Subgroups — Q₈×#261 #88241

Order 416.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#261	C₂	1	3	yes	maximal
3	C₄×#261	C₂	1	3	yes	maximal
4	C₂×#261	C₂²	1	3	yes	—
5	C₂×#261	C₂²	1	1	yes	characteristic
6	Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₄×D₁₃	C₂²	1	3	yes	—
8	Dic₂₆	C₄	1	3	yes	complemented
9	C₂×D₁₃	C₂³	1	1	yes	characteristic
10	#261	—	2	3	no	—
11	#261	Q₈	1	2	yes	direct product factor
12	C₄×C₁₃	C₂×C₄	1	3	yes	—
13	Dic₁₃	C₂×C₄	1	3	yes	—
14	C₄×Q₈	—	13	1	no	maximal, Sylow
15	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
16	D₁₃	C₂×Q₈	1	1	yes	characteristic
17	D₁₃	#41	1	1	yes	characteristic
18	C₂×Q₈	—	13	1	no	—
19	C₄⋊C₄	—	13	3	no	—
20	C₄²	—	13	3	no	—
21	C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	13	3	no	—
23	Q₈	#261	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	13	1	no	—
25	C₂×C₄	—	13	3	no	—
26	C₂×C₄	—	13	3	no	—
27	C₂²	—	13	1	no	—
28	C₄	—	13	2	no	—
29	C₄	—	13	3	no	—
30	C₄	—	26	3	no	—
31	C₄	C₂×#261	1	3	yes	—
32	C₂	—	13	1	no	—
33	C₂	—	13	1	no	—
34	C₂	C₂²×#261	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.