Finite Group Databasebeta

← #15760473

Subgroups — #15760473

Order 3328.

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

normal subgroups only

This group has 620 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#13125286C211yesmaximal, characteristic
2#13113550C211yesmaximal, characteristic, complemented
3#13113382C212yesmaximal, complemented
4#13112700C212yesmaximal, complemented
5C13×#2380C211yesmaximal, characteristic, complemented
6C2×C13×#127C2211yescharacteristic
7C2×#88186—22no—
8#11719182C2211yescharacteristic
9C13×#386—22no—
10C13×#386—24no—
11C13×#383C2212yes—
12#11718737C412yescomplemented
13#11718735—22no—
14#11718734C412yescomplemented
15#11718587C2212yes—
16C4×#6099C2211yescharacteristic
17#11718136—22no—
18#11718043—24no—
19C22×D4×C13—22no—
20C22×D4×C13D412yes—
21C23×C4×C13—22no—
22C2×#6127—21no—
23C13×#127—22no—
24C13×#127C2×C412yes—
25C13×#127D412yes—
26C2×C13×C22⋊C4—24no—
27C2×C13×C22⋊C4—22no—
28C2×C42×C13C2311yescharacteristic
29C2×#6105—24no—
30#88186—44no—
31#88186—44no—
32C2×#6104—24no—
33#88184—22no—
34C2×#6099—21no—
35#88129—21no—
36#88128C2×C411yescharacteristic, complemented
37C4×D52—22no—
38#88123C2×C411yescharacteristic, complemented
39C13×#95—22no—
40C13×#95—22no—
41C13×#95D414yes—
42C22⋊#1055—22no—
43C4⋊#1055—22no—
44#88043—21no—
45#88043—22no—
46C4×#1055C2×C412yescomplemented
47#9428—131nomaximal, Sylow
48C24×C13—22no—
49C2×D4×C13—24no—
50C2×D4×C13—24no—
51C2×D4×C13—22no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—82no—
55C2×D4×C13—82no—
56C2×D4×C13C22⋊C414yes—
57C22×C4×C13—24no—
58C22×C4×C13—84no—
59C22×C4×C13—82no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C2×C22⋊D13—41no—
63#6127—42no—
64#6127—42no—
65C2×D52—21no—
66C2×D52—22no—
67C2×C4×D13—41no—
68C2×Dic26—21no—
69C13×C22⋊C4—84no—
70C13×C22⋊C4—82no—
71C42×C13C22×C411yescharacteristic
72C42×C13C2×D411yescharacteristic
73C42×C13#4112yes—
74#6105—48no—
75#6104—48no—
76#6103—42no—
77C4⋊Dic13—22no—
78#6099—24no—
79C2×#1055—22no—
80C2×#1055—42no—
81#3151—131no—
82#2380D1311yescharacteristic, complemented
83#1555—131no—
84#1514—132no—
85#1288—132no—
86C23×C13—24no—
87C23×C13—44no—
88C23×C13—44no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13#12011yescharacteristic
92C22×D13—41no—
93D4×C13—44no—
94D4×C13—82no—
95D4×C13—84no—
96D4×C13—84no—
97C2×C4×C13—22no—
98C2×C4×C13—42no—
99C2×C4×C13—48no—
100C2×C4×C13—44no—
101C2×C4×C13—88no—
102C2×C4×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13C4×D412yes—
104C2×C4×C13#12112yes—
105C2×C4×C13#12311yescharacteristic
106C22⋊D13—82no—
107C2×Dic13—41no—
108D52—42no—
109D52—82no—
110C4×D13—81no—
111C4×D13—81no—
112Dic26—42no—
113#1055—24no—
114#1055—82no—
115C2×AGL(1,ℤ/8)—262no—
116#532—131no—
117C2×#127C2×D1311yescharacteristic
118#496—262no—
119#493—132no—
120#492—132no—
121#432—132no—
122C4×M16—131no—
123#386—22no—
124#386—24no—
125#383C2×D1312yes—
126#331—262no—
127#327—264no—
128C22×C13—22no—
129C22×C13—44no—
130C22×C13—48no—
