Finite Group Databasebeta

← #15760783

Subgroups — #15760783

Order 3328.

454 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 115 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#13120198C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113266C212yesmaximal
4#13112695C212yesmaximal
5C13×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#446—24no—
9C13×#432—22no—
10C13×#431C2212yes—
11#11718891—21no—
12C2×#88076—21no—
13#11718647C412yes—
14#11718640C412yes—
15#11718634—21no—
16#11718597C2211yescharacteristic
17#11718594—22no—
18#11718585C2212yes—
19#11718122—21no—
20#11718048—24no—
21C22×Q8×C13D411yescharacteristic
22C22×Dic26C2×C411yescharacteristic
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101—22no—
32C2×#6101—21no—
33C2×C4×Dic13—21no—
34C2×#6099—22no—
35C4×Dic26—22no—
36C4×Dic26—22no—
37C13×C4⋊C8—24no—
38C13×C4⋊C8—22no—
39C13×C22⋊C8—22no—
40C13×#97—24no—
41C4×C8×C13D414yes—
42#88076—42no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—21no—
47#88071C2×C412yes—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50#9488—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—21no—
53C2×Q8×C13—21no—
54C2×Q8×C13—22no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—22no—
62C22×Dic13—21no—
63C2×Dic26—22no—
64C2×Dic26—42no—
65C2×C8×C13—24no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—22no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13C2×D412yes—
71C42×C13#4112yes—
72C4⋊Dic13—22no—
73C4⋊Dic13—41no—
74C4⋊Dic13—41no—
75#6101—44no—
76#6101—41no—
77#6101—41no—
78C4×Dic13—42no—
79#6099—42no—
80#6099—42no—
81C2×#1055—42no—
82#2983D1311yescharacteristic
83#2581—131no—
84#1801—131no—
85#1487—132no—
86#1286—132no—
87C23×C13C2×C22⋊C411yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13C4×D412yes—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13#12112yes—
100C2×C4×C13#12311yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C13#13712yes—
103C2×C4×C13#13711yescharacteristic
104C2×Dic13—22no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112Dic26—24no—
113Dic26—42no—
114C8×C13—44no—
115#1055—82no—
116C2×C4×Q8—131no—
117C2×C4×Q8C2×D1311yescharacteristic
118#446—24no—
119#432—22no—
120#431C2×D1312yes—
121#423—132no—
122C2×#101—261no—
123#400—132no—
124#395—132no—
125#391—261no—
126#389—261no—
127#387—262no—
128#382—131no—
129#343—261no—
130Q8⋊C8—264no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13#38611yescharacteristic
134C22×C13#41711yescharacteristic
135C22×C13#41911yescharacteristic
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—42no—
140C4×C13—42no—
141C4×C13#46812yes—
142C4×C13#47012yes—
143Dic13—42no—
144Dic13—82no—
145Dic13—81no—
146C22×Q8—131no—
147C22×Q8D5211yescharacteristic
148C2×M16—262no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—262no—
152C4×Q8—262no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4C4×D1312yes—
158C2×C4⋊C4D5211yescharacteristic
159C2×C42—261no—
160C2×C42C22⋊D1312yes—
161C2×C42C22×D1311yescharacteristic
162C4⋊C8—24no—
163C4⋊C8—22no—
164C4⋊C8—262no—
165C4⋊C8—262no—
166#101—522no—
167C22⋊C8—22no—
168#97—24no—
169C4×C8C22⋊D1314yes—
170#95—132no—
171#95—262no—
172#95—262no—
173#95—262no—
174#95—261no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13#189111yescharacteristic
178C2×C13#189411yescharacteristic
179C2×C13#191211yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—22no—
184C2×Q8—262no—
185C2×Q8—522no—
186C22×C4—261no—
187C22×C4—262no—
188C22×C4—261no—
189C22×C4#610312yes—
190C22×C4#610312yes—
191C22×C4C2×C4×D1311yescharacteristic
192C22×C4C2×D5211yescharacteristic
193C22×C4C2×C22⋊D1311yescharacteristic
194M16—522no—
195M16—522no—
196C2×C8—24no—
197C2×C8—522no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—262no—
201C4⋊C4—524no—
202C4⋊C4—521no—
203C4⋊C4—521no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C42—22no—
207C42—22no—
208C42—522no—
209C42#612712yes—
210C42C2×C22⋊D1312yes—
211C13#948811yescharacteristic, complemented, Sylow
212C23C2×#610311yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—264no—
216Q8—522no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—262no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—522no—
231C2×C4—521no—
232C2×C4#8816211yescharacteristic
233C2×C4#8816312yes—
234C2×C4#8816311yescharacteristic
235C2×C4C4×C22⋊D1312yes—
236C2×C4#8818311yescharacteristic
237C2×C4#8818412yes—
238C2×C4#8820711yescharacteristic
239C8—44no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22#1171878111yescharacteristic
244C22#1171879411yescharacteristic
245C22#1171887411yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—522no—
252C4—1042no—
253C4—1041no—
254C4#1171879512yes—
255C4#1171879812yes—
256C2—21no—
257C2—21no—
258C2#1311525411yescharacteristic
259C2#1311526911yescharacteristic
260C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9488
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
211. C13#9488semidirect

Maximal subgroups

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

subgroupindex
#131201982
#131148322
#131132662
#131126952
C13×#29832
#948813