Finite Group Databasebeta

← #15760591

Subgroups — #15760591

Order 3328.

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

normal subgroups only

This group has 424 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#13123921C211yesmaximal, characteristic
2#13120023C211yesmaximal, characteristic
3#13113462C212yesmaximal
4#13112693C212yesmaximal
5C13×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C2211yescharacteristic
8C13×#432C2212yes—
9#11718891C411yescharacteristic
10#11718891C411yescharacteristic
11#11718685—24no—
12#11718645—21no—
13#11718645—21no—
14#11718638C411yescharacteristic
15#11718637C411yescharacteristic
16C4×C4⋊Dic13C2211yescharacteristic
17#11718594—21no—
18#11718594—21no—
19#11718587—21no—
20#11718587C2212yes—
21#11718586—21no—
22C13×#324—21no—
23C13×#324—21no—
24#11718057—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43#88124—22no—
44#88124—22no—
45C13×C4⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#97—22no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59#88043—22no—
60#88043D414yes—
61C4×#1055—22no—
62#9450—131nomaximal, Sylow
63C2×Q8×C13—22no—
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×C8×C13—42no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13C2×D412yes—
86C42×C13#4112yes—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89C4⋊Dic13—42no—
90#6101—42no—
91#6101—42no—
92#6101—41no—
93#6101—42no—
94#6101—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C2×#1055—24no—
98#2983—131no—
99#2565—131no—
100#1534—132no—
101#1467D1311yescharacteristic
102#1285—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—44no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13#10112yes—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13#12311yescharacteristic
123C2×Dic13—22no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C8×C13—82no—
135#1055—44no—
136C2×#125—131no—
137C2×C4×Q8C2×D1311yescharacteristic
138#446—264no—
139#432—132no—
140#432—261no—
141#432C2×D1312yes—
142#431—261no—
143#398—261no—
144#398—261no—
145#391—131no—
146#391—131no—
147#387—261no—
148#387—261no—
149#384—131no—
150#382—131no—
151C4×C4⋊C4—131no—
152#330—264no—
153#324—21no—
154#324—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#38611yescharacteristic
158C22×C13C2×#10111yescharacteristic
159C22×C13#41311yescharacteristic
160C4×C13—22no—
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168Dic13—42no—
169Dic13—81no—
170Dic13—81no—
171Dic13—81no—
172C22×Q8C4×D1311yescharacteristic
173#125—262no—
174#125—262no—
175C4×Q8—22no—
176C4×Q8—22no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22⋊D1311yescharacteristic
187C2×C42—131no—
188C2×C42—131no—
189C2×C42D5211yescharacteristic
190C2×C42D5211yescharacteristic
191C2×C42C22×D1311yescharacteristic
192C4⋊C8—22no—
193C4⋊C8—262no—
194C4⋊C8—262no—
195C4⋊C8—262no—
196C22⋊C8—22no—
197C22⋊C8—262no—
198#97—22no—
199#97—134no—
200#97—262no—
201C4×C8—262no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13#188411yescharacteristic
212C2×C13#190111yescharacteristic
213C2×C13#191211yescharacteristic
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—41no—
217C22×C4—261no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×D5211yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C2×C8—42no—
229C2×C8—264no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—262no—
234C4⋊C4—262no—
235C4⋊C4—522no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C4⋊C4—522no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—521no—
246C42—521no—
247C42D4×D1312yes—
248C42#612912yes—
249C13#945011yescharacteristic, complemented, Sylow
250C23C2×#610311yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—262no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—522no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4#8806412yes—
277C2×C4#8813512yes—
278C2×C4#8813611yescharacteristic
279C2×C4#8814011yescharacteristic
280C2×C4#8819312yes—
281C8—82no—
282C8—524no—
283C22—21no—
284C22—21no—
285C22#1171861911yescharacteristic
286C22#1171879311yescharacteristic
287C22C2×#8806411yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—522no—
297C4—1041no—
298C4—1041no—
299C4—1041no—
300C2—21no—
301C2—21no—
302C2#1311521711yescharacteristic
303C2#1311530211yescharacteristic
304C2#1311537111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1467C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1467D13
hypocenterC13#9450
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
249. C13#9450semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131200232
#131134622
#131126932
C13×#14672
#945013