Subgroups — Q₈×#14524194 #31772709

Order 17312.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14524194	C₂	1	3	yes	maximal
2	C₄×#14524194	C₂	1	3	yes	maximal
3	Q₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14524194	C₂²	1	3	yes	—
5	C₂×#14524194	C₂²	1	1	yes	characteristic
6	Dic₁₀₈₂	C₄	1	3	yes	complemented
7	C₄×D₅₄₁	C₂²	1	3	yes	—
8	Q₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
9	C₂×D₅₄₁	C₂³	1	1	yes	characteristic
10	#14524194	—	2	3	no	—
11	#14524194	Q₈	1	2	yes	direct product factor
12	C₄×C₅₄₁	C₂×C₄	1	3	yes	—
13	Dic₅₄₁	C₂×C₄	1	3	yes	—
14	C₂×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
15	D₅₄₁	C₂×Q₈	1	1	yes	characteristic
16	D₅₄₁	#41	1	1	yes	characteristic
17	C₅₄₁	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	541	1	no	maximal, Sylow
19	C₂×Q₈	—	541	1	no	—
20	C₄⋊C₄	—	541	3	no	—
21	C₄²	—	541	3	no	—
22	Q₈	—	541	3	no	—
23	Q₈	#14524194	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	541	1	no	—
25	C₂×C₄	—	541	3	no	—
26	C₂×C₄	—	541	3	no	—
27	C₂²	—	541	1	no	—
28	C₄	—	541	2	no	—
29	C₄	—	541	3	no	—
30	C₄	—	1082	3	no	—
31	C₄	C₂×#14524194	1	3	yes	—
32	C₂	—	541	1	no	—
33	C₂	—	541	1	no	—
34	C₂	C₂²×#14524194	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.