Finite Group Databasebeta

← #15760446

Subgroups — #15760446

Order 3328.

540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125289C211yesmaximal, characteristic
2#13113549C212yesmaximal, complemented
3#13113471C211yesmaximal, characteristic, complemented
4#13112707C212yesmaximal, complemented
5C13×#2980C211yesmaximal, characteristic, complemented
6C13×#532C2211yescharacteristic
7C2×#88203—22no—
8C2×#88128C2211yescharacteristic
9C13×#435—24no—
10C13×#432C2212yes—
11C13×#408—22no—
12#11718746C412yes—
13#11718734C412yes—
14#11718719—22no—
15#11718587C2212yes—
16C4×#6099C2211yescharacteristic
17#11718132—22no—
18#11718077—24no—
19C2×C13×#41D412yes—
20C22×D52—21no—
21C22×D52—22no—
22C2×C13×M16—22no—
23C22×C8×C13—22no—
24C13×C4⋊Q8C2×C411yescharacteristic
25C13×#127C2×C411yescharacteristic
26C13×#124D412yes—
27C13×#121—22no—
28C4×D4×C13—22no—
29C2×C42×C13C2311yescharacteristic
30#88203—44no—
31#88203—44no—
32C2×#6106—24no—
33C2×#6104—24no—
34C2×#6099—21no—
35#88128—21no—
36#88128—22no—
37#88128C2×C412yes—
38C13×C4⋊C8D414yes—
39C13×C22⋊C8—24no—
40C13×C22⋊C8—22no—
41C13×#97—22no—
42C22⋊#1055—22no—
43C4⋊#1055—22no—
44#88043—21no—
45#88043—22no—
46C4×#1055C2×C412yes—
47#9423—131nomaximal, Sylow
48C23×D13—41no—
49C13×#41—42no—
50C13×#41—42no—
51C2×Q8×C13C22⋊C412yes—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13C22⋊C412yes—
55C22×C4×C13—22no—
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13#4112yes—
58C2×D52—22no—
59C2×D52—24no—
60C2×D52—42no—
61C2×D52—42no—
62C2×D52—41no—
63C2×D52—42no—
64C2×D52—84no—
65C13×M16—82no—
66C2×C8×C13—24no—
67C2×C8×C13—82no—
68C13×C4⋊C4—22no—
69C13×C22⋊C4—24no—
70C42×C13C22×C411yescharacteristic
71C42×C13C2×D411yescharacteristic
72C42×C13C2×D412yes—
73#6106—48no—
74#6104—48no—
75#6099—24no—
76C2×#1055—22no—
77C2×#1055—42no—
78#3151—131no—
79#2980D1311yescharacteristic, complemented
80#1555—132no—
81#1536—131no—
82#1291—132no—
83C23×C13—22no—
84C23×C13#12311yescharacteristic
85C22×D13—42no—
86C22×D13—81no—
87C22×D13—81no—
88C22×D13—84no—
89Q8×C13—42no—
90D4×C13—42no—
91D4×C13—82no—
92D4×C13—82no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C4×D412yes—
100C2×C4×C13#12011yescharacteristic
101C2×C4×C13#12112yes—
102D52—44no—
103D52—84no—
104D52—84no—
105D52—82no—
106C8×C13—44no—
107#1055—24no—
108#1055—82no—
109C2×AGL(1,ℤ/8)—262no—
110#532C2×D1311yescharacteristic
111C2×#127—131no—
112#496—262no—
113#493—132no—
114#492—132no—
115#435—24no—
116#432—132no—
117#432C2×D1312yes—
118#408—22no—
119C4×M16—131no—
120#331—264no—
121#329—262no—
122C22×C13—21no—
123C22×C13—22no—
124C22×C13—42no—
125C22×C13—44no—
126C22×C13#38611yescharacteristic
127C2×D13—82no—
128C2×D13—84no—
129C2×D13—162no—
130C2×D13—162no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—42no—
135C4×C13#45312yes—
136C2×#41C22⋊D1312yes—
137C22×D4—262no—
138C22×D4—261no—
139AGL(1,ℤ/8)—524no—
140AGL(1,ℤ/8)—524no—
141C2×SD16—264no—
142C2×D8—264no—
143C2×M16—22no—
144C2×M16—261no—
145C22×C8—22no—
146C4⋊Q8C4×D1311yescharacteristic
147#127—132no—
148#127—261no—
149#127—262no—
150#127C4×D1311yescharacteristic
151#124D5212yes—
152#121—22no—
153C4×D4—22no—
154C2×C42C22×D1311yescharacteristic
155C4⋊C8—262no—
156C4⋊C8C22⋊D1314yes—
157C22⋊C8—24no—
158C22⋊C8—22no—
159C22⋊C8—262no—
160#97—22no—
161#97—261no—
162#97—262no—
163C4×C8—132no—
164C2×C13—41no—
165C2×C13—82no—
166C2×C13#188711yescharacteristic
167C2×C13#190312yes—
168D13—162no—
169C24—521no—
170#41—42no—
171#41—42no—
172C2×Q8#610312yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—262no—
176C2×D4—264no—
177C2×D4—522no—
178C2×D4—522no—
179C2×D4—522no—
180C2×D4—521no—
181C2×D4—1044no—
182C2×D4#610312yes—
183C22×C4—22no—
184C22×C4#612712yes—
185C22×C4C2×C22⋊D1311yescharacteristic
186SD16—528no—
187D8—528no—
188M16—82no—
189M16—264no—
190C2×C8—24no—
191C2×C8—82no—
192C2×C8—262no—
193C2×C8—522no—
194C4⋊C4—22no—
195C22⋊C4—24no—
196C42C2×C4×D1311yescharacteristic
197C42C2×D5211yescharacteristic
198C42C2×C22⋊D1312yes—
199C13#942311yescharacteristic, complemented, Sylow
200C23—22no—
201C23—522no—
202C23—1041no—
203C23—1041no—
204C23—1044no—
205C23#8818311yescharacteristic
206Q8—42no—
207D4—42no—
208D4—82no—
209D4—82no—
210D4—524no—
211D4—1044no—
212D4—1044no—
213D4—1042no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4C2×#610311yescharacteristic
220C2×C4C4×C22⋊D1312yes—
221C2×C4#8818412yes—
222C2×C4#8820711yescharacteristic
223C8—44no—
224C8—264no—
225C8—1042no—
226C22—21no—
227C22—22no—
228C22—42no—
229C22—44no—
230C22—1042no—
231C22—1044no—
232C22—2082no—
233C22—2082no—
234C22#1171887411yescharacteristic
235C4—21no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4#1171890212yes—
240C2—41no—
241C2—82no—
242C2—2082no—
243C2#1311523411yescharacteristic
244C2#1311531612yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2980C2
socleC22×C13#386
prime radical#13125289C2
cosocleC2×C42×C13C23
hypercenter#2980D13
hypocenterC13#9423
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #13113549C2semidirect
3. #13113471C2semidirect
4. #13112707C2semidirect
5. C13×#2980C2semidirect
79. #2980D13semidirect
199. C13#9423semidirect

Maximal subgroups

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

subgroupindex
#131252892
#131135492
#131134712
#131127072
C13×#29802
#942313