Subgroups — (C₆₇⋊C₃)⋊#1181 #37552172

Order 23316.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₆₇⋊#1181	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₆₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₂₉×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₂₉×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₆₇⋊C₃)⋊C₄	—	29	1	no	maximal, Hall
7	C₂×C₆₇⋊C₃	—	29	1	no	—
8	C₃×#1181	—	67	1	no	maximal, Hall
9	Dic₆₇	—	29	1	no	Hall
10	C₆₇⋊C₃	#1181	1	1	yes	characteristic, complemented, Hall
11	C₃×D₂₉	—	134	1	no	—
12	C₂×C₆₇	—	29	1	no	—
13	#1181	—	67	1	no	Hall
14	C₃×C₂₉	—	134	1	no	Hall
15	C₆₇	C₃×#1181	1	1	yes	characteristic, complemented, Sylow
16	D₂₉	D₆₇⋊C₃	1	1	yes	characteristic
17	C₂₉	(C₆₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1943	1	no	Hall
19	C₂×C₃	—	3886	1	no	—
20	C₄	—	1943	1	no	Sylow
21	C₃	—	134	1	no	Sylow
22	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉×C₆₇	C₃×C₄
prime radical	D₂₉×C₆₇⋊C₃	C₂
cosocle	D₂₉×C₆₇	C₂×C₃
LCS	G ▷ C₂₉×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.