Finite Group Databasebeta

← #15760666

Subgroups — #15760666

Order 3328.

554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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#13119324C211yesmaximal, characteristic
2#13117439C211yesmaximal, characteristic, complemented
3#13113366C212yesmaximal
4#13112690C212yesmaximal, complemented
5C13×#1821C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C13×#407C2212yes—
9#11718874—21no—
10#11718874—21no—
11#11718873—21no—
12#11718872C2212yes—
13C4×C22⋊Dic13—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718654—22no—
16#11718649C412yescomplemented
17#11718642—24no—
18#11718638C412yescomplemented
19C13×#343—22no—
20#11718062—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C2×C13×M16—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—21no—
33#88184—22no—
34#88184—22no—
35C2×#6103—21no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4×Dic13—22no—
41C2×C4×Dic13C2×C412yes—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—22no—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071—22no—
50#88071D414yes—
51#9465—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C23×D13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—42no—
59C22×C4×C13—81no—
60C22×C4×C13—81no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D412yes—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4112yes—
67C2×C22⋊D13—44no—
68C2×C22⋊D13—41no—
69C2×C22⋊D13—41no—
70C22×Dic13—21no—
71C22×Dic13—22no—
72C22×Dic13—24no—
73C2×D52—22no—
74C2×D52—42no—
75C13×M16—44no—
76C2×C8×C13—42no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C22⋊Dic13—44no—
80C22⋊Dic13—42no—
81#6103—42no—
82#6103—82no—
83#6103—82no—
84C4⋊Dic13—22no—
85C4⋊Dic13—82no—
86C4×Dic13—42no—
87C4×Dic13—82no—
88#2504—131no—
89#2313—131no—
90#1821D1311yescharacteristic, complemented
91#1510—132no—
92#1284—132no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—41no—
96C23×C13C2×C22⋊C411yescharacteristic
97C23×C13#12011yescharacteristic
98C23×C13#12311yescharacteristic
99C22×D13—42no—
100C22×D13—42no—
101C22×D13—41no—
102C22×D13—42no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12112yes—
117C22⋊D13—82no—
118C22⋊D13—82no—
119C2×Dic13—44no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—44no—
123C2×Dic13—42no—
124C2×Dic13—41no—
125C2×Dic13—42no—
126C2×Dic13—44no—
127D52—82no—
128C8×C13—82no—
129C2×#121—131no—
130C22×C4⋊C4C2×D1311yescharacteristic
131#407C2×D1312yes—
132#397—262no—
133#390—132no—
134#387—264no—
135#386—261no—
136#386—261no—
137#382—132no—
138#381—132no—
139#380—261no—
140C4×C22⋊C4—131no—
141C4×C22⋊C4—261no—
142#343—22no—
143#327—264no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—44no—
152C22×C13#38611yescharacteristic
153C22×C13#41012yes—
154C22×C13#45412yes—
155C2×D13—84no—
156C2×D13—81no—
157C2×D13—81no—
158C2×D13—81no—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—42no—
162C4×C13—42no—
163Dic13—84no—
164Dic13—82no—
165Dic13—81no—
166C22×D4—131no—
167C22×D4—261no—
168C23×C4D5211yescharacteristic
169C23×C4D5211yescharacteristic
170C23×C4C22×D1311yescharacteristic
171C2×M16—22no—
172#121—262no—
173#121—262no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4C4×D1312yes—
179C2×C4⋊C4C22⋊D1312yes—
180C2×C22⋊C4—261no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—261no—
183C2×C22⋊C4—262no—
184C2×C22⋊C4—262no—
185C2×C42—132no—
186C2×C42—262no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189#95—134no—
190#95—262no—
191#95—262no—
192#95—262no—
193#95—262no—
194#95—262no—
195#95—261no—
196C2×C13—22no—
197C2×C13—22no—
198C2×C13—41no—
199C2×C13#188811yescharacteristic
200C2×C13#189911yescharacteristic
201C2×C13#191111yescharacteristic
202D13—161no—
203C24—261no—
204C24C2×D5211yescharacteristic
205C2×D4—262no—
206C2×D4—522no—
207C2×D4—524no—
208C2×D4—521no—
209C2×D4—521no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—42no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—264no—
218C22×C4—261no—
219C22×C4—262no—
220C22×C4#610312yes—
221C22×C4#610312yes—
222C22×C4C2×C4×D1311yescharacteristic
223C22×C4D4×D1312yes—
224C22×C4#612912yes—
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—44no—
227C2×C8—42no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—262no—
231C4⋊C4—1042no—
232C22⋊C4—524no—
233C22⋊C4—522no—
234C22⋊C4—522no—
235C22⋊C4—1042no—
236C22⋊C4—1042no—
237C42—522no—
238C42—1042no—
239C13#946511yescharacteristic, complemented, Sylow
240C23—22no—
241C23—22no—
242C23—41no—
243C23—522no—
244C23—522no—
245C23—522no—
246C23—521no—
247C23#8813611yescharacteristic
248C23#8814011yescharacteristic
249C23C2×#610311yescharacteristic
250D4—1042no—
251D4—1042no—
252D4—1042no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—524no—
266C2×C4—522no—
267C2×C4—524no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4—524no—
272C2×C4—521no—
273C2×C4#8813512yes—
274C2×C4#8819312yes—
275C8—82no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—1044no—
285C22—1041no—
286C22—1041no—
287C22—1041no—
288C22#1171841412yes—
289C22#1171861911yescharacteristic
290C22#1171866712yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—1044no—
296C4—1042no—
297C4—1041no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—2081no—
302C2#1311523711yescharacteristic
303C2#1311529211yescharacteristic
304C2#1311536611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1821C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#1821D13
hypocenterC13#9465
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #13117439C2semidirect
4. #13112690C2semidirect
5. C13×#1821C2semidirect
16. #11718649C4semidirect
18. #11718638C4semidirect
90. #1821D13semidirect
239. C13#9465semidirect

Maximal subgroups

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

subgroupindex
#131193242
#131174392
#131133662
#131126902
C13×#18212
#946513