Subgroups — #44567153

Order 32193.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24924362	C₃	1	1	yes	maximal, characteristic, complemented
2	C₇×#13095275	C₃	1	2	yes	maximal, complemented
3	C₇₃×#3862	C₃	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₈)×C₇₃⋊C₃	—	7	2	no	maximal
5	C₇²×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	#13095276	—	7	2	no	—
7	#13095276	—	21	2	no	—
8	#13095275	ΓL(1,𝔽₈)	1	2	yes	complemented
9	C₇×C₇₃⋊C₃	—	7	2	no	—
10	ΓL(1,𝔽₈)×C₇₃	—	7	2	no	—
11	C₃×C₇₃⋊C₃	—	49	1	no	Hall
12	C₇×C₇₃	—	3	2	no	—
13	C₇×C₇₃	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
14	ΓL(1,𝔽₈)²	—	73	1	no	maximal, Hall
15	C₃×C₇₃	—	49	1	no	—
16	C₇₃⋊C₃	—	7	2	no	—
17	C₇₃⋊C₃	—	49	1	no	—
18	#3862	C₇₃⋊C₃	1	1	yes	characteristic, complemented
19	#3861	—	73	1	no	—
20	C₇×ΓL(1,𝔽₈)	—	73	2	no	—
21	C₇₃	ΓL(1,𝔽₈)²	1	1	yes	characteristic, complemented, Sylow
22	C₃×ΓL(1,𝔽₈)	—	511	2	no	—
23	C₇²	C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	511	2	no	—
25	ΓL(1,𝔽₈)	—	7	2	no	—
26	ΓL(1,𝔽₈)	—	73	2	no	—
27	ΓL(1,𝔽₈)	—	1533	2	no	—
28	ΓL(1,𝔽₈)	—	511	2	no	—
29	C₃²	—	3577	1	no	Sylow
30	C₇	—	3	2	no	—
31	C₇	ΓL(1,𝔽₈)×C₇₃⋊C₃	1	2	yes	complemented
32	C₃	—	49	1	no	—
33	C₃	—	3577	1	no	—
34	C₃	—	511	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₇₃	C₃²
LCS	G ▷ C₇²×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.