Group #18087614 — subgroups

Subgroups — #18087614

Order 4864.

478 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 141 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	#14564441	C₂	1	3	yes	maximal
2	#14563763	C₂	1	3	yes	maximal, complemented
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597320	C₂²	1	1	yes	characteristic
5	C₂×#10597278	—	2	6	no	—
6	#11926414	C₂²	1	3	yes	—
7	#11926307	—	2	6	no	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₂²×D₇₆	—	2	3	no	—
10	C₂²×C₈×C₁₉	D₄	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	3	no	—
13	C₂×C₄⋊Dic₁₉	—	2	3	no	—
14	C₂×C₄⋊Dic₁₉	—	2	3	no	—
15	#10597320	—	2	3	no	—
16	#10597320	Q₈	1	2	yes	—
17	C₄×C₈×C₁₉	—	2	6	no	—
18	#10597278	—	4	12	no	—
19	C₂³×D₁₉	—	4	1	no	—
20	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
21	C₂²×Dic₁₉	—	4	3	no	—
22	C₂×D₇₆	—	2	6	no	—
23	C₂×D₇₆	—	4	6	no	—
24	C₂×D₇₆	—	4	6	no	—
25	C₂×D₇₆	—	4	3	no	—
26	C₂×C₈×C₁₉	—	2	6	no	—
27	C₂×C₈×C₁₉	—	2	6	no	—
28	C₂×C₈×C₁₉	—	2	6	no	—
29	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	C₄²×C₁₉	#41	1	3	yes	—
31	C₄⋊Dic₁₉	—	4	6	no	—
32	C₄⋊Dic₁₉	—	4	6	no	—
33	C₄⋊Dic₁₉	—	4	6	no	—
34	#10678	—	19	1	no	maximal, Sylow
35	C₂³×C₁₉	#127	1	1	yes	characteristic
36	C₂²×D₁₉	—	4	2	no	—
37	C₂²×D₁₉	—	8	3	no	—
38	C₂²×D₁₉	—	8	3	no	—
39	C₂×C₄×C₁₉	C₂²⋊Q₈	1	3	yes	—
40	C₂×C₄×C₁₉	#123	1	3	yes	—
41	C₂×C₄×C₁₉	#135	1	6	yes	—
42	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	6	yes	—
43	C₂×Dic₁₉	—	8	3	no	—
44	C₂×Dic₁₉	—	8	3	no	—
45	C₂×Dic₁₉	—	8	3	no	—
46	D₇₆	—	4	12	no	—
47	D₇₆	—	8	6	no	—
48	C₈×C₁₉	—	4	6	no	—
49	#1957	—	19	3	no	—
50	#1834	—	19	3	no	—
51	#1273	D₁₉	1	1	yes	characteristic, complemented
52	C₂²×C₁₉	#399	1	1	yes	characteristic
53	C₂²×C₁₉	#495	1	3	yes	—
54	C₂²×C₁₉	#496	1	3	yes	—
55	C₂×D₁₉	—	8	6	no	—
56	C₂×D₁₉	—	16	1	no	—
57	C₂×D₁₉	—	16	3	no	—
58	C₄×C₁₉	#478	1	6	yes	—
59	C₄×C₁₉	#482	1	6	yes	—
60	Dic₁₉	—	16	3	no	—
61	C₂×#127	—	19	1	no	—
62	C₂×#102	—	38	6	no	—
63	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
64	#384	—	19	3	no	—
65	#340	—	38	6	no	—
66	C₂×C₁₉	#1711	1	1	yes	characteristic
67	C₂×C₁₉	#1717	1	3	yes	—
68	C₂×C₁₉	#2092	1	3	yes	—
69	D₁₉	—	16	2	no	—
70	C₂²×D₄	—	38	3	no	—
71	C₂²×C₈	D₇₆	1	6	yes	—
72	#127	—	19	2	no	—
73	#127	—	38	3	no	—
74	C₂×C₄⋊C₄	—	38	3	no	—
75	C₂×C₄⋊C₄	—	38	3	no	—
76	C₂×C₄⋊C₄	—	38	3	no	—
77	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
78	#102	—	76	12	no	—
79	C₄×C₈	—	2	6	no	—
80	C₁₉	#10678	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	—	76	1	no	—
82	C₂×D₄	—	38	6	no	—
83	C₂×D₄	—	76	3	no	—
84	C₂×D₄	—	76	6	no	—
85	C₂×D₄	—	76	6	no	—
86	C₂²×C₄	—	76	3	no	—
87	C₂²×C₄	C₂×D₇₆	1	3	yes	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	—	2	6	no	—
90	C₂×C₈	—	2	6	no	—
91	C₄⋊C₄	—	76	6	no	—
92	C₄⋊C₄	—	76	6	no	—
93	C₄⋊C₄	—	76	6	no	—
94	C₄²	#64543	1	3	yes	—
95	C₄²	Q₈×D₁₉	1	1	yes	characteristic
96	C₂³	—	76	2	no	—
97	C₂³	—	152	3	no	—
98	C₂³	—	152	3	no	—
99	C₂³	#10597320	1	1	yes	characteristic
100	D₄	—	76	12	no	—
101	D₄	—	152	6	no	—
102	C₂×C₄	—	152	3	no	—
103	C₂×C₄	—	152	3	no	—
104	C₂×C₄	—	152	3	no	—
105	C₂×C₄	#10597332	1	3	yes	—
106	C₂×C₄	#10597343	1	3	yes	—
107	C₂×C₄	#10597350	1	6	yes	—
108	C₂×C₄	#10597354	1	6	yes	—
109	C₈	—	4	6	no	—
110	C₂²	—	304	1	no	—
111	C₂²	—	304	3	no	—
112	C₂²	—	152	6	no	—
113	C₂²	#11926481	1	1	yes	characteristic
114	C₂²	#11926928	1	3	yes	—
115	C₂²	#11926933	1	3	yes	—
116	C₄	—	304	3	no	—
117	C₄	#11926845	1	6	yes	—
118	C₄	#11926869	1	6	yes	—
119	C₂	—	304	2	no	—
120	C₂	#14563247	1	1	yes	characteristic
121	C₂	#14563274	1	3	yes	—
122	C₂	#14565155	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564441

