Group #16819541 — subgroups

Subgroups — #16819541

Order 3712.

252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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×#11745269	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745170	C₂	1	2	yes	maximal, complemented
3	#14271145	C₂	1	2	yes	maximal
4	#14270921	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90805	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	#11745269	—	2	4	no	—
12	C₂×#90772	C₄	1	2	yes	—
13	C₂×C₈×D₂₉	C₄	1	2	yes	—
14	#11745172	—	2	2	no	—
15	#11745171	—	2	2	no	—
16	#11745170	—	2	4	no	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×C₂²⋊D₂₉	Q₈	1	2	yes	—
19	#90805	—	2	2	no	—
20	#90805	—	2	2	no	—
21	C₂×D₁₁₆	D₄	1	1	yes	characteristic
22	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
23	C₂×Dic₅₈	D₄	1	1	yes	characteristic
24	M₁₆×C₂₉	—	2	2	no	—
25	M₁₆×C₂₉	—	2	2	no	—
26	M₁₆×C₂₉	—	2	2	no	—
27	C₂×C₈×C₂₉	—	2	2	no	—
28	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
29	#90777	—	2	2	no	—
30	#90777	—	2	2	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	C₂×C₄	1	1	yes	characteristic
33	C₂×#6597	C₂×C₄	1	1	yes	characteristic
34	C₂×#6597	D₄	1	4	yes	—
35	#90772	—	2	4	no	—
36	C₈×D₂₉	—	2	4	no	—
37	C₂³×C₂₉	C₂×Q₈	1	1	yes	characteristic
38	C₂²×D₂₉	C₄⋊C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	#41	1	2	yes	—
43	C₂²⋊D₂₉	—	2	4	no	—
44	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
45	D₁₁₆	—	2	2	no	—
46	C₄×D₂₉	—	2	2	no	—
47	C₄×D₂₉	—	2	2	no	—
48	Dic₅₈	—	2	2	no	—
49	C₈×C₂₉	—	2	2	no	—
50	C₈×C₂₉	—	4	2	no	—
51	#6597	—	4	2	no	—
52	#6597	C₂²⋊C₄	1	2	yes	—
53	#6597	C₂²⋊C₄	1	2	yes	—
54	#1813	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	—	4	1	no	—
56	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₂₉	C₂²⋊Q₈	1	2	yes	—
58	C₂×D₂₉	—	2	2	no	—
59	C₂×D₂₉	—	4	2	no	—
60	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄×C₂₉	#117	1	1	yes	characteristic
62	C₄×C₂₉	#121	1	2	yes	—
63	Dic₂₉	—	2	2	no	—
64	C₂×#131	—	29	1	no	—
65	C₂×#108	—	29	2	no	—
66	#413	—	29	2	no	—
67	#338	—	29	1	no	—
68	#338	D₂₉	1	1	yes	characteristic, complemented
69	C₂×C₂₉	—	2	1	no	—
70	C₂×C₂₉	—	2	2	no	—
71	C₂×C₂₉	#380	1	1	yes	characteristic
72	D₂₉	—	4	2	no	—
73	C₂×#41	—	29	1	no	—
74	#131	—	58	4	no	—
75	C₂×M₁₆	—	29	2	no	—
76	C₂×M₁₆	—	29	2	no	—
77	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
78	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
79	C₂²×C₈	—	29	1	no	—
80	C₂²×C₈	—	29	2	no	—
81	#108	—	58	4	no	—
82	#101	—	58	2	no	—
83	#100	—	58	2	no	—
84	C₂₉	#1813	1	1	yes	characteristic, complemented, Sylow
85	#41	—	58	2	no	—
86	#41	—	58	2	no	—
87	C₂×Q₈	—	29	1	no	—
88	C₂×D₄	—	29	2	no	—
89	C₂×D₄	—	29	1	no	—
90	C₂²×C₄	—	29	2	no	—
91	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
92	M₁₆	—	2	2	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	58	4	no	—
96	M₁₆	—	58	2	no	—
97	M₁₆	—	58	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	29	1	no	—
100	C₂×C₈	—	29	1	no	—
101	C₂×C₈	—	29	4	no	—
102	C₂×C₈	—	58	4	no	—
103	C₂×C₈	—	58	2	no	—
104	C₂×C₈	C₄×D₂₉	1	2	yes	—
105	C₂³	—	29	2	no	—
106	C₂³	Q₈×D₂₉	1	1	yes	characteristic
107	Q₈	—	58	2	no	—
108	D₄	—	58	4	no	—
109	D₄	—	58	2	no	—
110	C₂×C₄	—	29	2	no	—
111	C₂×C₄	—	58	2	no	—
112	C₂×C₄	—	58	2	no	—
113	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
114	C₂×C₄	#90805	1	2	yes	—
115	C₂×C₄	D₄×D₂₉	1	2	yes	—
116	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	29	2	no	—
120	C₈	—	29	2	no	—
121	C₈	—	116	2	no	—
122	C₂²	—	4	1	no	—
123	C₂²	—	58	2	no	—
124	C₂²	—	116	2	no	—
125	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
126	C₂²	#11745258	1	2	yes	—
127	C₄	—	58	2	no	—
128	C₄	#11745234	1	1	yes	characteristic
129	C₄	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
130	C₄	#11745246	1	2	yes	—
131	C₂	—	2	1	no	—
132	C₂	—	2	2	no	—
133	C₂	—	116	2	no	—
134	C₂	#14271022	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745269

