Finite Group Databasebeta

← #15778075

Subgroups — #15778075

Order 3328.

456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123542C211yesmaximal, characteristic
2#13116475C212yesmaximal
3#13114638C212yesmaximal, complemented
4#13112959C211yesmaximal, characteristic, complemented
5C13×#1391C211yesmaximal, characteristic, complemented
6#11719533C2211yescharacteristic
7C2×#88202C2211yescharacteristic
8C22×#6094C411yescharacteristic, complemented
9C13×#410C2212yes—
10C13×#408C2211yescharacteristic
11#11718898C2212yes—
12#11718787C411yescharacteristic, complemented
13#11718783C411yescharacteristic, complemented
14#11718763C411yescharacteristic, complemented
15#11718658—22no—
16#11718391—22no—
17#11718390—22no—
18#11718125—22no—
19#11718064C414yescomplemented
20#11718063C414yescomplemented
21C2×C13×#41C2311yescharacteristic
22C22×C4×D13C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C13×#117—22no—
26#88202—42no—
27#88200—21no—
28#88192—21no—
29#88191C2×C412yes—
30#88189C2×C412yes—
31C4×C22⋊D13—22no—
32#88180C2×C411yescharacteristic
33C2×#6099—22no—
34C2×#6099C2×C411yescharacteristic
35C2×#6099D412yes—
36C22×#1055C2×C411yescharacteristic
37C22×#1055D412yes—
38C2×#6094—21no—
39C2×#6094—21no—
40C2×#6094—42no—
41C13×#99—22no—
42C13×#99C2×C414yes—
43C13×C22⋊C8—22no—
44#88076—22no—
45#88073C2×C414yes—
46#88060—22no—
47#88055—21no—
48#88054—22no—
49C8×Dic13—21no—
50#88043—42no—
51C4×#1055—42no—
52#12624—131nomaximal, Sylow
53C23×D13C4211yescharacteristic
54C13×#41—41no—
55C13×#41—41no—
56C2×Q8×C13#4111yescharacteristic
57C2×D4×C13C22×C412yes—
58C2×D4×C13#4111yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C2×C22⋊D13—22no—
62C22×Dic13C4211yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C13×M16—41no—
68C2×C8×C13—21no—
69C2×C8×C13—21no—
70C2×C8×C13—41no—
71C13×C4⋊C4—42no—
72C13×C22⋊C4—24no—
73C42×C13—42no—
74C22⋊Dic13—22no—
75C22⋊Dic13C4212yes—
76#6103—22no—
77C4⋊Dic13—21no—
78#6101—22no—
79C4×Dic13—21no—
80#6099—24no—
81#6099—41no—
82#6099—42no—
83#6099—42no—
84C2×#1055—22no—
85C2×#1055—22no—
86C2×#1055—22no—
87C2×#1055—42no—
88C2×#1055C22⋊C411yescharacteristic
89C2×#1055C22⋊C412yes—
90C2×#1055C22⋊C411yescharacteristic
91#6094—42no—
92#6094—42no—
93#2930—131no—
94#2120—132no—
95#1757—132no—
96#1392—131no—
97#1391D1311yescharacteristic, complemented
98C23×C13C2×C4211yescharacteristic
99C23×C13C4×D412yes—
100C22×D13—21no—
101C22×D13—41no—
102C22×D13—81no—
103Q8×C13—41no—
104D4×C13—42no—
105D4×C13—41no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—21no—
110C2×C4×C13—44no—
111C2×C4×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13#11711yescharacteristic
113C2×C4×C13C4×D412yes—
114C22⋊D13—82no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—41no—
118C4×D13—42no—
119C4×D13—41no—
120C4×D13—41no—
121C8×C13—41no—
122C8×C13—41no—
123#1055—21no—
124#1055—22no—
125#1055—44no—
126#1055#9912yes—
127C2×#131—131no—
128C22×M16—131no—
129#525—131no—
130#436—262no—
131#435—262no—
132#424—131no—
133#413—132no—
134#410C2×D1312yes—
135#408C2×D1311yescharacteristic
136#407—131no—
137#405—131no—
138#405—262no—
139#352—134no—
140AΣL(1,𝔽16)—134no—
141#344—262no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—42no—
145C22×C13—41no—