C₂

yes

maximal

#14563763

C₂

yes

maximal, complemented

C₁₉×#1273

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

characteristic

C₂×#10597278

—

#11926414

C₂²

yes

—

#11926307

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597320

—

#10597320

Q₈

yes

—

C₄×C₈×C₁₉

—

#10597278

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

#1957

—

#1834

—

#1273

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#399

yes

characteristic

C₂²×C₁₉

#495

yes

—

C₂²×C₁₉

#496

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#478

yes

—

C₄×C₁₉

#482

yes

—

Dic₁₉

—

C₂×#127

—

C₂×#102

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

#384

—

#340

—

C₂×C₁₉

#1711

yes

characteristic

C₂×C₁₉

#1717

yes

—

C₂×C₁₉

#2092

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×C₈

D₇₆

yes

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#102

—

C₄×C₈

—

C₁₉

#10678

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₇₆

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#64543

yes

—

C₄²

Q₈×D₁₉

yes

characteristic

C₂³

—

C₂³

—

152

—

C₂³

—

152

—

C₂³

#10597320

yes

characteristic

100

D₄

—

101

D₄

—

152

—

102

C₂×C₄

—

152

—

103

C₂×C₄

—

152

—

104

C₂×C₄

—

152

—

105

C₂×C₄

#10597332

yes

—

106

C₂×C₄

#10597343

yes

—

107

C₂×C₄

#10597350

yes

—

108

C₂×C₄

#10597354

yes

—

109

C₈

—

110

C₂²

—

304

—

111

C₂²

—

304

—

112

C₂²

—

152

—

113

C₂²

#11926481

yes

characteristic

114

C₂²

#11926928

yes

—

115

C₂²

#11926933

yes

—

116

C₄

—

304

—

117

C₄

#11926845

yes

—

118

C₄

#11926869

yes

—

119

C₂

—

304

—

120

C₂

#14563247

yes

characteristic

121

C₂

#14563274

yes

—

122

C₂

#14565155

yes

—

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10678
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#10597320

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1273

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. #14563763	C₂	semidirect
3. C₁₉×#1273	C₂	semidirect
51. #1273	D₁₉	semidirect
80. C₁₉	#10678	semidirect

H ≅ G/N

type

2. #14563763

C₂

semidirect

3. C₁₉×#1273

C₂

semidirect

51. #1273

D₁₉

semidirect

80. C₁₉

#10678

semidirect

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

subgroup	index
#14564441	2
#14563763	2
C₁₉×#1273	2
#10678	19

subgroup

index

#14564441

#14563763

C₁₉×#1273

#10678

Subgroups — #18087614

Conjugacy classes of subgroups

Complements

Maximal subgroups