Finite Group Databasebeta

← #15753909

Subgroups — #15753909

Order 3328.

510 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 121 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#13123526C211yesmaximal, characteristic
2#13114614C212yesmaximal, complemented
3#13113325C212yesmaximal
4#13112723C211yesmaximal, characteristic, complemented
5C13×#1297C211yesmaximal, characteristic, complemented
6#11719496C2211yescharacteristic
7C23×#1055C2211yescharacteristic
8C2×#88161C411yescharacteristic, complemented
9C13×#407C2211yescharacteristic
10C4×C13×C22⋊C4C2212yes—
11C2×C22⋊#1055C2212yes—
12#11718790C411yescharacteristic, complemented
13#11718783C411yescharacteristic, complemented
14#11718780C411yescharacteristic, complemented
15C2×#88043—22no—
16#11718391—22no—
17#11718386—22no—
18#11718116—22no—
19#11718044C414yescomplemented
20#11718043C414yescomplemented
21C23×C4×C13C2311yescharacteristic
22C2×#6127C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C2×C13×M16C2×C411yescharacteristic
25C2×C13×C22⋊C4—22no—
26C2×C42×C13—22no—
27#88207—21no—
28#88184C2×C412yes—
29#88183—21no—
30C4×C22⋊D13—22no—
31#88180C2×C411yescharacteristic
32#88178C2×C412yes—
33C22×#1055—22no—
34C22×#1055—42no—
35C22×#1055C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C22×#1055D412yes—
38C22×#1055D412yes—
39#88161—42no—
40C2×#6094—21no—
41C2×C8×D13—21no—
42C13×C22⋊C8—22no—
43C13×#95C2×C414yes—
44C22⋊#1055—22no—
45C22⋊#1055C2×C414yes—
46#88060—22no—
47#88055—21no—
48#88054—22no—
49C8×Dic13—21no—
50#88043—44no—
51#8239—131nomaximal, Sylow
52C24×C13#4111yescharacteristic
53C22×C4×C13—24no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C22×C412yes—
58C22×C4×C13C2×D412yes—
59C22×C4×C13#4111yescharacteristic
60C2×C22⋊D13—21no—
61C2×C22⋊D13—22no—
62#6127—41no—
63#6127—41no—
64C2×D52C4211yescharacteristic
65C2×C4×D13—21no—
66C2×Dic26C4211yescharacteristic
67C13×M16—41no—
68C13×M16—41no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C13×C22⋊C4—44no—
72C42×C13—42no—
73C42×C13—42no—
74C22⋊Dic13—21no—
75C22⋊Dic13—22no—
76#6103—22no—
77C4⋊Dic13C4212yes—
78#6101—22no—
79C4×Dic13—21no—
80C2×#1055—22no—
81C2×#1055—24no—
82C2×#1055—24no—
83C2×#1055—41no—
84C2×#1055—42no—
85C2×#1055—42no—
86C2×#1055—42no—
87C2×#1055C22⋊C411yescharacteristic
88C2×#1055C22⋊C412yes—
89C2×#1055C22⋊C411yescharacteristic
90#6094—42no—
91C8×D13—42no—
92#2929—131no—
93#1752—132no—
94#1501—132no—
95#1298—131no—
96#1297D1311yescharacteristic, complemented
97C23×C13—24no—
98C23×C13—41no—
99C23×C13#11711yescharacteristic
100C23×C13C4×D412yes—
101C22×D13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—44no—
109C2×C4×C13—44no—
110C2×C4×C13—44no—
111C2×C4×C13C2×C4211yescharacteristic
112C2×C4×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13C4×D412yes—
114C22⋊D13—42no—
115C22⋊D13—44no—
116C2×Dic13—22no—
117C2×Dic13—21no—
118D52—41no—
119C4×D13—41no—
120C4×D13—41no—
121Dic26—41no—
122C8×C13—41no—
123C8×C13—41no—
124#1055—21no—
125#1055—22no—
126#1055—44no—
127#1055#9912yes—
128C2×#131—131no—
129C23×C8—131no—
130#525—131no—
131#435—262no—
132C8×D4—262no—
133#424—131no—
134#408—131no—
135#407C2×D1311yescharacteristic
136C2×C22⋊C8—132no—
137#405—131no—
138C2×#97—262no—
139C4×C22⋊C4C2×D1312yes—
140#336—262no—
141#328—134no—