131C22×C13—82no—
132C22×C13—82no—
133C22×C13—84no—
134C22×C13#38611yescharacteristic
135C22×C13#45312yes—
136C2×D13—81no—
137C2×D13—82no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—22no—
141C4×C13—22no—
142C4×C13—84no—
143Dic13—81no—
144C2×#41—261no—
145C22×D4—22no—
146C22×D4C22⋊D1312yes—
147C23×C4—22no—
148AGL(1,ℤ/8)—524no—
149AGL(1,ℤ/8)—524no—
150C2×SD16—264no—
151C2×D8—264no—
152C2×M16—261no—
153C4⋊Q8—131no—
154#127—22no—
155#127—131no—
156#127C4×D1312yes—
157#127D5212yes—
158#124—261no—
159#121—262no—
160C4×D4—262no—
161C2×C22⋊C4—24no—
162C2×C22⋊C4—22no—
163C2×C42C22×D1311yescharacteristic
164C4⋊C8—262no—
165C22⋊C8—262no—
166#97—261no—
167#97—262no—
168C4×C8—132no—
169#95—22no—
170#95—22no—
171#95C22⋊D1314yes—
172C2×C13—22no—
173C2×C13—84no—
174C2×C13#188711yescharacteristic
175C2×C13#190412yes—
176D13—161no—
177C24—22no—
178#41—522no—
179#41—522no—
180C2×Q8—261no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—24no—
184C2×D4—42no—
185C2×D4—42no—
186C2×D4—82no—
187C2×D4—82no—
188C2×D4—261no—
189C2×D4—262no—
190C2×D4—521no—
191C2×D4#610314yes—
192C22×C4—24no—
193C22×C4—84no—
194C22×C4—82no—
195C22×C4—521no—
196C22×C4C2×C22⋊D1311yescharacteristic
197C22×C4C2×C22⋊D1312yes—
198SD16—528no—
199D8—528no—
200M16—264no—
201C2×C8—262no—
202C2×C8—522no—
203C4⋊C4—262no—
204C22⋊C4—84no—
205C22⋊C4—82no—
206C22⋊C4—522no—
207C42C2×C4×D1311yescharacteristic
208C42C2×D5211yescharacteristic
209C42#612712yes—
210C13#942811yescharacteristic, complemented, Sylow
211C23—24no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—521no—
217C23#8820711yescharacteristic
218Q8—522no—
219D4—44no—
220D4—82no—
221D4—84no—
222D4—84no—
223D4—522no—
224D4—1042no—
225D4—1042no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—48no—
229C2×C4—44no—
230C2×C4—88no—
231C2×C4—521no—
232C2×C4—1041no—
233C2×C4—1041no—
234C2×C4C2×#610311yescharacteristic
235C2×C4C4×C22⋊D1312yes—
236C2×C4#8818311yescharacteristic
237C2×C4#8818412yes—
238C8—264no—
239C8—1042no—
240C22—22no—
241C22—44no—
242C22—48no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—1041no—
247C22—1042no—
248C22#1171887411yescharacteristic
249C22#1171890212yes—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—84no—
255C4—1041no—
256C2—22no—
257C2—84no—
258C2—2081no—
259C2#1311523411yescharacteristic
260C2#1311532312yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2380C2
socleC22×C13#386
prime radical#13125286C2
cosocleC2×C42×C13C23
hypercenter#2380D13
hypocenterC13#9428
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
2. #13113550C2semidirect
3. #13113382C2semidirect
4. #13112700C2semidirect
5. C13×#2380C2semidirect
12. #11718737C4semidirect
14. #11718734C4semidirect
36. #88128C2×C4semidirect
38. #88123C2×C4semidirect
46. C4×#1055C2×C4semidirect
82. #2380D13semidirect
210. C13#9428semidirect

Maximal subgroups

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

subgroupindex
#131252862
#131135502
#131133822
#131127002
C13×#23802
#942813