Subgroups — C₄⋊(C₃⋊D₆₉) #13110264

Order 1656.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₆₉	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₇₆	—	3	4	no	maximal
4	C₂×C₃²×C₂₃	C₂²	1	1	yes	characteristic
5	C₃⋊D₆₉	—	2	2	no	—
6	C₂×D₆₉	—	3	8	no	—
7	C₃×C₄×C₂₃	D₃	1	4	yes	complemented
8	C₃²×C₂₃	D₄	1	1	yes	characteristic, complemented, Hall
9	D₉₂	—	9	1	no	Hall
10	C₂×C₃×C₂₃	C₂×D₃	1	4	yes	—
11	D₆₉	—	6	8	no	—
12	C₂×D₂₃	—	9	2	no	—
13	C₄×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₄⋊(C₃⋊D₃)	—	23	1	no	maximal, Hall
15	C₃×C₂₃	D₁₂	1	4	yes	complemented
16	C₂×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic
17	D₂₃	—	18	2	no	—
18	C₂×C₃⋊D₃	—	23	2	no	—
19	C₃²×C₄	D₂₃	1	1	yes	characteristic, complemented
20	D₁₂	—	69	4	no	—
21	C₂₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃²	C₂×D₂₃	1	1	yes	characteristic
23	C₃⋊D₃	—	46	2	no	—
24	C₂×D₃	—	69	8	no	—
25	C₃×C₄	D₆₉	1	4	yes	complemented
26	C₃²	D₉₂	1	1	yes	characteristic, complemented, Sylow
27	D₄	—	207	1	no	Sylow
28	C₂×C₃	C₂×D₆₉	1	4	yes	—
29	D₃	—	138	8	no	—
30	C₂²	—	207	2	no	—
31	C₄	C₃⋊D₆₉	1	1	yes	characteristic, complemented
32	C₃	D₂₇₆	1	4	yes	complemented
33	C₂	—	414	2	no	—
34	C₂	C₂×C₃⋊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.