Finite Group Databasebeta

← #14739002

Subgroups — #14739002

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079741C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13077640C211yesmaximal, characteristic, complemented
4#13068023C214yesmaximal, complemented
5#13067989C214yesmaximal, complemented
6#13067388C211yesmaximal, characteristic, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3036C211yesmaximal, characteristic
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#532C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#463—22no—
15C11×#461C2212yes—
16C11×#459C2212yes—
17C11×#423C2211yescharacteristic
18C11×#417—21no—
19C2×#66896—21no—
20C2×C22⋊(C11⋊C8)—22no—
21#10622692C2212yescomplemented
22#10622683C2212yescomplemented
23#10622647—22no—
24D4×C11⋊C8—22no—
25D4×C11⋊C8C2214yes—
26#10622621—22no—
27#10622621—22no—
28#10622621C2214yes—
29C2×#66872—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yescomplemented
34#10622182C2212yescomplemented
35#10622119C2214yescomplemented
36#10622118C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C22×Dic22—21no—
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—22no—
43C2×C11×D8—22no—
44C2×C11×M16—21no—
45C11×C4⋊Q8C2311yescharacteristic
46C11×#127C2311yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11D412yes—
55C4×D4×C11C2312yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—24no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×#103—22no—
70C11×#102—22no—
71#66896—24no—
72#66896—24no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)D412yes—
76#66872—24no—
77#66872—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19391—111nomaximal, Sylow
85C24×C11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11SD1614yes—
96C2×D4×C11C2×D412yes—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—41no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C11×SD16—44no—
110C11×D8—44no—
111C11×M16—42no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—84no—
133C2×C11⋊C8C2×D414yes—
134#3227—111no—
135C2×#476—111no—
136#3036D1111yescharacteristic
137#2972—111no—
138#1677—114no—
139#1671—114no—
140#1570—111no—
141#1548—111no—
142#1540—111no—
143C23×C11—22no—
144C23×C11—24no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149Q8×C11—41no—
150Q8×C11—41no—
151D4×C11—22no—
152D4×C11—24no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—42no—
156D4×C11—81no—
157D4×C11—82no—
158D4×C11C2×SD1614yes—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—44no—
163C2×C4×C11—41no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11—82no—
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11C2×SD1612yes—
171C2×C4×C11#13512yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×Dic11—42no—
176C2×Dic11—82no—
177Dic22—82no—
178Dic22—82no—
179C8×C11—42no—
180C11⋊C8—24no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C2×AGL(1,ℤ/8)—21no—
184#532C2×D1111yescharacteristic
185C2×C4⋊Q8—111no—
186C2×C4×D4C2×D1111yescharacteristic
187#498—112no—
188#486—112no—
189#481—222no—
190#476—114no—
191#476—222no—
192#476—222no—
193#463—22no—
194#461C2×D1112yes—
195#459C2×D1112yes—
196C8×D4—114no—
197C8×D4—222no—
198#431—111no—
199#431—111no—
200C2×#106—221no—
201#423C2×D1111yescharacteristic
202C2×C4⋊C8—111no—
203#417—21no—
204C2×#102—221no—
205C2×C22⋊C8—222no—
206#334—114no—
207#333—114no—
208#332—112no—
209#331—112no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—24no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—84no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#46512yes—
220C22×C11C2×#12111yescharacteristic
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—81no—
226C4×C11#46512yes—
227C4×C11C22×SD1611yescharacteristic
228C4×C11C2×#13511yescharacteristic
229C4×C11#57712yes—
230Dic11—82no—
231C2×#41—21no—
232C22×Q8—221no—
233C22×D4C22⋊D1111yescharacteristic
234C23×C4—21no—
235AGL(1,ℤ/8)—44no—
236C2×SD16—22no—
237C2×D8—22no—
238C2×M16—21no—
239C22×C8—224no—
240C22×C8—221no—
241C4⋊Q8—112no—
242C4⋊Q8—221no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8C22×D1111yescharacteristic
246#127C22×D1111yescharacteristic
247#124—21no—
248#121—21no—
249#121—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4C22⋊D1112yes—
255C4×D4C22×D1112yes—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#106—224no—
262#106—224no—
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269#103—22no—
270#102—22no—
271#102—224no—
272#102—224no—
273C22⋊C8—112no—
274C22⋊C8—224no—
275C22⋊C8—221no—
276C4×C8—112no—
277C4×C8—221no—
278C2×C11—22no—
279C2×C11—44no—
280C2×C11—161no—
281C2×C11#304211yescharacteristic
282C2×C11C2×#46511yescharacteristic
283C2×C11#306811yescharacteristic
284C24—21no—
285#41—42no—
286#41—42no—
287C2×Q8—21no—
288C2×Q8—222no—
289C2×Q8—441no—
290C2×Q8—882no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4#432414yes—
298C2×D4C2×C22⋊D1112yes—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—82no—
304C22×C4—441no—
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—44no—
309D8—44no—
310M16—42no—
311C2×C8—22no—
312C2×C8—114no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—442no—
316C2×C8—884no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4C2×C22⋊D1112yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C42D4×D1111yescharacteristic
330C42#434111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C23×D1111yescharacteristic
333C11#1939111yescharacteristic, complemented, Sylow
334C23—22no—
335C23—24no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23#6699211yescharacteristic
340Q8—41no—
341Q8—41no—
342Q8—882no—
343Q8—882no—
344D4—22no—
345D4—24no—
346D4—42no—
347D4—41no—
348D4—41no—
349D4—81no—
350D4—82no—
351D4C2×#432414yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—442no—
361C2×C4—882no—
362C2×C4C2×#432412yes—
363C2×C4#6699211yescharacteristic
364C2×C4#6699211yescharacteristic
365C2×C4#6699211yescharacteristic
366C2×C4#6700312yes—
367C2×C4C2×D4×D1111yescharacteristic
368C2×C4C2×#434111yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—42no—
371C8—224no—
372C8—442no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#1062265412yes—
384C22C2×#6699211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—882no—
391C4#1062265412yes—
392C4#1062330612yes—
393C4C22×#432411yescharacteristic
394C4C2×#6700311yescharacteristic
395C2—22no—
396C2—44no—
397C2—161no—
398C2#1307813011yescharacteristic
399C2C2×#1062265411yescharacteristic
400C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622621C2semidirect
3. #13077640C2semidirect
4. #13068023C2semidirect
5. #13067989C2semidirect
6. #13067388C2semidirect
7. #13067298C2semidirect
8. #13067265C2semidirect
21. #10622692C22semidirect
22. #10622683C22semidirect
33. #10622185C22semidirect
34. #10622182C22semidirect
35. #10622119C22semidirect
36. #10622118C22semidirect
333. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226212
#130776402
#130680232
#130679892
#130673882
#130672982
#130672652
C11×#30362
#1939111