Finite Group Databasebeta

← #15760340

Subgroups — #15760340

Order 3328.

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

normal subgroups only

This group has 450 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#13113521C212yesmaximal
4#13112739C212yesmaximal
5C13×#2568C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400C414yes—
9C13×#391—21no—
10C13×#391—22no—
11C13×#382—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88076—21no—
14#11718685—24no—
15#11718587—22no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718139—24no—
19#11718122—21no—
20C22×Q8×C13—21no—
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⋊C4C2×C412yes—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13D412yes—
33C2×C42×C13C2311yescharacteristic
34C2×#6099—22no—
35C13×#95—24no—
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#9404—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—21no—
49C2×Q8×C13—21no—
50C2×Q8×C13—22no—
51C2×Q8×C13—44no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C13×C4⋊C4—24no—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C42×C13—22no—
67C42×C13—22no—
68C42×C13—41no—
69C42×C13—41no—
70C42×C13C2×D412yes—
71C42×C13#4112yes—
72#6099—42no—
73#6099—42no—
74C2×#1055—24no—
75C2×#1055—42no—
76#2983—131no—
77#2568D1311yescharacteristic
78#1801—131no—
79#1549—132no—
80#1303—132no—
81C23×C13C2×C22⋊C411yescharacteristic
82Q8×C13—42no—
83Q8×C13—42no—
84Q8×C13—82no—
85Q8×C13—82no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—44no—
96C2×C4×C13—42no—
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#400Dic1314yes—
115#391—21no—
116#391—22no—
117#382—21no—
118C4×C4⋊C4C2×D1311yescharacteristic
119#343—261no—
120#332—264no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#38611yescharacteristic
124C22×C13#41711yescharacteristic
125C22×C13#41911yescharacteristic
126C4×C13—21no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13—42no—
130C4×C13—82no—
131C4×C13—82no—
132C4×C13#45412yes—
133C4×C13#46812yes—
134C4×C13#47012yes—
135C22×Q8—21no—
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⋊C4C2×Dic1312yes—
145C2×C4⋊C4C2×Dic1312yes—
146C2×C4⋊C4C22⋊D1311yescharacteristic
147C2×C42—21no—
148C2×C42C22⋊D1312yes—
149C2×C42C22×D1311yescharacteristic
150C4⋊C8—134no—
151C4⋊C8—264no—
152C4⋊C8—262no—
153C4⋊C8—262no—
154#101—522no—
155C22⋊C8—262no—
156#97—264no—
157C4×C8—262no—
158#95—24no—
159#95—24no—
160#95C2×Dic1312yes—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#188811yescharacteristic
164C2×C13#189411yescharacteristic
165C2×C13#191511yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—44no—
171C2×Q8—41no—
172C2×Q8—41no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4C22⋊Dic1312yes—
176C22×C4C22⋊Dic1312yes—
177C22×C4C22×Dic1311yescharacteristic
178C22×C4C2×C22⋊D1311yescharacteristic
179C22×C4C2×C22⋊D1311yescharacteristic
180M16—522no—
181M16—522no—
182C2×C8—264no—
183C2×C8—522no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C42—22no—
190C42—22no—
191C42—41no—
192C42—41no—
193C42D4×D1312yes—
194C42#612912yes—
195C13#940411yescharacteristic, complemented, Sylow
196C23C2×C22⋊Dic1311yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—82no—
200Q8—82no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
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—42no—
230C4—42no—
231C4—82no—
232C4—82no—
233C4#1171871012yes—
234C4#1171871312yes—
235C4#1171872312yes—
236C2—21no—
237C2—21no—
238C2#1311524011yescharacteristic
239C2#1311527011yescharacteristic
240C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2568C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2568D13
hypocenterC13#9404
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
195. C13#9404semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131148322
#131135212
#131127392
C13×#25682
#940413