Group #16819374 — subgroups

Subgroups — #16819374

Order 3712.

232 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 117 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	#14271201	C₂	1	1	yes	maximal, characteristic
2	#14271121	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	#14270924	C₂	1	2	yes	maximal
5	C₂×C₂₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745288	C₂²	1	2	yes	—
9	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
10	C₂²×#6597	C₂²	1	1	yes	characteristic
11	C₂₉×#108	C₄	1	4	yes	complemented
12	#11745166	C₄	1	2	yes	complemented
13	#11745165	C₄	1	2	yes	complemented
14	#11745163	—	2	2	no	—
15	C₈×Dic₂₉	—	2	2	no	—
16	C₈×Dic₂₉	C₄	1	4	yes	complemented
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₂₉	—	2	1	no	—
19	M₁₆×C₂₉	—	2	2	no	—
20	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₂²⋊Dic₂₉	—	2	2	no	—
27	C₄⋊Dic₂₉	C₂×C₄	1	4	yes	—
28	C₄×Dic₂₉	—	2	2	no	—
29	C₄×Dic₂₉	—	2	1	no	—
30	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
31	C₂×#6597	C₂×C₄	1	2	yes	—
32	C₂×#6597	D₄	1	1	yes	characteristic
33	C₂×#6597	D₄	1	1	yes	characteristic
34	C₂×#6597	Q₈	1	2	yes	—
35	C₂³×C₂₉	#41	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
42	C₂×Dic₂₉	—	2	4	no	—
43	C₂×Dic₂₉	—	2	2	no	—
44	C₂×Dic₂₉	—	2	4	no	—
45	C₈×C₂₉	—	2	4	no	—
46	C₈×C₂₉	C₄²	1	2	yes	—
47	C₈×C₂₉	C₄²	1	2	yes	—
48	#6597	C₄⋊C₄	1	2	yes	—
49	#6597	C₄⋊C₄	1	2	yes	—
50	#1772	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	2	2	no	—
52	C₂²×C₂₉	#117	1	1	yes	characteristic
53	C₂²×C₂₉	C₄×D₄	1	1	yes	characteristic
54	C₂²×C₂₉	C₄×Q₈	1	1	yes	characteristic
55	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
56	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
58	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
59	Dic₂₉	—	2	4	no	—
60	Dic₂₉	—	4	4	no	—
61	C₂×#108	D₂₉	1	1	yes	characteristic
62	#427	—	29	1	no	—
63	#405	—	29	2	no	—
64	C₂×C₄×C₈	—	29	1	no	—
65	#339	—	29	2	no	—
66	C₂×C₂₉	—	2	1	no	—
67	C₂×C₂₉	—	2	1	no	—
68	C₂×C₂₉	C₄×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₂₉	#443	1	2	yes	—
70	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
71	C₂²×C₈	—	29	1	no	—
72	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
73	#117	—	29	2	no	—
74	C₂×C₄²	—	29	1	no	—
75	#108	Dic₂₉	1	4	yes	complemented
76	#107	—	29	2	no	—
77	#106	—	29	2	no	—
78	#97	—	58	2	no	—
79	C₄×C₈	—	29	4	no	—
80	C₄×C₈	—	58	2	no	—
81	C₂₉	#1772	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	58	1	no	—
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	C₂×Dic₂₉	1	4	yes	—
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	29	2	no	—
88	C₂×C₈	—	29	1	no	—
89	C₂×C₈	—	29	1	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	C₄×D₂₉	1	2	yes	—
92	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
93	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
94	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
95	C₄⋊C₄	—	29	4	no	—
96	C₂²⋊C₄	—	58	2	no	—
97	C₄²	—	29	2	no	—
98	C₄²	—	58	2	no	—
99	C₄²	—	58	1	no	—
100	C₂³	#90809	1	1	yes	characteristic
101	C₂×C₄	—	58	4	no	—
102	C₂×C₄	—	58	2	no	—
103	C₂×C₄	—	58	4	no	—
104	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
105	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
106	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
107	C₂×C₄	#90807	1	1	yes	characteristic
108	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
109	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
110	C₈	—	2	4	no	—
111	C₈	—	29	2	no	—
112	C₈	—	29	2	no	—
113	C₈	C₄×Dic₂₉	1	2	yes	—
114	C₈	C₄×Dic₂₉	1	2	yes	—
115	C₂²	—	2	2	no	—
116	C₂²	#11745254	1	1	yes	characteristic
117	C₂²	#11745255	1	1	yes	characteristic
118	C₂²	Q₈×Dic₂₉	1	1	yes	characteristic
119	C₄	—	58	4	no	—
120	C₄	—	116	4	no	—
121	C₄	#11745249	1	1	yes	characteristic
122	C₄	C₄⋊C₄×D₂₉	1	1	yes	characteristic
123	C₄	C₂×C₄×Dic₂₉	1	1	yes	characteristic
124	C₄	D₄×Dic₂₉	1	1	yes	characteristic
125	C₂	—	2	1	no	—
126	C₂	—	2	1	no	—
127	C₂	C₄⋊C₄×Dic₂₉	1	1	yes	characteristic
128	C₂	#14271279	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271201

