Finite Group Databasebeta

← #15766018

Subgroups — #15766018

Order 3328.

438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123199C211yesmaximal, characteristic, complemented
2#13115664C211yesmaximal, characteristic
3#13113397C212yesmaximal
4#13112695C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×#88124—21no—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597C2212yes—
11#11718596—21no—
12#11718589—24no—
13C2×#88045—21no—
14C2×#88045—21no—
15#11718585C2211yescharacteristic
16#11718062—24no—
17C2×#6127—21no—
18C2×C42×C13—22no—
19C2×C42×C13D411yescharacteristic
20C2×C42×C13D411yescharacteristic
21C2×C42×C13C2311yescharacteristic
22#88184—22no—
23C2×C4⋊Dic13—24no—
24C2×C4⋊Dic13—22no—
25C2×#6101—24no—
26C2×#6099—21no—
27#88129—21no—
28#88128Q811yescharacteristic
29C4×D52—22no—
30#88124—42no—
31#88124—42no—
32#88123Q811yescharacteristic
33C13×C4⋊C8—22no—
34C13×C22⋊C8—22no—
35C4×C8×C13—22no—
36#88071—22no—
37#88071D414yes—
38#88045—42no—
39#88045—42no—
40C4⋊#1055—22no—
41#10364—131nomaximal, Sylow
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13C2×D412yes—
46C2×C22⋊D13—41no—
47C22×Dic13—24no—
48#6127—41no—
49#6127—41no—
50#6127—41no—
51#6127—41no—
52C2×D52—21no—
53C2×D52—22no—
54C2×C4×D13—41no—
55C2×Dic26—21no—
56C2×C8×C13—42no—
57C42×C13—21no—
58C42×C13—21no—
59C42×C13—44no—
60C42×C13D812yes—
61C42×C13SD1612yes—
62C42×C13C2×Q811yescharacteristic
63C42×C13#4112yes—
64C42×C13#4111yescharacteristic
65#6103—42no—
66C4⋊Dic13—22no—
67C4⋊Dic13—48no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70#6101—48no—
71#6099—41no—
72#6099—41no—
73C2×#1055—41no—
74#2859—131no—
75#1962—131no—
76#1517—132no—
77#1286—132no—
78#1276D1311yescharacteristic, complemented
79C23×C13#12011yescharacteristic
80C22×D13—41no—
81C2×C4×C13—24no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13C22⋊Q812yes—
87C2×C4×C13C22⋊Q811yescharacteristic
88C2×C4×C13#12412yes—
89C2×C4×C13#12411yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13C2×SD1611yescharacteristic
92C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C13#13711yescharacteristic
94C22⋊D13—81no—
95C22⋊D13—81no—
96C2×Dic13—48no—
97C2×Dic13—41no—
98C2×Dic13—44no—
99D52—41no—
100D52—41no—
101D52—82no—
102C4×D13—81no—
103C4×D13—81no—
104Dic26—41no—
105Dic26—41no—
106C8×C13—82no—
107#1055—81no—
108#532—131no—
109C2×#125—261no—
110#431C2×D1312yes—
111#423—131no—
112C2×#104—261no—
113C2×#104—261no—
114#389—264no—
115#384—261no—
116#382—132no—
117C43C2×D1311yescharacteristic
118#327—264no—
119C22×C13—22no—
120C22×C13#39311yescharacteristic
121C22×C13#44711yescharacteristic
122C22×C13#44811yescharacteristic
123C2×D13—81no—
124C2×D13—82no—
125C4×C13—24no—
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13#47411yescharacteristic
130C4×C13#47611yescharacteristic
131C4×C13#48611yescharacteristic
132C4×C13#48911yescharacteristic
133Dic13—84no—
134Dic13—81no—
135C2×#41—261no—
136C2×M16—261no—
137C4⋊Q8—131no—
138#127—131no—
139#125—522no—
140#125—522no—
141#124—261no—
142#121—262no—
143C4×D4—262no—
144C2×C4⋊C4—264no—
145C2×C4⋊C4—264no—
146C2×C4⋊C4—262no—
147C2×C42—22no—
148C2×C42D5211yescharacteristic
149C2×C42D5211yescharacteristic
150C2×C42C22×D1311yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—262no—
153#104—522no—
154#104—522no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—134no—
158#95—262no—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#202311yescharacteristic
162C2×C13#203112yes—
163D13—161no—
164#41—521no—
165#41—521no—
166#41—521no—
167#41—521no—
168C2×Q8—261no—
169C2×D4—262no—
170C2×D4—261no—
171C2×D4—521no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—264no—
175C22×C4—521no—
176C22×C4C2×D5211yescharacteristic
177C22×C4D4×D1312yes—
178M16—521no—
179M16—521no—
180C2×C8—42no—
181C2×C8—521no—
182C4⋊C4—262no—
183C4⋊C4—528no—
184C4⋊C4—528no—
185C4⋊C4—522no—
186C4⋊C4—522no—
187C22⋊C4—522no—
188C42—21no—
189C42—21no—
190C42—44no—
191C42#609512yes—
192C42D10412yes—
193C42#612712yes—
194C42#612911yescharacteristic
195C42Q8×D1311yescharacteristic
196C13#1036411yescharacteristic, complemented, Sylow
197C23—521no—
198C23#8813611yescharacteristic
199Q8—521no—
200Q8—521no—
201D4—521no—
202D4—521no—
203D4—1042no—
204D4—1041no—
205D4—1041no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—528no—
212C2×C4—521no—
213C2×C4—524no—
214C2×C4—1041no—
215C2×C4—1041no—
216C2×C4#8812911yescharacteristic
217C2×C4#8813912yes—
218C2×C4#8815012yes—
219C2×C4#8815111yescharacteristic
220C2×C4C2×#609511yescharacteristic
221C2×C4C2×D10411yescharacteristic
222C2×C4#8816211yescharacteristic
223C2×C4#8816311yescharacteristic
224C8—82no—
225C8—1041no—
226C22—22no—
227C22—1041no—
228C22—1042no—
229C22#1171833411yescharacteristic
230C22#1171839311yescharacteristic
231C22#1171839911yescharacteristic
232C4—24no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—1044no—
237C4—1041no—
238C4#1171835511yescharacteristic
239C4#1171837511yescharacteristic
240C4#1171850311yescharacteristic
241C4#1171850711yescharacteristic
242C2—21no—
243C2—21no—
244C2—2081no—
245C2#1311597311yescharacteristic
246C2#1311600912yes—
subgroupG/H
centerC22#11718334
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#393
prime radical#11719182C22
hypercenter#1276D13
hypocenterC13#10364
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
1. #13123199C2semidirect
4. #13112695C2semidirect
5. C13×#1276C2semidirect
78. #1276D13semidirect
196. C13#10364semidirect

Maximal subgroups

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

subgroupindex
#131231992
#131156642
#131133972
#131126952
C13×#12762
#1036413