Group #18070182 — subgroups

Subgroups — #18070182

Order 4864.

130 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14565896	C₂	1	1	yes	maximal, characteristic
2	#14561711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₁₅₂	C₄	1	1	yes	characteristic
5	C₂×#10597257	—	2	1	no	—
6	C₂×D₃₀₄	C₄	1	1	yes	characteristic
7	#11926928	—	2	1	no	—
8	#11926365	—	2	1	no	—
9	C₁₉×M₆₄	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	—	2	1	no	—
12	C₂×D₁₅₂	—	2	1	no	—
13	C₂×#64516	—	4	1	no	—
14	#10597321	—	4	1	no	—
15	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
18	#10597269	—	4	1	no	—
19	Dic₁₅₂	—	4	1	no	—
20	#10597257	—	4	1	no	—
21	#10597257	—	4	1	no	—
22	D₃₀₄	—	4	1	no	—
23	C₁₉×C₃₂	—	4	1	no	—
24	C₂×D₇₆	—	4	1	no	—
25	C₂×Dic₃₈	—	4	1	no	—
26	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
29	(C₂×D₁₉)⋊C₄	—	8	2	no	—
30	Dic₇₆	—	4	1	no	—
31	Dic₇₆	—	4	1	no	—
32	D₁₅₂	—	4	1	no	—
33	D₁₅₂	—	4	1	no	—
34	#64516	—	8	1	no	—
35	#64516	—	8	1	no	—
36	C₁₆×C₁₉	—	2	1	no	—
37	C₁₆×C₁₉	D₈	1	1	yes	characteristic
38	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
39	C₁₉⋊C₁₆	—	8	1	no	—
40	#7447	—	19	1	no	maximal, Sylow
41	C₂²×D₁₉	—	8	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
44	C₂×Dic₁₉	—	8	1	no	—
45	D₇₆	—	8	1	no	—
46	D₇₆	—	8	1	no	—
47	Dic₃₈	—	8	1	no	—
48	Dic₃₈	—	8	1	no	—
49	C₈×C₁₉	#100	1	1	yes	characteristic
50	C₈×C₁₉	#102	1	1	yes	characteristic
51	C₈×C₁₉	D₁₆	1	1	yes	characteristic
52	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
53	#2249	—	19	1	no	—
54	#1422	D₁₉	1	1	yes	characteristic, complemented
55	#1373	—	19	1	no	—
56	C₂²×C₁₉	#361	1	1	yes	characteristic
57	C₂×D₁₉	—	16	2	no	—
58	C₂×D₁₉	—	16	1	no	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	#331	1	1	yes	characteristic
61	C₄×C₁₉	#357	1	1	yes	characteristic
62	Dic₁₉	—	16	1	no	—
63	C₂×Q₃₂	—	19	1	no	—
64	C₂×SD₃₂	—	38	1	no	—
65	C₂×D₁₆	—	19	1	no	—
66	#495	—	38	1	no	—
67	M₆₄	—	2	1	no	—
68	#364	—	38	1	no	—
69	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	#1361	1	1	yes	characteristic
72	D₁₉	—	32	1	no	—
73	C₂×Q₁₆	—	38	1	no	—
74	C₂×SD₁₆	—	76	1	no	—
75	C₂×D₈	—	38	1	no	—
76	#124	—	76	1	no	—
77	Q₃₂	—	76	1	no	—
78	SD₃₂	—	76	1	no	—
79	SD₃₂	—	76	1	no	—
80	D₁₆	—	76	1	no	—
81	M₃₂	—	76	1	no	—
82	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
83	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
84	C₄×C₈	D₇₆	1	1	yes	characteristic
85	C₃₂	—	4	1	no	—
86	C₁₉	#7447	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	76	1	no	—
88	C₂×D₄	—	76	1	no	—
89	Q₁₆	—	76	1	no	—
90	Q₁₆	—	76	1	no	—
91	SD₁₆	—	152	1	no	—
92	SD₁₆	—	152	1	no	—
93	D₈	—	76	1	no	—
94	D₈	—	76	1	no	—
95	C₂×C₈	D₁₅₂	1	1	yes	characteristic
96	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
97	C₂²⋊C₄	—	152	2	no	—
98	C₄²	#64516	1	1	yes	characteristic
99	C₁₆	—	2	1	no	—
100	C₁₆	—	152	1	no	—
101	C₁₆	#64525	1	1	yes	characteristic
102	C₁₆	#64527	1	1	yes	characteristic
103	C₂³	—	152	1	no	—
104	Q₈	—	152	1	no	—
105	Q₈	—	152	1	no	—
106	D₄	—	152	1	no	—
107	D₄	—	152	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	152	1	no	—
110	C₂×C₄	#10597278	1	1	yes	characteristic
111	C₈	D₃₀₄	1	1	yes	characteristic
112	C₈	#10597257	1	1	yes	characteristic
113	C₈	#10597266	1	1	yes	characteristic
114	C₈	#10597280	1	1	yes	characteristic
115	C₂²	—	304	2	no	—
116	C₂²	—	304	1	no	—
117	C₂²	#11926358	1	1	yes	characteristic
118	C₄	—	4	1	no	—
119	C₄	—	304	1	no	—
120	C₄	#11926287	1	1	yes	characteristic
121	C₄	#11926346	1	1	yes	characteristic
122	C₂	—	2	1	no	—
123	C₂	—	608	1	no	—
124	C₂	#14561682	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565896

