Subgroups — #20295913

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#89137	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	D₁₀₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#89137	C₄	1	1	yes	characteristic
6	#13182032	C₄	1	2	yes	complemented
7	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
8	#13182004	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#89137	C₈	1	2	yes	—
11	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
12	#11724786	C₈	1	2	yes	—
13	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	#11724784	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₀₉	C₂×C₈	1	1	yes	characteristic
16	#89137	—	2	2	no	—
17	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
18	Dic₁₀₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
20	D₁₀₉	M₃₂	1	2	yes	—
21	C₁₀₉	#346	1	1	yes	characteristic, complemented, Sylow
22	#346	—	109	1	no	maximal, Sylow
23	C₂×C₁₆	—	109	1	no	—
24	C₂×C₁₆	—	109	1	no	—
25	C₄×C₈	—	109	1	no	—
26	C₂×C₈	—	109	1	no	—
27	C₂×C₈	—	109	1	no	—
28	C₄²	—	109	1	no	—
29	C₁₆	—	109	2	no	—
30	C₁₆	—	109	1	no	—
31	C₁₆	#89137	1	1	yes	characteristic, complemented
32	C₂×C₄	—	109	1	no	—
33	C₂×C₄	—	109	2	no	—
34	C₈	—	109	2	no	—
35	C₈	—	109	1	no	—
36	C₈	C₂×#89137	1	1	yes	characteristic
37	C₂²	—	109	1	no	—
38	C₄	—	109	1	no	—
39	C₄	—	218	2	no	—
40	C₄	C₄×#89137	1	1	yes	characteristic
41	C₂	—	109	2	no	—
42	C₂	C₈×#89137	1	1	yes	characteristic

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