Group #16819540 — subgroups

Subgroups — #16819540

Order 3712.

252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11745310	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745170	C₂	1	2	yes	maximal, complemented
3	#14271147	C₂	1	1	yes	maximal, characteristic
4	#14270921	C₂	1	2	yes	maximal, complemented
5	C₂₉×#413	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	#11745310	—	2	4	no	—
9	C₂×#90777	C₄	1	2	yes	—
10	C₂×#90777	C₂²	1	2	yes	—
11	C₂×#90777	C₂²	1	1	yes	characteristic
12	C₂²×#6597	C₄	1	2	yes	—
13	C₂²×#6597	C₂²	1	1	yes	characteristic
14	C₂₉×#101	—	2	1	no	—
15	C₂₉×#100	—	2	1	no	—
16	#11745184	—	2	1	no	—
17	#11745181	—	2	1	no	—
18	#11745170	—	2	4	no	—
19	#41×C₂₉	—	2	2	no	—
20	#41×C₂₉	—	2	2	no	—
21	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
22	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
23	C₂×D₄×C₂₉	Q₈	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₂₉	—	2	2	no	—
27	M₁₆×C₂₉	—	2	2	no	—
28	C₂×C₈×C₂₉	—	2	2	no	—
29	#90777	—	2	2	no	—
30	#90777	—	2	4	no	—
31	#90777	—	2	2	no	—
32	#90777	—	2	2	no	—
33	C₂×#6597	—	2	4	no	—
34	C₂×#6597	—	2	2	no	—
35	C₂×#6597	C₂×C₄	1	2	yes	—
36	C₂×#6597	C₂×C₄	1	1	yes	characteristic
37	C₂×#6597	C₂×C₄	1	1	yes	characteristic
38	C₂×#6597	D₄	1	4	yes	—
39	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
40	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
41	Q₈×C₂₉	—	2	2	no	—
42	D₄×C₂₉	—	2	4	no	—
43	D₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	—	2	2	no	—
46	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₂₉	#41	1	2	yes	—
51	C₈×C₂₉	—	4	2	no	—
52	#6597	—	2	2	no	—
53	#6597	—	4	2	no	—
54	#6597	C₂²⋊C₄	1	2	yes	—
55	#6597	C₂²⋊C₄	1	2	yes	—
56	#1813	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	—	2	2	no	—
58	C₂²×C₂₉	—	4	1	no	—
59	C₂²×C₂₉	—	4	2	no	—
60	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₂₉	C₂²⋊Q₈	1	2	yes	—
62	C₄×C₂₉	—	2	2	no	—
63	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₂₉	#117	1	1	yes	characteristic
65	C₄×C₂₉	#121	1	2	yes	—
66	C₂×#131	—	29	1	no	—
67	C₂×#108	—	29	2	no	—
68	#413	—	29	1	no	—
69	#413	D₂₉	1	1	yes	characteristic
70	#338	—	29	2	no	—
71	C₂×C₂₉	—	2	1	no	—
72	C₂×C₂₉	—	2	2	no	—
73	C₂×C₂₉	—	4	2	no	—
74	C₂×C₂₉	#380	1	1	yes	characteristic
75	C₂×#41	C₂×D₂₉	1	1	yes	characteristic
76	#131	—	58	4	no	—
77	C₂×M₁₆	—	29	2	no	—
78	C₂×M₁₆	—	29	1	no	—
79	C₂×M₁₆	—	29	2	no	—
80	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
81	C₂²×C₈	—	29	1	no	—
82	C₂²×C₈	—	29	2	no	—
83	#108	—	58	4	no	—
84	#101	—	2	1	no	—
85	#101	—	58	1	no	—
86	#100	—	2	1	no	—
87	#100	—	58	1	no	—
88	C₂₉	#1813	1	1	yes	characteristic, complemented, Sylow
89	#41	—	2	2	no	—
90	#41	—	2	2	no	—
91	C₂×Q₈	C₂²⋊D₂₉	1	1	yes	characteristic
92	C₂×D₄	Dic₅₈	1	2	yes	—
93	C₂×D₄	C₂²⋊D₂₉	1	1	yes	characteristic
94	C₂²×C₄	C₄×D₂₉	1	2	yes	—
95	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
96	M₁₆	—	2	2	no	—
97	M₁₆	—	2	2	no	—
98	M₁₆	—	58	4	no	—
99	M₁₆	—	58	2	no	—
100	M₁₆	—	58	2	no	—
101	M₁₆	—	58	2	no	—
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	29	1	no	—
104	C₂×C₈	—	29	1	no	—
105	C₂×C₈	—	29	4	no	—
106	C₂×C₈	—	29	2	no	—
107	C₂×C₈	—	58	4	no	—
108	C₂×C₈	—	58	2	no	—
109	C₂³	#90779	1	2	yes	—
110	C₂³	C₂×Dic₅₈	1	1	yes	characteristic
111	Q₈	—	2	2	no	—
112	D₄	—	2	4	no	—
113	D₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	#90779	1	2	yes	—
117	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
118	C₂×C₄	D₄×D₂₉	1	2	yes	—
119	C₂×C₄	#90807	1	2	yes	—
120	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
121	C₈	—	4	2	no	—
122	C₈	—	29	2	no	—
123	C₈	—	29	2	no	—
124	C₈	—	58	2	no	—
125	C₈	—	116	2	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	4	1	no	—
128	C₂²	—	4	2	no	—
129	C₂²	#11745240	1	2	yes	—
130	C₂²	C₂×#90779	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	#11745239	1	1	yes	characteristic
133	C₄	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
134	C₄	#11745301	1	2	yes	—
135	C₂	—	2	1	no	—
136	C₂	—	2	2	no	—
137	C₂	—	4	2	no	—
138	C₂	#14271021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745310

