Finite Group Databasebeta

← #15760290

Subgroups — #15760290

Order 3328.

506 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 139 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#13123917C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113508C212yesmaximal
4#13112739C212yesmaximal
5C13×#2546C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—21no—
7C2×C13×C4⋊Q8C2211yescharacteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C13×#398C414yes—
10C13×#391—21no—
11C13×#389—22no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88076—21no—
14Q8×#1055—24no—
15#11718586—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—
24C13×C4⋊Q8—42no—
25C13×C4⋊Q8—42no—
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—24no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13D412yes—
36C2×C42×C13C2311yescharacteristic
37C2×#6099—22no—
38C13×#95—24no—
39C13×#95C2×C412yes—
40#88076—42no—
41C22⋊#1055—22no—
42C4⋊#1055—24no—
43C4⋊#1055—22no—
44C4⋊#1055—22no—
45C4⋊#1055D414yes—
46C4×#1055—24no—
47C4×#1055—22no—
48#9394—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—42no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13—42no—
55C2×Q8×C13D812yes—
56C2×Q8×C13SD1612yes—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C13×C4⋊C4—24no—
65C13×C4⋊C4—24no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—48no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C42×C13—22no—
72C42×C13—22no—
73C42×C13—41no—
74C42×C13—41no—
75C42×C13C2×D412yes—
76C42×C13#4112yes—
77#6099—42no—
78#6099—42no—
79C2×#1055—24no—
80C2×#1055—42no—
81#2982—131no—
82#2546D1311yescharacteristic
83#1801—131no—
84#1546—132no—
85#1303—132no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—24no—
88Q8×C13—24no—
89Q8×C13—82no—
90Q8×C13—82no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—24no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13#10214yes—
104C2×C4×C13C4×D412yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12112yes—
107C2×C4×C13#12311yescharacteristic
108C2×C4×C13C2×D811yescharacteristic
109C2×C4×C13C2×SD1611yescharacteristic
110C2×C4×C13#13512yes—
111#1055—44no—
112#1055—82no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8C2×D1311yescharacteristic
115C2×C4×Q8C2×D1311yescharacteristic
116C8×Q8—264no—
117#431—132no—
118#431—262no—
119#423—132no—
120C2×#101—261no—
121#398Dic1314yes—
122#391—21no—
123#389—22no—
124C4×C4⋊C4C2×D1311yescharacteristic
125#343—261no—
126#332—264no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13#38611yescharacteristic
130C22×C13C2×#10211yescharacteristic
131C22×C13#41611yescharacteristic
132C4×C13—21no—
133C4×C13—24no—
134C4×C13—22no—
135C4×C13—44no—
136C4×C13—42no—
137C4×C13—82no—
138C4×C13#45612yes—
139C4×C13#46512yes—
140C4×C13#46612yes—
141C22×Q8—21no—
142C22×Q8C22⋊D1311yescharacteristic
143C2×M16—262no—
144C4⋊Q8—22no—
145C4⋊Q8—22no—
146C4⋊Q8—42no—
147C4⋊Q8—42no—
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic1312yes—
154C2×C4⋊C4C2×Dic1312yes—
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C42—21no—
157C2×C42C22⋊D1312yes—
158C2×C42C22×D1311yescharacteristic
159C4⋊C8—134no—
160C4⋊C8—264no—
161C4⋊C8—262no—
162C4⋊C8—262no—
163#101—522no—
164C22⋊C8—262no—
165C4×C8—264no—
166C4×C8—262no—
167#95—24no—
168#95C2×Dic1312yes—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13#188611yescharacteristic
172C2×C13#189311yescharacteristic
173C2×C13#191511yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8#610412yes—
181C2×Q8#610512yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4C22⋊Dic1312yes—
185C22×C4C22⋊Dic1312yes—
186C22×C4C22×Dic1311yescharacteristic
187C22×C4C2×C22⋊D1311yescharacteristic
188C22×C4C2×C22⋊D1311yescharacteristic
189M16—522no—
190M16—522no—
191C2×C8—264no—
192C2×C8—522no—
193C4⋊C4—24no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—48no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42D4×D1312yes—
205C42#612912yes—
206C13#939411yescharacteristic, complemented, Sylow
207C23C2×C22⋊Dic1311yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#8807214yes—
225C2×C4C2×#610411yescharacteristic
226C2×C4C2×#610511yescharacteristic
227C2×C4D4×Dic1312yes—
228C2×C4#8818911yescharacteristic
229C2×C4#8819111yescharacteristic
230C2×C4#8819312yes—
231C2×C4#8820412yes—
232C8—524no—
233C8—1042no—
234C22—21no—
235C22—21no—
236C22C2×#8807211yescharacteristic
237C22#1171888111yescharacteristic
238C22#1171889411yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4#1171869912yes—
246C4#1171870212yes—
247C4#1171875612yes—
248C2—21no—
249C2—21no—
250C2#1311523011yescharacteristic
251C2#1311526511yescharacteristic
252C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2546C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2546D13
hypocenterC13#9394
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
206. C13#9394semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131148322
#131135082
#131127392
C13×#25462
#939413