Group #14574081 — subgroups

Subgroups — #14574081

Order 2432.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597350	C₂	1	4	yes	maximal, complemented
2	#11927094	C₂	1	2	yes	maximal, complemented
3	#11926938	C₂	1	4	yes	maximal, complemented
4	#11926933	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	#10597376	—	2	4	no	—
10	C₂×Dic₇₆	C₂²	1	4	yes	—
11	#10597350	—	2	16	no	—
12	C₂×D₁₅₂	C₂²	1	4	yes	—
13	C₂×#64516	C₂²	1	8	yes	—
14	#10597321	C₂²	1	4	yes	—
15	#10597320	C₂²	1	2	yes	—
16	C₄×D₇₆	—	2	4	no	—
17	#10597315	C₂²	1	2	yes	—
18	C₁₉×#97	C₂²	1	4	yes	—
19	C₂²×C₄×C₁₉	D₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₁₉	—	2	4	no	—
22	#64541	—	2	16	no	—
23	C₂×D₇₆	—	2	4	no	—
24	C₂×D₇₆	C₂³	1	4	yes	—
25	C₂×C₄×D₁₉	—	2	4	no	—
26	C₂×Dic₃₈	C₂³	1	4	yes	—
27	C₂×C₈×C₁₉	D₄	1	8	yes	complemented
28	C₂×C₈×C₁₉	C₂³	1	4	yes	—
29	C₄²×C₁₉	D₄	1	2	yes	—
30	C₄²×C₁₉	C₂³	1	2	yes	—
31	(C₂×D₁₉)⋊C₄	—	2	8	no	—
32	C₄⋊Dic₁₉	—	2	4	no	—
33	Dic₇₆	—	2	8	no	—
34	D₁₅₂	—	2	8	no	—
35	#64516	—	2	16	no	—
36	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂²×D₁₉	—	2	4	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
43	C₂²⋊D₁₉	—	4	8	no	—
44	C₂×Dic₁₉	—	2	4	no	—
45	D₇₆	—	2	8	no	—
46	D₇₆	—	4	8	no	—
47	C₄×D₁₉	—	4	8	no	—
48	Dic₃₈	—	2	8	no	—
49	C₈×C₁₉	C₂×D₄	1	8	yes	—
50	#3150	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	#127	1	2	yes	—
53	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
54	C₂×D₁₉	—	4	4	no	—
55	C₂×D₁₉	—	4	8	no	—
56	C₄×C₁₉	—	2	4	no	—
57	C₄×C₁₉	#127	1	2	yes	—
58	C₄×C₁₉	C₂²×D₄	1	2	yes	—
59	Dic₁₉	—	4	4	no	—
60	C₂×#135	—	19	4	no	—
61	#532	—	19	2	no	—
62	#497	—	19	4	no	—
63	#496	—	19	4	no	—
64	C₂×#97	D₁₉	1	1	yes	characteristic, complemented
65	C₂×C₁₉	—	2	2	no	—
66	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
67	C₂×C₁₉	#575	1	2	yes	—
68	D₁₉	—	8	4	no	—
69	C₂×#41	—	19	4	no	—
70	#135	—	38	16	no	—
71	C₂×Q₁₆	—	19	4	no	—
72	C₂×SD₁₆	—	19	8	no	—
73	C₂×D₈	—	19	4	no	—
74	C₂²×C₈	C₂×D₁₉	1	2	yes	—
75	C₄⋊Q₈	—	19	2	no	—
76	#127	—	19	2	no	—
77	#124	—	19	4	no	—
78	#121	—	38	4	no	—
79	C₄×D₄	—	38	4	no	—
80	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
81	#97	C₂×D₁₉	1	4	yes	—
82	C₁₉	#3150	1	1	yes	characteristic, complemented, Sylow
83	#41	—	38	16	no	—
84	C₂×Q₈	—	19	4	no	—
85	C₂×D₄	—	19	4	no	—
86	C₂×D₄	—	38	4	no	—
87	C₂×D₄	—	38	4	no	—
88	C₂²×C₄	—	38	4	no	—
89	C₂²×C₄	D₇₆	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	Q₁₆	—	38	8	no	—
92	SD₁₆	—	38	16	no	—
93	D₈	—	38	8	no	—
94	C₂×C₈	D₇₆	1	8	yes	complemented
95	C₂×C₈	C₂²×D₁₉	1	4	yes	—
96	C₄⋊C₄	—	38	4	no	—
97	C₂²⋊C₄	—	38	8	no	—
98	C₄²	D₇₆	1	2	yes	—
99	C₄²	C₂²×D₁₉	1	2	yes	—
100	C₂³	—	38	4	no	—
101	C₂³	C₂×D₇₆	1	1	yes	characteristic
102	Q₈	—	38	8	no	—
103	D₄	—	38	8	no	—
104	D₄	—	76	8	no	—
105	D₄	—	76	8	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	38	4	no	—
108	C₂×C₄	—	76	8	no	—
109	C₂×C₄	C₂×D₇₆	1	4	yes	—
110	C₂×C₄	C₂×D₇₆	1	4	yes	—
111	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
112	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
113	C₈	C₂×D₇₆	1	8	yes	—
114	C₂²	—	2	2	no	—
115	C₂²	—	76	4	no	—
116	C₂²	—	76	8	no	—
117	C₂²	#10597320	1	2	yes	—
118	C₂²	C₂²×D₇₆	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	76	4	no	—
121	C₄	#10597320	1	2	yes	—
122	C₄	C₂²×D₇₆	1	2	yes	—
123	C₂	—	2	2	no	—
124	C₂	—	152	4	no	—
125	C₂	C₂×#10597320	1	1	yes	characteristic
126	C₂	#11927344	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597350

