Subgroups — #49181582

Order 37926.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34038921	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	#19129333	—	7	8	no	maximal
5	C₇²×D₄₃	C₉	1	1	yes	characteristic, complemented, Hall
6	#14582150	—	7	8	no	—
7	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₄₃	ΓL(1,𝔽₈)	1	8	yes	—
9	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
10	C₂×#89204	—	43	1	no	maximal, Hall
11	D₄₃⋊C₉	—	49	1	no	Hall
12	C₇×D₄₃	C₇⋊C₉	1	8	yes	complemented
13	#89204	—	43	1	no	Hall
14	C₄₃⋊C₉	—	49	1	no	Hall
15	C₇×C₄₃	C₂×C₇⋊C₉	1	8	yes	complemented
16	C₂×C₃×C₇²	—	43	1	no	—
17	C₃×D₄₃	#3861	1	1	yes	characteristic
18	C₃×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
19	C₃×C₄₃	C₂×#3861	1	1	yes	characteristic
20	C₂×C₇⋊C₉	—	301	8	no	—
21	C₂×C₇²	—	43	1	no	Hall
22	D₄₃	#89204	1	1	yes	characteristic, complemented, Hall
23	C₇⋊C₉	—	301	8	no	—
24	C₇²	D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₄₃	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₇	—	43	8	no	—
27	C₃×C₇	#14268587	1	8	yes	—
28	C₂×C₉	—	2107	1	no	Hall
29	C₂×C₇	—	43	8	no	—
30	C₉	—	2107	1	no	Sylow
31	C₇	#19129333	1	8	yes	complemented
32	C₂×C₃	—	43	1	no	—
33	C₃	#27162432	1	1	yes	characteristic
34	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#27162432
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇²×D₄₃	C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₃

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.