Subgroups — #16812787

Order 3488.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13182039	C₂	1	3	yes	maximal, complemented
2	D₁₀₉⋊C₈	C₂	1	3	yes	maximal, complemented
3	#13182030	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₀₉	C₄	1	1	yes	characteristic
5	D₄₃₆	C₄	1	3	yes	—
6	C₄×D₁₀₉	C₂²	1	3	yes	—
7	#11724786	C₂²	1	1	yes	characteristic
8	#11724786	C₂²	1	3	yes	—
9	C₂×D₁₀₉	C₂×C₄	1	3	yes	—
10	C₄×C₁₀₉	C₂×C₄	1	3	yes	—
11	Dic₁₀₉	C₂³	1	1	yes	characteristic
12	C₂×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
13	D₁₀₉	—	2	3	no	—
14	C₁₀₉	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	109	1	no	maximal, Sylow
16	#41	—	109	1	no	—
17	M₁₆	—	109	3	no	—
18	C₂×C₈	—	109	3	no	—
19	Q₈	#89137	1	1	yes	characteristic
20	D₄	—	109	3	no	—
21	C₂×C₄	—	109	3	no	—
22	C₈	—	109	1	no	—
23	C₈	—	109	3	no	—
24	C₂²	—	109	3	no	—
25	C₄	—	109	1	no	—
26	C₄	C₂×#89137	1	3	yes	—
27	C₂	—	218	3	no	—
28	C₂	C₂²×#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.