Group #16819542 — subgroups

Subgroups — #16819542

Order 3712.

252 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11745167	C₂	1	2	yes	maximal, complemented
2	#14271147	C₂	1	2	yes	maximal
3	#14270921	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₉×#131	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic
6	C₂₉×#131	—	2	4	no	—
7	C₂×M₁₆×C₂₉	C₄	1	2	yes	—
8	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₂₉	C₄	1	2	yes	—
10	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×#90777	C₂²	1	4	yes	—
12	#11745184	—	2	2	no	—
13	#11745181	—	2	2	no	—
14	#11745167	—	2	4	no	—
15	#41×C₂₉	—	2	2	no	—
16	#41×C₂₉	—	2	2	no	—
17	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
19	C₂×D₄×C₂₉	Q₈	1	2	yes	—
20	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₉	—	2	2	no	—
23	M₁₆×C₂₉	—	2	4	no	—
24	C₂×C₈×C₂₉	—	2	4	no	—
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₂₉	D₄	1	4	yes	—
29	#90777	—	2	4	no	—
30	#90777	—	2	4	no	—
31	C₂×#6597	—	2	4	no	—
32	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
33	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	Q₈×C₂₉	—	2	2	no	—
35	D₄×C₂₉	—	2	4	no	—
36	D₄×C₂₉	—	2	2	no	—
37	C₂×C₄×C₂₉	—	2	2	no	—
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₂₉	#41	1	2	yes	—
44	C₈×C₂₉	—	2	2	no	—
45	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
46	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
47	#6597	—	4	4	no	—
48	#1813	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	—	2	2	no	—
50	C₂²×C₂₉	—	4	1	no	—
51	C₂²×C₂₉	—	4	2	no	—
52	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₂₉	C₂²⋊Q₈	1	2	yes	—
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₄×C₂₉	#117	1	1	yes	characteristic
57	C₄×C₂₉	#121	1	2	yes	—
58	C₂×#131	D₂₉	1	1	yes	characteristic
59	C₂×#108	—	29	2	no	—
60	#413	—	29	2	no	—
61	#338	—	29	2	no	—
62	C₂×C₂₉	—	2	1	no	—
63	C₂×C₂₉	—	2	2	no	—
64	C₂×C₂₉	—	4	2	no	—
65	C₂×C₂₉	#380	1	1	yes	characteristic
66	C₂×#41	C₂×D₂₉	1	1	yes	characteristic
67	#131	—	2	4	no	—
68	C₂×M₁₆	—	29	4	no	—
69	C₂×M₁₆	Dic₂₉	1	2	yes	—
70	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
71	C₂²×C₈	Dic₂₉	1	2	yes	—
72	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
73	#108	—	58	4	no	—
74	#101	—	58	2	no	—
75	#100	—	58	2	no	—
76	C₂₉	#1813	1	1	yes	characteristic, complemented, Sylow
77	#41	—	2	2	no	—
78	#41	—	2	2	no	—
79	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
80	C₂×D₄	Dic₅₈	1	2	yes	—
81	C₂×D₄	D₁₁₆	1	1	yes	characteristic
82	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	2	4	no	—
86	M₁₆	—	58	4	no	—
87	M₁₆	—	58	4	no	—
88	C₂×C₈	—	2	4	no	—
89	C₂×C₈	—	58	4	no	—
90	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
91	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
92	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₂₉	1	4	yes	—
94	C₂³	C₄⋊Dic₂₉	1	2	yes	—
95	C₂³	C₂×Dic₅₈	1	1	yes	characteristic
96	Q₈	—	2	2	no	—
97	D₄	—	2	4	no	—
98	D₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	C₄⋊Dic₂₉	1	2	yes	—
102	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
103	C₂×C₄	#90805	1	2	yes	—
104	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
105	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
106	C₈	—	2	2	no	—
107	C₈	—	116	4	no	—
108	C₈	C₂²⋊Dic₂₉	1	2	yes	—
109	C₈	C₂²⋊Dic₂₉	1	2	yes	—
110	C₂²	—	2	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	2	no	—
113	C₂²	#11745286	1	2	yes	—
114	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	#11745288	1	1	yes	characteristic
117	C₄	#11745292	1	2	yes	—
118	C₄	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	2	no	—
121	C₂	—	4	2	no	—
122	C₂	#14271023	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745167

C₂

yes

maximal, complemented

#14271147

C₂

yes

maximal

#14270921

C₂

yes

maximal, complemented

C₂×C₂₉×#131

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

characteristic

C₂₉×#131

—

C₂×M₁₆×C₂₉

C₄

yes

—

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂²×C₈×C₂₉

C₄

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

#11745184

—

#11745181

—

#11745167

—

#41×C₂₉

—

#41×C₂₉

—

C₂×Q₈×C₂₉

D₄

yes

characteristic

C₂×D₄×C₂₉

D₄

yes

characteristic

C₂×D₄×C₂₉

Q₈

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

#90777

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

C₄⋊C₄

yes

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₈×C₂₉

—

C₈×C₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

C₂²⋊C₄

yes

—

#6597

—

#1813

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

C₂×#131

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#380

yes

characteristic

C₂×#41

C₂×D₂₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

Dic₂₉

yes

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂²×C₈

Dic₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

—

—

—

C₂₉

#1813

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

D₁₁₆

yes

characteristic

C₂×D₄

Dic₅₈

yes

—

C₂×D₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₂×C₈

C₂×Dic₂₉

yes

characteristic

C₂×C₈

C₂×Dic₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

—

C₂³

C₄⋊Dic₂₉

yes

—

C₂³

C₂×Dic₅₈

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄⋊Dic₂₉

yes

—

102

C₂×C₄

C₂×D₁₁₆

yes

characteristic

103

C₂×C₄

#90805

yes

—

104

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

105

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

106

C₈

—

107

C₈

—

116

—

108

C₈

C₂²⋊Dic₂₉

yes

—

109

C₈

C₂²⋊Dic₂₉

yes

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

#11745286

yes

—

114

C₂²

C₂×C₄⋊Dic₂₉

yes

characteristic

115

C₄

—

116

C₄

#11745288

yes

characteristic

117

C₄

#11745292

yes

—

118

C₄

C₂×C₂²⋊Dic₂₉

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

122

C₂

#14271023

yes

characteristic

	subgroup	G/H
center	C₄	#11745288
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#131	C₂
socle	C₂×C₂₉	#380
prime radical	C₂×#41×C₂₉	C₂²
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#131	D₂₉
hypocenter	C₂₉	#1813
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₂×#131

subgroup

G/H

center

C₄

#11745288

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#131

C₂

socle

C₂×C₂₉

#380

prime radical

C₂×#41×C₂₉

C₂²

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₂×#131

N	H ≅ G/N	type
1. C₂×#11745167	C₂	semidirect
3. #14270921	C₂	semidirect
76. C₂₉	#1813	semidirect

H ≅ G/N

type

1. C₂×#11745167

C₂

semidirect

3. #14270921

C₂

semidirect

76. C₂₉

#1813

semidirect

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

subgroup	index
C₂×#11745167	2
#14271147	2
#14270921	2
C₂×C₂₉×#131	2
#1813	29

subgroup

index

C₂×C₂₉×#131

Subgroups — #16819542

Conjugacy classes of subgroups

Complements

Maximal subgroups