Subgroups — #20295952

Order 6976.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812768	C₂	1	2	yes	maximal
2	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#89137	—	2	2	no	—
4	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
5	#13182004	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#89137	—	4	2	no	—
8	C₄×D₁₀₉	D₄	1	1	yes	characteristic
9	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	#11724784	Q₈	1	1	yes	characteristic
11	C₂×D₁₀₉	D₈	1	1	yes	characteristic
12	#89137	—	8	2	no	—
13	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
14	Dic₁₀₉	Q₁₆	1	1	yes	characteristic
15	C₂×C₁₀₉	#107	1	1	yes	characteristic
16	D₁₀₉	D₁₆	1	1	yes	characteristic
17	D₁₀₉	Q₃₂	1	1	yes	characteristic
18	C₁₀₉	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	109	1	no	maximal, Sylow
20	C₂×C₁₆	—	109	1	no	—
21	#107	—	109	2	no	—
22	C₂×C₈	—	109	1	no	—
23	C₄⋊C₄	—	218	2	no	—
24	C₁₆	—	109	1	no	—
25	C₁₆	#89137	1	1	yes	characteristic, complemented
26	C₂×C₄	—	109	1	no	—
27	C₂×C₄	—	436	2	no	—
28	C₈	—	109	1	no	—
29	C₈	C₂×#89137	1	1	yes	characteristic
30	C₂²	—	109	1	no	—
31	C₄	—	872	2	no	—
32	C₄	—	109	1	no	—
33	C₄	C₄⋊#89137	1	1	yes	characteristic
34	C₂	—	109	1	no	—
35	C₂	—	109	1	no	—
36	C₂	#16812768	1	1	yes	characteristic

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