Subgroups — #45688592

Order 33348.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659822	C₂	1	1	yes	maximal, characteristic
2	C₇×#13097544	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#22552381	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₃₉₇	C₂×C₃	1	1	yes	characteristic
5	#13097544⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₃₉₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	D₃₉₇⋊C₃	—	7	1	no	—
8	#13097544	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	C₃₉₇⋊C₃	—	7	1	no	Hall
10	D₃₉₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃₉₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
12	C₄×ΓL(1,𝔽₈)	—	397	1	no	maximal, Hall
13	C₂×ΓL(1,𝔽₈)	—	397	1	no	—
14	C₄×C₇	—	397	1	no	Hall
15	ΓL(1,𝔽₈)	—	397	1	no	Hall
16	C₂×C₇	—	397	1	no	—
17	C₃×C₄	—	2779	1	no	Hall
18	C₇	#13097544⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2779	1	no	—
20	C₄	—	397	1	no	Sylow
21	C₃	—	2779	1	no	Sylow
22	C₂	—	397	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₃₉₇	C₃×C₄
prime radical	#30659822	C₂
cosocle	C₇×D₃₉₇	C₂×C₃
LCS	G ▷ C₇×C₃₉₇
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.