Subgroups — #16812767

Order 3488.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#89137	C₂	1	2	yes	maximal
2	C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#89137	—	2	2	no	—
4	C₄×D₁₀₉	C₂²	1	1	yes	characteristic
5	C₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
6	#11724784	C₄	1	1	yes	characteristic, complemented
7	C₂×D₁₀₉	D₄	1	1	yes	characteristic
8	#89137	—	4	2	no	—
9	C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	Dic₁₀₉	Q₈	1	1	yes	characteristic
11	C₂×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
12	D₁₀₉	SD₁₆	1	2	yes	—
13	C₁₀₉	#106	1	1	yes	characteristic, complemented, Sylow
14	#106	—	109	1	no	maximal, Sylow
15	C₂×C₈	—	109	1	no	—
16	C₄⋊C₄	—	109	2	no	—
17	C₂×C₄	—	109	1	no	—
18	C₂×C₄	—	218	2	no	—
19	C₈	—	109	1	no	—
20	C₈	#89137	1	1	yes	characteristic, complemented
21	C₂²	—	109	1	no	—
22	C₄	—	109	1	no	—
23	C₄	—	436	2	no	—
24	C₄	C₂×#89137	1	1	yes	characteristic
25	C₂	—	109	2	no	—
26	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.