Finite Group Databasebeta

← #15760324

Subgroups — #15760324

Order 3328.

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

normal subgroups only

This group has 534 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#13119828C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13113507C212yesmaximal, complemented
4#13112738C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88190—21no—
8C2×#88123C2211yescharacteristic
9C13×#436—24no—
10C13×#431C2212yes—
11C13×#407—22no—
12C2×#88073—21no—
13#11718873—22no—
14#11718635—21no—
15#11718614C414yes—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718585C2212yes—
18#11718122—21no—
19#11718078—24no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D412yes—
22C22×Dic26—21no—
23C2×C13×M16—24no—
24C4×D4×C13—22no—
25C4×D4×C13—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4C2×C412yes—
28C2×C42×C13C2311yescharacteristic
29C2×C22⋊Dic13—24no—
30#88190—44no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C412yes—
34C2×C4×Dic13—21no—
35C2×#6099—22no—
36#88123—22no—
37#88123—22no—
38C13×C4⋊C8D414yes—
39C13×C22⋊C8—24no—
40C13×C22⋊C8—22no—
41C4×C8×C13—22no—
42#88073—42no—
43#88071—24no—
44#88071C2×C412yes—
45C4⋊#1055—22no—
46C4⋊#1055—22no—
47#9401—131nomaximal, Sylow
48C24×C13C22⋊C412yes—
49C2×D4×C13—22no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—44no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C2×Dic26—42no—
63C2×Dic26—42no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C13×M16—84no—
67C2×C8×C13—24no—
68C13×C4⋊C4—22no—
69C13×C22⋊C4—24no—
70C42×C13C2×D412yes—
71C42×C13#4112yes—
72C22⋊Dic13—48no—
73C4⋊Dic13—24no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77C4×Dic13—42no—
78#6099—42no—
79#6099—42no—
80C2×#1055—42no—
81#2975D1311yescharacteristic
82#2547—131no—
83#1800—131no—
84#1546—132no—
85#1303—132no—
86C23×C13—22no—
87C23×C13—22no—
88C23×C13—22no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×C22⋊C411yescharacteristic
92D4×C13—42no—
93D4×C13—42no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—41no—
97C2×C4×C13—44no—
98C2×C4×C13—42no—
99C2×C4×C13—82no—
100C2×C4×C13C4×D412yes—
101C2×C4×C13#12011yescharacteristic
102C2×C4×C13#12112yes—
103C2×C4×C13#12311yescharacteristic
104C2×C4×C13AGL(1,ℤ/8)12yes—
105C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C13#13711yescharacteristic
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113Dic26—82no—
114Dic26—82no—
115C8×C13—44no—
116#1055—82no—
117C2×C4⋊Q8—131no—
118C2×#124—261no—
119C2×C4×D4C2×D1311yescharacteristic
120#436—24no—
121#431C2×D1312yes—
122#423—132no—
123C2×#100—261no—
124#407—22no—
125#397—134no—
126#391—261no—
127#380—262no—
128C4×C4⋊C4—131no—
129#343—261no—
130#332—264no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—44no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—82no—
138C22×C13#38611yescharacteristic
139C22×C13#41711yescharacteristic
140C22×C13#41811yescharacteristic
141C4×C13—21no—
142C4×C13—22no—
143C4×C13—42no—
144C4×C13#45512yes—
145C4×C13#46812yes—
146C4×C13#46912yes—
147Dic13—82no—
148Dic13—82no—
149C22×Q8—261no—
150C22×D4D5211yescharacteristic
151C23×C4C22⋊D1312yes—
152C2×M16—24no—
153C2×M16—262no—
154C4⋊Q8—262no—
155C4⋊Q8—262no—
156#124—524no—
157C4×D4—22no—
158C4×D4—22no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4—261no—
162C2×C4⋊C4D5211yescharacteristic
163C2×C22⋊C4—264no—
164C2×C22⋊C4C4×D1312yes—
165C2×C42—261no—
166C2×C42C22×D1311yescharacteristic
167C4⋊C8—262no—
168C4⋊C8—262no—
169C4⋊C8C22⋊D1314yes—
170#100—522no—
171C22⋊C8—24no—
172C22⋊C8—22no—
173C4×C8—22no—
174#95—132no—
175#95—264no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13—82no—
179C2×C13#188511yescharacteristic
180C2×C13#189511yescharacteristic
181C2×C13#191511yescharacteristic
182C24#610312yes—
183C2×Q8—522no—
184C2×Q8—521no—
185C2×Q8—521no—
186C2×Q8—522no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—44no—
194C22×C4—262no—
195C22×C4—262no—
196C22×C4#610312yes—
197C22×C4C2×C4×D1311yescharacteristic
198C22×C4C2×D5211yescharacteristic
199C22×C4C2×C22⋊D1311yescharacteristic
200M16—84no—
201M16—522no—
202M16—522no—
203C2×C8—24no—
204C2×C8—522no—
205C4⋊C4—22no—
206C4⋊C4—264no—
207C4⋊C4—522no—
208C4⋊C4—521no—
209C4⋊C4—521no—
210C22⋊C4—24no—
211C22⋊C4—528no—
212C42—522no—
213C42#612712yes—
214C42C2×C22⋊D1312yes—
215C13#940111yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23C2×#610311yescharacteristic
222Q8—1042no—
223Q8—1042no—
224D4—42no—
225D4—42no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4#8816212yes—
239C2×C4#8816211yescharacteristic
240C2×C4#8816311yescharacteristic
241C2×C4C4×C22⋊D1312yes—
242C2×C4#8818311yescharacteristic
243C2×C4#8818412yes—
244C2×C4#8820711yescharacteristic
245C8—44no—
246C8—1042no—
247C22—21no—
248C22—21no—
249C22—44no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—82no—
254C22#1171879211yescharacteristic
255C22#1171879411yescharacteristic
256C22#1171887411yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—1042no—
261C4—1042no—
262C4#1171879512yes—
263C4#1171879612yes—
264C4#1171890312yes—
265C2—21no—
266C2—21no—
267C2—82no—
268C2#1311522411yescharacteristic
269C2#1311527411yescharacteristic
270C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2975C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2975D13
hypocenterC13#9401
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #13113507C2semidirect
4. #13112738C2semidirect
215. C13#9401semidirect

Maximal subgroups

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

subgroupindex
#131198282
#131148282
#131135072
#131127382
C13×#29752
#940113