Group #14573946 — subgroups

Subgroups — C₂×#11926895 #14573946

Order 2432.

424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597315	C₂	1	1	yes	maximal, characteristic
3	#11926895	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10597273	C₂	1	4	yes	maximal
5	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	—	2	1	no	—
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	—	2	1	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	#10597315	—	2	2	no	—
15	#10597315	—	2	2	no	—
16	#10597315	C₂²	1	4	yes	—
17	#10597315	C₂²	1	4	yes	—
18	C₄×C₈×C₁₉	C₂²	1	4	yes	—
19	#10597273	C₂²	1	16	yes	—
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₂²×Dic₁₉	—	2	2	no	—
25	C₂×Dic₃₈	—	2	8	no	—
26	C₂×Dic₃₈	—	2	4	no	—
27	C₂×Dic₃₈	—	2	2	no	—
28	C₂×Dic₃₈	—	4	4	no	—
29	C₂×Dic₃₈	C₂³	1	4	yes	—
30	C₂×C₈×C₁₉	—	2	4	no	—
31	C₂×C₈×C₁₉	C₂³	1	4	yes	—
32	C₄²×C₁₉	D₄	1	2	yes	—
33	C₄²×C₁₉	C₂³	1	2	yes	—
34	C₄⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	4	no	—
36	C₄⋊Dic₁₉	—	2	4	no	—
37	C₄⋊Dic₁₉	—	2	4	no	—
38	C₄⋊Dic₁₉	C₂³	1	4	yes	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	SD₁₆	1	4	yes	—
41	C₂×C₄×C₁₉	Q₁₆	1	4	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	#41	1	4	yes	—
46	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	4	4	no	—
50	C₂×Dic₁₉	—	4	4	no	—
51	Dic₃₈	—	2	8	no	—
52	Dic₃₈	—	4	4	no	—
53	Dic₃₈	—	4	8	no	—
54	C₈×C₁₉	—	2	4	no	—
55	C₂×#487	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	#124	1	2	yes	—
57	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
58	C₂²×C₁₉	C₂×Q₁₆	1	2	yes	—
59	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
60	C₄×C₁₉	#124	1	2	yes	—
61	C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
62	C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
63	C₄×C₁₉	C₂×#41	1	2	yes	—
64	Dic₁₉	—	4	4	no	—
65	Dic₁₉	—	4	4	no	—
66	C₂×C₄⋊Q₈	—	19	1	no	—
67	C₂×C₄⋊Q₈	—	19	1	no	—
68	#487	—	19	8	no	—
69	C₂×#103	—	19	4	no	—
70	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
71	C₂×C₁₉	#487	1	4	yes	complemented
72	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
73	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
74	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
75	C₂²×Q₈	—	19	2	no	—
76	C₂²×Q₈	—	38	1	no	—
77	C₂²×C₈	C₂×D₁₉	1	2	yes	—
78	C₄⋊Q₈	—	19	4	no	—
79	C₄⋊Q₈	—	19	4	no	—
80	C₄⋊Q₈	—	38	2	no	—
81	C₄⋊Q₈	—	38	2	no	—
82	C₂×C₄⋊C₄	—	19	2	no	—
83	C₂×C₄⋊C₄	—	38	1	no	—
84	C₂×C₄⋊C₄	—	38	1	no	—
85	C₂×C₄⋊C₄	—	38	1	no	—
86	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
87	#103	—	19	16	no	—
88	C₄×C₈	C₂×D₁₉	1	4	yes	—
89	C₁₉	C₂×#487	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	19	4	no	—
91	C₂×Q₈	—	38	4	no	—
92	C₂×Q₈	—	38	2	no	—
93	C₂×Q₈	—	38	8	no	—
94	C₂×Q₈	—	76	4	no	—
95	C₂²×C₄	—	38	2	no	—
96	C₂²×C₄	—	38	2	no	—
97	C₂²×C₄	D₇₆	1	1	yes	characteristic
98	C₂²×C₄	D₇₆	1	1	yes	characteristic
99	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
100	C₂×C₈	—	2	4	no	—
101	C₂×C₈	C₂²×D₁₉	1	4	yes	—
102	C₄⋊C₄	—	19	4	no	—
103	C₄⋊C₄	—	38	2	no	—
104	C₄⋊C₄	—	38	4	no	—
105	C₄⋊C₄	—	38	4	no	—
106	C₄⋊C₄	—	38	4	no	—
107	C₄²	D₇₆	1	2	yes	—
108	C₄²	C₂²×D₁₉	1	2	yes	—
109	C₂³	C₂×D₇₆	1	1	yes	characteristic
110	Q₈	—	38	8	no	—
111	Q₈	—	76	4	no	—
112	Q₈	—	76	8	no	—
113	C₂×C₄	—	38	4	no	—
114	C₂×C₄	—	38	4	no	—
115	C₂×C₄	—	76	4	no	—
116	C₂×C₄	—	76	4	no	—
117	C₂×C₄	#64516	1	4	yes	—
118	C₂×C₄	Dic₇₆	1	4	yes	—
119	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
120	C₂×C₄	C₂×D₇₆	1	2	yes	—
121	C₂×C₄	C₂×D₇₆	1	2	yes	—
122	C₂×C₄	#64541	1	4	yes	—
123	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
124	C₈	—	2	4	no	—
125	C₂²	#10597321	1	2	yes	—
126	C₂²	C₂×#64516	1	2	yes	—
127	C₂²	C₂×Dic₇₆	1	2	yes	—
128	C₂²	C₂²×D₇₆	1	1	yes	characteristic
129	C₄	—	76	4	no	—
130	C₄	—	76	4	no	—
131	C₄	#10597321	1	2	yes	—
132	C₄	C₂×#64516	1	4	yes	—
133	C₄	C₂×Dic₇₆	1	4	yes	—
134	C₄	C₂×#64541	1	2	yes	—
135	C₂	#11926895	1	4	yes	direct product factor
136	C₂	C₂×#10597321	1	1	yes	characteristic
137	C₂	C₂²×#64516	1	1	yes	characteristic
138	C₂	C₂²×Dic₇₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×#10597315

