Group #14574149 — subgroups

Subgroups — #14574149

Order 2432.

356 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 173 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	#11927101	C₂	1	2	yes	maximal
2	#11926949	C₂	1	2	yes	maximal, complemented
3	#11926946	C₂	1	4	yes	maximal, complemented
4	#11926942	C₂	1	2	yes	maximal, complemented
5	#11926582	C₂	1	4	yes	maximal
6	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	4	yes	—
10	#10597370	—	2	4	no	—
11	#10597316	C₂²	1	4	yes	—
12	#10597315	C₂²	1	4	yes	—
13	C₄×Dic₃₈	—	2	4	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₉	C₂²	1	2	yes	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	#10597275	C₂²	1	8	yes	—
18	#10597274	C₂²	1	8	yes	—
19	C₂²×C₄×C₁₉	D₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₃₈	—	2	4	no	—
22	C₂×C₈×C₁₉	Q₈	1	8	yes	complemented
23	C₂×C₈×C₁₉	C₂³	1	2	yes	—
24	C₂×C₈×C₁₉	C₂³	1	2	yes	—
25	C₄²×C₁₉	D₄	1	2	yes	—
26	C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²⋊Dic₁₉	—	2	4	no	—
29	C₄⋊Dic₁₉	—	2	4	no	—
30	C₄⋊Dic₁₉	C₂³	1	8	yes	—
31	Dic₁₉⋊C₄	—	2	8	no	—
32	C₄×Dic₁₉	—	2	4	no	—
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
39	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂×Dic₁₉	—	2	8	no	—
41	Dic₃₈	—	4	8	no	—
42	C₈×C₁₉	C₂×Q₈	1	4	yes	—
43	C₈×C₁₉	C₂×Q₈	1	4	yes	—
44	#3160	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	—	2	2	no	—
46	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
47	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
50	C₄×C₁₉	#135	1	4	yes	—
51	C₄×C₁₉	C₂²×Q₈	1	2	yes	—
52	Dic₁₉	—	4	8	no	—
53	#533	—	19	2	no	—
54	#500	—	19	2	no	—
55	#499	—	19	4	no	—
56	#498	—	19	2	no	—
57	#427	—	19	4	no	—
58	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
59	C₂×C₁₉	—	2	2	no	—
60	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
61	C₂×C₁₉	C₂×#135	1	2	yes	—
62	C₂²×C₈	C₂×D₁₉	1	2	yes	—
63	C₄⋊Q₈	—	19	4	no	—
64	#125	—	19	4	no	—
65	C₂²⋊Q₈	—	38	4	no	—
66	C₄×Q₈	—	38	4	no	—
67	#117	—	19	4	no	—
68	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
69	#107	—	19	8	no	—
70	#106	—	19	8	no	—
71	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₄×C₈	C₂×D₁₉	1	2	yes	—
73	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
74	C₁₉	#3160	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	38	4	no	—
76	C₂²×C₄	D₇₆	1	2	yes	—
77	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
78	C₂×C₈	Dic₃₈	1	8	yes	complemented
79	C₂×C₈	C₂²×D₁₉	1	2	yes	—
80	C₂×C₈	C₂²×D₁₉	1	2	yes	—
81	C₄⋊C₄	—	19	8	no	—
82	C₄⋊C₄	—	38	8	no	—
83	C₄⋊C₄	—	38	4	no	—
84	C₂²⋊C₄	—	38	4	no	—
85	C₄²	—	38	4	no	—
86	C₄²	D₇₆	1	2	yes	—
87	C₄²	C₂²×D₁₉	1	1	yes	characteristic
88	C₄²	C₂²×D₁₉	1	1	yes	characteristic
89	C₂³	C₂×D₇₆	1	1	yes	characteristic
90	Q₈	—	76	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	38	8	no	—
93	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
94	C₂×C₄	C₂×D₇₆	1	2	yes	—
95	C₂×C₄	C₂×D₇₆	1	2	yes	—
96	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
97	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
98	C₈	C₂×Dic₃₈	1	4	yes	—
99	C₈	C₂×Dic₃₈	1	4	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	#10597315	1	2	yes	—
102	C₂²	C₂²×D₇₆	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	—	76	8	no	—
105	C₄	#10597315	1	2	yes	—
106	C₄	#10597350	1	4	yes	—
107	C₄	C₂²×Dic₃₈	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	C₂×#10597315	1	1	yes	characteristic
110	C₂	C₂×#10597350	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal

#11926949

C₂

yes

maximal, complemented

#11926946

C₂

yes

maximal, complemented

#11926942

C₂

yes

maximal, complemented

#11926582

C₂

yes

maximal

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

—

#10597316

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂×Q₈

yes

—

C₈×C₁₉

C₂×Q₈

yes

—

#3160

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

C₂²×Q₈

yes

—

Dic₁₉

—

—

—

—

—

—

C₂×C₄×C₈

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

C₂×#135

yes

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#107

—

#106

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#3160

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

Dic₃₈

yes

complemented

C₂×C₈

C₂²×D₁₉

yes

—

C₂×C₈

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

D₇₆

yes

—

C₄²

C₂²×D₁₉

yes

characteristic

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

C₂×D₇₆

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×D₇₆

yes

—

C₂×C₄

C₂×D₇₆

yes

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

C₂³×D₁₉

yes

characteristic

C₈

C₂×Dic₃₈

yes

—

C₈

C₂×Dic₃₈

yes

—

100

C₂²

—

101

C₂²

#10597315

yes

—

102

C₂²

C₂²×D₇₆

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

#10597315

yes

—

106

C₄

#10597350

yes

—

107

C₄

C₂²×Dic₃₈

yes

—

108

C₂

—

109

C₂

C₂×#10597315

yes

characteristic

110

C₂

C₂×#10597350

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#3160
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄×C₈

D₁₉

hypocenter

C₁₉

#3160

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #11926949	C₂	semidirect
3. #11926946	C₂	semidirect
4. #11926942	C₂	semidirect
22. C₂×C₈×C₁₉	Q₈	semidirect
74. C₁₉	#3160	semidirect
78. C₂×C₈	Dic₃₈	semidirect

H ≅ G/N

type

2. #11926949

C₂

semidirect

3. #11926946

C₂

semidirect

4. #11926942

C₂

semidirect

22. C₂×C₈×C₁₉

Q₈

semidirect

74. C₁₉

#3160

semidirect

78. C₂×C₈

Dic₃₈

semidirect

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

subgroup	index
#11927101	2
#11926949	2
#11926946	2
#11926942	2
#11926582	2
C₂×C₄×C₈×C₁₉	2
#3160	19

subgroup

index

C₂×C₄×C₈×C₁₉

Subgroups — #14574149

Conjugacy classes of subgroups

Complements

Maximal subgroups