Group #14574381 — subgroups

Subgroups — #14574381

Order 2432.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11927099	C₂	1	2	yes	maximal
2	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926896	C₂	1	2	yes	maximal, complemented
4	#11926803	C₂	1	4	yes	maximal
5	#11926650	C₂	1	4	yes	maximal, complemented
6	C₄×#64515	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
9	#10597392	—	2	2	no	—
10	Q₈×Dic₁₉	—	2	2	no	—
11	C₂×Dic₇₆	C₂²	1	4	yes	—
12	C₂×#64515	C₂²	1	2	yes	—
13	#10597343	C₂²	1	4	yes	—
14	#10597338	—	2	2	no	—
15	#10597336	—	2	2	no	—
16	#10597333	C₂²	1	4	yes	—
17	C₄²×D₁₉	C₂²	1	1	yes	characteristic
18	#10597315	C₂²	1	2	yes	—
19	C₁₉×#106	C₂²	1	4	yes	—
20	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	#10597272	C₂²	1	2	yes	—
22	#10597267	C₂²	1	8	yes	—
23	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	—	2	2	no	—
25	C₂×C₄×D₁₉	D₄	1	2	yes	—
26	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₃₈	C₂³	1	4	yes	—
28	C₂×C₈×C₁₉	C₂³	1	2	yes	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
31	C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	(C₂×D₁₉)⋊C₄	—	2	4	no	—
33	C₄⋊Dic₁₉	—	2	2	no	—
34	C₄⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	4	no	—
36	Dic₁₉⋊C₄	—	2	4	no	—
37	C₄×Dic₁₉	—	2	4	no	—
38	C₄×Dic₁₉	D₄	1	2	yes	—
39	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
41	Dic₇₆	—	2	8	no	—
42	#64515	—	2	4	no	—
43	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₁₉	—	4	4	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
50	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
51	C₄×D₁₉	—	2	4	no	—
52	C₄×D₁₉	—	2	2	no	—
53	Dic₃₈	—	2	8	no	—
54	C₈×C₁₉	#41	1	4	yes	—
55	C₁₉⋊C₈	—	2	2	no	—
56	#3185	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
58	C₂×D₁₉	—	2	1	no	—
59	C₂×D₁₉	—	2	2	no	—
60	C₄×C₁₉	—	4	4	no	—
61	C₄×C₁₉	#137	1	4	yes	—
62	C₄×C₁₉	C₂×#41	1	2	yes	—
63	Dic₁₉	—	2	1	no	—
64	Dic₁₉	—	2	2	no	—
65	Dic₁₉	—	4	4	no	—
66	#533	—	19	2	no	—
67	#498	D₁₉	1	1	yes	characteristic, complemented
68	#494	—	19	1	no	—
69	#487	—	19	2	no	—
70	#470	—	19	4	no	—
71	#441	—	19	4	no	—
72	C₄×M₁₆	—	19	1	no	—
73	C₂×C₁₉	#532	1	1	yes	characteristic
74	C₂×C₁₉	C₂×#137	1	2	yes	—
75	D₁₉	—	4	1	no	—
76	C₂×Q₁₆	—	19	4	no	—
77	C₂×M₁₆	—	19	2	no	—
78	C₄⋊Q₈	—	19	2	no	—
79	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
80	#125	—	38	2	no	—
81	C₂²⋊Q₈	—	19	4	no	—
82	C₂²⋊Q₈	—	38	2	no	—
83	C₄×Q₈	—	19	4	no	—
84	C₄×Q₈	—	38	2	no	—
85	#117	—	38	2	no	—
86	C₂×C₄²	—	19	1	no	—
87	#106	C₂×D₁₉	1	4	yes	—
88	#103	—	19	8	no	—
89	#97	—	19	2	no	—
90	C₄×C₈	—	19	1	no	—
91	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
92	C₁₉	#3185	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	—	19	4	no	—
95	C₂²×C₄	—	19	2	no	—
96	C₂²×C₄	—	19	1	no	—
97	Q₁₆	—	38	8	no	—
98	M₁₆	—	38	4	no	—
99	C₂×C₈	—	19	2	no	—
100	C₂×C₈	C₂²×D₁₉	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	38	4	no	—
103	C₄⋊C₄	—	38	4	no	—
104	C₄⋊C₄	—	38	2	no	—
105	C₄⋊C₄	—	38	2	no	—
106	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
107	C₂²⋊C₄	—	38	4	no	—
108	C₄²	—	19	2	no	—
109	C₄²	—	19	1	no	—
110	C₄²	—	38	4	no	—
111	C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	C₂³	—	19	1	no	—
113	Q₈	—	4	4	no	—
114	Q₈	—	38	8	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	19	2	no	—
117	C₂×C₄	—	19	1	no	—
118	C₂×C₄	—	38	2	no	—
119	C₂×C₄	—	38	4	no	—
120	C₂×C₄	—	38	4	no	—
121	C₂×C₄	D₄×D₁₉	1	2	yes	—
122	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
123	C₈	—	38	2	no	—
124	C₈	#64545	1	4	yes	—
125	C₂²	—	38	2	no	—
126	C₂²	—	38	1	no	—
127	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
128	C₄	—	4	4	no	—
129	C₄	—	38	2	no	—
130	C₄	—	38	1	no	—
131	C₄	—	76	4	no	—
132	C₄	#10597361	1	4	yes	—
133	C₄	C₂×#64545	1	2	yes	—
134	C₂	—	76	1	no	—
135	C₂	#11927095	1	1	yes	characteristic
136	C₂	C₂×#10597361	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal

#11926924

C₂

yes

maximal, characteristic, complemented

#11926896

C₂

yes

maximal, complemented

#11926803

C₂

yes

maximal

#11926650

C₂

yes

maximal, complemented

C₄×#64515

C₂

yes

maximal, characteristic

C₁₉×#498

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

—

#10597392

—

Q₈×Dic₁₉

—

C₂×Dic₇₆

C₂²

yes

—

C₂×#64515

C₂²

yes

—

#10597343

C₂²

yes

—

#10597338

—

#10597336

—

#10597333

C₂²

yes

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

—

C₁₉×#106

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597272

C₂²

yes

—

#10597267

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

Dic₇₆

—

#64515

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#3185

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#137

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#533

—

#498

D₁₉

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂×C₁₉

#532

yes

characteristic

C₂×C₁₉

C₂×#137

yes

—

D₁₉

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#106

C₂×D₁₉

yes

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#3185

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₁₉

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂²×D₁₉

yes

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₂²×D₁₉

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

D₄×D₁₉

yes

—

122

C₂×C₄

C₂³×D₁₉

yes

characteristic

123

C₈

—

124

C₈

#64545

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂×D₄×D₁₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

#10597361

yes

—

133

C₄

C₂×#64545

yes

—

134

C₂

—

135

C₂

#11927095

yes

characteristic

136

C₂

C₂×#10597361

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#498	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#498	D₁₉
hypocenter	C₁₉	#3185
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#498

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂²×D₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #11926924	C₂	semidirect
3. #11926896	C₂	semidirect
5. #11926650	C₂	semidirect
7. C₁₉×#498	C₂	semidirect
67. #498	D₁₉	semidirect
92. C₁₉	#3185	semidirect

H ≅ G/N

type

2. #11926924

C₂

semidirect

3. #11926896

C₂

semidirect

5. #11926650

C₂

semidirect

7. C₁₉×#498

C₂

semidirect

67. #498

D₁₉

semidirect

92. C₁₉

#3185

semidirect

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

subgroup	index
#11927099	2
#11926924	2
#11926896	2
#11926803	2
#11926650	2
C₄×#64515	2
C₁₉×#498	2
#3185	19

subgroup

index

C₁₉×#498

Subgroups — #14574381

Conjugacy classes of subgroups

Complements

Maximal subgroups