Group #14572655 — subgroups

Subgroups — #14572655

Order 2432.

402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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	Q₈×C₁₉⋊C₈	C₂	1	2	yes	maximal, complemented
2	#11926622	C₂	1	6	yes	maximal, complemented
3	#11926601	C₂	1	3	yes	maximal, complemented
4	C₄×#64520	C₂	1	3	yes	maximal, complemented
5	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
8	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₄×D₄×C₁₉	C₄	1	3	yes	—
10	C₄×D₄×C₁₉	C₂²	1	3	yes	—
11	C₁₉×#117	C₄	1	3	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
13	C₂×#64520	C₂²	1	6	yes	—
14	C₂²⋊(C₁₉⋊C₈)	C₂²	1	6	yes	—
15	C₄⋊(C₁₉⋊C₈)	C₂²	1	6	yes	—
16	#10597260	C₂²	1	3	yes	—
17	#10597260	C₂²	1	1	yes	characteristic
18	C₄×C₁₉⋊C₈	C₂²	1	6	yes	—
19	#41×C₁₉	—	2	4	no	—
20	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×D₄×C₁₉	C₂×C₄	1	3	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	3	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
25	C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
26	C₄⋊C₄×C₁₉	C₂×C₄	1	3	yes	—
27	C₂²⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
28	C₄²×C₁₉	C₂×C₄	1	3	yes	—
29	C₄²×C₁₉	C₂×C₄	1	3	yes	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₄²×C₁₉	C₂³	1	3	yes	—
32	#64520	—	2	12	no	—
33	C₂×C₁₉⋊C₈	C₂³	1	6	yes	—
34	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
35	C₂³×C₁₉	C₂²×C₄	1	3	yes	—
36	Q₈×C₁₉	M₁₆	1	4	yes	complemented
37	D₄×C₁₉	—	2	6	no	—
38	C₂×C₄×C₁₉	—	2	6	no	—
39	C₂×C₄×C₁₉	—	2	6	no	—
40	C₂×C₄×C₁₉	—	4	3	no	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
44	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
45	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
46	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
47	C₁₉⋊C₈	—	2	6	no	—
48	C₁₉⋊C₈	#41	1	4	yes	complemented
49	#2971	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	3	no	—
51	C₂²×C₁₉	—	2	3	no	—
52	C₂²×C₁₉	—	2	3	no	—
53	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
54	C₄×C₁₉	—	2	3	no	—
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	—	2	3	no	—
58	C₄×C₁₉	C₂×M₁₆	1	6	yes	—
59	C₄×C₁₉	C₂×#41	1	2	yes	—
60	C₄×#41	D₁₉	1	1	yes	characteristic
61	C₈×Q₈	—	19	2	no	—
62	#436	—	19	6	no	—
63	#432	—	19	3	no	—
64	C₄×M₁₆	—	19	3	no	—
65	C₂×C₁₉	—	4	3	no	—
66	C₂×C₁₉	C₄×#41	1	1	yes	characteristic
67	C₂×C₁₉	C₂²×M₁₆	1	1	yes	characteristic
68	C₂×C₁₉	#568	1	1	yes	characteristic
69	C₂×#41	Dic₁₉	1	1	yes	characteristic
70	C₂×M₁₆	—	19	6	no	—
71	C₄×Q₈	Dic₁₉	1	1	yes	characteristic
72	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
73	C₄×D₄	Dic₁₉	1	3	yes	—
74	C₄×D₄	C₂×D₁₉	1	3	yes	—
75	#117	Dic₁₉	1	3	yes	—
76	C₂×C₄²	C₂×D₁₉	1	3	yes	—
77	C₄⋊C₈	—	19	6	no	—
78	C₂²⋊C₈	—	19	6	no	—
79	#97	—	19	1	no	—
80	#97	—	19	3	no	—
81	C₄×C₈	—	19	6	no	—
82	C₁₉	#2971	1	1	yes	characteristic, complemented, Sylow
83	#41	—	2	4	no	—
84	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
85	C₂×D₄	C₂×Dic₁₉	1	3	yes	—
86	C₂²×C₄	C₂×Dic₁₉	1	3	yes	—
87	C₂²×C₄	C₂×Dic₁₉	1	3	yes	—
88	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
89	M₁₆	—	38	12	no	—
90	C₂×C₈	—	19	2	no	—
91	C₂×C₈	—	19	6	no	—
92	C₄⋊C₄	C₂×Dic₁₉	1	3	yes	—
93	C₄⋊C₄	C₂×Dic₁₉	1	3	yes	—
94	C₂²⋊C₄	C₂×Dic₁₉	1	6	yes	—
95	C₄²	C₂×Dic₁₉	1	3	yes	—
96	C₄²	C₂×Dic₁₉	1	3	yes	—
97	C₄²	C₂²×D₁₉	1	3	yes	—
98	C₄²	C₂²×D₁₉	1	1	yes	characteristic
99	C₂³	C₂²×Dic₁₉	1	3	yes	—
100	Q₈	#64520	1	4	yes	complemented
101	D₄	—	2	6	no	—
102	C₂×C₄	—	2	6	no	—
103	C₂×C₄	—	2	6	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
106	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
107	C₂×C₄	C₂²×Dic₁₉	1	3	yes	—
108	C₂×C₄	C₂²×Dic₁₉	1	3	yes	—
109	C₂×C₄	C₂²×Dic₁₉	1	3	yes	—
110	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
111	C₈	—	19	4	no	—
112	C₈	—	38	6	no	—
113	C₂²	—	2	3	no	—
114	C₂²	—	2	3	no	—
115	C₂²	—	2	3	no	—
116	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
117	C₄	—	2	1	no	—
118	C₄	—	2	1	no	—
119	C₄	—	2	3	no	—
120	C₄	—	2	3	no	—
121	C₄	C₂×#64520	1	6	yes	—
122	C₄	#41×D₁₉	1	2	yes	—
123	C₂	—	4	3	no	—
124	C₂	#41×Dic₁₉	1	1	yes	characteristic
125	C₂	C₂²×#64520	1	1	yes	characteristic
126	C₂	#11927311	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×C₁₉⋊C₈

