Subgroups — C₃×C₃₇×#3862 #30654591

Order 16317.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#3862	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₇²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×ΓL(1,𝔽₈)×C₃₇	—	7	2	no	maximal
4	C₇²×C₃₇	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₃₇	—	3	2	no	—
6	C₃×C₇×C₃₇	ΓL(1,𝔽₈)	1	2	yes	complemented
7	ΓL(1,𝔽₈)×C₃₇	—	7	6	no	—
8	C₃×#3862	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃²×C₃₇	—	49	1	no	Hall
10	C₇×C₃₇	—	3	2	no	—
11	C₇×C₃₇	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
12	C₃×C₇²	C₃×C₃₇	1	1	yes	characteristic, complemented
13	#3862	C₃×C₃₇	1	3	yes	direct product factor
14	C₃×C₃₇	—	49	3	no	—
15	C₃×C₃₇	#3862	1	1	yes	characteristic, direct product factor
16	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
17	C₇²	C₃²×C₃₇	1	1	yes	characteristic, complemented, Sylow
18	C₃₇	C₃×#3862	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₇	—	3	2	no	—
20	C₃×C₇	ΓL(1,𝔽₈)×C₃₇	1	2	yes	complemented
21	ΓL(1,𝔽₈)	—	7	6	no	—
22	C₃²	—	49	1	no	Sylow
23	C₇	—	3	2	no	—
24	C₇	C₃×ΓL(1,𝔽₈)×C₃₇	1	2	yes	complemented
25	C₃	—	49	3	no	—
26	C₃	C₃₇×#3862	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₃₇	#3862
commutator, cosocle, hypocenter	C₇²	C₃²×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₃₇

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.