142#327—134no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—44no—
148C22×C13C4×C22⋊C411yescharacteristic
149C22×C13#44414yes—
150C2×D13—41no—
151C2×D13—42no—
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—84no—
155C4×C13C2×#9911yescharacteristic
156C4×C13#41011yescharacteristic
157Dic13—41no—
158Dic13—42no—
159C2×#41—131no—
160C23×C4C22×D1311yescharacteristic
161#131—522no—
162C2×M16—261no—
163C2×M16C4×D1311yescharacteristic
164C2×M16C4×D1311yescharacteristic
165C22×C8—131no—
166C22×C8—132no—
167C22×C8—131no—
168C22×C8—132no—
169C22×C8—261no—
170C22×C8—262no—
171C22×C8—522no—
172#123—261no—
173C22⋊Q8—132no—
174#121—132no—
175#120—261no—
176C4×D4—262no—
177#117—131no—
178C2×C22⋊C4—22no—
179C2×C42—22no—
180C4⋊C8—262no—
181C22⋊C8—22no—
182C22⋊C8—134no—
183C22⋊C8—262no—
184C22⋊C8—262no—
185#97—261no—
186#97—524no—
187C4×C8—261no—
188#95C4×D1314yes—
189C2×C13—24no—
190C2×C13—41no—
191C2×C13C4×#9911yescharacteristic
192C2×C13#176512yes—
193D13—81no—
194C24#612911yescharacteristic
195#41—521no—
196#41—521no—
197C2×Q8—131no—
198C2×D4—131no—
199C2×D4—262no—
200C2×D4—261no—
201C22×C4—24no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—261no—
205C22×C4C2×C4×D1311yescharacteristic
206C22×C4C2×C4×D1312yes—
207C22×C4D4×D1312yes—
208C22×C4#613111yescharacteristic
209M16—41no—
210M16—41no—
211M16—522no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—131no—
215C2×C8—131no—
216C2×C8—132no—
217C2×C8—264no—
218C2×C8—262no—
219C2×C8—264no—
220C2×C8—522no—
221C2×C8—521no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—132no—
226C4⋊C4—262no—
227C22⋊C4—44no—
228C22⋊C4—262no—
229C22⋊C4—261no—
230C22⋊C4—262no—
231C42—42no—
232C42—42no—
233C42—261no—
234C13#823911yescharacteristic, complemented, Sylow
235C23—24no—
236C23—41no—
237C23—261no—
238C23#8813512yes—
239C23#8814611yescharacteristic
240Q8—521no—
241D4—521no—
242D4—522no—
243D4—524no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—44no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—262no—
254C2×C4—261no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4C42×D1311yescharacteristic
258C2×C4C22⋊C4×D1311yescharacteristic
259C2×C4#8814712yes—
260C8—41no—
261C8—41no—
262C8—132no—
263C8—262no—
264C8—261no—
265C8—524no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—21no—
270C22—44no—
271C22—522no—
272C22—521no—
273C22#1171832711yescharacteristic
274C22#1171848414yes—
275C4—22no—
276C4—21no—
277C4—84no—
278C4—522no—
279C4—521no—
280C4#1171840111yescharacteristic
281C4D13×#9911yescharacteristic
282C2—24no—
283C2—41no—
284C2—1041no—
285C2#1311462311yescharacteristic
286C2#1311467712yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1297C2
socleC22×C13C4×C22⋊C4
prime radical#11719496C22
cosocleC23×C4×C13C23
hypercenter#1297D13
hypocenterC13#8239
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #13114614C2semidirect
4. #13112723C2semidirect
5. C13×#1297C2semidirect
8. C2×#88161C4semidirect
12. #11718790C4semidirect
13. #11718783C4semidirect
14. #11718780C4semidirect
19. #11718044C4semidirect
20. #11718043C4semidirect
96. #1297D13semidirect
234. C13#8239semidirect

Maximal subgroups

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

subgroupindex
#131235262
#131146142
#131133252
#131127232
C13×#12972
#823913