Subgroups — #14572024

Order 2432.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926435	C₂	1	7	yes	maximal
2	#11926428	C₂	1	7	yes	maximal, complemented
3	C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×C₁₉	C₂²	1	7	yes	—
5	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	7	yes	—
6	C₂×Dic₁₉⋊C₄	C₂²	1	7	yes	—
7	C₁₉⋊#95	C₂²	1	14	yes	—
8	C₂³×D₁₉	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₁₉	C₂³	1	7	yes	—
10	C₂²×Dic₁₉	C₂³	1	7	yes	—
11	C₄²×C₁₉	—	2	14	no	—
12	(C₂×D₁₉)⋊C₄	—	2	14	no	—
13	Dic₁₉⋊C₄	—	2	14	no	—
14	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
15	C₂²×D₁₉	—	2	7	no	—
16	C₂×C₄×C₁₉	—	2	14	no	—
17	C₂×C₄×C₁₉	#41	1	14	yes	—
18	C₂×Dic₁₉	—	2	14	no	—
19	C₂×Dic₁₉	—	2	7	no	—
20	#2865	—	19	1	no	maximal, Sylow
21	C₂²×C₁₉	C₂×#41	1	7	yes	—
22	C₂×D₁₉	—	4	7	no	—
23	C₄×C₁₉	—	2	14	no	—
24	Dic₁₉	—	4	7	no	—
25	#388	—	19	7	no	—
26	#387	—	19	7	no	—
27	C₄³	D₁₉	1	1	yes	characteristic, complemented
28	C₂×C₁₉	#529	1	7	yes	—
29	D₁₉	—	8	1	no	—
30	C₂×C₄⋊C₄	—	19	7	no	—
31	C₂×C₂²⋊C₄	—	19	7	no	—
32	C₂×C₄²	C₂×D₁₉	1	7	yes	—
33	#95	—	19	14	no	—
34	C₁₉	#2865	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	19	1	no	—
36	C₂²×C₄	—	19	7	no	—
37	C₂²×C₄	C₂²×D₁₉	1	7	yes	—
38	C₄⋊C₄	—	38	14	no	—
39	C₂²⋊C₄	—	38	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	38	7	no	—
42	C₂³	C₂³×D₁₉	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	38	7	no	—
45	C₂×C₄	—	38	14	no	—
46	C₂×C₄	#64541	1	14	yes	—
47	C₂²	—	76	7	no	—
48	C₂²	C₂×#64541	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	76	7	no	—
51	C₂	—	152	1	no	—
52	C₂	#11927078	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄³×C₁₉	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₄³	D₁₉
hypocenter	C₁₉	#2865
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #11926428	C₂	semidirect
3. C₄³×C₁₉	C₂	semidirect
27. C₄³	D₁₉	semidirect
34. C₁₉	#2865	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11926435	2
#11926428	2
C₄³×C₁₉	2
#2865	19