Group #14563619 — subgroups

Subgroups — #14563619

Order 2432.

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

normal subgroups only

This group has 312 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	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
3	#11926299	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#117	—	2	4	no	—
7	C₂×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
12	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
14	C₂⁴×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	4	no	—
24	C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₄²×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	D₄	1	4	yes	—
27	C₂×C₁₉⋊C₈	—	2	4	no	—
28	C₂×C₁₉⋊C₈	—	2	4	no	—
29	C₂×C₁₉⋊C₈	—	2	4	no	—
30	C₂³×C₁₉	—	2	1	no	—
31	C₂³×C₁₉	—	2	1	no	—
32	C₂³×C₁₉	—	2	4	no	—
33	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
34	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	4	no	—
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
43	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₁₉⋊C₈	—	4	4	no	—
49	#1798	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	2	no	—
51	C₂²×C₁₉	—	2	4	no	—
52	C₂²×C₁₉	—	4	2	no	—
53	C₂²×C₁₉	—	4	2	no	—
54	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₉	#117	1	1	yes	characteristic
57	C₂²×C₁₉	#131	1	4	yes	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	2	4	no	—
60	C₄×C₁₉	—	4	2	no	—
61	C₄×C₁₉	#121	1	2	yes	—
62	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
63	C₂×#117	D₁₉	1	1	yes	characteristic
64	C₂×C₄⋊C₈	—	19	2	no	—
65	C₂×C₂²⋊C₈	—	19	2	no	—
66	#336	—	19	2	no	—
67	C₂×C₁₉	—	4	2	no	—
68	C₂×C₁₉	#380	1	1	yes	characteristic
69	C₂×C₁₉	#408	1	2	yes	—
70	C₂×C₁₉	#424	1	2	yes	—
71	C₂×C₁₉	#433	1	2	yes	—
72	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
73	C₂²×C₈	—	19	4	no	—
74	#117	—	2	4	no	—
75	C₂×C₄⋊C₄	Dic₁₉	1	2	yes	—
76	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
77	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
79	C₄⋊C₈	—	38	4	no	—
80	C₂²⋊C₈	—	38	4	no	—
81	C₁₉	#1798	1	1	yes	characteristic, complemented, Sylow
82	C₂⁴	C₂×Dic₁₉	1	1	yes	characteristic
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	Dic₃₈	1	2	yes	—
86	C₂²×C₄	D₇₆	1	2	yes	—
87	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
88	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂×C₈	—	38	4	no	—
92	C₂×C₈	—	38	4	no	—
93	C₂×C₈	—	38	4	no	—
94	C₄⋊C₄	—	2	4	no	—
95	C₂²⋊C₄	—	2	4	no	—
96	C₄²	—	2	2	no	—
97	C₄²	C₂²⋊D₁₉	1	4	yes	—
98	C₂³	—	2	4	no	—
99	C₂³	—	2	1	no	—
100	C₂³	—	2	1	no	—
101	C₂³	C₄⋊Dic₁₉	1	2	yes	—
102	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
111	C₂×C₄	C₂²⋊Dic₁₉	1	4	yes	—
112	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
113	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
114	C₂×C₄	#64541	1	2	yes	—
115	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
116	C₈	—	76	4	no	—
117	C₂²	—	2	4	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	4	2	no	—
120	C₂²	—	4	2	no	—
121	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
122	C₂²	#10597372	1	1	yes	characteristic
123	C₂²	#10597394	1	4	yes	—
124	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	2	4	no	—
127	C₄	—	4	2	no	—
128	C₄	#10597370	1	2	yes	—
129	C₄	#10597376	1	2	yes	—
130	C₂	—	4	2	no	—
131	C₂	#11926404	1	1	yes	characteristic
132	C₂	#11926511	1	2	yes	—
133	C₂	#11926571	1	2	yes	—
134	C₂	#11926605	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

C₂×C₂²⋊(C₁₉⋊C₈)

C₂

yes

maximal

#11926299

C₂

yes

maximal, complemented

C₂×C₁₉×#117

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#1798

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×#117

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

#380

yes

characteristic

C₂×C₁₉

#408

yes

—

C₂×C₁₉

#424

yes

—

C₂×C₁₉

#433

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

Dic₁₉

yes

—

C₂×C₂²⋊C₄

Dic₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₁₉

#1798

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₃₈

yes

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₄⋊Dic₁₉

yes

—

102

C₂³

C₂²×Dic₁₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₄⋊Dic₁₉

yes

—

111

C₂×C₄

C₂²⋊Dic₁₉

yes

—

112

C₂×C₄

C₂×Dic₃₈

yes

characteristic

113

C₂×C₄

C₂×D₇₆

yes

characteristic

114

C₂×C₄

#64541

yes

—

115

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

122

C₂²

#10597372

yes

characteristic

123

C₂²

#10597394

yes

—

124

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

#10597370

yes

—

129

C₄

#10597376

yes

—

130

C₂

—

131

C₂

#11926404

yes

characteristic

132

C₂

#11926511

yes

—

133

C₂

#11926571

yes

—

134

C₂

#11926605

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle	C₂³×C₁₉	C₂²×C₄
Fitting	C₂×C₁₉×#117	C₂
prime radical	C₂⁴×C₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#117	D₁₉
hypocenter	C₁₉	#1798
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator, socle

C₂³×C₁₉

C₂²×C₄

Fitting

C₂×C₁₉×#117

C₂

prime radical

C₂⁴×C₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×#117

N	H ≅ G/N	type
1. C₂×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
3. #11926299	C₂	semidirect
81. C₁₉	#1798	semidirect

H ≅ G/N

type

1. C₂×C₄⋊(C₁₉⋊C₈)

C₂

semidirect

3. #11926299

C₂

semidirect

81. C₁₉

#1798

semidirect

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

subgroup	index
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
#11926299	2
C₂×C₁₉×#117	2
#1798	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₂×C₂²⋊(C₁₉⋊C₈)

#11926299

C₂×C₁₉×#117

#1798

Subgroups — #14563619

Conjugacy classes of subgroups

Complements

Maximal subgroups