Subgroups — Q₈×#89137 #16812780

Order 3488.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#89137	C₂	1	3	yes	maximal
2	C₄×#89137	C₂	1	3	yes	maximal
3	Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#89137	C₂²	1	3	yes	—
5	C₂×#89137	C₂²	1	1	yes	characteristic
6	Q₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₄×D₁₀₉	C₂²	1	3	yes	—
8	Dic₂₁₈	C₄	1	3	yes	complemented
9	C₂×D₁₀₉	C₂³	1	1	yes	characteristic
10	#89137	—	2	3	no	—
11	#89137	Q₈	1	2	yes	direct product factor
12	C₄×C₁₀₉	C₂×C₄	1	3	yes	—
13	Dic₁₀₉	C₂×C₄	1	3	yes	—
14	C₂×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
15	D₁₀₉	C₂×Q₈	1	1	yes	characteristic
16	D₁₀₉	#41	1	1	yes	characteristic
17	C₁₀₉	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	109	1	no	maximal, Sylow
19	C₂×Q₈	—	109	1	no	—
20	C₄⋊C₄	—	109	3	no	—
21	C₄²	—	109	3	no	—
22	Q₈	—	109	3	no	—
23	Q₈	#89137	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	109	1	no	—
25	C₂×C₄	—	109	3	no	—
26	C₂×C₄	—	109	3	no	—
27	C₂²	—	109	1	no	—
28	C₄	—	109	2	no	—
29	C₄	—	109	3	no	—
30	C₄	—	218	3	no	—
31	C₄	C₂×#89137	1	3	yes	—
32	C₂	—	109	1	no	—
33	C₂	—	109	1	no	—
34	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.