Subgroups — #261×C₆₇⋊C₉ #44535600

Order 31356.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₆₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#261×C₆₇	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₆₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
5	#261×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic
7	C₄×C₆₇⋊C₉	—	13	1	no	maximal, Hall
8	D₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic
9	C₂×C₆₇⋊C₉	—	13	1	no	—
10	C₁₃×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₆₇	—	13	1	no	—
12	C₆₇⋊C₉	#261	1	1	yes	characteristic, direct product factor, Hall
13	C₉×#261	—	67	1	no	maximal, Hall
14	C₂×C₃×C₆₇	—	13	1	no	—
15	C₄×C₆₇	—	13	1	no	Hall
16	C₉×D₁₃	—	67	1	no	—
17	C₃×C₆₇	C₃×#261	1	1	yes	characteristic
18	C₃×#261	C₆₇⋊C₃	1	1	yes	characteristic
19	C₂×C₆₇	—	13	1	no	—
20	C₉×C₁₃	—	67	1	no	Hall
21	C₃×D₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic
22	C₆₇	C₉×#261	1	1	yes	characteristic, complemented, Sylow
23	#261	C₆₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₃	C₄×C₆₇⋊C₃	1	1	yes	characteristic
25	C₄×C₉	—	871	1	no	Hall
26	D₁₃	C₂×C₆₇⋊C₉	1	1	yes	characteristic
27	C₂×C₉	—	871	1	no	—
28	C₁₃	C₄×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	—	67	1	no	Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	13	1	no	Sylow
33	C₃	#261×C₆₇⋊C₃	1	1	yes	characteristic
34	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#261×C₆₇⋊C₃
commutator, hypocenter	C₁₃×C₆₇	C₄×C₉
Fitting, socle	C₃×C₁₃×C₆₇	C₃×C₄
prime radical, cosocle	C₃×D₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃

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.