Finite Group Databasebeta

← #15760633

Subgroups — #15760633

Order 3328.

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

normal subgroups only

This group has 536 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#13119835C211yesmaximal, characteristic
2#13113549C212yesmaximal
3#13113180C211yesmaximal, characteristic, complemented
4#13112693C212yesmaximal, complemented
5C13×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201C412yes—
8C2×#88128C2211yescharacteristic
9C13×#446—24no—
10C13×#432—21no—
11C13×#432C2212yes—
12C13×#431—21no—
13#11718652—21no—
14#11718652—21no—
15#11718649C412yes—
16#11718600—21no—
17#11718600—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2212yes—
20#11718120—21no—
21#11718120—21no—
22#11718077—24no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D52—21no—
25C22×D52—21no—
26C22×D52C2×C412yes—
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35#88201—44no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×#6103—22no—
40C2×C4⋊Dic13—21no—
41C2×C4×Dic13C2×C412yes—
42#88128—22no—
43#88128—22no—
44C13×C4⋊C8—22no—
45C13×C4⋊C8—22no—
46C13×C4⋊C8D414yes—
47C13×C22⋊C8—22no—
48C13×#97—22no—
49C13×#97—22no—
50C4×C8×C13—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54#88043—22no—
55#9458—131nomaximal, Sylow
56C23×D13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C2×D52—24no—
69C2×D52—42no—
70C2×D52—42no—
71C2×D52—42no—
72C2×D52—42no—
73C2×D52—41no—
74C2×D52—42no—
75C2×D52—41no—
76C2×D52—82no—
77C2×C8×C13—24no—
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—
87#6103—44no—
88#6103—44no—
89#6103—82no—
90#6103—82no—
91C4⋊Dic13—42no—
92C4×Dic13—42no—
93C2×#1055—42no—
94#2983D1311yescharacteristic, complemented
95#2548—131no—
96#1555—132no—
97#1467—131no—
98#1285—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—42no—
105C22×D13—42no—
106C22×D13—42no—
107Q8×C13—44no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#10012yes—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12311yescharacteristic
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129D52—82no—
130D52—84no—
131D52—84no—
132D52—82no—
133C8×C13—44no—
134#1055—82no—
135C2×#127—131no—
136C2×#124—132no—
137C2×C4×Q8C2×D1311yescharacteristic
138#446—24no—
139#432—21no—
140#432—132no—
141#432C2×D1312yes—
142#431—21no—
143#394—261no—
144#394—261no—
145#390—132no—
146#390—261no—
147#390—261no—
148C4×C4⋊C4—131no—
149#331—264no—
150#324—261no—
151#324—261no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13#38611yescharacteristic
155C22×C13C2×#10011yescharacteristic
156C22×C13#41311yescharacteristic
157C2×D13—82no—
158C2×D13—82no—
159C2×D13—82no—
160C2×D13—82no—
161C2×D13—82no—
162C2×D13—82no—
163C2×D13—82no—
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13#45412yes—
172Dic13—82no—
173C22×Q8C4×D1311yescharacteristic
174C22×D4—132no—
175C22×D4—261no—
176C22×D4—261no—
177#127—262no—
178#127—262no—
179#124—524no—
180C4×Q8—22no—
181C4×Q8—22no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4C4×D1311yescharacteristic
184C2×C4⋊C4D5211yescharacteristic
185C2×C4⋊C4D5211yescharacteristic
186C2×C22⋊C4—262no—
187C2×C22⋊C4—262no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—262no—
190C2×C42—132no—
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C2×C42C22×D1311yescharacteristic
194C4⋊C8—22no—
195C4⋊C8—22no—
196C4⋊C8—262no—
197C4⋊C8C22⋊D1314yes—
198C22⋊C8—22no—
199C22⋊C8—262no—
200#97—22no—
201#97—22no—
202#97—262no—
203C4×C8—22no—
204#95—261no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#188811yescharacteristic
208C2×C13#190011yescharacteristic
209C2×C13#191011yescharacteristic
210D13—162no—
211C24—262no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×D4—264no—
216C2×D4—522no—
217C2×D4—522no—
218C2×D4—522no—
219C2×D4—522no—
220C2×D4—521no—
221C2×D4—522no—
222C2×D4—521no—
223C2×D4—1042no—
224C22×C4—262no—
225C22×C4#610311yescharacteristic
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4C2×C4×D1311yescharacteristic
230C22×C4C2×D5211yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—24no—
233C2×C8—522no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—522no—
238C22⋊C4—524no—
239C22⋊C4—524no—
240C22⋊C4—1042no—
241C22⋊C4—1042no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—522no—
247C42#612712yes—
248C42C2×C22⋊D1312yes—
249C13#945811yescharacteristic, complemented, Sylow
250C23—522no—
251C23—522no—
252C23—522no—
253C23—522no—
254C23—522no—
255C23—522no—
256C23—522no—
257C23C2×#610311yescharacteristic
258Q8—44no—
259D4—1044no—
260D4—1042no—
261D4—1044no—
262D4—1042no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4#8806312yes—
280C2×C4C4×C22⋊D1312yes—
281C2×C4#8818311yescharacteristic
282C2×C4#8818412yes—
283C2×C4#8820711yescharacteristic
284C8—44no—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22—1042no—
289C22—1042no—
290C22—1042no—
291C22—1042no—
292C22—1042no—
293C22—1042no—
294C22—1042no—
295C22C2×#8806311yescharacteristic
296C22#1171879311yescharacteristic
297C22#1171887411yescharacteristic
298C4—21no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—1042no—
306C4#1171890612yes—
307C2—21no—
308C2—21no—
309C2—2082no—
310C2#1311523911yescharacteristic
311C2#1311529911yescharacteristic
312C2#1311536311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9458
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
3. #13113180C2semidirect
4. #13112693C2semidirect
5. C13×#2983C2semidirect
94. #2983D13semidirect
249. C13#9458semidirect

Maximal subgroups

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

subgroupindex
#131198352
#131135492
#131131802
#131126932
C13×#29832
#945813