Subgroups — C₁₃×(C₁₁⋊Dic₁₁)⋊C₃ #34038367

Order 18876.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₁⋊Dic₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₁⋊Dic₁₁)⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁²⋊C₃	C₂×C₁₃	1	1	yes	characteristic
8	C₁₃×Dic₁₁	—	33	4	no	—
9	C₁₁⋊Dic₁₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₁²⋊C₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₁₃	—	3	4	no	—
12	C₂×C₁₁²	C₂×C₃×C₁₃	1	1	yes	characteristic
13	C₃×C₄×C₁₃	—	121	1	no	maximal, Hall
14	C₁₁×C₁₃	—	3	4	no	—
15	C₁₁²	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₁₃	—	121	1	no	—
17	C₄×C₁₃	—	121	1	no	Hall
18	Dic₁₁	—	33	4	no	—
19	C₃×C₁₃	—	121	1	no	Hall
20	C₂×C₁₃	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
21	C₂×C₁₁	—	3	4	no	—
22	C₁₃	(C₁₁⋊Dic₁₁)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₄	—	121	1	no	Hall
24	C₁₁	—	3	4	no	—
25	C₂×C₃	—	121	1	no	—
26	C₄	—	121	1	no	Sylow
27	C₃	—	121	1	no	Sylow
28	C₂	C₁₃×(C₁₁⋊D₁₁)⋊C₃	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.