Finite Group Databasebeta

← #14738997

Subgroups — #14738997

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#13079744C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic, complemented
4#13068027C214yesmaximal, complemented
5#13067993C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C2×C11×#476C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66985—21no—
13#10623008C2211yescharacteristic
14C11×#476—22no—
15C11×#476C2214yes—
16C2×C11×#106—21no—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19C2×C22⋊(C11⋊C8)—22no—
20#10622701C2212yescomplemented
21#10622697—22no—
22#10622692C2212yescomplemented
23#10622632C2212yes—
24#10622629—22no—
25#10622628C2212yes—
26D4×C11⋊C8—22no—
27D4×C11⋊C8C2214yes—
28#10622581—22no—
29#10622579—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622184C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622118C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×#4339—21no—
41C22×C8×C11—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11D412yes—
49C4×D4×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C22⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4324—22no—
56#66985—44no—
57C2×#4323—22no—
58#66983—21no—
59#66983—21no—
60C2×#4318—21no—
61C22×C11⋊C8—24no—
62#66928—21no—
63#66927C2311yescharacteristic
64C4×D44—21no—
65C4×D44—21no—
66#66922C2311yescharacteristic
67C11×#106—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#102—24no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—24no—
73C22⋊(C11⋊C8)D412yes—
74#66874—22no—
75#66873—22no—
76#66873—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—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—82no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11SD1614yes—
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—41no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—41no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C2×C8×C11—22no—
110C2×C8×C11—42no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4C2×D412yes—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4324—44no—
124#4323—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—84no—
133C2×C11⋊C8C2×D414yes—
134#3227—111no—
135C2×#476D1111yescharacteristic, complemented
136#3036—111no—
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—81no—
146C23×C11—81no—
147C23×C11#12111yescharacteristic
148C22×D11—41no—
149Q8×C11—82no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—24no—
153D4×C11C2×SD1614yes—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—44no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11—82no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11#13512yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—41no—
172D44—41no—
173D44—41no—
174D44—42no—
175D44—81no—
176C4×D11—82no—
177Dic22—41no—
178Dic22—41no—
179C8×C11—42no—
180C11⋊C8—24no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C2×AGL(1,ℤ/8)—221no—
184#532—111no—
185C2×C4⋊Q8C2×D1111yescharacteristic
186C2×C4×D4C2×D1111yescharacteristic
187#498—112no—
188#486—112no—
189#481—222no—
190#476—22no—
191#476—222no—
192#476C2×D1114yes—
193#463—222no—
194#461—112no—
195#459—112no—
196C8×D4—114no—
197C8×D4—222no—
198#431—111no—
199#431—111no—
200C2×#106—21no—
201#423—111no—
202C2×C4⋊C8C2×D1111yescharacteristic
203#417—221no—
204C2×#102—21no—
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#46512yes—
217C22×C11C2×#12111yescharacteristic
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—42no—
225C4×C11—82no—
226C4×C11#46512yes—
227C4×C11C22×SD1611yescharacteristic
228C4×C11C2×#13511yescharacteristic
229C4×C11#57712yes—
230Dic11—81no—
231C2×#41—221no—
232C22×Q8—21no—
233C22×D4C22⋊D1111yescharacteristic
234C23×C4—21no—
235AGL(1,ℤ/8)—444no—
236C2×SD16—222no—
237C2×D8—222no—
238C2×M16—221no—
239C22×C8—21no—
240C22×C8—224no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—111no—
245C4⋊Q8C22×D1112yes—
246#127—111no—
247#124—221no—
248#121—221no—
249#121—221no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—221no—
253C4×D4—221no—
254C4×D4C22⋊D1112yes—
255C4×D4C22×D1112yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#106—24no—
262#106—224no—
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269#103—222no—
270#102—24no—
271#102—224no—
272#102—222no—
273C22⋊C8—112no—
274C22⋊C8—224no—
275C22⋊C8—221no—
276C4×C8—112no—
277C4×C8—221no—
278C2×C11—22no—
279C2×C11—44no—
280C2×C11#304211yescharacteristic
281C2×C11C2×#46511yescharacteristic
282C2×C11#306811yescharacteristic
283D11—161no—
284C24—21no—
285#41—442no—
286#41—442no—
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—82no—
290C2×Q8—221no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—441no—
297C2×D4#432514yes—
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—444no—
309D8—444no—
310M16—442no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—114no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—884no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4C2×C22⋊D1112yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42D4×D1111yescharacteristic
330C42#434111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C23×D1111yescharacteristic
333C11#1939111yescharacteristic, complemented, Sylow
334C23—22no—
335C23—24no—
336C23—81no—
337C23—81no—
338C23—441no—
339C23#6699211yescharacteristic
340Q8—82no—
341Q8—82no—
342Q8—441no—
343Q8—441no—
344D4—22no—
345D4—24no—
346D4—442no—
347D4—441no—
348D4—441no—
349D4—881no—
350D4—882no—
351D4C2×#432514yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—441no—
361C2×C4—882no—
362C2×C4#6699211yescharacteristic
363C2×C4#6699211yescharacteristic
364C2×C4#6699211yescharacteristic
365C2×C4C2×#432512yes—
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—881no—
381C22—881no—
382C22—881no—
383C22#1062266112yes—
384C22C2×#6699211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—82no—
390C4—881no—
391C4#1062266112yes—
392C4#1062329312yes—
393C4C22×#432511yescharacteristic
394C4C2×#6700311yescharacteristic
395C2—22no—
396C2—44no—
397C2—1761no—
398C2#1307812511yescharacteristic
399C2C2×#1062266111yescharacteristic
400C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenterC2×#476D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
3. #13077640C2semidirect
4. #13068027C2semidirect
5. #13067993C2semidirect
6. #13067386C2semidirect
7. #13067297C2semidirect
8. #13067266C2semidirect
9. C2×C11×#476C2semidirect
20. #10622701C22semidirect
22. #10622692C22semidirect
33. #10622184C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622118C22semidirect
135. C2×#476D11semidirect
333. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130780802
#130776402
#130680272
#130679932
#130673862
#130672972
#130672662
C2×C11×#4762
#1939111