Finite Group Databasebeta

← #15758950

Subgroups — #15758950

Order 3328.

624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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#13123400C211yesmaximal, characteristic, complemented
2#13120586C211yesmaximal, characteristic
3#13113503C212yesmaximal, complemented
4#13112695C212yesmaximal, complemented
5C13×#1458C211yesmaximal, characteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C2×#88184—21no—
8C22×#6099—21no—
9C2×#88128C2211yescharacteristic
10C13×#431C2212yes—
11#11718660—24no—
12#11718652—21no—
13#11718652C412yes—
14#11718621—21no—
15#11718621C412yes—
16#11718600—21no—
17#11718597C2211yescharacteristic
18#11718585—21no—
19#11718585C2212yes—
20C13×#324—21no—
21C13×#323—21no—
22#11718077—24no—
23C23×C4×C13D411yescharacteristic
24C22×C22⋊D13—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52C2×C412yes—
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36#88184—42no—
37#88184—42no—
38C2×#6103—22no—
39C2×#6103—22no—
40C2×#6103—22no—
41C2×C4⋊Dic13—21no—
42C2×#6099—22no—
43C2×#6099—22no—
44C2×#6099—42no—
45C2×#6099—42no—
46C22×#1055—22no—
47#88128—22no—
48#88128—22no—
49C13×C4⋊C8—22no—
50C13×C22⋊C8—22no—
51C4×C8×C13—22no—
52#88071—21no—
53#88071C2×C412yes—
54C4⋊#1055—24no—
55C4⋊#1055—22no—
56C4⋊#1055D414yescomplemented
57#9197—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C23×D13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13D812yes—
68C22×C4×C13SD1612yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C2×C22⋊D13—44no—
73C2×C22⋊D13—82no—
74C2×C22⋊D13—82no—
75C22×Dic13—22no—
76C2×D52—24no—
77C2×D52—41no—
78C2×D52—42no—
79C2×D52—41no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—82no—
85C2×D52—82no—
86C2×C8×C13—42no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13C2×D412yes—
94C42×C13#4112yes—
95#6103—44no—
96#6103—82no—
97#6103—82no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6099—44no—
101#6099—42no—
102#6099—42no—
103C2×#1055—24no—
104C2×#1055—44no—
105#2905—131no—
106#2619—131no—
107#1545—132no—
108#1458D1311yescharacteristic, complemented
109#1286—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#10212yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—42no—
121C22×D13—42no—
122C22×D13—42no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13#10212yes—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12112yes—
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×D811yescharacteristic
141C2×C4×C13C2×SD1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C22⋊D13—88no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148D52—84no—
149D52—84no—
150D52—81no—
151D52—81no—
152D52—81no—
153D52—81no—
154C8×C13—82no—
155#1055—44no—
156C22×M16—261no—
157C2×#127—131no—
158C2×#121—261no—
159C2×#117C2×D1311yescharacteristic
160#431C2×D1312yes—
161#424—264no—
162#423—132no—
163#423—261no—
164#394—132no—
165#394—261no—
166#392—132no—
167#392—261no—
168#390—261no—
169#382—131no—
170#331—264no—
171#324—21no—
172#323—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—81no—
180C22×C13#38611yescharacteristic
181C22×C13C2×#10211yescharacteristic
182C22×C13#41711yescharacteristic
183C2×D13—82no—
184C2×D13—82no—
185C2×D13—82no—
186C2×D13—82no—
187C2×D13—82no—
188C2×D13—82no—
189C2×D13—82no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—22no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13#44711yescharacteristic
196C4×C13#44811yescharacteristic
197C4×C13#48011yescharacteristic
198C4×C13#48111yescharacteristic
199Dic13—82no—
200C22×D4—132no—
201C22×D4—262no—
202C22×D4—261no—
203C22×D4—261no—
204C23×C4D5211yescharacteristic
205C2×M16—262no—
206C2×M16—262no—
207C2×M16—522no—
208C2×M16—522no—
209C22×C8—262no—
210#127—262no—
211#127—262no—
212#121—522no—
213#121—522no—
214#117—22no—
215#117—22no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4C4×D1311yescharacteristic
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C22⋊C4—262no—
220C2×C22⋊C4—262no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4C4×D1311yescharacteristic
223C2×C22⋊C4C22⋊D1311yescharacteristic
224C2×C42D5211yescharacteristic
225C2×C42C22×D1311yescharacteristic
226C4⋊C8—22no—
227C4⋊C8—134no—
228C4⋊C8—264no—
229C4⋊C8—262no—
230C22⋊C8—22no—
231C4×C8—22no—
232#95—132no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—42no—
237C2×C13#187411yescharacteristic
238C2×C13#191011yescharacteristic
239C2×C13#191411yescharacteristic
240D13—162no—
241C24—262no—
242C24#610311yescharacteristic
243C2×D4—264no—
244C2×D4—524no—
245C2×D4—521no—
246C2×D4—521no—
247C2×D4—521no—
248C2×D4—521no—
249C2×D4—521no—
250C2×D4—521no—
251C2×D4—522no—
252C2×D4—1042no—
253C2×D4—1042no—
254C2×D4—1042no—
255C2×D4—1042no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—262no—
261C22×C4#609512yes—
262C22×C4D10412yes—
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4C2×C4×D1311yescharacteristic
267C22×C4C2×D5211yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269M16—524no—
270M16—522no—
271M16—522no—
272C2×C8—42no—
273C2×C8—264no—
274C2×C8—524no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—524no—
282C22⋊C4—1042no—
283C22⋊C4—1042no—
284C42—21no—
285C42—21no—
286C42D4×D1312yes—
287C42#612912yes—
288C13#919711yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—522no—
294C23—522no—
295C23—522no—
296C23—522no—
297C23—522no—
298C23—522no—
299C23—522no—
300C23#8806112yes—
301C23C2×#610311yescharacteristic
302D4—1044no—
303D4—1044no—
304D4—1048no—
305D4—1041no—
306D4—1041no—
307D4—1041no—
308D4—1041no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—522no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4#8806112yes—
325C2×C4#8813512yes—
326C2×C4#8813611yescharacteristic
327C2×C4#8814011yescharacteristic
328C2×C4C2×#609511yescharacteristic
329C2×C4C2×D10411yescharacteristic
330C2×C4#8816211yescharacteristic
331C2×C4#8816311yescharacteristic
332C2×C4#8819312yes—
333C8—82no—
334C8—524no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—1042no—
343C22—1042no—
344C22—1042no—
345C22—1042no—
346C22—1042no—
347C22—1042no—
348C22—1042no—
349C22#1171861911yescharacteristic
350C22C2×#8806111yescharacteristic
351C22#1171879411yescharacteristic
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—1042no—
358C4#1171839311yescharacteristic
359C4#1171839611yescharacteristic
360C4#1171839711yescharacteristic
361C4#1171839911yescharacteristic
362C2—21no—
363C2—21no—
364C2—42no—
365C2—2082no—
366C2#1311515111yescharacteristic
367C2#1311536111yescharacteristic
368C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1458C2
socleC22×C13#386
prime radical#13120586C2
cosocleC2×C42×C13C23
hypercenter#1458D13
hypocenterC13#9197
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
1. #13123400C2semidirect
3. #13113503C2semidirect
4. #13112695C2semidirect
5. C13×#1458C2semidirect
56. C4⋊#1055D4semidirect
108. #1458D13semidirect
288. C13#9197semidirect

Maximal subgroups

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

subgroupindex
#131234002
#131205862
#131135032
#131126952
C13×#14582
#919713