C₂

yes

maximal, characteristic

#14561711

C₂

yes

maximal, characteristic, complemented

C₁₉×#1422

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₅₂

C₄

yes

characteristic

C₂×#10597257

—

C₂×D₃₀₄

C₄

yes

characteristic

#11926928

—

#11926365

—

C₁₉×M₆₄

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×D₁₅₂

—

C₂×#64516

—

#10597321

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597269

—

Dic₁₅₂

—

#10597257

—

#10597257

—

D₃₀₄

—

C₁₉×C₃₂

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

(C₂×D₁₉)⋊C₄

—

Dic₇₆

—

Dic₇₆

—

D₁₅₂

—

D₁₅₂

—

#64516

—

#64516

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7447

—

maximal, Sylow

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

#2249

—

#1422

D₁₉

yes

characteristic, complemented

#1373

—

C₂²×C₁₉

#361

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×Q₃₂

—

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1361

yes

characteristic

D₁₉

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

D₇₆

yes

characteristic

C₃₂

—

C₁₉

#7447

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

152

—

SD₁₆

—

152

—

D₈

—

D₈

—

C₂×C₈

D₁₅₂

yes

characteristic

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂²⋊C₄

—

152

—

C₄²

#64516

yes

characteristic

C₁₆

—

100

C₁₆

—

152

—

101

C₁₆

#64525

yes

characteristic

102

C₁₆

#64527

yes

characteristic

103

C₂³

—

152

—

104

Q₈

—

152

—

105

Q₈

—

152

—

106

D₄

—

152

—

107

D₄

—

152

—

108

C₂×C₄

—

109

C₂×C₄

—

152

—

110

C₂×C₄

#10597278

yes

characteristic

111

C₈

D₃₀₄

yes

characteristic

112

C₈

#10597257

yes

characteristic

113

C₈

#10597266

yes

characteristic

114

C₈

#10597280

yes

characteristic

115

C₂²

—

304

—

116

C₂²

—

304

—

117

C₂²

#11926358

yes

characteristic

118

C₄

—

119

C₄

—

304

—

120

C₄

#11926287

yes

characteristic

121

C₄

#11926346

yes

characteristic

122

C₂

—

123

C₂

—

608

—

124

C₂

#14561682

yes

characteristic

	subgroup	G/H
center	C₂	#14561682
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1422	C₂
socle	C₂×C₁₉	#1361
prime radical	C₂×D₃₀₄	C₄
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1422	D₁₉
hypocenter	C₁₉	#7447
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

subgroup

G/H

center

C₂

#14561682

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1422

C₂

socle

C₂×C₁₉

#1361

prime radical

C₂×D₃₀₄

C₄

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

N	H ≅ G/N	type
2. #14561711	C₂	semidirect
3. C₁₉×#1422	C₂	semidirect
54. #1422	D₁₉	semidirect
86. C₁₉	#7447	semidirect

H ≅ G/N

type

2. #14561711

C₂

semidirect

3. C₁₉×#1422

C₂

semidirect

54. #1422

D₁₉

semidirect

86. C₁₉

#7447

semidirect

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

subgroup	index
#14565896	2
#14561711	2
C₁₉×#1422	2
#7447	19

subgroup

index

#14565896

#14561711

C₁₉×#1422

#7447

Subgroups — #18070182

Conjugacy classes of subgroups

Complements

Maximal subgroups