Group #14571627 — subgroups

Subgroups — #14571627

Order 2432.

432 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926464	C₂	1	3	yes	maximal
2	#11926463	C₂	1	2	yes	maximal
3	#11926449	C₂	1	3	yes	maximal
4	#11926448	C₂	1	6	yes	maximal
5	C₁₉×#395	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	3	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
12	C₁₉×#95	C₂²	1	3	yes	—
13	C₁₉⋊#95	C₂²	1	6	yes	—
14	C₁₉⋊#95	C₂²	1	6	yes	—
15	C₁₉⋊#95	C₂²	1	3	yes	—
16	C₂×Q₈×C₁₉	—	4	3	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
20	C₂²×Dic₁₉	C₂³	1	2	yes	—
21	C₂²×Dic₁₉	C₂³	1	6	yes	—
22	C₂×Dic₃₈	—	4	3	no	—
23	C₂×Dic₃₈	—	4	3	no	—
24	C₂×Dic₃₈	—	4	3	no	—
25	C₂×Dic₃₈	Q₈	1	12	yes	complemented
26	C₄⋊C₄×C₁₉	—	4	3	no	—
27	Dic₁₉⋊C₄	—	4	6	no	—
28	C₄×Dic₁₉	—	4	3	no	—
29	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
30	Q₈×C₁₉	—	4	4	no	—
31	C₂×C₄×C₁₉	—	2	3	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	—	2	6	no	—
34	C₂×C₄×C₁₉	—	2	3	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	C₂×Q₈	1	6	yes	—
37	C₂×Dic₁₉	—	2	6	no	—
38	C₂×Dic₁₉	—	2	6	no	—
39	C₂×Dic₁₉	—	2	6	no	—
40	C₂×Dic₁₉	C₂×Q₈	1	12	yes	—
41	Dic₃₈	—	4	12	no	—
42	Dic₃₈	—	4	4	no	—
43	#2811	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	C₂²×Q₈	1	3	yes	—
45	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
47	C₄×C₁₉	—	2	6	no	—
48	C₄×C₁₉	—	4	1	no	—
49	C₄×C₁₉	—	4	3	no	—
50	Dic₁₉	—	2	12	no	—
51	Dic₁₉	—	4	2	no	—
52	#395	—	19	2	no	—
53	#395	—	19	3	no	—
54	#395	D₁₉	1	1	yes	characteristic
55	#391	—	19	3	no	—
56	#391	—	19	6	no	—
57	C₂×C₁₉	#543	1	3	yes	—
58	C₂×C₁₉	Q₈²	1	3	yes	—
59	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
60	C₂²×Q₈	—	19	3	no	—
61	C₂²×Q₈	—	19	1	no	—
62	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
63	C₂×C₄⋊C₄	—	19	6	no	—
64	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
65	C₂×C₄²	—	19	3	no	—
66	#95	—	19	3	no	—
67	#95	—	19	6	no	—
68	#95	—	19	6	no	—
69	#95	C₂×D₁₉	1	3	yes	—
70	C₁₉	#2811	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₈	—	4	3	no	—
72	C₂×Q₈	—	19	12	no	—
73	C₂×Q₈	—	76	3	no	—
74	C₂×Q₈	—	76	3	no	—
75	C₂×Q₈	—	76	3	no	—
76	C₂²×C₄	—	19	6	no	—
77	C₂²×C₄	—	19	2	no	—
78	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
80	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
81	C₄⋊C₄	—	4	3	no	—
82	C₄⋊C₄	—	76	6	no	—
83	C₄²	—	76	3	no	—
84	C₂³	C₂³×D₁₉	1	1	yes	characteristic
85	Q₈	—	4	4	no	—
86	Q₈	—	76	12	no	—
87	Q₈	—	76	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	19	12	no	—
94	C₂×C₄	—	38	6	no	—
95	C₂×C₄	—	38	6	no	—
96	C₂×C₄	—	38	6	no	—
97	C₂×C₄	Q₈×D₁₉	1	6	yes	—
98	C₂²	#10597430	1	3	yes	—
99	C₂²	C₂×Q₈×D₁₉	1	3	yes	—
100	C₂²	#10597435	1	1	yes	characteristic
101	C₄	—	2	6	no	—
102	C₄	—	4	3	no	—
103	C₄	—	4	1	no	—
104	C₄	—	38	12	no	—
105	C₄	—	76	2	no	—
106	C₂	#11927169	1	3	yes	—
107	C₂	#11927274	1	3	yes	—
108	C₂	#11927287	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926464

C₂

yes

maximal

#11926463

C₂

yes

maximal

#11926449

C₂

yes

maximal

#11926448

C₂

yes

maximal

C₁₉×#395

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₄⋊C₄×C₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

Dic₃₈

—

#2811

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#395

—

#395

—

#395

D₁₉

yes

characteristic

#391

—

#391

—

C₂×C₁₉

#543

yes

—

C₂×C₁₉

Q₈²

yes

—

C₂×C₁₉

H(3,𝔽₄)

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2811

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Q₈×D₁₉

yes

—

C₂²

#10597430

yes

—

C₂²

C₂×Q₈×D₁₉

yes

—

100

C₂²

#10597435

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₂

#11927169

yes

—

107

C₂

#11927274

yes

—

108

C₂

#11927287

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#395	C₂
hypercenter	#395	D₁₉
hypocenter	C₁₉	#2811
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#395

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
25. C₂×Dic₃₈	Q₈	semidirect
70. C₁₉	#2811	semidirect

H ≅ G/N

type

25. C₂×Dic₃₈

Q₈

semidirect

70. C₁₉

#2811

semidirect

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

subgroup	index
#11926464	2
#11926463	2
#11926449	2
#11926448	2
C₁₉×#395	2
#2811	19

subgroup

index

C₁₉×#395

Subgroups — #14571627

Conjugacy classes of subgroups

Complements

Maximal subgroups