Subgroups — #34038366

Order 18876.

40 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	C₁₁×Dic₁₄₃	—	3	1	no	maximal, Hall
3	C₁₃×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₃	D₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	#13089712	—	13	1	no	maximal, Hall
7	C₂×C₁₁²⋊C₃	D₁₃	1	1	yes	characteristic
8	Dic₁₄₃	—	3	1	no	—
9	C₁₁×Dic₁₃	—	33	1	no	—
10	C₁₁×Dic₁₁	—	39	1	no	Hall
11	C₁₁²⋊C₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₃	—	3	1	no	—
13	C₂×C₁₁×C₁₃	—	6	1	no	—
14	C₂×C₁₁×C₁₃	—	6	1	no	—
15	C₂×C₁₁²	D₃₉	1	1	yes	characteristic
16	Dic₃₉	—	121	1	no	maximal, Hall
17	C₁₁×C₁₃	—	3	1	no	—
18	C₁₁×C₁₃	—	6	1	no	—
19	C₁₁×C₁₃	—	6	1	no	—
20	C₁₁²	Dic₃₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₁₃	—	242	1	no	—
22	Dic₁₃	—	33	1	no	Hall
23	C₄×C₁₁	—	429	1	no	—
24	Dic₁₁	—	39	1	no	—
25	C₃×C₁₃	—	242	1	no	Hall
26	C₂×C₁₃	#10624391	1	1	yes	characteristic
27	C₂×C₁₁	—	3	1	no	—
28	C₂×C₁₁	—	6	1	no	—
29	C₂×C₁₁	—	6	1	no	—
30	C₁₃	#13089712	1	1	yes	characteristic, complemented, Sylow
31	Dic₃	—	1573	1	no	Hall
32	C₁₁	—	3	1	no	—
33	C₁₁	—	6	1	no	—
34	C₁₁	—	6	1	no	—
35	C₂×C₃	—	242	1	no	—
36	C₄	—	429	1	no	Sylow
37	C₃	—	242	1	no	Sylow
38	C₂	C₁₃⋊#10624391	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₃⋊#10624391
commutator, hypocenter	C₁₃×C₁₁²⋊C₃	C₄
Fitting, socle	C₂×C₁₁²×C₁₃	D₃
prime radical, cosocle	C₂×C₁₃×C₁₁²⋊C₃	C₂
LCS	G ▷ C₁₃×C₁₁²⋊C₃
UCS	C₁ ◁ C₂

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.