C₂

yes

maximal, characteristic

#14271121

C₂

yes

maximal

C₂×C₈×Dic₂₉

C₂

yes

maximal, characteristic

#14270924

C₂

yes

maximal

C₂×C₂₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

characteristic

C₂₉×#108

C₄

yes

complemented

#11745166

C₄

yes

complemented

#11745165

C₄

yes

complemented

#11745163

—

C₈×Dic₂₉

—

C₈×Dic₂₉

C₄

yes

complemented

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

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

C₂×C₄

yes

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

—

C₂×#6597

D₄

yes

characteristic

C₂×#6597

D₄

yes

characteristic

C₂×#6597

Q₈

yes

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

C₄²

yes

—

C₈×C₂₉

C₄²

yes

—

#6597

C₄⋊C₄

yes

—

#6597

C₄⋊C₄

yes

—

#1772

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

#117

yes

characteristic

C₂²×C₂₉

C₄×D₄

yes

characteristic

C₂²×C₂₉

C₄×Q₈

yes

characteristic

C₄×C₂₉

C₂×C₄²

yes

characteristic

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

C₄×Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂×#108

D₂₉

yes

characteristic

#427

—

#405

—

C₂×C₄×C₈

—

#339

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₂₉

#443

yes

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

—

C₂×C₄²

—

#108

Dic₂₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#1772

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

C₂×Dic₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₂×Dic₂₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

100

C₂³

#90809

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

105

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

106

C₂×C₄

D₄×D₂₉

yes

characteristic

107

C₂×C₄

#90807

yes

characteristic

108

C₂×C₄

Q₈×D₂₉

yes

characteristic

109

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₄×Dic₂₉

yes

—

114

C₈

C₄×Dic₂₉

yes

—

115

C₂²

—

116

C₂²

#11745254

yes

characteristic

117

C₂²

#11745255

yes

characteristic

118

C₂²

Q₈×Dic₂₉

yes

characteristic

119

C₄

—

120

C₄

—

116

—

121

C₄

#11745249

yes

characteristic

122

C₄

C₄⋊C₄×D₂₉

yes

characteristic

123

C₄

C₂×C₄×Dic₂₉

yes

characteristic

124

C₄

D₄×Dic₂₉

yes

characteristic

125

C₂

—

126

C₂

—

127

C₂

C₄⋊C₄×Dic₂₉

yes

characteristic

128

C₂

#14271279

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#108	C₂
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#108	D₂₉
hypocenter	C₂₉	#1772
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₂₉

commutator

C₄×C₂₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#108

C₂

socle

C₂²×C₂₉

C₄×D₄

prime radical

C₂³×C₂₉

#41

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₂₉×#108	C₄	semidirect
12. #11745166	C₄	semidirect
13. #11745165	C₄	semidirect
16. C₈×Dic₂₉	C₄	semidirect
75. #108	Dic₂₉	semidirect
81. C₂₉	#1772	semidirect

H ≅ G/N

type

11. C₂₉×#108

C₄

semidirect

12. #11745166

C₄

semidirect

13. #11745165

C₄

semidirect

16. C₈×Dic₂₉

C₄

semidirect

75. #108

Dic₂₉

semidirect

81. C₂₉

#1772

semidirect

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

subgroup	index
#14271201	2
#14271121	2
C₂×C₈×Dic₂₉	2
#14270924	2
C₂×C₂₉×#108	2
#1772	29

subgroup

index

C₂×C₈×Dic₂₉

C₂×C₂₉×#108

Subgroups — #16819374

Conjugacy classes of subgroups

Complements

Maximal subgroups