C₂

yes

maximal, complemented

#11927094

C₂

yes

maximal, complemented

#11926938

C₂

yes

maximal, complemented

#11926933

C₂

yes

maximal, complemented

C₂×C₁₉×#97

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

—

C₂×Dic₇₆

C₂²

yes

—

#10597350

—

C₂×D₁₅₂

C₂²

yes

—

C₂×#64516

C₂²

yes

—

#10597321

C₂²

yes

—

#10597320

C₂²

yes

—

C₄×D₇₆

—

#10597315

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

D₄

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

—

#3150

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

—

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

—

—

—

—

C₂×#97

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#575

yes

—

D₁₉

—

C₂×#41

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#97

C₂×D₁₉

yes

—

C₁₉

#3150

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

D₇₆

yes

complemented

C₂×C₈

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₇₆

yes

—

C₄²

C₂²×D₁₉

yes

—

100

C₂³

—

101

C₂³

C₂×D₇₆

yes

characteristic

102

Q₈

—

103

D₄

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×D₇₆

yes

—

110

C₂×C₄

C₂×D₇₆

yes

—

111

C₂×C₄

C₂×D₇₆

yes

characteristic

112

C₂×C₄

C₂³×D₁₉

yes

characteristic

113

C₈

C₂×D₇₆

yes

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

#10597320

yes

—

118

C₂²

C₂²×D₇₆

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

#10597320

yes

—

122

C₄

C₂²×D₇₆

yes

—

123

C₂

—

124

C₂

—

152

—

125

C₂

C₂×#10597320

yes

characteristic

126

C₂

#11927344

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#3150
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle

C₂²×C₁₉

C₂²×D₄

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

#3150

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
1. C₂×#10597350	C₂	semidirect
2. #11927094	C₂	semidirect
3. #11926938	C₂	semidirect
4. #11926933	C₂	semidirect
5. C₂×C₁₉×#97	C₂	semidirect
27. C₂×C₈×C₁₉	D₄	semidirect
64. C₂×#97	D₁₉	semidirect
82. C₁₉	#3150	semidirect
94. C₂×C₈	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597350

C₂

semidirect

2. #11927094

C₂

semidirect

3. #11926938

C₂

semidirect

4. #11926933

C₂

semidirect

5. C₂×C₁₉×#97

C₂

semidirect

27. C₂×C₈×C₁₉

D₄

semidirect

64. C₂×#97

D₁₉

semidirect

82. C₁₉

#3150

semidirect

94. C₂×C₈

D₇₆

semidirect

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

subgroup	index
C₂×#10597350	2
#11927094	2
#11926938	2
#11926933	2
C₂×C₁₉×#97	2
#3150	19

subgroup

index

C₂×C₁₉×#97

Subgroups — #14574081

Conjugacy classes of subgroups

Complements

Maximal subgroups