C₂

yes

maximal, complemented

#11926622

C₂

yes

maximal, complemented

#11926601

C₂

yes

maximal, complemented

C₄×#64520

C₂

yes

maximal, complemented

C₄×#41×C₁₉

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₄

yes

characteristic

C₄×Q₈×C₁₉

C₄

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

C₄

yes

—

C₄×D₄×C₁₉

C₂²

yes

—

C₁₉×#117

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597260

C₂²

yes

—

#10597260

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂²×C₄

yes

—

Q₈×C₁₉

M₁₆

yes

complemented

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

C₂×#41

yes

—

C₄×#41

D₁₉

yes

characteristic

C₈×Q₈

—

#436

—

#432

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₄×#41

yes

characteristic

C₂×C₁₉

C₂²×M₁₆

yes

characteristic

C₂×C₁₉

#568

yes

characteristic

C₂×#41

Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

Dic₁₉

yes

characteristic

C₄×Q₈

C₂×D₁₉

yes

characteristic

C₄×D₄

Dic₁₉

yes

—

C₄×D₄

C₂×D₁₉

yes

—

#117

Dic₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₁₉

#2971

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

C₂×Dic₁₉

yes

characteristic

C₂×D₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₂²⋊C₄

C₂×Dic₁₉

yes

—

C₄²

C₂×Dic₁₉

yes

—

C₄²

C₂×Dic₁₉

yes

—

C₄²

C₂²×D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

C₂²×Dic₁₉

yes

—

100

Q₈

#64520

yes

complemented

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

106

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

107

C₂×C₄

C₂²×Dic₁₉

yes

—

108

C₂×C₄

C₂²×Dic₁₉

yes

—

109

C₂×C₄

C₂²×Dic₁₉

yes

—

110

C₂×C₄

C₂³×D₁₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

C₂³×Dic₁₉

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂×#64520

yes

—

122

C₄

#41×D₁₉

yes

—

123

C₂

—

124

C₂

#41×Dic₁₉

yes

characteristic

125

C₂

C₂²×#64520

yes

characteristic

126

C₂

#11927311

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₄×#41×C₁₉	C₂
prime radical	C₂×#41×C₁₉	C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	#2971
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₄×#41×C₁₉

C₂

prime radical

C₂×#41×C₁₉

C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

hypercenter

C₄×#41

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ C₄×#41

N	H ≅ G/N	type
1. Q₈×C₁₉⋊C₈	C₂	semidirect
2. #11926622	C₂	semidirect
3. #11926601	C₂	semidirect
4. C₄×#64520	C₂	semidirect
36. Q₈×C₁₉	M₁₆	semidirect
48. C₁₉⋊C₈	#41	semidirect
82. C₁₉	#2971	semidirect
100. Q₈	#64520	semidirect

H ≅ G/N

type

1. Q₈×C₁₉⋊C₈

C₂

semidirect

2. #11926622

C₂

semidirect

3. #11926601

C₂

semidirect

4. C₄×#64520

C₂

semidirect

36. Q₈×C₁₉

M₁₆

semidirect

48. C₁₉⋊C₈

#41

semidirect

82. C₁₉

#2971

semidirect

100. Q₈

#64520

semidirect

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

subgroup	index
Q₈×C₁₉⋊C₈	2
#11926622	2
#11926601	2
C₄×#64520	2
C₄×#41×C₁₉	2
#2971	19

subgroup

index

Q₈×C₁₉⋊C₈

C₄×#41×C₁₉

Subgroups — #14572655

Conjugacy classes of subgroups

Complements

Maximal subgroups