Finite Group Databasebeta

← #15757878

Subgroups — #15757878

Order 3328.

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

normal subgroups only

This group has 502 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#13125281C211yesmaximal, characteristic
2#13113498C211yesmaximal, characteristic, complemented
3#13113304C212yesmaximal, complemented
4#13112734C212yesmaximal, complemented
5C13×#2980C211yesmaximal, characteristic, complemented
6C13×#532C2211yescharacteristic
7C2×#88204—22no—
8#11719182C2211yescharacteristic
9C13×#435—24no—
10C13×#432C2212yes—
11C13×#408—22no—
12#11718747—21no—
13#11718735—21no—
14#11718721C412yes—
15#11718719C412yes—
16#11718586C2212yes—
17C2×#88043C2211yescharacteristic
18#11718138—21no—
19#11718136—21no—
20#11718075—24no—
21C2×C13×#41D412yes—
22C2×#6127—21no—
23C2×C13×M16—22no—
24C22×C8×C13—22no—
25C13×C4⋊Q8D411yescharacteristic
26C13×#127D411yescharacteristic
27C13×#124C2×C412yes—
28C13×#121—22no—
29C4×D4×C13—22no—
30C2×C42×C13C2311yescharacteristic
31#88204—44no—
32#88204—44no—
33C2×#6107—22no—
34C2×#6106—22no—
35C2×#6105—22no—
36C2×#6104—22no—
37#88184—22no—
38C22×#1055—21no—
39#88129—21no—
40#88128C2×C411yescharacteristic
41C4×D52—22no—
42#88123C2×C411yescharacteristic
43C13×C4⋊C8D414yes—
44C13×C22⋊C8—24no—
45C13×C22⋊C8—22no—
46C13×#97—22no—
47C22⋊#1055—22no—
48C4⋊#1055—22no—
49#88043—21no—
50#88043C2×C412yes—
51C4×#1055—22no—
52#9007—131nomaximal, Sylow
53C13×#41—42no—
54C13×#41—42no—
55C2×Q8×C13C22⋊C412yes—
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13C22⋊C412yes—
59C22×C4×C13—22no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4112yes—
62C2×C22⋊D13—41no—
63#6127—42no—
64#6127—42no—
65C2×D52—21no—
66C2×D52—22no—
67C2×C4×D13—41no—
68C2×Dic26—21no—
69C13×M16—82no—
70C2×C8×C13—24no—
71C2×C8×C13—82no—
72C13×C4⋊C4—22no—
73C13×C22⋊C4—24no—
74C42×C13C22×C411yescharacteristic
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D412yes—
77#6107—44no—
78#6106—44no—
79#6105—44no—
80#6104—44no—
81#6103—42no—
82C4⋊Dic13—22no—
83C2×#1055—24no—
84C2×#1055—22no—
85C2×#1055—42no—
86#3150—131no—
87#2980D1311yescharacteristic, complemented
88#1543—131no—
89#1496—132no—
90#1302—132no—
91C23×C13—22no—
92C23×C13#12311yescharacteristic
93C22×D13—41no—
94Q8×C13—42no—
95D4×C13—42no—
96D4×C13—82no—
97D4×C13—82no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13C4×D412yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12112yes—
107C22⋊D13—81no—
108C22⋊D13—81no—
109C2×Dic13—41no—
110D52—42no—
111D52—44no—
112C4×D13—82no—
113Dic26—42no—
114C8×C13—44no—
115#1055—24no—
116#1055—82no—
117C2×#135—262no—
118#532—131no—
119#532C2×D1311yescharacteristic
120#497—132no—
121#497—261no—
122#496—132no—
123#496—261no—
124#435—24no—
125#432C2×D1312yes—
126#431—132no—
127#408—22no—
128C2×#97—131no—
129#333—261no—
130#331—261no—
131D4⋊C8—264no—
132C22×C13—22no—
133C22×C13—21no—
134C22×C13—44no—
135C22×C13—42no—
136C22×C13#38611yescharacteristic
137C2×D13—82no—
138C2×D13—81no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13#45312yes—
144Dic13—81no—
145C2×#41—261no—
146C2×#41C22⋊D1312yes—
147#135—524no—
148#135—524no—
149C2×Q16—262no—
150C2×SD16—262no—
151C2×SD16—262no—
152C2×D8—262no—
153C2×M16—22no—
154C22×C8—22no—
155C22×C8—261no—
156C4⋊Q8—131no—
157C4⋊Q8D5211yescharacteristic
158#127—131no—
159#127D5211yescharacteristic
160#124—261no—
161#124C4×D1312yes—
162#121—22no—
163#121—262no—
164C4×D4—22no—
165C4×D4—262no—
166C2×C42C22×D1311yescharacteristic
167C4⋊C8—262no—
168C4⋊C8C22⋊D1314yes—
169C22⋊C8—24no—
170C22⋊C8—22no—
171C22⋊C8—262no—
172#97—22no—
173#97—132no—
174#97—261no—
175C4×C8—262no—
176C2×C13—41no—
177C2×C13—82no—
178C2×C13#188112yes—
179C2×C13#188711yescharacteristic
180D13—161no—
181#41—42no—
182#41—42no—
183#41—522no—
184#41—522no—
185C2×Q8—261no—
186C2×Q8#610312yes—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—261no—
190C2×D4—262no—
191C2×D4—521no—
192C2×D4#610312yes—
193C22×C4—22no—
194C22×C4—521no—
195C22×C4#612712yes—
196C22×C4C2×C22⋊D1311yescharacteristic
197Q16—524no—
198SD16—524no—
199SD16—524no—
200D8—524no—
201M16—82no—
202C2×C8—24no—
203C2×C8—82no—
204C2×C8—264no—
205C2×C8—262no—
206C2×C8—522no—
207C4⋊C4—22no—
208C4⋊C4—262no—
209C22⋊C4—24no—
210C22⋊C4—522no—
211C42C2×C4×D1311yescharacteristic
212C42C2×D5211yescharacteristic
213C42C2×C22⋊D1312yes—
214C13#900711yescharacteristic, complemented, Sylow
215C23—22no—
216C23—521no—
217C23#8818311yescharacteristic
218Q8—42no—
219Q8—522no—
220D4—42no—
221D4—82no—
222D4—82no—
223D4—522no—
224D4—524no—
225D4—1041no—
226D4—1041no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—521no—
233C2×C4—1042no—
234C2×C4C2×#610311yescharacteristic
235C2×C4C4×C22⋊D1312yes—
236C2×C4#8818412yes—
237C2×C4#8820711yescharacteristic
238C8—44no—
239C8—264no—
240C8—1042no—
241C22—22no—
242C22—21no—
243C22—44no—
244C22—42no—
245C22—1042no—
246C22—1041no—
247C22#1171887411yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—42no—
252C4—1041no—
253C4#1171890212yes—
254C2—41no—
255C2—82no—
256C2—2081no—
257C2#1311519812yes—
258C2#1311523411yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2980C2
socleC22×C13#386
prime radical#13125281C2
cosocleC2×C42×C13C23
hypercenter#2980D13
hypocenterC13#9007
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #13113498C2semidirect
3. #13113304C2semidirect
4. #13112734C2semidirect
5. C13×#2980C2semidirect
87. #2980D13semidirect
214. C13#9007semidirect

Maximal subgroups

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

subgroupindex
#131252812
#131134982
#131133042
#131127342
C13×#29802
#900713