Finite Group Databasebeta

← #15758957

Subgroups — #15758957

Order 3328.

578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 115 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#13120586C211yesmaximal, characteristic
2#13113505C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic, complemented
4#13112696C212yesmaximal, complemented
5C13×#2921C211yesmaximal, characteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C2×#88184—21no—
8C2×#88128C2211yescharacteristic
9C13×#433—24no—
10C13×#423C2212yes—
11C13×#407—21no—
12C4×C13×M16—21no—
13#11718652—21no—
14#11718652C412yes—
15#11718621—21no—
16#11718621C412yes—
17#11718600—21no—
18#11718597C2211yescharacteristic
19#11718586C2212yes—
20#11718120—21no—
21#11718117—21no—
22#11718077—24no—
23C23×C4×C13D411yescharacteristic
24C22×C22⋊D13—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52C2×C412yes—
28C2×C13×M16—22no—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13C2311yescharacteristic
37#88184—44no—
38C2×#6103—22no—
39C2×#6103—22no—
40C2×#6103—22no—
41C2×C4⋊Dic13—21no—
42#88128—22no—
43#88128—22no—
44C13×C4⋊C8—22no—
45C13×C4⋊C8D414yescomplemented
46C13×C22⋊C8—24no—
47C13×#97—22no—
48C4×C8×C13—22no—
49#88071—21no—
50#88071C2×C412yes—
51C22⋊#1055—22no—
52C4⋊#1055—22no—
53C4×#1055—22no—
54#9198—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C23×D13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C2×C22⋊D13—44no—
68C2×C22⋊D13—82no—
69C2×C22⋊D13—82no—
70C22×Dic13—22no—
71C2×D52—24no—
72C2×D52—41no—
73C2×D52—42no—
74C2×D52—41no—
75C2×D52—42no—
76C2×D52—42no—
77C2×D52—82no—
78C2×D52—82no—
79C13×M16—42no—
80C13×M16—42no—
81C2×C8×C13—24no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13C2×D412yes—
89C42×C13#4112yes—
90#6103—44no—
91#6103—82no—
92#6103—82no—
93C4⋊Dic13—42no—
94C2×#1055—42no—
95#2921D1311yescharacteristic, complemented
96#2619—131no—
97#1545—132no—
98#1458—131no—
99#1286—132no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106C22×D13—42no—
107C22×D13—42no—
108C22×D13—42no—
109C22×D13—42no—
110C22×D13—42no—
111C22×D13—42no—
112C22×D13—42no—
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—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12011yescharacteristic
126C2×C4×C13#12112yes—
127C2×C4×C13#12311yescharacteristic
128C2×C4×C13#13512yes—
129C2×C4×C13AGL(1,ℤ/8)12yes—
130C22⋊D13—88no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134D52—84no—
135D52—84no—
136D52—82no—
137D52—82no—
138C8×C13—44no—
139#1055—82no—
140C2×#127—131no—
141C2×#121—261no—
142C2×#117C2×D1311yescharacteristic
143#433—24no—
144#431—132no—
145#423C2×D1312yes—
146#407—21no—
147C4×M16—21no—
148#394—132no—
149#394—261no—
150#392—132no—
151#392—261no—
152#390—261no—
153#382—131no—
154#331—264no—
155#324—261no—
156#323—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—81no—
164C22×C13#38611yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#41811yescharacteristic
167C2×D13—82no—
168C2×D13—82no—
169C2×D13—82no—
170C2×D13—82no—
171C2×D13—82no—
172C2×D13—82no—
173C2×D13—82no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13#44912yes—
180C4×C13#48212yes—
181Dic13—82no—
182C22×D4—132no—
183C22×D4—262no—
184C22×D4—261no—
185C22×D4—261no—
186C23×C4C22⋊D1311yescharacteristic
187C2×M16—22no—
188#127—262no—
189#127—262no—
190#121—524no—
191#117—22no—
192#117—22no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4C4×D1311yescharacteristic
195C2×C4⋊C4D5211yescharacteristic
196C2×C22⋊C4—262no—
197C2×C22⋊C4—262no—
198C2×C22⋊C4—262no—
199C2×C22⋊C4C4×D1311yescharacteristic
200C2×C22⋊C4D5211yescharacteristic
201C2×C42C22⋊D1311yescharacteristic
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—22no—
204C4⋊C8—262no—
205C4⋊C8C22⋊D1314yescomplemented
206C22⋊C8—24no—
207C22⋊C8—262no—
208#97—22no—
209C4×C8—22no—
210C4×C8—262no—
211#95—132no—
212#95—261no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—81no—
216C2×C13#187511yescharacteristic
217C2×C13#191011yescharacteristic
218C2×C13#191411yescharacteristic
219D13—162no—
220C24—262no—
221C24#610311yescharacteristic
222C2×D4—264no—
223C2×D4—524no—
224C2×D4—521no—
225C2×D4—522no—
226C2×D4—522no—
227C2×D4—522no—
228C2×D4—521no—
229C2×D4—1042no—
230C2×D4—1042no—
231C2×D4—1042no—
232C2×D4—1042no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—262no—
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4C2×C4×D1311yescharacteristic
242C22×C4C2×D5211yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244M16—42no—
245M16—42no—
246C2×C8—24no—
247C2×C8—522no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—522no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—524no—
254C22⋊C4—1042no—
255C22⋊C4—1042no—
256C42—21no—
257C42—21no—
258C42#612712yes—
259C42C2×C22⋊D1312yes—
260C13#919811yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—522no—
267C23—522no—
268C23—522no—
269C23—522no—
270C23—522no—
271C23—522no—
272C23—522no—
273C23C2×#610311yescharacteristic
274D4—1044no—
275D4—1044no—
276D4—1048no—
277D4—1042no—
278D4—1042no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4C4×C22⋊D1312yes—
294C2×C4#8818311yescharacteristic
295C2×C4#8818412yes—
296C2×C4#8820312yes—
297C2×C4#8820412yes—
298C2×C4#8820711yescharacteristic
299C8—44no—
300C8—1042no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—1042no—
309C22—1042no—
310C22—1042no—
311C22—1042no—
312C22—1042no—
313C22—1042no—
314C22—1042no—
315C22#1171866211yescharacteristic
316C22#1171866311yescharacteristic
317C22#1171887411yescharacteristic
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1042no—
324C4#1171866412yes—
325C4#1171889912yes—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—2082no—
330C2#1311515811yescharacteristic
331C2#1311536311yescharacteristic
332C2#1311538311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2921C2
socleC22×C13#386
prime radical#13120586C2
cosocleC2×C42×C13C23
hypercenter#2921D13
hypocenterC13#9198
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #13113505C2semidirect
3. #13113150C2semidirect
4. #13112696C2semidirect
5. C13×#2921C2semidirect
45. C13×C4⋊C8D4semidirect
95. #2921D13semidirect
205. C4⋊C8C22⋊D13semidirect
260. C13#9198semidirect

Maximal subgroups

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

subgroupindex
#131205862
#131135052
#131131502
#131126962
C13×#29212
#919813