Group #16822795 — subgroups

Subgroups — #16822795

Order 3712.

432 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14271104	C₂	1	3	yes	maximal, complemented
2	#14271092	C₂	1	3	yes	maximal
3	#14271087	C₂	1	1	yes	maximal, characteristic
4	#14271014	C₂	1	3	yes	maximal, complemented
5	#14271010	C₂	1	3	yes	maximal
6	#14271008	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#401	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90781	C₂²	1	3	yes	—
10	C₂×#90781	C₂²	1	3	yes	—
11	C₂×#90779	C₂²	1	3	yes	—
12	C₂×#90779	C₂²	1	3	yes	—
13	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
14	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
15	C₂₉×#95	C₂²	1	1	yes	characteristic
16	C₂₉×#95	C₂²	1	3	yes	—
17	C₂₉×#95	C₂²	1	3	yes	—
18	#11745179	C₂²	1	3	yes	—
19	#11745179	C₂²	1	3	yes	—
20	#11745179	C₂²	1	3	yes	—
21	C₂³×D₂₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
24	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₂₉	C₂³	1	3	yes	—
26	C₂²×Dic₂₉	C₂³	1	3	yes	—
27	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×D₂₉	—	2	6	no	—
29	#90781	—	2	6	no	—
30	#90781	—	2	6	no	—
31	#90779	—	2	6	no	—
32	#90779	—	2	6	no	—
33	C₄×Dic₂₉	—	2	6	no	—
34	C₄×Dic₂₉	—	2	6	no	—
35	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
36	C₂²×D₂₉	—	2	3	no	—
37	C₂²×D₂₉	—	2	3	no	—
38	C₂²×D₂₉	#41	1	2	yes	—
39	C₂×C₄×C₂₉	—	2	3	no	—
40	C₂×C₄×C₂₉	—	2	3	no	—
41	C₂×C₄×C₂₉	—	2	3	no	—
42	C₂×C₄×C₂₉	—	2	3	no	—
43	C₂×C₄×C₂₉	—	2	3	no	—
44	C₂×C₄×C₂₉	—	2	3	no	—
45	C₂×C₄×C₂₉	—	2	3	no	—
46	C₂×Dic₂₉	—	2	3	no	—
47	C₂×Dic₂₉	—	2	3	no	—
48	C₂×Dic₂₉	—	2	3	no	—
49	C₂×Dic₂₉	—	2	3	no	—
50	C₂×Dic₂₉	—	2	3	no	—
51	C₂×Dic₂₉	#41	1	6	yes	—
52	C₂×Dic₂₉	#41	1	6	yes	—
53	C₄×D₂₉	—	4	4	no	—
54	#2401	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	C₂×#41	1	3	yes	—
56	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
57	C₂²×C₂₉	C₂×#41	1	3	yes	—
58	C₂×D₂₉	—	2	6	no	—
59	C₂×D₂₉	—	4	1	no	—
60	C₂×D₂₉	—	4	3	no	—
61	C₄×C₂₉	—	4	1	no	—
62	C₄×C₂₉	—	4	3	no	—
63	C₄×C₂₉	—	4	3	no	—
64	Dic₂₉	—	2	6	no	—
65	Dic₂₉	—	4	3	no	—
66	Dic₂₉	#126	1	4	yes	—
67	#401	D₂₉	1	1	yes	characteristic, complemented
68	#400	—	29	3	no	—
69	#397	—	29	3	no	—
70	#396	—	29	1	no	—
71	C₄×C₄⋊C₄	—	29	3	no	—
72	C₄×C₂²⋊C₄	—	29	3	no	—
73	#376	—	29	1	no	—
74	C₂×C₂₉	C₂×#126	1	1	yes	characteristic
75	C₂×C₂₉	#529	1	3	yes	—
76	C₂×C₂₉	#529	1	3	yes	—
77	D₂₉	—	4	2	no	—
78	C₂³×C₄	—	29	1	no	—
79	C₂×C₄⋊C₄	—	29	3	no	—
80	C₂×C₄⋊C₄	—	29	3	no	—
81	C₂×C₂²⋊C₄	—	29	3	no	—
82	C₂×C₂²⋊C₄	—	29	3	no	—
83	C₂×C₄²	—	29	3	no	—
84	C₂×C₄²	—	29	3	no	—
85	#95	—	29	3	no	—
86	#95	—	29	3	no	—
87	#95	—	29	3	no	—
88	#95	C₂×D₂₉	1	1	yes	characteristic
89	#95	C₂×D₂₉	1	3	yes	—
90	#95	C₂×D₂₉	1	3	yes	—
91	C₂₉	#2401	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	—	29	1	no	—
93	C₂²×C₄	—	29	1	no	—
94	C₂²×C₄	—	29	3	no	—
95	C₂²×C₄	—	29	3	no	—
96	C₂²×C₄	—	58	6	no	—
97	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
99	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
100	C₄⋊C₄	—	58	6	no	—
101	C₄⋊C₄	—	58	6	no	—
102	C₂²⋊C₄	—	58	6	no	—
103	C₂²⋊C₄	—	58	6	no	—
104	C₄²	—	58	6	no	—
105	C₄²	—	58	6	no	—
106	C₂³	—	29	2	no	—
107	C₂³	—	58	3	no	—
108	C₂³	—	58	3	no	—
109	C₂³	C₂³×D₂₉	1	1	yes	characteristic
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	3	no	—
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	29	6	no	—
118	C₂×C₄	—	29	6	no	—
119	C₂×C₄	—	58	3	no	—
120	C₂×C₄	—	58	3	no	—
121	C₂×C₄	—	58	3	no	—
122	C₂×C₄	—	58	3	no	—
123	C₂×C₄	—	58	3	no	—
124	C₂×C₄	—	116	4	no	—
125	C₂²	—	58	6	no	—
126	C₂²	—	116	1	no	—
127	C₂²	—	116	3	no	—
128	C₂²	#41×D₂₉	1	3	yes	—
129	C₂²	#41×D₂₉	1	3	yes	—
130	C₂²	#41×D₂₉	1	1	yes	characteristic
131	C₄	—	4	1	no	—
132	C₄	—	4	3	no	—
133	C₄	—	4	3	no	—
134	C₄	—	29	4	no	—
135	C₄	—	58	6	no	—
136	C₄	—	116	3	no	—
137	C₂	—	116	2	no	—
138	C₂	#126×D₂₉	1	1	yes	characteristic
139	C₂	#14271696	1	3	yes	—
140	C₂	#14271696	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271104

