Finite Group Databasebeta

← #14739000

Subgroups — #14739000

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#13079746C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13068025C214yesmaximal, complemented
5#13067991C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067296C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C8×D4×C11—22no—
15C8×D4×C11C2214yes—
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C22⋊C8—22no—
19C2×#66896—21no—
20#10622632C2212yes—
21#10622629—22no—
22#10622628C2212yes—
23#10622621—22no—
24#10622621C2214yes—
25#10622579—21no—
26C2×#66872—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622455—22no—
30#10622348—22no—
31#10622307C2212yescomplemented
32#10622293C2212yescomplemented
33#10622124C2212yescomplemented
34#10622123C2212yescomplemented
35#10622119C2214yescomplemented
36#10622095C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C2×#4339—21no—
40C22×Dic22—21no—
41C22×C8×C11—24no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11D412yes—
45C4×D4×C11C2312yes—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4324—22no—
50#66985—44no—
51C2×#4323—22no—
52#66983—21no—
53#66983—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58#66928—21no—
59#66927C2311yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922C2312yes—
66#66922C2311yescharacteristic
67C11×C4⋊C8D412yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—24no—
71C11×C22⋊C8D412yes—
72C4×C8×C11—21no—
73C4×C8×C11C2312yes—
74#66896—24no—
75#66885—24no—
76#66881—24no—
77#66874—22no—
78#66873—22no—
79#66872—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19391—111nomaximal, Sylow
85C24×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11SD1614yes—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—41no—
98C22×Dic11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C2×C8×C11—22no—
110C2×C8×C11—84no—
111C2×C8×C11C2×D414yes—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C2×D412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4324—44no—
121#4323—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134#3227—111no—
135C2×#476—111no—
136#3036—111no—
137#2972D1111yescharacteristic, complemented
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—
149D4×C11—22no—
150D4×C11—24no—
151D4×C11C2×SD1614yes—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—44no—
156C2×C4×C11—82no—
157C2×C4×C11—81no—
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11#13512yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C22⋊D11—82no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—82no—
170D44—41no—
171D44—41no—
172D44—42no—
173D44—81no—
174C4×D11—82no—
175Dic22—41no—
176Dic22—41no—
177Dic22—82no—
178Dic22—82no—
179C8×C11—24no—
180C8×C11—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C2×AGL(1,ℤ/8)—221no—
184#532—111no—
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—222no—
194#461—112no—
195#459—112no—
196C8×D4—22no—
197C8×D4C2×D1114yes—
198#431C2×D1111yescharacteristic
199#431C2×D1111yescharacteristic
200C2×#106—221no—
201#423—111no—
202C2×C4⋊C8—111no—
203#417—221no—
204C2×#102—221no—
205C2×C22⋊C8—22no—
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#46512yes—
226C4×C11C22×SD1611yescharacteristic
227C4×C11C2×#13511yescharacteristic
228C4×C11#57712yes—
229Dic11—81no—
230Dic11—82no—
231C2×#41—221no—
232C22×Q8—221no—
233C22×D4D4411yescharacteristic
234C23×C4—21no—
235AGL(1,ℤ/8)—444no—
236C2×SD16—222no—
237C2×D8—222no—
238C2×M16—221no—
239C22×C8—24no—
240C22×C8—221no—
241C4⋊Q8—112no—
242C4⋊Q8—111no—
243C4⋊Q8—221no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
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×D4D4412yes—
255C4×D4C22×D1112yes—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4D4411yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#106—224no—
262#106—224no—
263C4⋊C8—112no—
264C4⋊C8—112no—
265C4⋊C8—221no—
266C4⋊C8—221no—
267C4⋊C8C22⋊D1112yes—
268C4⋊C8C22×D1112yes—
269#103—222no—
270#102—224no—
271#102—224no—
272#102—222no—
273C22⋊C8—21no—
274C22⋊C8—24no—
275C22⋊C8C22⋊D1112yes—
276C4×C8—21no—
277C4×C8C22×D1112yes—
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—221no—
288C2×Q8—222no—
289C2×Q8—441no—
290C2×Q8—882no—
291C2×D4—22no—
292C2×D4—21no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—221no—
296C2×D4—441no—
297C2×D4#431414yes—
298C2×D4C2×D4412yes—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—82no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4C2×D4411yescharacteristic
306C22×C4#433911yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308SD16—444no—
309D8—444no—
310M16—442no—
311C2×C8—22no—
312C2×C8—84no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—442no—
316C2×C8C2×C22⋊D1114yes—
317C4⋊C4—21no—
318C4⋊C4—222no—
319C4⋊C4—221no—
320C4⋊C4—222no—
321C4⋊C4—221no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4C2×D4412yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42C2×D4411yescharacteristic
330C42#433911yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C23×D1111yescharacteristic
333C11#1939111yescharacteristic, complemented, Sylow
334C23—22no—
335C23—24no—
336C23—81no—
337C23—81no—
338C23—441no—
339C23#6698311yescharacteristic
340Q8—441no—
341Q8—441no—
342Q8—882no—
343Q8—882no—
344D4—24no—
345D4—22no—
346D4—441no—
347D4—441no—
348D4—442no—
349D4—881no—
350D4—882no—
351D4C2×#431414yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—82no—
357C2×C4—81no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4C2×#431412yes—
363C2×C4#6695712yes—
364C2×C4#6698311yescharacteristic
365C2×C4#6698311yescharacteristic
366C2×C4#6698311yescharacteristic
367C2×C4C22×D4411yescharacteristic
368C2×C4C2×#433911yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—24no—
371C8—42no—
372C8—442no—
373C8—442no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22#1062272712yes—
384C22C2×#6698311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—882no—
390C4—881no—
391C4#1062272712yes—
392C4C22×#431411yescharacteristic
393C4C2×#6695711yescharacteristic
394C4#1062336712yes—
395C2—22no—
396C2—44no—
397C2—1761no—
398C2#1307812811yescharacteristic
399C2C2×#1062272711yescharacteristic
400C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenter#2972D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13079746C2semidirect
2. C2×#10622621C2semidirect
4. #13068025C2semidirect
5. #13067991C2semidirect
6. #13067387C2semidirect
7. #13067296C2semidirect
8. #13067263C2semidirect
9. C11×#2972C2semidirect
31. #10622307C22semidirect
32. #10622293C22semidirect
33. #10622124C22semidirect
34. #10622123C22semidirect
35. #10622119C22semidirect
36. #10622095C22semidirect
137. #2972D11semidirect
333. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106226212
#130780802
#130680252
#130679912
#130673872
#130672962
#130672632
C11×#29722
#1939111