Finite Group Databasebeta

← #13124767

Subgroups — #13124767

Order 1664.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#117C211yesmaximal, characteristic, complemented
2#11719496C211yesmaximal, characteristic
3#11718868C211yesmaximal, characteristic, complemented
4#11718664C214yesmaximal, complemented
5#11718657C214yesmaximal, complemented
6#11718627C212yesmaximal, complemented
7#11718625C212yesmaximal, complemented
8C23×C4×C13C2211yescharacteristic
9C2×#6127C2211yescharacteristic
10C13×#117—22no—
11C13×#117C2214yes—
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C22⋊C4—21no—
14C2×C42×C13—21no—
15#88207—21no—
16#88184C2212yes—
17#88183—21no—
18C4×C22⋊D13—22no—
19#88180C2211yescharacteristic
20#88178C2212yes—
21C2×#6099C2212yes—
22C22⋊#1055C2214yes—
23#88050C2214yescomplemented
24#88049C2214yescomplemented
25#88048C2214yescomplemented
26#88047C2214yescomplemented
27C24×C13D411yescharacteristic
28C22×C4×C13—24no—
29C22×C4×C13—22no—
30C22×C4×C13D412yes—
31C22×C4×C13D411yescharacteristic
32C22×C4×C13C2312yes—
33C22×C4×C13C2311yescharacteristic
34C2×C22⋊D13—22no—
35C2×C22⋊D13—21no—
36#6127—24no—
37C2×D52C2311yescharacteristic
38C2×C4×D13—21no—
39C2×Dic26C2311yescharacteristic
40C13×C4⋊C4—22no—
41C13×C4⋊C4C2314yes—
42C13×C22⋊C4—24no—
43C42×C13—24no—
44C22⋊Dic13—22no—
45C22⋊Dic13—21no—
46#6103—22no—
47C4⋊Dic13C2312yes—
48#6101—22no—
49C4×Dic13—21no—
50#6099—24no—
51C2×#1055C2314yes—
52#3093—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—42no—
55C23×C13C2×D412yes—
56C23×C13C2×D411yescharacteristic
57C22×D13—21no—
58C2×C4×C13—22no—
59C2×C4×C13—24no—
60C2×C4×C13—24no—
61C2×C4×C13—24no—
62C2×C4×C13—44no—
63C2×C4×C13C2×D412yes—
64C2×C4×C13C2×D411yescharacteristic
65C2×C4×C13#4114yes—
66C2×C4×C13C2411yescharacteristic
67C22⋊D13—44no—
68C22⋊D13—42no—
69C2×Dic13—22no—
70C2×Dic13—21no—
71D52—22no—
72C4×D13—42no—
73Dic26—22no—
74#1055—24no—
75#525—131no—
76C2×#117D1311yescharacteristic, complemented
77#485—134no—
78#482—134no—
79#428—132no—
80#417—132no—
81#407—131no—
82C22×C13—22no—
83C22×C13—22no—
84C22×C13—22no—
85C22×C13—22no—
86C22×C13—44no—
87C22×C13#12312yes—
88C22×C13C22×D411yescharacteristic
89C2×D13—41no—
90C2×D13—42no—
91C4×C13—22no—
92C4×C13—44no—
93C4×C13#12312yes—
94C4×C13C2×#4112yes—
95Dic13—41no—
96Dic13—42no—
97C2×#41—131no—
98C23×C4C2×D1311yescharacteristic
99C2×M16—132no—
100#123—261no—
101C22⋊Q8—132no—
102#121—132no—
103#120—261no—
104C4×D4—262no—
105#117—22no—
106#117—131no—
107#117C2×D1314yes—
108C2×C4⋊C4C2×D1312yes—
109C2×C22⋊C4—21no—
110C2×C42—21no—
111#107—134no—
112#106—134no—
113#103—134no—
114#102—134no—
115C22⋊C8—134no—
116C2×C13—22no—
117C2×C13—42no—
118C2×C13C2×#12311yescharacteristic
119C2×C13#57512yes—
120D13—81no—
121C24C22⋊D1311yescharacteristic
122#41—264no—
123C2×Q8—131no—
124C2×D4—131no—
125C2×D4—262no—
126C2×D4—261no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—261no—
130C22×C4C22⋊D1311yescharacteristic
131C22×C4C22⋊D1312yes—
132C22×C4C22×D1312yes—
133C22×C4C22×D1311yescharacteristic
134M16—264no—
135C2×C8—134no—
136C4⋊C4—22no—
137C4⋊C4—132no—
138C4⋊C4—262no—
139C4⋊C4C22×D1314yes—
140C22⋊C4—24no—
141C22⋊C4—261no—
142C22⋊C4—262no—
143C22⋊C4—262no—
144C42—24no—
145C42—261no—
146C13#309311yescharacteristic, complemented, Sylow
147C23—22no—
148C23—42no—
149C23—261no—
150C23C2×C22⋊D1312yes—
151C23C2×C22⋊D1311yescharacteristic
152Q8—262no—
153D4—262no—
154D4—524no—
155D4—522no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—262no—
162C2×C4—261no—
163C2×C4—522no—
164C2×C4#612714yes—
165C2×C4C2×C22⋊D1312yes—
166C2×C4C2×C22⋊D1311yescharacteristic
167C2×C4C23×D1311yescharacteristic
168C8—264no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—521no—
175C22—522no—
176C22#8818312yes—
177C22C22×C22⋊D1311yescharacteristic
178C4—22no—
179C4—44no—
180C4—521no—
181C4—522no—
182C4#8818312yes—
183C4C2×#612712yes—
184C2—22no—
185C2—42no—
186C2—1041no—
187C2C2×#8818311yescharacteristic
188C2#1171952712yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#117C2
socleC22×C13C22×D4
prime radical#11719496C2
hypercenterC2×#117D13
hypocenterC13#3093
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#117C2semidirect
3. #11718868C2semidirect
4. #11718664C2semidirect
5. #11718657C2semidirect
6. #11718627C2semidirect
7. #11718625C2semidirect
23. #88050C22semidirect
24. #88049C22semidirect
25. #88048C22semidirect
26. #88047C22semidirect
76. C2×#117D13semidirect
146. C13#3093semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1172
#117194962
#117188682
#117186642
#117186572
#117186272
#117186252
#309313