Group #14573971 — subgroups

Subgroups — C₂×#11926910 #14573971

Order 2432.

488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597320	C₂	1	1	yes	maximal, characteristic
2	#11926910	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597266	C₂	1	4	yes	maximal, complemented
4	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	—	2	2	no	—
7	C₂²×D₇₆	C₂²	1	2	yes	—
8	C₁₉×#125	—	2	2	no	—
9	C₁₉×#125	C₂²	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	#10597320	—	2	2	no	—
15	#10597320	C₂²	1	4	yes	—
16	#10597266	C₂²	1	16	yes	complemented
17	#10597260	C₂²	1	4	yes	complemented
18	C₂³×D₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×D₇₆	—	2	8	no	—
23	C₂×D₇₆	—	2	8	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	4	8	no	—
26	C₂×D₇₆	C₂³	1	4	yes	—
27	C₄⋊C₄×C₁₉	—	2	8	no	—
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
30	C₄²×C₁₉	D₄	1	2	yes	—
31	C₄²×C₁₉	C₂³	1	2	yes	—
32	C₂×C₁₉⋊C₈	—	2	4	no	—
33	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
34	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×D₁₉	—	2	4	no	—
36	C₂²×D₁₉	—	4	4	no	—
37	C₂²×D₁₉	—	4	8	no	—
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	4	4	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	4	yes	—
44	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
45	D₇₆	—	2	8	no	—
46	D₇₆	—	4	16	no	—
47	D₇₆	—	4	4	no	—
48	C₁₉⋊C₈	—	2	4	no	—
49	C₂×#490	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	#124	1	2	yes	—
51	C₂²×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
52	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
53	C₂×D₁₉	—	4	4	no	—
54	C₂×D₁₉	—	4	8	no	—
55	C₂×D₁₉	—	8	8	no	—
56	C₄×C₁₉	—	2	4	no	—
57	C₄×C₁₉	—	4	4	no	—
58	C₄×C₁₉	#124	1	2	yes	—
59	C₄×C₁₉	C₂×#41	1	2	yes	—
60	C₂×#127	—	19	1	no	—
61	C₂×#125	D₁₉	1	1	yes	characteristic, complemented
62	#490	—	19	8	no	—
63	C₂×#102	—	19	4	no	—
64	C₂×#97	—	19	1	no	—
65	C₂×C₁₉	#490	1	4	yes	complemented
66	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
67	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
68	D₁₉	—	8	4	no	—
69	C₂²×D₄	—	19	2	no	—
70	C₂²×D₄	—	38	2	no	—
71	C₂²×C₈	—	19	2	no	—
72	#127	—	19	4	no	—
73	#127	—	38	2	no	—
74	#125	—	2	2	no	—
75	#125	C₂×D₁₉	1	4	yes	complemented
76	C₂×C₄⋊C₄	—	2	2	no	—
77	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
78	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
79	#102	—	19	16	no	—
80	#97	—	19	4	no	—
81	C₁₉	C₂×#490	1	1	yes	characteristic, complemented, Sylow
82	C₂⁴	—	38	2	no	—
83	C₂×D₄	—	19	4	no	—
84	C₂×D₄	—	38	8	no	—
85	C₂×D₄	—	38	8	no	—
86	C₂×D₄	—	38	2	no	—
87	C₂×D₄	—	76	8	no	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂×C₈	—	19	4	no	—
92	C₂×C₈	—	38	4	no	—
93	C₄⋊C₄	—	2	8	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
96	C₄²	C₂²⋊D₁₉	1	2	yes	—
97	C₄²	C₂²×D₁₉	1	2	yes	—
98	C₂³	—	38	4	no	—
99	C₂³	—	76	4	no	—
100	C₂³	—	76	8	no	—
101	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
102	D₄	—	38	8	no	—
103	D₄	—	76	16	no	—
104	D₄	—	76	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	#64545	1	4	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
112	C₈	—	38	4	no	—
113	C₂²	—	76	4	no	—
114	C₂²	—	76	8	no	—
115	C₂²	—	152	8	no	—
116	C₂²	#10597393	1	2	yes	—
117	C₂²	#10597395	1	4	yes	—
118	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	4	4	no	—
121	C₄	#10597393	1	2	yes	—
122	C₄	C₂×#64545	1	2	yes	—
123	C₂	—	152	4	no	—
124	C₂	#11926910	1	4	yes	direct product factor
125	C₂	C₂×#10597393	1	1	yes	characteristic
126	C₂	C₂×#10597395	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

#11926910

C₂

yes

maximal, direct product factor

C₂×#10597266

C₂

yes

maximal, complemented

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#125

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

—

C₂²×D₇₆

C₂²

yes

—

C₁₉×#125

—

C₁₉×#125

C₂²

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597320

—

#10597320

C₂²

yes

—

#10597266

C₂²

yes

complemented

#10597260

C₂²

yes

complemented

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

C₂×#490

—

maximal, Sylow

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×#41

yes

—

C₂×#127

—

C₂×#125

D₁₉

yes

characteristic, complemented

#490

—

C₂×#102

—

C₂×#97

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

—

—

—

C₂×D₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#102

—

#97

—

C₁₉

C₂×#490

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₄²

C₂²⋊D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#64545

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

111

C₂×C₄

C₂³×D₁₉

yes

characteristic

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

152

—

116

C₂²

#10597393

yes

—

117

C₂²

#10597395

yes

—

118

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

#10597393

yes

—

122

C₄

C₂×#64545

yes

—

123

C₂

—

152

—

124

C₂

#11926910

yes

direct product factor

125

C₂

C₂×#10597393

yes

characteristic

126

C₂

C₂×#10597395

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂×#10597320	C₂
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	C₂×#490
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle

C₂³×C₁₉

C₂×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #11926910	C₂	direct (N × H)
3. C₂×#10597266	C₂	semidirect
4. C₂×#10597260	C₂	semidirect
5. C₂×C₁₉×#125	C₂	semidirect
9. C₁₉×#125	C₂²	semidirect
16. #10597266	C₂²	semidirect
17. #10597260	C₂²	semidirect
61. C₂×#125	D₁₉	semidirect
65. C₂×C₁₉	#490	semidirect
75. #125	C₂×D₁₉	semidirect
81. C₁₉	C₂×#490	semidirect
124. C₂	#11926910	direct (N × H)

H ≅ G/N

type

2. #11926910

C₂

direct (N × H)

3. C₂×#10597266

C₂

semidirect

4. C₂×#10597260

C₂

semidirect

5. C₂×C₁₉×#125

C₂

semidirect

9. C₁₉×#125

C₂²

semidirect

16. #10597266

C₂²

semidirect

17. #10597260

C₂²

semidirect

61. C₂×#125

D₁₉

semidirect

65. C₂×C₁₉

#490

semidirect

75. #125

C₂×D₁₉

semidirect

81. C₁₉

C₂×#490

semidirect

124. C₂

#11926910

direct (N × H)

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

subgroup	index
C₂×#10597320	2
#11926910	2
C₂×#10597266	2
C₂×#10597260	2
C₂×C₁₉×#125	2
C₂×#490	19

subgroup

index

C₂×C₁₉×#125

Subgroups — C₂×#11926910 #14573971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926910 #14573971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926910 #14573971