Finite Group Databasebeta

← #15760669

Subgroups — #15760669

Order 3328.

554 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117439C211yesmaximal, characteristic, complemented
2#13114916C211yesmaximal, characteristic, complemented
3#13113365C212yesmaximal
4#13112689C212yesmaximal, complemented
5C13×#2504C211yesmaximal, characteristic
6C2×C13×#121C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#397—22no—
9C13×#390C412yescomplemented
10C13×#386—21no—
11C13×#386—21no—
12C13×#382C412yescomplemented
13C4×C13×C22⋊C4C2211yescharacteristic
14#11718873—21no—
15#11718872C2212yes—
16C4×C22⋊Dic13—21no—
17#11718868C2212yes—
18#11718642—24no—
19#11718129—24no—
20#11718122—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#121—22no—
27C13×#121—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13C2×C412yes—
38C2×C22⋊Dic13—22no—
39C2×C4⋊Dic13—22no—
40C2×C4×Dic13—22no—
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—21no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071D414yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9465—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13C2×D411yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—42no—
56C2×D4×C13—44no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—42no—
66C22×C4×C13—81no—
67C22×C4×C13—81no—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C22×Dic13—24no—
75C13×C4⋊C4—24no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—82no—
81C13×C22⋊C4—82no—
82C42×C13—42no—
83C22⋊Dic13—44no—
84C4⋊Dic13—82no—
85C4×Dic13—82no—
86#6099—44no—
87C2×#1055—42no—
88#2504D1311yescharacteristic
89#2313—131no—
90#1821—131no—
91#1510—132no—
92#1284—132no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—41no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#12011yescharacteristic
102C23×C13#12311yescharacteristic
103D4×C13—82no—
104D4×C13—82no—
105D4×C13—82no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C4×D412yes—
124C2×C4×C13#12112yes—
125C2×Dic13—44no—
126C2×Dic13—44no—
127C2×Dic13—44no—
128#1055—82no—
129C2×#121C2×D1311yescharacteristic
130C22×C4⋊C4C2×D1311yescharacteristic
131#407—132no—
132#397—22no—
133#390Dic1312yescomplemented
134#387—264no—
135#386—21no—
136#386—21no—
137#382Dic1312yescomplemented
138#381—132no—
139#380—261no—
140C4×C22⋊C4—261no—
141C4×C22⋊C4C2×D1311yescharacteristic
142#343—262no—
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—84no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13#38611yescharacteristic
157C22×C13#41012yes—
158C22×C13#45412yes—
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—42no—
162C4×C13—42no—
163C4×C13—82no—
164C4×C13—81no—
165Dic13—84no—
166C22×D4—21no—
167C22×D4C2×Dic1311yescharacteristic
168C23×C4C22⋊D1311yescharacteristic
169C23×C4C22⋊D1311yescharacteristic
170C23×C4C22×D1311yescharacteristic
171C2×M16—262no—
172#121—22no—
173#121—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—262no—
177C2×C4⋊C4C2×Dic1311yescharacteristic
178C2×C4⋊C4C2×Dic1312yes—
179C2×C4⋊C4C22⋊D1312yes—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—262no—
185C2×C42—262no—
186C2×C42C2×Dic1312yes—
187C22⋊C8—262no—
188C22⋊C8—262no—
189#95—22no—
190#95—22no—
191#95—21no—
192#95—134no—
193#95—262no—
194#95—262no—
195#95—262no—
196C2×C13—22no—
197C2×C13—22no—
198C2×C13—41no—
199C2×C13—161no—
200C2×C13#188811yescharacteristic
201C2×C13#189911yescharacteristic
202C2×C13#191111yescharacteristic
203C24—21no—
204C24C2×C22⋊D1311yescharacteristic
205C2×D4—22no—
206C2×D4—42no—
207C2×D4—44no—
208C2×D4—41no—
209C2×D4—41no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—264no—
220C22×C4C22⋊Dic1312yes—
221C22×C4C22⋊Dic1312yes—
222C22×C4D4×D1312yes—
223C22×C4#612912yes—
224C22×C4C22×Dic1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—524no—
227C2×C8—522no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—22no—
231C4⋊C4—1042no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C22⋊C4—524no—
237C42—42no—
238C42—1042no—
239C13#946511yescharacteristic, complemented, Sylow
240C23—22no—
241C23—22no—
242C23—41no—
243C23—42no—
244C23—42no—
245C23—41no—
246C23—42no—
247C23#8818911yescharacteristic
248C23#8819111yescharacteristic
249C23C2×C22⋊Dic1311yescharacteristic
250D4—82no—
251D4—82no—
252D4—82no—
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—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—524no—
271C2×C4—524no—
272C2×C4—524no—
273C2×C4D4×Dic1312yes—
274C2×C4#8819312yes—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—84no—
285C22—81no—
286C22—81no—
287C22—81no—
288C22#1171872312yes—
289C22#1171888111yescharacteristic
290C22#1171890112yes—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—82no—
296C4—81no—
297C4—1044no—
298C2—22no—
299C2—22no—
300C2—41no—
301C2—161no—
302C2#1311524011yescharacteristic
303C2#1311529511yescharacteristic
304C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2504C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2504D13
hypocenterC13#9465
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2504

Complements

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

NH ≅ G/Ntype
1. #13117439C2semidirect
2. #13114916C2semidirect
4. #13112689C2semidirect
9. C13×#390C4semidirect
12. C13×#382C4semidirect
133. #390Dic13semidirect
137. #382Dic13semidirect
239. C13#9465semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131149162
#131133652
#131126892
C13×#25042
#946513