Subgroups — #32913821

Order 18396.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22604108	C₂	1	1	yes	maximal, characteristic
2	#20259505	C₃	1	1	yes	maximal, characteristic
3	#17987163	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₇₃⋊C₃	C₂×C₃	1	1	yes	characteristic
5	#14581496	—	7	1	no	maximal, Hall
6	C₇⋊#64408	C₉	1	1	yes	characteristic, complemented, Hall
7	C₇×C₇₃⋊C₃	C₃×C₄	1	1	yes	characteristic
8	#10620323⋊C₂	—	7	1	no	—
9	C₇×D₇₃	C₂×C₉	1	1	yes	characteristic
10	#64408⋊C₃	—	21	1	no	—
11	#10620323	—	7	1	no	Hall
12	C₇×C₇₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	D₇₃⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
14	#64408	—	21	1	no	Hall
15	Dic₇⋊C₉	—	73	1	no	maximal, Hall
16	C₇₃⋊C₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
17	D₇₃	D₇⋊C₉	1	1	yes	characteristic
18	C₂×C₇⋊C₉	—	73	1	no	—
19	C₃×Dic₇	—	73	1	no	—
20	C₇₃	Dic₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
21	C₇⋊C₉	—	73	1	no	Hall
22	C₂×C₃×C₇	—	73	1	no	—
23	C₄×C₉	—	511	1	no	Hall
24	Dic₇	—	657	1	no	Hall
25	C₃×C₇	—	73	1	no	—
26	C₂×C₉	—	511	1	no	—
27	C₂×C₇	—	657	1	no	—
28	C₃×C₄	—	1533	1	no	—
29	C₉	—	511	1	no	Sylow
30	C₇	#14581496	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	73	1	no	—
32	C₄	—	4599	1	no	Sylow
33	C₃	—	73	1	no	—
34	C₂	—	73	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₇₃	C₄×C₉
prime radical, cosocle	C₇×D₇₃⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₇₃
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.