C₂

yes

maximal, characteristic

C₂×#11745170

C₂

yes

maximal, complemented

#14271145

C₂

yes

maximal

#14270921

C₂

yes

maximal, characteristic, complemented

C₂₉×#338

C₂

yes

maximal, characteristic, complemented

C₂×#90805

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

#11745269

—

C₂×#90772

C₄

yes

—

C₂×C₈×D₂₉

C₄

yes

—

#11745172

—

#11745171

—

#11745170

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₂²⋊D₂₉

Q₈

yes

—

#90805

—

#90805

—

C₂×D₁₁₆

D₄

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×Dic₅₈

D₄

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

D₄

yes

—

#90772

—

C₈×D₂₉

—

C₂³×C₂₉

C₂×Q₈

yes

characteristic

C₂²×D₂₉

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

—

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

#6597

—

#6597

C₂²⋊C₄

yes

—

#6597

C₂²⋊C₄

yes

—

#1813

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

Dic₂₉

—

—

—

—

—

D₂₉

yes

characteristic, complemented

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#380

yes

characteristic

D₂₉

—

C₂×#41

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#108

—

#101

—

#100

—

C₂₉

#1813

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₄×D₂₉

yes

—

105

C₂³

—

106

C₂³

Q₈×D₂₉

yes

characteristic

107

Q₈

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

114

C₂×C₄

#90805

yes

—

115

C₂×C₄

D₄×D₂₉

yes

—

116

C₂×C₄

D₄×D₂₉

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

116

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

116

—

125

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

126

C₂²

#11745258

yes

—

127

C₄

—

128

C₄

#11745234

yes

characteristic

129

C₄

C₂²⋊C₄×D₂₉

yes

characteristic

130

C₄

#11745246

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

116

—

134

C₂

#14271022

yes

characteristic

	subgroup	G/H
center	C₄	#11745234
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#338	C₂
socle	C₂×C₂₉	#380
prime radical	C₂×#90805	C₂²
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#338	D₂₉
hypocenter	C₂₉	#1813
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#11745234

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#338

C₂

C₂×C₂₉

C₂²

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
2. C₂×#11745170	C₂	semidirect
4. #14270921	C₂	semidirect
5. C₂₉×#338	C₂	semidirect
68. #338	D₂₉	semidirect
84. C₂₉	#1813	semidirect

H ≅ G/N

type

2. C₂×#11745170

C₂

semidirect

4. #14270921

C₂

semidirect

5. C₂₉×#338

C₂

semidirect

68. #338

D₂₉

semidirect

84. C₂₉

#1813

semidirect

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

subgroup	index
C₂×#11745269	2
C₂×#11745170	2
#14271145	2
#14270921	2
C₂₉×#338	2
#1813	29

subgroup

index

C₂₉×#338

Subgroups — #16819541

Conjugacy classes of subgroups

Complements

Maximal subgroups