Subgroups — C₄²×#89137 #20295960

Order 6976.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#89137	C₂	1	6	yes	maximal
2	C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#89137	C₂²	1	4	yes	—
4	C₄×#89137	C₄	1	24	yes	direct product factor
5	C₂×C₄×D₁₀₉	C₂²	1	3	yes	—
6	C₄×Dic₁₀₉	C₄	1	3	yes	complemented
7	C₄²×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂²×D₁₀₉	C₂³	1	1	yes	characteristic
9	C₂×#89137	C₂×C₄	1	24	yes	—
10	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
11	C₂×Dic₁₀₉	C₂×C₄	1	3	yes	—
12	C₄×D₁₀₉	C₂×C₄	1	12	yes	—
13	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₁₀₉	C₂²×C₄	1	6	yes	—
15	#89137	C₄²	1	16	yes	direct product factor
16	C₄×C₁₀₉	C₄²	1	6	yes	complemented
17	Dic₁₀₉	C₄²	1	6	yes	complemented
18	C₂×C₁₀₉	C₂×C₄²	1	3	yes	—
19	D₁₀₉	C₂×C₄²	1	4	yes	—
20	C₁₀₉	C₄³	1	1	yes	characteristic, complemented, Sylow
21	C₄³	—	109	1	no	maximal, Sylow
22	C₂×C₄²	—	109	6	no	—
23	C₂×C₄²	—	109	1	no	—
24	C₂²×C₄	—	109	4	no	—
25	C₂²×C₄	—	109	3	no	—
26	C₄²	—	109	24	no	—
27	C₄²	—	109	3	no	—
28	C₄²	#89137	1	1	yes	characteristic, direct product factor
29	C₂³	—	109	1	no	—
30	C₂×C₄	—	109	24	no	—
31	C₂×C₄	—	109	3	no	—
32	C₂×C₄	—	109	12	no	—
33	C₂×C₄	C₂×#89137	1	3	yes	—
34	C₂²	—	109	6	no	—
35	C₂²	C₂²×#89137	1	1	yes	characteristic
36	C₄	—	109	16	no	—
37	C₄	—	109	6	no	—
38	C₄	C₄×#89137	1	6	yes	direct product factor
39	C₂	—	109	4	no	—
40	C₂	C₂×C₄×#89137	1	3	yes	—

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