Subgroups — D₁₅₄₇₇ #44526244

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁₅₉	—	3	1	no	maximal, Hall
3	C₇×C₁₁×C₆₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₂₁₁	—	7	1	no	maximal, Hall
5	D₁₄₀₇	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₆₇	D₇	1	1	yes	characteristic, complemented, Hall
7	D₇₃₇	—	21	1	no	Hall
8	C₃×C₇×C₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
9	D₄₆₉	—	33	1	no	Hall
10	C₁₁×C₆₇	D₂₁	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	D₃₃	1	1	yes	characteristic, complemented, Hall
12	D₂₃₁	—	67	1	no	maximal, Hall
13	D₂₀₁	—	77	1	no	Hall
14	C₃×C₇×C₁₁	D₆₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₇	D₇₇	1	1	yes	characteristic, complemented, Hall
16	D₇₇	—	201	1	no	Hall
17	D₆₇	—	231	1	no	Hall
18	C₇×C₁₁	D₂₀₁	1	1	yes	characteristic, complemented, Hall
19	C₆₇	D₂₃₁	1	1	yes	characteristic, complemented, Sylow
20	D₃₃	—	469	1	no	Hall
21	D₂₁	—	737	1	no	Hall
22	C₃×C₁₁	D₄₆₉	1	1	yes	characteristic, complemented, Hall
23	D₁₁	—	1407	1	no	Hall
24	C₃×C₇	D₇₃₇	1	1	yes	characteristic, complemented, Hall
25	D₇	—	2211	1	no	Hall
26	C₁₁	D₁₄₀₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₂₂₁₁	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	5159	1	no	Hall
29	C₃	D₅₁₅₉	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15477	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁×C₆₇	C₂
LCS	G ▷ C₃×C₇×C₁₁×C₆₇
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.