Subgroups — C₁₇×(C₁₁⋊Dic₁₁)⋊C₃ #37590586

Order 24684.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₁⋊Dic₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₁⋊Dic₁₁)⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×Dic₁₁	—	33	4	no	—
8	C₂×C₁₁²⋊C₃	C₂×C₁₇	1	1	yes	characteristic
9	C₁₁⋊Dic₁₁	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₇	—	3	4	no	—
11	C₁₁²⋊C₃	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁²	C₂×C₃×C₁₇	1	1	yes	characteristic
13	C₃×C₄×C₁₇	—	121	1	no	maximal, Hall
14	C₁₁×C₁₇	—	3	4	no	—
15	C₁₁²	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₁₇	—	121	1	no	—
17	C₄×C₁₇	—	121	1	no	Hall
18	C₃×C₁₇	—	121	1	no	Hall
19	Dic₁₁	—	33	4	no	—
20	C₂×C₁₇	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
21	C₂×C₁₁	—	3	4	no	—
22	C₁₇	(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	C₁₇×(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.