Subgroups — #20295424

Order 6976.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812699	C₂	1	2	yes	maximal
2	#16812631	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₈	—	2	2	no	—
5	C₄⋊Dic₁₀₉	—	2	2	no	—
6	C₄⋊Dic₁₀₉	C₂²	1	4	yes	—
7	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
8	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
10	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
11	C₂×Dic₁₀₉	—	2	4	no	—
12	Dic₂₁₈	—	4	4	no	—
13	C₈×C₁₀₉	Q₈	1	4	yes	complemented
14	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₀₉	SD₁₆	1	4	yes	—
16	C₄×C₁₀₉	C₂×Q₈	1	2	yes	—
17	Dic₁₀₉	—	4	4	no	—
18	C₂×C₁₀₉	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₁₀₉	C₂×SD₁₆	1	2	yes	—
20	C₁₀₉	#498	1	1	yes	characteristic, complemented, Sylow
21	#498	—	109	1	no	maximal, Sylow
22	C₄⋊Q₈	—	109	2	no	—
23	#106	—	109	4	no	—
24	C₄×C₈	D₁₀₉	1	1	yes	characteristic
25	C₂×Q₈	—	218	2	no	—
26	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
27	C₄⋊C₄	—	109	4	no	—
28	C₄⋊C₄	—	218	2	no	—
29	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
30	Q₈	—	436	4	no	—
31	C₂×C₄	—	218	4	no	—
32	C₂×C₄	D₄₃₆	1	2	yes	—
33	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
34	C₈	Dic₂₁₈	1	4	yes	complemented
35	C₂²	C₂×D₄₃₆	1	1	yes	characteristic
36	C₄	—	436	4	no	—
37	C₄	#13182018	1	4	yes	—
38	C₄	C₂×Dic₂₁₈	1	2	yes	—
39	C₂	#16812699	1	1	yes	characteristic
40	C₂	C₂×#13182018	1	2	yes	—

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