Finite Group Databasebeta

← #15760784

Subgroups — #15760784

Order 3328.

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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#13113265C212yesmaximal
4#13112694C212yesmaximal
5C13×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400C412yes—
9C13×#395C412yes—
10C13×#391—21no—
11C13×#389—21no—
12C13×#387—22no—
13C13×#382C2211yescharacteristic
14C2×#88076—21no—
15#11718685—24no—
16#11718587—22no—
17#11718586C2212yes—
18#11718585C2212yes—
19Q8⋊#1055—24no—
20#11718122—21no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13D411yescharacteristic
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C2×#6099—22no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—21no—
41C13×#95C2×C412yes—
42#88076—42no—
43C22⋊#1055—22no—
44C4⋊#1055—24no—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48#88043—24no—
49C4×#1055D414yes—
50#9488—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×Q8×C13—21no—
53C2×Q8×C13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—42no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—24no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—44no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13—42no—
76C42×C13C2×D412yes—
77C42×C13#4112yes—
78#6099—42no—
79#6099—42no—
80C2×#1055—24no—
81C2×#1055—42no—
82#2983—131no—
83#2581D1311yescharacteristic
84#1801—131no—
85#1487—132no—
86#1286—132no—
87C23×C13C2×C22⋊C411yescharacteristic
88Q8×C13—24no—
89Q8×C13—42no—
90Q8×C13—42no—
91Q8×C13—42no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13C4×D412yes—
108C2×C4×C13#12011yescharacteristic
109C2×C4×C13#12112yes—
110C2×C4×C13#12311yescharacteristic
111C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C13#13712yes—
113C2×C4×C13#13711yescharacteristic
114#1055—44no—
115#1055—82no—
116C2×C4×Q8C2×D1311yescharacteristic
117C2×C4×Q8C2×D1311yescharacteristic
118#446—264no—
119#432—262no—
120#431—132no—
121#423—132no—
122C2×#101—261no—
123#400Dic1312yes—
124#395Dic1312yes—
125#391—21no—
126#389—21no—
127#387—22no—
128#382C2×D1311yescharacteristic
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—42no—
142C4×C13—82no—
143C4×C13—81no—
144C4×C13#46812yes—
145C4×C13#47012yes—
146C22×Q8C2×Dic1311yescharacteristic
147C22×Q8C22⋊D1311yescharacteristic
148C2×M16—262no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×Dic1311yescharacteristic
157C2×C4⋊C4C2×Dic1312yes—
158C2×C4⋊C4C22⋊D1311yescharacteristic
159C2×C42—21no—
160C2×C42C22⋊D1312yes—
161C2×C42C22×D1311yescharacteristic
162C4⋊C8—264no—
163C4⋊C8—262no—
164C4⋊C8—262no—
165C4⋊C8—262no—
166#101—522no—
167C22⋊C8—262no—
168#97—264no—
169C4×C8—134no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—21no—
174#95C2×Dic1312yes—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13#189111yescharacteristic
178C2×C13#189411yescharacteristic
179C2×C13#191211yescharacteristic
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—42no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4C22⋊Dic1312yes—
190C22×C4C22⋊Dic1312yes—
191C22×C4C22×Dic1311yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193C22×C4C2×C22⋊D1311yescharacteristic
194M16—522no—
195M16—522no—
196C2×C8—264no—
197C2×C8—522no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C42—22no—
207C42—22no—
208C42—42no—
209C42D4×D1312yes—
210C42#612912yes—
211C13#948811yescharacteristic, complemented, Sylow
212C23C2×C22⋊Dic1311yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4D4×Dic1312yes—
233C2×C4#8818911yescharacteristic
234C2×C4#8819111yescharacteristic
235C2×C4#8819312yes—
236C2×C4#8819612yes—
237C2×C4#8820311yescharacteristic
238C2×C4#8820511yescharacteristic
239C8—524no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22#1171888111yescharacteristic
244C22#1171888611yescharacteristic
245C22#1171889311yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#1171871012yes—
255C4#1171871312yes—
256C2—21no—
257C2—21no—
258C2#1311525511yescharacteristic
259C2#1311527011yescharacteristic
260C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2581C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2581D13
hypocenterC13#9488
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

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
#131239212
#131148322
#131132652
#131126942
C13×#25812
#948813