Group #16819236 — subgroups

Subgroups — #16819236

Order 3712.

296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₈×Dic₂₉	C₂	1	2	yes	maximal
2	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270918	C₂	1	1	yes	maximal, characteristic
4	#14270917	C₂	1	2	yes	maximal
5	C₂₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂²×#6597	C₂²	1	2	yes	—
13	C₈×Dic₂₉	C₄	1	8	yes	complemented
14	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
17	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
22	C₄²×C₂₉	—	2	2	no	—
23	C₄×Dic₂₉	—	2	1	no	—
24	C₄×Dic₂₉	—	2	1	no	—
25	C₄×Dic₂₉	—	2	4	no	—
26	C₄×Dic₂₉	C₈	1	8	yes	complemented
27	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
28	C₂×#6597	—	2	2	no	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	C₂×C₄	1	4	yes	—
31	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₉	—	2	2	no	—
33	C₂×C₄×C₂₉	—	2	2	no	—
34	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
35	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₂₉	#41	1	2	yes	—
37	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
38	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
39	C₂×Dic₂₉	—	2	2	no	—
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	C₄²	1	2	yes	—
42	C₂×Dic₂₉	C₄²	1	2	yes	—
43	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
44	C₂×Dic₂₉	C₂×C₈	1	4	yes	—
45	C₂×Dic₂₉	M₁₆	1	4	yes	—
46	C₈×C₂₉	—	2	4	no	—
47	#6597	—	2	4	no	—
48	#1744	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
50	C₂²×C₂₉	#117	1	1	yes	characteristic
51	C₂²×C₂₉	#117	1	1	yes	characteristic
52	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
53	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
54	C₄×C₂₉	—	2	4	no	—
55	C₄×C₂₉	#117	1	2	yes	—
56	C₄×C₂₉	#117	1	2	yes	—
57	Dic₂₉	—	2	4	no	—
58	Dic₂₉	C₄×C₈	1	4	yes	—
59	Dic₂₉	#97	1	4	yes	—
60	C₂×C₄×C₈	—	29	2	no	—
61	C₄³	—	29	1	no	—
62	#336	—	29	2	no	—
63	#336	—	29	1	no	—
64	#336	D₂₉	1	1	yes	characteristic
65	C₂×C₂₉	#376	1	1	yes	characteristic
66	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
67	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
68	C₂×C₂₉	#431	1	2	yes	—
69	C₂×C₂₉	#431	1	2	yes	—
70	C₂²×C₈	—	29	2	no	—
71	C₂²×C₈	C₂×D₂₉	1	2	yes	—
72	C₂×C₄²	—	29	2	no	—
73	C₂×C₄²	—	29	1	no	—
74	C₂×C₄²	—	29	2	no	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
77	C₄×C₈	—	29	8	no	—
78	C₂₉	#1744	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	29	1	no	—
80	C₂²×C₄	—	29	1	no	—
81	C₂²×C₄	—	29	2	no	—
82	C₂²×C₄	C₄×D₂₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	29	4	no	—
87	C₂×C₈	—	58	2	no	—
88	C₂×C₈	—	58	2	no	—
89	C₂×C₈	C₄×D₂₉	1	4	yes	—
90	C₄²	—	2	2	no	—
91	C₄²	—	29	8	no	—
92	C₄²	—	29	4	no	—
93	C₄²	—	58	4	no	—
94	C₄²	—	58	1	no	—
95	C₄²	—	58	1	no	—
96	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	29	2	no	—
100	C₂×C₄	—	29	2	no	—
101	C₂×C₄	—	29	4	no	—
102	C₂×C₄	—	29	4	no	—
103	C₂×C₄	—	29	4	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	—	58	2	no	—
106	C₂×C₄	C₈×D₂₉	1	4	yes	—
107	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
108	C₂×C₄	#90807	1	1	yes	characteristic
109	C₂×C₄	#90807	1	2	yes	—
110	C₂×C₄	#90809	1	1	yes	characteristic
111	C₈	—	2	4	no	—
112	C₈	—	58	4	no	—
113	C₂²	C₄²×D₂₉	1	1	yes	characteristic
114	C₂²	#11745239	1	1	yes	characteristic
115	C₂²	#11745254	1	1	yes	characteristic
116	C₂²	C₂×C₈×D₂₉	1	2	yes	—
117	C₂²	M₁₆×D₂₉	1	2	yes	—
118	C₄	—	2	4	no	—
119	C₄	—	29	4	no	—
120	C₄	—	29	4	no	—
121	C₄	—	58	4	no	—
122	C₄	#11745239	1	2	yes	—
123	C₄	#11745254	1	2	yes	—
124	C₂	#14271008	1	1	yes	characteristic
125	C₂	C₄×C₈×D₂₉	1	1	yes	characteristic
126	C₂	#97×D₂₉	1	1	yes	characteristic
127	C₂	#14271213	1	2	yes	—
128	C₂	#14271215	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₂₉

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal

C₂₉×#336

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

—

C₈×Dic₂₉

C₄

yes

complemented

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₈

yes

complemented

C₄×Dic₂₉

C₂×C₄

yes

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₂×Dic₂₉

M₁₆

yes

—

C₈×C₂₉

—

#6597

—

#1744

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

C₂²×C₈

yes

—

C₂²×C₂₉

C₂×M₁₆

yes

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

C₄×C₂₉

#117

yes

—

Dic₂₉

—

Dic₂₉

C₄×C₈

yes

—

Dic₂₉

#97

yes

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

—

#336

D₂₉

yes

characteristic

C₂×C₂₉

#376

yes

characteristic

C₂×C₂₉

C₂×C₄×C₈

yes

characteristic

C₂×C₂₉

C₂×#97

yes

characteristic

C₂×C₂₉

#431

yes

—

C₂×C₂₉

#431

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄×C₈

—

C₂₉

#1744

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₂₉

yes

—

107

C₂×C₄

C₂×C₄×D₂₉

yes

—

108

C₂×C₄

#90807

yes

characteristic

109

C₂×C₄

#90807

yes

—

110

C₂×C₄

#90809

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

C₄²×D₂₉

yes

characteristic

114

C₂²

#11745239

yes

characteristic

115

C₂²

#11745254

yes

characteristic

116

C₂²

C₂×C₈×D₂₉

yes

—

117

C₂²

M₁₆×D₂₉

yes

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11745239

yes

—

123

C₄

#11745254

yes

—

124

C₂

#14271008

yes

characteristic

125

C₂

C₄×C₈×D₂₉

yes

characteristic

126

C₂

#97×D₂₉

yes

characteristic

127

C₂

#14271213

yes

—

128

C₂

#14271215

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂×C₄×C₈
Fitting	C₂₉×#336	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#336	D₂₉
hypocenter	C₂₉	#1744
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator

C₂×C₂₉

C₂×C₄×C₈

Fitting

C₂₉×#336

C₂

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
13. C₈×Dic₂₉	C₄	semidirect
26. C₄×Dic₂₉	C₈	semidirect
78. C₂₉	#1744	semidirect

H ≅ G/N

type

13. C₈×Dic₂₉

C₄

semidirect

26. C₄×Dic₂₉

C₈

semidirect

78. C₂₉

#1744

semidirect

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

subgroup	index
C₂×C₈×Dic₂₉	2
C₄²×Dic₂₉	2
#14270918	2
#14270917	2
C₂₉×#336	2
#1744	29

subgroup

index

C₂×C₈×Dic₂₉

C₄²×Dic₂₉

#14270918

#14270917

C₂₉×#336

#1744

Subgroups — #16819236

Conjugacy classes of subgroups

Complements

Maximal subgroups