Subgroups — C₃⋊(C₁₉⋊#5997) #26014028

Order 11172.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#5997	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
5	C₇²×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×C₁₉	—	14	4	no	—
7	C₃⋊#5997	—	19	1	no	maximal, Hall
8	C₃×C₇×C₁₉	—	2	4	no	—
9	C₃×C₇⋊D₇	D₁₉	1	1	yes	characteristic
10	D₇×C₁₉	—	14	4	no	—
11	Dic₅₇	—	49	1	no	maximal, Hall
12	#5997	—	57	1	no	Hall
13	C₃×C₇²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₉	—	2	4	no	—
15	C₂×C₃×C₁₉	—	49	1	no	—
16	C₇⋊D₇	D₅₇	1	1	yes	characteristic
17	Dic₁₉	—	147	1	no	Hall
18	C₃×C₁₉	#5997	1	1	yes	characteristic, complemented, Hall
19	C₇²	Dic₅₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₇	—	14	4	no	—
21	C₂×C₁₉	—	49	1	no	—
22	C₃×C₇	—	2	4	no	—
23	C₁₉	C₃⋊#5997	1	1	yes	characteristic, complemented, Sylow
24	D₇	—	14	4	no	—
25	Dic₃	—	931	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	49	1	no	—
28	C₄	—	2793	1	no	Sylow
29	C₃	C₁₉⋊#5997	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇²×C₁₉	C₄
prime radical, cosocle	C₃×C₁₉×C₇⋊D₇	C₂
LCS	G ▷ C₃×C₇²×C₁₉
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.