Subgroups — #30660600

Order 16758.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22552710	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	#14558781	—	7	8	no	maximal
5	C₇²×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	#11924777	—	7	8	no	—
7	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×#89204	—	19	1	no	maximal, Hall
9	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	8	yes	—
10	#89204	—	19	1	no	Hall
11	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	—
12	#4294⋊C₂	—	49	1	no	Hall
13	C₂×C₃×C₇²	—	57	1	no	—
14	C₇×D₁₉	C₇⋊C₉	1	8	yes	complemented
15	#4294	—	49	1	no	Hall
16	C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic
17	C₇×C₁₉	C₂×C₇⋊C₉	1	8	yes	complemented
18	C₂×C₇⋊C₉	—	133	8	no	—
19	C₃×D₁₉	#3861	1	1	yes	characteristic
20	C₂×C₇²	—	57	1	no	Hall
21	C₇⋊C₉	—	133	8	no	—
22	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic
23	C₇²	#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₇	—	57	8	no	—
25	D₁₉	#89204	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇	#11716322	1	8	yes	—
27	C₁₉	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	931	1	no	Hall
29	C₂×C₇	—	57	8	no	—
30	C₉	—	931	1	no	Sylow
31	C₇	#14558781	1	8	yes	complemented
32	C₂×C₃	—	57	1	no	—
33	C₃	#19150312	1	1	yes	characteristic
34	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#19150312
commutator, hypocenter	C₇²×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₇²×D₁₉	C₃
LCS	G ▷ C₇²×C₁₉
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.