C₂

yes

maximal, characteristic

#11926895

C₂

yes

maximal, direct product factor

C₂×#10597273

C₂

yes

maximal

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597315

—

#10597315

—

#10597315

C₂²

yes

—

#10597315

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₂×#487

—

maximal, Sylow

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

C₂×Q₁₆

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

—

#487

—

C₂×#103

—

C₂×C₄×C₈

D₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

C₂²×SD₁₆

yes

characteristic

C₂×C₁₉

C₂²×Q₁₆

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

C₂×D₁₉

yes

—

C₁₉

C₂×#487

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

C₂²×D₁₉

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

D₇₆

yes

—

108

C₄²

C₂²×D₁₉

yes

—

109

C₂³

C₂×D₇₆

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#64516

yes

—

118

C₂×C₄

Dic₇₆

yes

—

119

C₂×C₄

C₂×D₇₆

yes

characteristic

120

C₂×C₄

C₂×D₇₆

yes

—

121

C₂×C₄

C₂×D₇₆

yes

—

122

C₂×C₄

#64541

yes

—

123

C₂×C₄

C₂³×D₁₉

yes

characteristic

124

C₈

—

125

C₂²

#10597321

yes

—

126

C₂²

C₂×#64516

yes

—

127

C₂²

C₂×Dic₇₆

yes

—

128

C₂²

C₂²×D₇₆

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

#10597321

yes

—

132

C₄

C₂×#64516

yes

—

133

C₄

C₂×Dic₇₆

yes

—

134

C₄

C₂×#64541

yes

—

135

C₂

#11926895

yes

direct product factor

136

C₂

C₂×#10597321

yes

characteristic

137

C₂

C₂²×#64516

yes

characteristic

138

C₂

C₂²×Dic₇₆

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	C₂×#487
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄×C₈

D₁₉

hypocenter

C₁₉

C₂×#487

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
3. #11926895	C₂	direct (N × H)
71. C₂×C₁₉	#487	semidirect
89. C₁₉	C₂×#487	semidirect
135. C₂	#11926895	direct (N × H)

H ≅ G/N

type

3. #11926895

C₂

direct (N × H)

71. C₂×C₁₉

#487

semidirect

89. C₁₉

C₂×#487

semidirect

135. C₂

#11926895

direct (N × H)

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

subgroup	index
C₂×#10597315	2
#11926895	2
C₂×#10597273	2
C₂×C₄×C₈×C₁₉	2
C₂×#487	19

subgroup

index

C₂×C₄×C₈×C₁₉

Subgroups — C₂×#11926895 #14573946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926895 #14573946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926895 #14573946