Finite Group Databasebeta

← #15760320

Subgroups — #15760320

Order 3328.

466 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123921C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113517C212yesmaximal
4#13112739C212yesmaximal
5C13×#2567C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#395C414yes—
9C13×#391—21no—
10C13×#389—22no—
11C13×#384—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88076—21no—
14#11718685—24no—
15#11718587—22no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718138—24no—
19#11718122—21no—
20C22×Q8×C13C2×C412yes—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—24no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13D412yes—
34C2×C42×C13C2311yescharacteristic
35C2×#6099—22no—
36C13×#95—24no—
37C13×#95C2×C412yes—
38#88076—42no—
39C22⋊#1055—22no—
40C4⋊#1055—24no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055D414yes—
44#88043—24no—
45C4×#1055—22no—
46#9400—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—21no—
49C2×Q8×C13—21no—
50C2×Q8×C13—22no—
51C2×Q8×C13—24no—
52C2×Q8×C13—82no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C13×C4⋊C4—24no—
61C13×C4⋊C4—24no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—84no—
67C42×C13—22no—
68C42×C13—22no—
69C42×C13—41no—
70C42×C13—41no—
71C42×C13C2×D412yes—
72C42×C13#4112yes—
73#6099—42no—
74#6099—42no—
75C2×#1055—24no—
76C2×#1055—42no—
77#2983—131no—
78#2567D1311yescharacteristic
79#1801—131no—
80#1548—132no—
81#1303—132no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—42no—
84Q8×C13—42no—
85Q8×C13—84no—
86C2×C4×C13—22no—
87C2×C4×C13—24no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—44no—
97C2×C4×C13—42no—
98C2×C4×C13C4×D412yes—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13#12112yes—
101C2×C4×C13#12311yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C13#13712yes—
104C2×C4×C13#13711yescharacteristic
105#1055—44no—
106#1055—82no—
107C2×C4⋊Q8C2×D1311yescharacteristic
108C2×C4×Q8C2×D1311yescharacteristic
109#446—264no—
110#432—262no—
111#431—132no—
112#423—132no—
113C2×#101—261no—
114#395Dic1314yes—
115#391—21no—
116#389—22no—
117#384—21no—
118C4×C4⋊C4C2×D1311yescharacteristic
119#343—261no—
120#333—264no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#38611yescharacteristic
124C22×C13#41711yescharacteristic
125C22×C13#41911yescharacteristic
126C4×C13—21no—
127C4×C13—22no—
128C4×C13—44no—
129C4×C13—42no—
130C4×C13—42no—
131C4×C13—82no—
132C4×C13#45612yes—
133C4×C13#46812yes—
134C4×C13#47012yes—
135C22×Q8C2×Dic1312yes—
136C22×Q8C22⋊D1311yescharacteristic
137C2×M16—262no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4C2×Dic1312yes—
147C2×C4⋊C4C22⋊D1311yescharacteristic
148C2×C42—21no—
149C2×C42C22⋊D1312yes—
150C2×C42C22×D1311yescharacteristic
151C4⋊C8—134no—
152C4⋊C8—264no—
153C4⋊C8—262no—
154C4⋊C8—262no—
155#101—522no—
156C22⋊C8—262no—
157#97—264no—
158C4×C8—262no—
159#95—24no—
160#95C2×Dic1312yes—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#188611yescharacteristic
164C2×C13#189411yescharacteristic
165C2×C13#191411yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—24no—
171C2×Q8—82no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4C22⋊Dic1312yes—
175C22×C4C22⋊Dic1312yes—
176C22×C4C22×Dic1311yescharacteristic
177C22×C4C2×C22⋊D1311yescharacteristic
178C22×C4C2×C22⋊D1311yescharacteristic
179M16—522no—
180M16—522no—
181C2×C8—264no—
182C2×C8—522no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—84no—
190C42—22no—
191C42—22no—
192C42—41no—
193C42—41no—
194C42D4×D1312yes—
195C42#612912yes—
196C13#940011yescharacteristic, complemented, Sylow
197C23C2×C22⋊Dic1311yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—84no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4D4×Dic1312yes—
214C2×C4#8818911yescharacteristic
215C2×C4#8819111yescharacteristic
216C2×C4#8819312yes—
217C2×C4#8819612yes—
218C2×C4#8820311yescharacteristic
219C2×C4#8820511yescharacteristic
220C8—524no—
221C8—1042no—
222C22—21no—
223C22—21no—
224C22#1171888111yescharacteristic
225C22#1171888611yescharacteristic
226C22#1171889311yescharacteristic
227C4—21no—
228C4—22no—
229C4—44no—
230C4—42no—
231C4—42no—
232C4—82no—
233C4#1171871012yes—
234C4#1171871312yes—
235C4#1171875612yes—
236C2—21no—
237C2—21no—
238C2#1311523011yescharacteristic
239C2#1311527011yescharacteristic
240C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2567C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2567D13
hypocenterC13#9400
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2567

Complements

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

NH ≅ G/Ntype
196. C13#9400semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131148322
#131135172
#131127392
C13×#25672
#940013