Subgroups — C₃⋊(C₃⋊(C₇⋊#87604)) #37567979

Order 24444.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₉₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#87604)	—	3	4	no	maximal
3	C₃²×C₇×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₉₇	D₃	1	4	yes	—
5	C₃⋊(C₃⋊#87604)	—	7	1	no	maximal, Hall
6	C₇⋊#87604	—	9	1	no	Hall
7	C₃×C₇×C₉₇	Dic₃	1	4	yes	complemented
8	C₃²×D₉₇	D₇	1	1	yes	characteristic
9	C₇×D₉₇	C₃⋊D₃	1	1	yes	characteristic
10	C₃⋊#87604	—	21	4	no	—
11	C₃²×C₉₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₉₇	D₂₁	1	4	yes	—
14	#87604	—	63	1	no	Hall
15	C₃×C₉₇	Dic₂₁	1	4	yes	complemented
16	C₃⋊Dic₂₁	—	97	1	no	maximal, Hall
17	D₉₇	C₃⋊D₂₁	1	1	yes	characteristic
18	C₂×C₃²×C₇	—	97	1	no	—
19	C₉₇	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
20	Dic₂₁	—	291	4	no	—
21	C₃²×C₇	#87604	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	—	97	4	no	—
23	C₃⋊Dic₃	—	679	1	no	Hall
24	Dic₇	—	873	1	no	Hall
25	C₃×C₇	C₃⋊#87604	1	4	yes	complemented
26	C₂×C₃²	—	97	1	no	—
27	C₂×C₇	—	97	1	no	—
28	Dic₃	—	2037	4	no	—
29	C₃²	C₇⋊#87604	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊(C₃⋊#87604)	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	97	4	no	—
32	C₄	—	6111	1	no	Sylow
33	C₃	C₃⋊(C₇⋊#87604)	1	4	yes	complemented
34	C₂	—	97	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₉₇	C₄
prime radical, cosocle	C₃²×C₇×D₉₇	C₂
LCS	G ▷ C₃²×C₇×C₉₇
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.