Finite Group Databasebeta

← #15765595

Subgroups — #15765595

Order 3328.

566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#13125763C212yesmaximal
2#13123214C211yesmaximal, characteristic, complemented
3#13115664C211yesmaximal, characteristic
4#13113516C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597—22no—
11#11718590—24no—
12C2×#88045—22no—
13#11718585C2211yescharacteristic
14#11718502—24no—
15#11718399—24no—
16#11718354—22no—
17#11718342—22no—
18#11718073—24no—
19C2×#6127—21no—
20C22×Dic26D414yes—
21C2×C42×C13—22no—
22C2×C42×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24#88184—22no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13—22no—
27C2×#6099—21no—
28C2×#6095—28no—
29#88129—21no—
30#88128D411yescharacteristic
31C4×D52—22no—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123—22no—
36#88123D411yescharacteristic
37C13×C4⋊C8D414yes—
38C13×C22⋊C8—22no—
39C4×C8×C13—22no—
40#88071—28no—
41#88056—28no—
42#88045—44no—
43C4⋊#1055—22no—
44#10287—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C2×C22⋊D13—41no—
49C22×Dic13—24no—
50#6127—42no—
51#6127—42no—
52C2×D52—22no—
53C2×D52—21no—
54C2×C4×D13—41no—
55C2×Dic26—24no—
56C2×Dic26—21no—
57C2×Dic26—24no—
58C2×Dic26—48no—
59C2×C8×C13—24no—
60C42×C13—22no—
61C42×C13—44no—
62C42×C13SD1614yescomplemented
63C42×C13C2×D412yes—
64C42×C13C2×D411yescharacteristic
65C42×C13#4111yescharacteristic
66#6103—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72#6099—42no—
73C2×#1055—41no—
74#6095—88no—
75#3206—132no—
76#2862—131no—
77#1962—131no—
78#1548—132no—
79#1276D1311yescharacteristic, complemented
80C23×C13#12011yescharacteristic
81C22×D13—41no—
82C2×C4×C13—24no—
83C2×C4×C13—24no—
84C2×C4×C13—44no—
85C2×C4×C13#12012yes—
86C2×C4×C13#12112yes—
87C2×C4×C13#12111yescharacteristic
88C2×C4×C13#12711yescharacteristic
89C2×C4×C13C2×SD1612yes—
90C2×C4×C13#13712yes—
91C22⋊D13—82no—
92C2×Dic13—48no—
93C2×Dic13—41no—
94C2×Dic13—44no—
95D52—44no—
96D52—42no—
97C4×D13—81no—
98C4×D13—81no—
99Dic26—48no—
100Dic26—42no—
101Dic26—84no—
102C8×C13—44no—
103#1055—81no—
104#532—131no—
105C2×C4⋊Q8—132no—
106#492—262no—
107#487—262no—
108#461—264no—
109#448—264no—
110#431C2×D1312yes—
111#423—131no—
112C2×#104—262no—
113#391—264no—
114#382—262no—
115C43C2×D1311yescharacteristic
116#333—264no—
117C22×C13—22no—
118C22×C13#39211yescharacteristic
119C22×C13#44812yes—
120C2×D13—82no—
121C2×D13—81no—
122C4×C13—22no—
123C4×C13—44no—
124C4×C13#45514yes—
125C4×C13#46112yes—
126C4×C13#49211yescharacteristic
127C4×C13#49711yescharacteristic
128Dic13—84no—
129Dic13—81no—
130C2×#41—261no—
131C22×Q8—134no—
132C2×SD16—268no—
133C2×M16—261no—
134C4⋊Q8—131no—
135C4⋊Q8—262no—
136C4⋊Q8—262no—
137C4⋊Q8—262no—
138C4⋊Q8—262no—
139#127—131no—
140#124—261no—
141#121—262no—
142C4×D4—262no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—262no—
145C2×C42—22no—
146C2×C42D5212yes—
147C2×C42C22×D1311yescharacteristic
148C4⋊C8—262no—
149C4⋊C8D5214yes—
150#104—524no—
151#103—268no—
152C22⋊C8—22no—
153C4×C8—22no—
154#95—268no—
155C2×C13—22no—
156C2×C13#200412yes—
157C2×C13#201311yescharacteristic
158D13—161no—
159#41—522no—
160#41—522no—
161C2×Q8—264no—
162C2×Q8—261no—
163C2×Q8—264no—
164C2×Q8—528no—
165C2×D4—262no—
166C2×D4—261no—
167C2×D4—521no—
168C22×C4—22no—
169C22×C4—264no—
170C22×C4—521no—
171C22×C4C2×D5211yescharacteristic
172C22×C4D4×D1312yes—
173SD16—1048no—
174M16—522no—
175C2×C8—24no—
176C2×C8—521no—
177C4⋊C4—262no—
178C4⋊C4—522no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C22⋊C4—522no—
183C42—22no—
184C42—44no—
185C42#609514yescomplemented
186C42C2×D5212yes—
187C42D4×D1311yescharacteristic
188C42#613111yescharacteristic
189C13#1028711yescharacteristic, complemented, Sylow
190C23—521no—
191C23#8813611yescharacteristic
192Q8—528no—
193Q8—522no—
194Q8—1044no—
195D4—524no—
196D4—522no—
197D4—1042no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—44no—
201C2×C4—528no—
202C2×C4—521no—
203C2×C4—524no—
204C2×C4—1041no—
205C2×C4—1041no—
206C2×C4#8812811yescharacteristic
207C2×C4#8813612yes—
208C2×C4#8814912yes—
209C2×C4#8814911yescharacteristic
210C2×C4C2×#609512yes—
211C2×C4#8816312yes—
212C8—44no—
213C8—1041no—
214C22—22no—
215C22—1041no—
216C22—1042no—
217C22#1171833211yescharacteristic
218C22#1171839912yes—
219C4—22no—
220C4—44no—
221C4—1041no—
222C4—1044no—
223C4#1171835411yescharacteristic
224C4#1171837611yescharacteristic
225C4#1171848614yes—
226C4#1171850212yes—
227C2—22no—
228C2—2081no—
229C2#1311586812yes—
230C2#1311592111yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#1276D13
hypocenterC13#10287
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
2. #13123214C2semidirect
4. #13113516C2semidirect
5. C13×#1276C2semidirect
62. C42×C13SD16semidirect
79. #1276D13semidirect
185. C42#6095semidirect
189. C13#10287semidirect

Maximal subgroups

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

subgroupindex
#131257632
#131232142
#131156642
#131135162
C13×#12762
#1028713