Subgroups — #16812762

Order 3488.

42 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	Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#89137	—	2	1	no	—
5	Q₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
6	C₄×D₁₀₉	—	2	1	no	—
7	C₄×D₁₀₉	C₂²	1	1	yes	characteristic
8	Dic₂₁₈	—	2	1	no	—
9	Dic₂₁₈	C₄	1	1	yes	characteristic, complemented
10	#11724786	—	2	1	no	—
11	C₂×D₁₀₉	D₄	1	1	yes	characteristic
12	#89137	—	4	1	no	—
13	C₄×C₁₀₉	—	2	1	no	—
14	C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	Dic₁₀₉	—	2	1	no	—
16	Dic₁₀₉	D₄	1	1	yes	characteristic
17	C₂×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₀₉	SD₁₆	1	1	yes	characteristic
19	D₁₀₉	Q₁₆	1	1	yes	characteristic
20	C₁₀₉	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	109	1	no	maximal, Sylow
22	C₂×Q₈	—	109	1	no	—
23	C₂×C₈	—	109	1	no	—
24	C₄⋊C₄	—	109	1	no	—
25	Q₈	—	109	1	no	—
26	Q₈	—	218	1	no	—
27	Q₈	#89137	1	1	yes	characteristic, complemented
28	C₂×C₄	—	109	1	no	—
29	C₂×C₄	—	218	1	no	—
30	C₂×C₄	—	218	1	no	—
31	C₈	—	218	1	no	—
32	C₂²	—	109	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	109	1	no	—
35	C₄	—	436	1	no	—
36	C₄	—	218	1	no	—
37	C₄	C₂×#89137	1	1	yes	characteristic
38	C₂	—	109	1	no	—
39	C₂	—	109	1	no	—
40	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.