Finite Group Databasebeta

← #14739006

Subgroups — #14739006

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic, complemented
4#13068055C214yesmaximal, complemented
5#13068003C214yesmaximal, complemented
6#13067390C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C2×C11×#461C211yesmaximal, characteristic, complemented
10C22×C11×SD16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66985—21no—
14#10623008C2211yescharacteristic
15C11×#461—22no—
16C11×#461C2214yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19C2×C22⋊(C11⋊C8)—22no—
20#10622701C2212yescomplemented
21#10622700—22no—
22#10622691C2212yescomplemented
23#10622632C2212yes—
24#10622629—22no—
25#10622628C2212yes—
26D4×C11⋊C8—22no—
27D4×C11⋊C8C2214yes—
28#10622580—22no—
29#10622579—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622185C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622117C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×#4339—21no—
41C2×C11×SD16—24no—
42C2×C11×SD16—44no—
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11D412yes—
51C4×D4×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4324—22no—
58#66985—44no—
59C2×#4323—22no—
60#66983—21no—
61#66983—21no—
62C2×#4318—21no—
63C22×C11⋊C8—24no—
64#66928—21no—
65#66927C2311yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68#66922C2311yescharacteristic
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#103—24no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—24no—
74C22⋊(C11⋊C8)D412yes—
75#66874—22no—
76#66873—22no—
77#66873—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8C2312yes—
85#19392—111nomaximal, Sylow
86C24×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×D4×C11—21no—
92C2×D4×C11—22no—
93C2×D4×C11D814yes—
94C2×D4×C11C2×D412yes—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11—82no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—41no—
104#4339—42no—
105#4339—42no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×C4×D11—41no—
110C2×Dic22—21no—
111C11×SD16—48no—
112C2×C8×C11—22no—
113C2×C8×C11—42no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4C2×D412yes—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—22no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126#4324—44no—
127#4323—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132#4318—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—84no—
136C2×C11⋊C8C2×D414yes—
137#3226—111no—
138#3036—111no—
139C2×#461D1111yescharacteristic, complemented
140#2972—111no—
141#1681—114no—
142#1673—114no—
143#1571—111no—
144#1546—111no—
145#1540—111no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11#12111yescharacteristic
151C22×D11—41no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—82no—
155D4×C11—22no—
156D4×C11—24no—
157D4×C11C2×D814yes—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—81no—
165C2×C4×C11—82no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11C2×D812yes—
170C2×C4×C11#13512yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C22⋊D11—82no—
175C2×Dic11—41no—
176D44—41no—
177D44—41no—
178D44—42no—
179D44—81no—
180C4×D11—82no—
181Dic22—41no—
182Dic22—41no—
183C8×C11—42no—
184C11⋊C8—24no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—221no—
188C22×SD16—21no—
189#532—111no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191C2×C4×D4C2×D1111yescharacteristic
192#500—112no—
193#486—112no—
194#480—222no—
195#474—222no—
196#463—222no—
197#461—22no—
198#461—112no—
199#461C2×D1114yes—
200#459—112no—
201C8×D4—114no—
202C8×D4—222no—
203#431—111no—
204#431—111no—
205#423—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207#417—221no—
208C2×#103—21no—
209C2×C22⋊C8—222no—
210#335—114no—
211#332—114no—
212#332—112no—
213#331—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—24no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—84no—
220C22×C11#46612yes—
221C22×C11C2×#12111yescharacteristic
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11#46612yes—
231C4×C11C22×D811yescharacteristic
232C4×C11C2×#13511yescharacteristic
233C4×C11#57712yes—
234Dic11—81no—
235C2×#41—221no—
236C22×Q8—21no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239AGL(1,ℤ/8)—444no—
240C2×SD16—24no—
241C2×SD16—44no—
242C2×SD16—222no—
243C2×D8—222no—
244C2×M16—221no—
245C22×C8—21no—
246C22×C8—224no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—111no—
251C4⋊Q8C22×D1112yes—
252#127—111no—
253#124—221no—
254#121—221no—
255#121—221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4C22⋊D1112yes—
261C4×D4C22×D1112yes—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C22⋊D1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8—112no—
271C4⋊C8—112no—
272C4⋊C8—221no—
273C4⋊C8C22×D1112yes—
274#103—24no—
275#103—222no—
276#102—224no—
277#102—222no—
278C22⋊C8—112no—
279C22⋊C8—224no—
280C22⋊C8—221no—
281C4×C8—112no—
282C4×C8—221no—
283C2×C11—22no—
284C2×C11—44no—
285C2×C11#304211yescharacteristic
286C2×C11C2×#46611yescharacteristic
287C2×C11#306911yescharacteristic
288D11—161no—
289C24—21no—
290#41—442no—
291#41—442no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—42no—
295C2×Q8—42no—
296C2×Q8—221no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4#432314yes—
304C2×D4C2×C22⋊D1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4—441no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—48no—
315SD16—444no—
316D8—444no—
317M16—442no—
318C2×C8—22no—
319C2×C8—42no—
320C2×C8—114no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—884no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4C2×C22⋊D1112yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—22no—
342C23—24no—
343C23—81no—
344C23—81no—
345C23—441no—
346C23#6699211yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—82no—
350Q8—441no—
351Q8—441no—
352D4—22no—
353D4—24no—
354D4—442no—
355D4—441no—
356D4—441no—
357D4—881no—
358D4—882no—
359D4C2×#432314yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—441no—
369C2×C4—882no—
370C2×C4C2×#432312yes—
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C2×C4#6699211yescharacteristic
374C2×C4#6700312yes—
375C2×C4C2×D4×D1111yescharacteristic
376C2×C4C2×#434111yescharacteristic
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—42no—
379C8—224no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062265112yes—
392C22C2×#6699211yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—82no—
398C4—881no—
399C4#1062265112yes—
400C4#1062329312yes—
401C4C22×#432311yescharacteristic
402C4C2×#6700311yescharacteristic
403C2—22no—
404C2—44no—
405C2—1761no—
406C2#1307812511yescharacteristic
407C2C2×#1062265111yescharacteristic
408C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#461C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenterC2×#461D11
hypocenterC11#19392
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13077640C2semidirect
4. #13068055C2semidirect
5. #13068003C2semidirect
6. #13067390C2semidirect
7. #13067288C2semidirect
8. #13067266C2semidirect
9. C2×C11×#461C2semidirect
20. #10622701C22semidirect
22. #10622691C22semidirect
33. #10622185C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622117C22semidirect
139. C2×#461D11semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780802
#130776402
#130680552
#130680032
#130673902
#130672882
#130672662
C2×C11×#4612
#1939211