Group #18076357 — subgroups

Subgroups — #18076357

Order 4864.

306 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 155 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	#14563773	C₂	1	2	yes	maximal
2	#14562394	C₂	1	2	yes	maximal
3	#14562391	C₂	1	2	yes	maximal
4	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
5	#11926568	C₂²	1	4	yes	—
6	#11926309	—	2	4	no	—
7	#11926297	—	2	4	no	—
8	#11926295	—	2	4	no	—
9	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#322	C₄	1	4	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
15	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×#64520	—	2	4	no	—
18	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₉	D₄	1	2	yes	—
22	C₄×C₈×C₁₉	D₄	1	2	yes	—
23	C₄×C₈×C₁₉	Q₈	1	2	yes	—
24	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
25	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
26	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₈×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
33	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
34	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
35	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	#64520	—	4	8	no	—
40	C₂×C₁₉⋊C₈	—	4	4	no	—
41	#8827	—	19	1	no	maximal, Sylow
42	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#135	1	4	yes	—
52	C₈×C₁₉	—	2	4	no	—
53	C₈×C₁₉	—	2	4	no	—
54	C₈×C₁₉	—	2	4	no	—
55	C₁₉⋊C₈	—	8	4	no	—
56	#1837	—	19	2	no	—
57	#1567	—	19	2	no	—
58	#1566	—	19	2	no	—
59	C₂×#322	D₁₉	1	1	yes	characteristic
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	#384	1	1	yes	characteristic
63	C₂²×C₁₉	#499	1	2	yes	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	#427	1	2	yes	—
67	C₄×C₁₉	#430	1	2	yes	—
68	C₄×C₁₉	#430	1	2	yes	—
69	C₄×C₁₉	#495	1	2	yes	—
70	#423	—	19	4	no	—
71	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
74	#341	—	38	4	no	—
75	#335	—	38	4	no	—
76	#334	—	38	4	no	—
77	#322	Dic₁₉	1	4	yes	—
78	C₂×C₁₉	—	2	2	no	—
79	C₂×C₁₉	#1846	1	1	yes	characteristic
80	C₂×C₁₉	#1849	1	1	yes	characteristic
81	C₂×C₁₉	#1849	1	1	yes	characteristic
82	C₂×M₁₆	—	38	4	no	—
83	C₂²×C₈	Dic₃₈	1	2	yes	—
84	C₂²×C₈	Dic₃₈	1	2	yes	—
85	C₂²×C₈	D₇₆	1	2	yes	—
86	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
87	C₄⋊C₈	—	38	4	no	—
88	C₄⋊C₈	—	38	4	no	—
89	C₄×C₈	Dic₃₈	1	2	yes	—
90	C₄×C₈	D₇₆	1	2	yes	—
91	C₄×C₈	D₇₆	1	2	yes	—
92	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
93	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
94	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
95	C₁₉	#8827	1	1	yes	characteristic, complemented, Sylow
96	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
97	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
98	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
99	M₁₆	—	76	8	no	—
100	C₂×C₈	—	2	4	no	—
101	C₂×C₈	—	4	2	no	—
102	C₂×C₈	—	4	2	no	—
103	C₂×C₈	—	76	4	no	—
104	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
105	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
106	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
107	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
108	C₄²	C₂×D₇₆	1	1	yes	characteristic
109	C₄²	C₂×D₇₆	1	1	yes	characteristic
110	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
111	C₂³	#10597315	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	#10597315	1	1	yes	characteristic
115	C₂×C₄	#10597315	1	1	yes	characteristic
116	C₂×C₄	#10597320	1	1	yes	characteristic
117	C₂×C₄	#10597350	1	4	yes	—
118	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
119	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
120	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
121	C₈	—	2	4	no	—
122	C₈	—	2	4	no	—
123	C₈	—	2	4	no	—
124	C₈	—	152	4	no	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	#11926414	1	1	yes	characteristic
128	C₂²	#11926946	1	2	yes	—
129	C₄	—	2	1	no	—
130	C₄	—	2	1	no	—
131	C₄	#11926582	1	2	yes	—
132	C₄	#11926593	1	2	yes	—
133	C₄	#11926593	1	2	yes	—
134	C₄	#11926928	1	2	yes	—
135	C₂	—	2	2	no	—
136	C₂	#14563799	1	1	yes	characteristic
137	C₂	#14563810	1	1	yes	characteristic
138	C₂	#14563810	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563773

C₂

yes

maximal

#14562394

C₂

yes

maximal

#14562391

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

#11926309

—

#11926297

—

#11926295

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂²×C₈×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

#8827

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#499

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#427

yes

—

C₄×C₁₉

#430

yes

—

C₄×C₁₉

#430

yes

—

C₄×C₁₉

#495

yes

—

#423

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

—

—

—

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

Dic₃₈

yes

—

C₂²×C₈

Dic₃₈

yes

—

C₂²×C₈

D₇₆

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

D₇₆

yes

—

C₄×C₈

D₇₆

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₄×C₈

C₂×Dic₁₉

yes

—

C₁₉

#8827

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

characteristic

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₄⋊Dic₁₉

yes

—

105

C₂×C₈

C₄⋊Dic₁₉

yes

—

106

C₂×C₈

C₄⋊Dic₁₉

yes

—

107

C₄²

C₂×Dic₃₈

yes

characteristic

108

C₄²

C₂×D₇₆

yes

characteristic

109

C₄²

C₂×D₇₆

yes

characteristic

110

C₄²

C₂²×Dic₁₉

yes

characteristic

111

C₂³

#10597315

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#10597315

yes

characteristic

115

C₂×C₄

#10597315

yes

characteristic

116

C₂×C₄

#10597320

yes

characteristic

117

C₂×C₄

#10597350

yes

—

118

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

119

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

120

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

152

—

125

C₂²

—

126

C₂²

—

127

C₂²

#11926414

yes

characteristic

128

C₂²

#11926946

yes

—

129

C₄

—

130

C₄

—

131

C₄

#11926582

yes

—

132

C₄

#11926593

yes

—

133

C₄

#11926593

yes

—

134

C₄

#11926928

yes

—

135

C₂

—

136

C₂

#14563799

yes

characteristic

137

C₂

#14563810

yes

characteristic

138

C₂

#14563810

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#8827
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#10597320

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
95. C₁₉	#8827	semidirect

H ≅ G/N

type

95. C₁₉

#8827

semidirect

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

subgroup	index
#14563773	2
#14562394	2
#14562391	2
C₂×C₁₉×#322	2
#8827	19

subgroup

index

C₂×C₁₉×#322

Subgroups — #18076357

Conjugacy classes of subgroups

Complements

Maximal subgroups