C₂

yes

maximal, complemented

#14271092

C₂

yes

maximal

#14271087

C₂

yes

maximal, characteristic

#14271014

C₂

yes

maximal, complemented

#14271010

C₂

yes

maximal

#14271008

C₂

yes

maximal, characteristic, complemented

C₂₉×#401

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₂₉

C₂²

yes

characteristic

C₂×#90781

C₂²

yes

—

C₂×#90781

C₂²

yes

—

C₂×#90779

C₂²

yes

—

C₂×#90779

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂₉×#95

C₂²

yes

characteristic

C₂₉×#95

C₂²

yes

—

C₂₉×#95

C₂²

yes

—

#11745179

C₂²

yes

—

#11745179

C₂²

yes

—

#11745179

C₂²

yes

—

C₂³×D₂₉

C₂³

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

characteristic

C₂×C₄×D₂₉

—

—

—

—

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂²×D₂₉

#41

yes

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

#41

yes

—

C₂×Dic₂₉

#41

yes

—

C₄×D₂₉

—

#2401

—

maximal, Sylow

C₂²×C₂₉

C₂×#41

yes

—

C₂²×C₂₉

C₂×#41

yes

characteristic

C₂²×C₂₉

C₂×#41

yes

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#126

yes

—

#401

D₂₉

yes

characteristic, complemented

#400

—

#397

—

#396

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

C₂×C₂₉

C₂×#126

yes

characteristic

C₂×C₂₉

#529

yes

—

C₂×C₂₉

#529

yes

—

D₂₉

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

C₂×D₂₉

yes

characteristic

#95

C₂×D₂₉

yes

—

#95

C₂×D₂₉

yes

—

C₂₉

#2401

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂³×D₂₉

yes

characteristic

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

116

—

125

C₂²

—

126

C₂²

—

116

—

127

C₂²

—

116

—

128

C₂²

#41×D₂₉

yes

—

129

C₂²

#41×D₂₉

yes

—

130

C₂²

#41×D₂₉

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

116

—

137

C₂

—

116

—

138

C₂

#126×D₂₉

yes

characteristic

139

C₂

#14271696

yes

—

140

C₂

#14271696

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂₉×#401	C₂
prime radical	C₂³×D₂₉	C₂³
hypercenter	#401	D₂₉
hypocenter	C₂₉	#2401
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₂₉×#401

C₂

prime radical

C₂³×D₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
1. #14271104	C₂	semidirect
4. #14271014	C₂	semidirect
6. #14271008	C₂	semidirect
7. C₂₉×#401	C₂	semidirect
67. #401	D₂₉	semidirect
91. C₂₉	#2401	semidirect

H ≅ G/N

type

1. #14271104

C₂

semidirect

4. #14271014

C₂

semidirect

6. #14271008

C₂

semidirect

7. C₂₉×#401

C₂

semidirect

67. #401

D₂₉

semidirect

91. C₂₉

#2401

semidirect

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

subgroup	index
#14271104	2
#14271092	2
#14271087	2
#14271014	2
#14271010	2
#14271008	2
C₂₉×#401	2
#2401	29

subgroup

index

C₂₉×#401

Subgroups — #16822795

Conjugacy classes of subgroups

Complements

Maximal subgroups