Subgroups — Q₈×D₆₉ #11764277

Order 1104.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₆₉	C₂	1	3	yes	maximal
3	Dic₁₃₈	C₂	1	3	yes	maximal, complemented
4	Q₈×D₂₃	—	3	1	no	maximal, Hall
5	C₂×D₆₉	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₂₃	C₂²	1	3	yes	—
7	Dic₆₉	C₂²	1	3	yes	—
8	Q₈×C₂₃	D₃	1	1	yes	characteristic, complemented
9	C₄×D₂₃	—	3	3	no	—
10	Dic₄₆	—	3	3	no	—
11	C₂×C₃×C₂₃	C₂³	1	1	yes	characteristic
12	D₆₉	Q₈	1	2	yes	direct product factor
13	C₂×D₂₃	—	3	1	no	—
14	C₄×C₂₃	C₂×D₃	1	3	yes	—
15	Dic₂₃	—	3	3	no	—
16	C₃×C₂₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
17	D₃×Q₈	—	23	1	no	maximal, Hall
18	C₂×C₂₃	C₂²×D₃	1	1	yes	characteristic
19	D₂₃	—	3	2	no	—
20	C₃×Q₈	D₂₃	1	1	yes	characteristic, complemented
21	C₄×D₃	—	23	3	no	—
22	Dic₆	—	23	3	no	—
23	C₂₃	D₃×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×Q₈	—	69	1	no	Sylow
25	C₂×D₃	—	23	1	no	—
26	C₃×C₄	C₂×D₂₃	1	3	yes	—
27	Dic₃	—	23	3	no	—
28	Q₈	—	69	3	no	—
29	Q₈	D₆₉	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	69	3	no	—
31	C₂×C₃	C₂²×D₂₃	1	1	yes	characteristic
32	D₃	—	23	2	no	—
33	C₂²	—	69	1	no	—
34	C₄	—	69	3	no	—
35	C₄	C₂×D₆₉	1	3	yes	—
36	C₃	Q₈×D₂₃	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	69	2	no	—
38	C₂	C₂²×D₆₉	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.