Subgroups — C₈×#89137 #16812751

Order 3488.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.