C₂

yes

maximal, characteristic

C₂×#11745170

C₂

yes

maximal, complemented

#14271147

C₂

yes

maximal, characteristic

#14270921

C₂

yes

maximal, complemented

C₂₉×#413

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

#11745310

—

C₂×#90777

C₄

yes

—

C₂×#90777

C₂²

yes

—

C₂×#90777

C₂²

yes

characteristic

C₂²×#6597

C₄

yes

—

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#101

—

C₂₉×#100

—

#11745184

—

#11745181

—

#11745170

—

#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×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

D₄

yes

—

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

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₈×C₂₉

—

#6597

—

#6597

—

#6597

C₂²⋊C₄

yes

—

#6597

C₂²⋊C₄

yes

—

#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

—

—

—

—

D₂₉

yes

characteristic

#338

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#380

yes

characteristic

C₂×#41

C₂×D₂₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

—

—

—

—

—

—

C₂₉

#1813

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂²⋊D₂₉

yes

characteristic

C₂×D₄

Dic₅₈

yes

—

C₂×D₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂³

#90779

yes

—

110

C₂³

C₂×Dic₅₈

yes

characteristic

111

Q₈

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

#90779

yes

—

117

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

118

C₂×C₄

D₄×D₂₉

yes

—

119

C₂×C₄

#90807

yes

—

120

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

—

116

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#11745240

yes

—

130

C₂²

C₂×#90779

yes

characteristic

131

C₄

—

132

C₄

#11745239

yes

characteristic

133

C₄

C₂²⋊C₄×D₂₉

yes

characteristic

134

C₄

#11745301

yes

—

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#14271021

yes

characteristic

	subgroup	G/H
center	C₄	#11745239
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#413	C₂
socle	C₂×C₂₉	#380
prime radical	C₂×#41×C₂₉	C₂²
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#413	D₂₉
hypocenter	C₂₉	#1813
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₄

#11745239

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#413

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 ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
2. C₂×#11745170	C₂	semidirect
4. #14270921	C₂	semidirect
88. C₂₉	#1813	semidirect

H ≅ G/N

type

2. C₂×#11745170

C₂

semidirect

4. #14270921

C₂

semidirect

88. C₂₉

#1813

semidirect

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

subgroup	index
C₂×#11745310	2
C₂×#11745170	2
#14271147	2
#14270921	2
C₂₉×#413	2
#1813	29

subgroup

index

C₂₉×#413

Subgroups — #16819540

Conjugacy classes of subgroups

Complements

Maximal subgroups