Subgroups — C₈×#11724786 #20295866

Order 6976.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11724786	C₂	1	2	yes	maximal
2	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724786	C₄	1	4	yes	—
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
9	#11724786	C₈	1	8	yes	direct product factor
10	C₈×C₁₀₉	C₈	1	2	yes	complemented
11	#11724784	C₈	1	2	yes	complemented
12	C₂²×C₁₀₉	C₄²	1	1	yes	characteristic
13	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
15	Dic₁₀₉	C₂×C₈	1	4	yes	—
16	C₂×C₁₀₉	C₄×C₈	1	2	yes	—
17	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
18	C₁₀₉	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	109	1	no	maximal, Sylow
20	C₄×C₈	—	109	2	no	—
21	C₄×C₈	—	109	1	no	—
22	C₂×C₈	—	109	4	no	—
23	C₂×C₈	—	109	1	no	—
24	C₂×C₈	#89137	1	1	yes	characteristic
25	C₄²	—	109	1	no	—
26	C₂×C₄	—	109	2	no	—
27	C₂×C₄	C₂×#89137	1	1	yes	characteristic
28	C₈	—	109	8	no	—
29	C₈	—	109	2	no	—
30	C₈	#11724786	1	2	yes	direct product factor
31	C₂²	C₄×#89137	1	1	yes	characteristic
32	C₄	—	109	4	no	—
33	C₄	C₂×#11724786	1	1	yes	characteristic
34	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
35	C₂	C₈×#89137	1	2	yes	—
36	C₂	C₄×#11724786	1	1	yes	characteristic

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