146C22×C13C4×C22⋊C411yescharacteristic
147C2×D13—41no—
148C2×D13—41no—
149C2×D13—41no—
150C2×D13—82no—
151C4×C13—22no—
152C4×C13—21no—
153C4×C13—84no—
154C4×C13C2×#9911yescharacteristic
155C4×C13#41011yescharacteristic
156Dic13—42no—
157Dic13—41no—
158C2×#41C22×D1311yescharacteristic
159C23×C4—131no—
160#131—522no—
161C2×M16—131no—
162C2×M16—132no—
163C2×M16—261no—
164C2×M16—261no—
165C2×M16—262no—
166C2×M16—522no—
167C2×M16C4×D1311yescharacteristic
168C22×C8—131no—
169C22×C8—132no—
170C22×C8C4×D1311yescharacteristic
171#123—132no—
172C22⋊Q8—261no—
173#121—261no—
174#120—132no—
175C4×D4—262no—
176#117—22no—
177#117—131no—
178C4⋊C8—262no—
179#101—262no—
180#100—134no—
181#99—22no—
182#99C4×D1314yes—
183C22⋊C8—22no—
184C22⋊C8—262no—
185#97—261no—
186#97—522no—
187C4×C8—261no—
188C4×C8—522no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13—41no—
192C2×C13C4×#9911yescharacteristic
193D13—81no—
194C24—131no—
195#41—41no—
196#41—41no—
197C2×Q8#613111yescharacteristic
198C2×D4—262no—
199C2×D4C2×C4×D1312yes—
200C2×D4#612911yescharacteristic
201C22×C4—131no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—521no—
205C22×C4—521no—
206C22×C4C2×C4×D1311yescharacteristic
207C22×C4D4×D1312yes—
208M16—41no—
209M16—264no—
210M16—522no—
211M16—522no—
212M16—521no—
213M16—522no—
214M16—522no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—131no—
219C2×C8—131no—
220C2×C8—132no—
221C2×C8—262no—
222C2×C8—262no—
223C2×C8—262no—
224C2×C8—522no—
225C4⋊C4—42no—
226C4⋊C4—261no—
227C4⋊C4—262no—
228C22⋊C4—24no—
229C22⋊C4—132no—
230C22⋊C4—262no—
231C22⋊C4—262no—
232C42—42no—
233C42—261no—
234C13#1262411yescharacteristic, complemented, Sylow
235C23—261no—
236C23—521no—
237C23—1041no—
238C23C42×D1311yescharacteristic
239C23#8813512yes—
240Q8—41no—
241D4—42no—
242D4—41no—
243D4—1042no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—44no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4C22⋊C4×D1311yescharacteristic
256C2×C4#8814611yescharacteristic
257C2×C4#8814712yes—
258C8—41no—
259C8—41no—
260C8—132no—
261C8—262no—
262C8—261no—
263C8—524no—
264C22—22no—
265C22—21no—
266C22—42no—
267C22—41no—
268C22—521no—
269C22—521no—
270C22—521no—
271C22—1042no—
272C22#1171832711yescharacteristic
273C4—22no—
274C4—21no—
275C4—84no—
276C4—522no—
277C4—521no—
278C4#1171840111yescharacteristic
279C4D13×#9911yescharacteristic
280C2—21no—
281C2—42no—
282C2—41no—
283C2—1041no—
284C2#1311462311yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC23×C13C2×C42
FrattiniC2×#41C22×D13
FittingC13×#1391C2
socleC2×C13C4×#99
prime radical#11719533C22
cosocleC2×C13×#41C23
hypercenter#1391D13
hypocenterC13#12624
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

Complements

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

NH ≅ G/Ntype
3. #13114638C2semidirect
4. #13112959C2semidirect
5. C13×#1391C2semidirect
8. C22×#6094C4semidirect
12. #11718787C4semidirect
13. #11718783C4semidirect
14. #11718763C4semidirect
19. #11718064C4semidirect
20. #11718063C4semidirect
97. #1391D13semidirect
234. C13#12624semidirect

Maximal subgroups

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

subgroupindex
#131235422
#131164752
#131146382
#131129592
C13×#13912
#1262413