Group #16820241 — subgroups

Subgroups — #16820241

Order 3712.

208 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 97 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	1	yes	maximal, characteristic
2	#14271190	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270922	C₂	1	2	yes	maximal
5	C₂₉×#427	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#117	C₂²	1	2	yes	—
8	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90777	C₂²	1	2	yes	—
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	C₂₉×#107	C₄	1	2	yes	complemented
12	C₂₉×#106	C₄	1	2	yes	complemented
13	#11745167	—	2	2	no	—
14	C₈×Dic₂₉	—	2	2	no	—
15	C₄⋊#6597	—	2	4	no	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₂₉	—	2	1	no	—
18	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₉	D₄	1	2	yes	—
21	C₂×C₈×C₂₉	Q₈	1	2	yes	—
22	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
23	C₂²⋊C₄×C₂₉	—	2	2	no	—
24	C₄²×C₂₉	—	2	2	no	—
25	C₄×Dic₂₉	—	2	1	no	—
26	C₄×Dic₂₉	Q₈	1	2	yes	—
27	#90777	—	2	2	no	—
28	#90777	—	2	2	no	—
29	C₂×#6597	—	2	1	no	—
30	C₂×#6597	—	2	1	no	—
31	C₂×#6597	—	2	2	no	—
32	C₂×#6597	D₄	1	2	yes	—
33	C₂³×C₂₉	#41	1	1	yes	characteristic
34	C₂×C₄×C₂₉	—	2	4	no	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
41	C₂×Dic₂₉	—	2	4	no	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
44	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
45	#6597	—	2	2	no	—
46	#6597	—	4	2	no	—
47	#1945	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	—	2	2	no	—
49	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
50	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
51	C₂²×C₂₉	#125	1	1	yes	characteristic
52	C₄×C₂₉	—	4	4	no	—
53	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
55	C₄×C₂₉	#121	1	1	yes	characteristic
56	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
57	Dic₂₉	—	2	4	no	—
58	C₂×#108	—	29	1	no	—
59	#427	D₂₉	1	1	yes	characteristic
60	#424	—	29	2	no	—
61	C₂×C₄×C₈	—	29	1	no	—
62	#339	—	29	2	no	—
63	C₂×C₂₉	—	2	1	no	—
64	C₂×C₂₉	—	2	1	no	—
65	C₂×C₂₉	#389	1	1	yes	characteristic
66	C₂×C₂₉	#443	1	2	yes	—
67	C₂×M₁₆	—	29	2	no	—
68	C₂²×C₈	—	29	1	no	—
69	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
70	#117	C₂×D₂₉	1	2	yes	—
71	C₂×C₄²	—	29	1	no	—
72	#108	—	58	2	no	—
73	#107	Dic₂₉	1	2	yes	complemented
74	#106	Dic₂₉	1	2	yes	complemented
75	C₄⋊C₈	—	58	4	no	—
76	C₄×C₈	—	58	2	no	—
77	C₂₉	#1945	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	58	1	no	—
79	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
80	M₁₆	—	58	2	no	—
81	M₁₆	—	58	2	no	—
82	C₂×C₈	—	29	2	no	—
83	C₂×C₈	—	58	1	no	—
84	C₂×C₈	—	58	1	no	—
85	C₂×C₈	—	58	2	no	—
86	C₂×C₈	Dic₅₈	1	2	yes	—
87	C₂×C₈	D₁₁₆	1	2	yes	—
88	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
89	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
90	C₄⋊C₄	C₂×Dic₂₉	1	4	yes	—
91	C₂²⋊C₄	—	2	2	no	—
92	C₄²	—	2	2	no	—
93	C₄²	—	29	2	no	—
94	C₄²	—	58	1	no	—
95	C₂³	#90807	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	58	4	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
100	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
101	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
102	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
103	C₂×C₄	#90809	1	1	yes	characteristic
104	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
105	C₈	—	58	2	no	—
106	C₈	—	116	2	no	—
107	C₈	C₄⋊Dic₂₉	1	2	yes	—
108	C₈	C₄⋊Dic₂₉	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	#11745252	1	1	yes	characteristic
111	C₂²	#11745259	1	1	yes	characteristic
112	C₂²	D₄×Dic₂₉	1	1	yes	characteristic
113	C₄	—	4	4	no	—
114	C₄	—	58	4	no	—
115	C₄	#11745250	1	1	yes	characteristic
116	C₄	#11745257	1	1	yes	characteristic
117	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
118	C₄	Q₈×Dic₂₉	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#14271062	1	1	yes	characteristic
122	C₂	#14271280	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745167

C₂

yes

maximal, characteristic

#14271190

C₂

yes

maximal

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14270922

C₂

yes

maximal

C₂₉×#427

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#107

C₄

yes

complemented

C₂₉×#106

C₄

yes

complemented

#11745167

—

C₈×Dic₂₉

—

C₄⋊#6597

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

Q₈

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

Q₈

yes

—

—

—

—

—

—

D₄

yes

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂²×C₂₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₉

#125

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

C₄×C₂₉

#121

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

C₂×#108

—

#427

D₂₉

yes

characteristic

#424

—

C₂×C₄×C₈

—

#339

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#389

yes

characteristic

C₂×C₂₉

#443

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

C₂×D₂₉

yes

—

C₂×C₄²

—

#108

—

#107

Dic₂₉

yes

complemented

#106

Dic₂₉

yes

complemented

C₄⋊C₈

—

C₄×C₈

—

C₂₉

#1945

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

C₂×Dic₂₉

yes

characteristic

C₂×C₈

C₂×Dic₂₉

yes

characteristic

C₄⋊C₄

C₂×Dic₂₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#90807

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₅₈

yes

characteristic

100

C₂×C₄

C₂×D₁₁₆

yes

characteristic

101

C₂×C₄

D₄×D₂₉

yes

characteristic

102

C₂×C₄

Q₈×D₂₉

yes

characteristic

103

C₂×C₄

#90809

yes

characteristic

104

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

105

C₈

—

106

C₈

—

116

—

107

C₈

C₄⋊Dic₂₉

yes

—

108

C₈

C₄⋊Dic₂₉

yes

—

109

C₂²

—

110

C₂²

#11745252

yes

characteristic

111

C₂²

#11745259

yes

characteristic

112

C₂²

D₄×Dic₂₉

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

#11745250

yes

characteristic

116

C₄

#11745257

yes

characteristic

117

C₄

C₂×C₄⋊Dic₂₉

yes

characteristic

118

C₄

Q₈×Dic₂₉

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#14271062

yes

characteristic

122

C₂

#14271280

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#427	C₂
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#427	D₂₉
hypocenter	C₂₉	#1945
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#427

C₂

socle

C₂²×C₂₉

C₄×D₄

prime radical

C₂³×C₂₉

#41

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
11. C₂₉×#107	C₄	semidirect
12. C₂₉×#106	C₄	semidirect
73. #107	Dic₂₉	semidirect
74. #106	Dic₂₉	semidirect
77. C₂₉	#1945	semidirect

H ≅ G/N

type

11. C₂₉×#107

C₄

semidirect

12. C₂₉×#106

C₄

semidirect

73. #107

Dic₂₉

semidirect

74. #106

Dic₂₉

semidirect

77. C₂₉

#1945

semidirect

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

subgroup	index
C₂×#11745167	2
#14271190	2
C₂×C₈×Dic₂₉	2
#14270922	2
C₂₉×#427	2
#1945	29

subgroup

index

C₂×C₈×Dic₂₉

C₂₉×#427

Subgroups — #16820241

Conjugacy classes of subgroups

Complements

Maximal subgroups