182014	1	1	yes	characteristic
32	C₂²	—	1744	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#16812640	1	1	yes	characteristic
35	C₂	—	3488	1	no	—
36	C₂	#20294861	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.