Finite Group Databasebeta

← #15760793

Subgroups — #15760793

Order 3328.

522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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#13119741C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic, complemented
3#13113262C212yesmaximal
4#13112695C212yesmaximal, complemented
5C13×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88200—21no—
8C2×C4×D52C2211yescharacteristic
9C13×#446—24no—
10C13×#432—22no—
11C13×#431C2212yes—
12C2×#88076—21no—
13#11718652C412yes—
14#11718648—21no—
15#11718644C412yes—
16#11718601—22no—
17#11718597C2211yescharacteristic
18#11718585C2212yes—
19#11718122—21no—
20#11718051—24no—
21C22×Q8×C13D411yescharacteristic
22C22×D52C2×C411yescharacteristic
23C22×C4×D13—21no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4C2×C412yes—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30#88200—44no—
31C2×#6103—22no—
32C2×#6103—22no—
33C2×#6103—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—22no—
37C2×#6099—22no—
38C4×D52—22no—
39C4×D52—22no—
40C13×C4⋊C8—24no—
41C13×C4⋊C8—22no—
42C13×C22⋊C8—22no—
43C13×#97—24no—
44C4×C8×C13D414yes—
45#88076—42no—
46#88071—22no—
47#88071—21no—
48#88071C2×C412yes—
49C4⋊#1055—22no—
50C4⋊#1055—22no—
51#9490—131nomaximal, Sylow
52C23×D13—21no—
53C2×Q8×C13—22no—
54C2×Q8×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—21no—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—21no—
64C2×D52—22no—
65C2×D52—42no—
66C2×C4×D13—42no—
67C2×C4×D13—42no—
68C2×C4×D13—41no—
69C2×C4×D13—41no—
70C2×C8×C13—24no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—22no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13C2×D412yes—
76C42×C13#4112yes—
77#6103—44no—
78#6103—44no—
79#6103—41no—
80#6103—41no—
81C4⋊Dic13—22no—
82C4⋊Dic13—42no—
83#6101—44no—
84#6099—42no—
85#6099—42no—
86C2×#1055—42no—
87#2983D1311yescharacteristic, complemented
88#2536—131no—
89#1801—131no—
90#1486—132no—
91#1286—132no—
92C23×C13C2×C22⋊C411yescharacteristic
93C22×D13—22no—
94C22×D13—41no—
95C22×D13—41no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100Q8×C13—42no—
101Q8×C13—42no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13C4×D412yes—
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13#12112yes—
112C2×C4×C13#12311yescharacteristic
113C2×C4×C13AGL(1,ℤ/8)12yes—
114C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C13#13711yescharacteristic
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122D52—24no—
123D52—42no—
124C4×D13—82no—
125C4×D13—82no—
126C8×C13—44no—
127#1055—82no—
128C2×C22⋊Q8—261no—
129C2×C4×Q8C2×D1311yescharacteristic
130C2×C4×D4—131no—
131#446—24no—
132#432—22no—
133#431C2×D1312yes—
134#423—132no—
135C2×#101—261no—
136#398—132no—
137#394—132no—
138#388—262no—
139#382—131no—
140#380—261no—
141#343—261no—
142D4⋊C8—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13#38611yescharacteristic
146C22×C13#41711yescharacteristic
147C22×C13#41811yescharacteristic
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—42no—
151C2×D13—81no—
152C2×D13—81no—
153C2×D13—81no—
154C2×D13—81no—
155C4×C13—22no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—42no—
159C4×C13—42no—
160C4×C13#46812yes—
161C4×C13#46912yes—
162Dic13—82no—
163Dic13—81no—
164C22×Q8D5211yescharacteristic
165C22×D4—131no—
166C23×C4—261no—
167C2×M16—262no—
168C22⋊Q8—524no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—262no—
172C4×D4—262no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C4×D1312yes—
177C2×C4⋊C4D5211yescharacteristic
178C2×C22⋊C4—262no—
179C2×C22⋊C4—262no—
180C2×C22⋊C4—261no—
181C2×C42C22⋊D1312yes—
182C2×C42C22×D1311yescharacteristic
183C4⋊C8—24no—
184C4⋊C8—22no—
185C4⋊C8—262no—
186C4⋊C8—262no—
187#101—522no—
188C22⋊C8—22no—
189#97—24no—
190C4×C8C22⋊D1314yes—
191#95—132no—
192#95—262no—
193#95—261no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13#189111yescharacteristic
197C2×C13#189511yescharacteristic
198C2×C13#191211yescharacteristic
199D13—82no—
200C24—261no—
201C2×Q8—21no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×D4—262no—
206C2×D4—522no—
207C22×C4—262no—
208C22×C4—261no—
209C22×C4—522no—
210C22×C4—521no—
211C22×C4—521no—
212C22×C4—522no—
213C22×C4#610312yes—
214C22×C4#610312yes—
215C22×C4C2×C4×D1311yescharacteristic
216C22×C4C2×D5211yescharacteristic
217C22×C4C2×C22⋊D1311yescharacteristic
218M16—522no—
219M16—522no—
220C2×C8—24no—
221C2×C8—522no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—262no—
225C4⋊C4—524no—
226C4⋊C4—522no—
227C22⋊C4—524no—
228C22⋊C4—524no—
229C22⋊C4—521no—
230C22⋊C4—521no—
231C42—22no—
232C42—22no—
233C42#612712yes—
234C42C2×C22⋊D1312yes—
235C13#949011yescharacteristic, complemented, Sylow
236C23—262no—
237C23—521no—
238C23—521no—
239C23—521no—
240C23—521no—
241C23—521no—
242C23—521no—
243C23C2×#610311yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—264no—
247D4—522no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—1042no—
262C2×C4—1042no—
263C2×C4#8816212yes—
264C2×C4#8816211yescharacteristic
265C2×C4#8816311yescharacteristic
266C2×C4C4×C22⋊D1312yes—
267C2×C4#8818311yescharacteristic
268C2×C4#8818412yes—
269C2×C4#8820711yescharacteristic
270C8—44no—
271C8—1042no—
272C22—21no—
273C22—21no—
274C22—522no—
275C22—522no—
276C22—522no—
277C22—1041no—
278C22—1041no—
279C22—1041no—
280C22—1041no—
281C22#1171879211yescharacteristic
282C22#1171879411yescharacteristic
283C22#1171887411yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—1042no—
290C4—1041no—
291C4#1171879512yes—
292C4#1171879612yes—
293C2—21no—
294C2—21no—
295C2—1042no—
296C2#1311525411yescharacteristic
297C2#1311527411yescharacteristic
298C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9490
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #13114832C2semidirect
4. #13112695C2semidirect
5. C13×#2983C2semidirect
87. #2983D13semidirect
235. C13#9490semidirect

Maximal subgroups

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

subgroupindex
#131197412
#131148322
#131132622
#131126952
C13×#29832
#949013