Subgroups — #34038413

Order 18876.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊(C₁₁⋊#261)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₁⋊Dic₁₁)⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₁²⋊C₃	—	13	1	no	—
8	C₁₁⋊#261	—	33	4	no	—
9	C₁₁⋊Dic₁₁	—	13	1	no	Hall
10	C₁₁²⋊C₃	#261	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₁₃	—	3	4	no	—
12	C₂×C₁₁²	—	13	1	no	—
13	C₃×#261	—	121	1	no	maximal, Hall
14	C₁₁×C₁₃	—	3	4	no	—
15	C₁₁²	C₃×#261	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₁₃	—	242	1	no	—
17	#261	—	121	1	no	Hall
18	Dic₁₁	—	429	4	no	—
19	C₃×C₁₃	—	242	1	no	Hall
20	D₁₃	(C₁₁⋊D₁₁)⋊C₃	1	1	yes	characteristic
21	C₂×C₁₁	—	39	4	no	—
22	C₁₃	(C₁₁⋊Dic₁₁)⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₄	—	1573	1	no	Hall
24	C₁₁	—	3	4	no	—
25	C₂×C₃	—	3146	1	no	—
26	C₄	—	1573	1	no	Sylow
27	C₃	—	242	1	no	Sylow
28	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₁₃	C₃×C₄
prime radical	D₁₃×C₁₁²⋊C₃	C₂
cosocle	C₁₁²×D₁₃	C₂×C₃
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁

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.