Group #16819636 — subgroups

Subgroups — #16819636

Order 3712.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14271009	C₂	1	1	yes	maximal, characteristic
2	#14270918	C₂	1	1	yes	maximal, characteristic
3	#14270917	C₂	1	2	yes	maximal
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	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
10	C₂²×#6597	C₂²	1	2	yes	—
11	#11745179	C₄	1	2	yes	—
12	#11745179	C₄	1	2	yes	—
13	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₉	—	2	2	no	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₄²×C₂₉	—	2	2	no	—
22	C₄×Dic₂₉	—	2	2	no	—
23	C₄×Dic₂₉	—	2	1	no	—
24	C₄×Dic₂₉	—	2	1	no	—
25	C₂×#6597	—	2	2	no	—
26	C₂×#6597	—	2	2	no	—
27	C₂×#6597	—	2	2	no	—
28	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	2	no	—
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	#41	1	2	yes	—
33	C₂×C₄×C₂₉	#41	1	2	yes	—
34	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
35	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
36	C₂×Dic₂₉	—	2	1	no	—
37	C₂×Dic₂₉	—	2	1	no	—
38	C₂×Dic₂₉	—	2	2	no	—
39	C₂×Dic₂₉	—	2	2	no	—
40	C₂×Dic₂₉	—	2	2	no	—
41	C₂×Dic₂₉	—	2	2	no	—
42	C₂×Dic₂₉	—	2	2	no	—
43	C₈×C₂₉	—	4	2	no	—
44	#6597	—	4	2	no	—
45	#1840	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	#117	1	1	yes	characteristic
47	C₂²×C₂₉	#117	1	1	yes	characteristic
48	C₂²×C₂₉	#117	1	1	yes	characteristic
49	C₂²×C₂₉	#131	1	2	yes	—
50	C₂²×C₂₉	#131	1	2	yes	—
51	C₄×C₂₉	—	4	2	no	—
52	C₄×C₂₉	#126	1	2	yes	—
53	C₄×C₂₉	#126	1	2	yes	—
54	Dic₂₉	—	4	1	no	—
55	Dic₂₉	—	4	2	no	—
56	Dic₂₉	—	4	1	no	—
57	#376	—	29	1	no	—
58	#336	—	29	2	no	—
59	#336	—	29	2	no	—
60	#336	—	29	1	no	—
61	#336	D₂₉	1	1	yes	characteristic
62	C₂×C₂₉	#383	1	1	yes	characteristic
63	C₂×C₂₉	#433	1	2	yes	—
64	C₂×C₂₉	#433	1	1	yes	characteristic
65	C₂×C₂₉	#433	1	2	yes	—
66	C₂×C₂₉	#433	1	1	yes	characteristic
67	C₂²×C₈	—	29	2	no	—
68	C₂²×C₈	C₂×D₂₉	1	2	yes	—
69	C₂×C₄²	—	29	1	no	—
70	C₂×C₄²	—	29	1	no	—
71	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
72	#95	—	29	2	no	—
73	#95	—	29	2	no	—
74	C₂₉	#1840	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	29	1	no	—
76	C₂²×C₄	—	29	1	no	—
77	C₂²×C₄	—	29	2	no	—
78	C₂²×C₄	C₄×D₂₉	1	2	yes	—
79	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	—	58	2	no	—
85	C₂×C₈	—	58	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	58	2	no	—
88	C₄²	—	58	1	no	—
89	C₄²	—	58	1	no	—
90	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	58	1	no	—
95	C₂×C₄	—	58	1	no	—
96	C₂×C₄	—	58	2	no	—
97	C₂×C₄	—	58	2	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	—	58	2	no	—
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	#90805	1	2	yes	—
102	C₂×C₄	#90807	1	1	yes	characteristic
103	C₂×C₄	#90807	1	2	yes	—
104	C₂×C₄	#90809	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	116	2	no	—
107	C₂²	#11745234	1	1	yes	characteristic
108	C₂²	#11745239	1	1	yes	characteristic
109	C₂²	#11745254	1	1	yes	characteristic
110	C₂²	#11745263	1	2	yes	—
111	C₂²	#11745269	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	116	1	no	—
114	C₄	—	116	2	no	—
115	C₄	—	116	1	no	—
116	C₄	#11745241	1	2	yes	—
117	C₄	#11745260	1	2	yes	—
118	C₂	#14271030	1	1	yes	characteristic
119	C₂	#14271221	1	2	yes	—
120	C₂	#14271222	1	1	yes	characteristic
121	C₂	#14271223	1	2	yes	—
122	C₂	#14271225	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271009

C₂

yes

maximal, characteristic

#14270918

C₂

yes

maximal, characteristic

#14270917

C₂

yes

maximal

#14270917

C₂

yes

maximal

C₂₉×#336

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂²×#6597

C₂²

yes

—

#11745179

C₄

yes

—

#11745179

C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₂²×C₂₉

#131

yes

—

C₄×C₂₉

—

C₄×C₂₉

#126

yes

—

C₄×C₂₉

#126

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

—

D₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#433

yes

characteristic

C₂×C₂₉

#433

yes

—

C₂×C₂₉

#433

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#95

—

#95

—

C₂₉

#1840

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

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂×C₄×D₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

#90805

yes

—

102

C₂×C₄

#90807

yes

characteristic

103

C₂×C₄

#90807

yes

—

104

C₂×C₄

#90809

yes

characteristic

105

C₈

—

106

C₈

—

116

—

107

C₂²

#11745234

yes

characteristic

108

C₂²

#11745239

yes

characteristic

109

C₂²

#11745254

yes

characteristic

110

C₂²

#11745263

yes

—

111

C₂²

#11745269

yes

—

112

C₄

—

113

C₄

—

116

—

114

C₄

—

116

—

115

C₄

—

116

—

116

C₄

#11745241

yes

—

117

C₄

#11745260

yes

—

118

C₂

#14271030

yes

characteristic

119

C₂

#14271221

yes

—

120

C₂

#14271222

yes

characteristic

121

C₂

#14271223

yes

—

122

C₂

#14271225

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#336	C₂
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#336	D₂₉
hypocenter	C₂₉	#1840
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₉

commutator, socle, prime radical

C₂³×C₂₉

C₂²×C₄

Fitting

C₂₉×#336

C₂

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
74. C₂₉	#1840	semidirect

H ≅ G/N

type

74. C₂₉

#1840

semidirect

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

subgroup	index
#14271009	2
#14270918	2
#14270917	2
C₂₉×#336	2
#1840	29

subgroup

index

C₂₉×#336

Subgroups — #16819636

Conjugacy classes of subgroups

Complements

Maximal subgroups