Subgroups — #34038416

Order 18876.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	#20262574	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#92150	—	13	1	no	maximal, Hall
7	D₁₁×C₁₃⋊C₃	—	22	6	no	—
8	C₃×C₁₁⋊D₁₁	—	26	1	no	—
9	#92150	—	13	1	no	Hall
10	C₁₁×C₁₃⋊C₃	—	2	6	no	—
11	C₃×C₁₁²	—	26	1	no	Hall
12	C₁₃×D₁₁	—	22	6	no	—
13	C₁₁⋊D₁₁	D₁₃⋊C₃	1	1	yes	characteristic
14	Dic₁₃⋊C₃	—	121	1	no	maximal, Hall
15	C₁₁×C₁₃	—	2	6	no	—
16	C₁₁²	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₃⋊C₃	—	121	1	no	—
18	C₃×D₁₁	—	286	6	no	—
19	Dic₁₃	—	121	1	no	Hall
20	C₁₃⋊C₃	#92150	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	—	26	6	no	—
22	C₂×C₁₃	—	121	1	no	—
23	D₁₁	—	22	6	no	—
24	C₁₃	C₃×#92150	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₄	—	1573	1	no	Hall
26	C₁₁	—	2	6	no	—
27	C₂×C₃	—	3146	1	no	—
28	C₄	—	1573	1	no	Sylow
29	C₃	—	26	1	no	Sylow
30	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₁₃	C₃×C₄
prime radical	C₁₃⋊C₃×C₁₁⋊D₁₁	C₂
cosocle	C₁₃×C₁₁⋊D₁₁	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.