Finite Group Databasebeta

← #14739009

Subgroups — #14739009

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#13079739C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13068053C214yesmaximal, complemented
5#13068005C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067287C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4324—21no—
12C2×#66985—21no—
13#10623008C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C8×D4×C11—22no—
16C8×D4×C11C2214yes—
17C11×#431C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C22⋊C8—22no—
20#10622632—22no—
21#10622632C2214yes—
22#10622632C2212yes—
23#10622629—22no—
24#10622628C2212yes—
25C2×#66874—21no—
26#10622579—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622459—22no—
30#10622349—22no—
31#10622307C2212yescomplemented
32#10622295C2212yescomplemented
33#10622124C2214yescomplemented
34#10622124C2212yescomplemented
35#10622123C2212yescomplemented
36#10622096C2214yescomplemented
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—
50C2×#4324—24no—
51C2×#4324—44no—
52#66985—44no—
53C2×#4323—22no—
54#66983—21no—
55#66983—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×#4318—21no—
59C22×C11⋊C8—21no—
60#66928—21no—
61#66927C2311yescharacteristic
62C4×D44—21no—
63C4×D44—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68#66922C2311yescharacteristic
69C11×C4⋊C8D412yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C11×C22⋊C8—24no—
73C11×C22⋊C8D412yes—
74C4×C8×C11—21no—
75C4×C8×C11C2312yes—
76#66885—24no—
77#66882—24no—
78#66874—22no—
79#66874—24no—
80#66873—22no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)C2312yes—
84C4⋊(C11⋊C8)C2312yes—
85#19392—111nomaximal, Sylow
86C24×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11D814yes—
90C2×D4×C11C2×D412yes—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—82no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100#4339—42no—
101#4339—42no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—22no—
107C2×Dic22—21no—
108C2×Dic22—41no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C2×C8×C11—22no—
112C2×C8×C11—84no—
113C2×C8×C11C2×D414yes—
114C11×C4⋊C4—21no—
115C11×C4⋊C4C2×D412yes—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121C42×C11C2411yescharacteristic
122#4324—44no—
123#4324—48no—
124#4323—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—21no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133#4318—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—42no—
137#3226—111no—
138#3036—111no—
139C2×#461—111no—
140#2972D1111yescharacteristic, complemented
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—
152D4×C11—22no—
153D4×C11—24no—
154D4×C11C2×D814yes—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—44no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C2×D812yes—
165C2×C4×C11#13512yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C22⋊D11—82no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—82no—
173D44—41no—
174D44—41no—
175D44—42no—
176D44—81no—
177C4×D11—82no—
178Dic22—42no—
179Dic22—41no—
180Dic22—42no—
181Dic22—41no—
182Dic22—82no—
183C8×C11—24no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—221no—
188C22×SD16—221no—
189#532—111no—
190C2×C4⋊Q8—111no—
191C2×C4×D4C2×D1111yescharacteristic
192#500—112no—
193#486—112no—
194#480—222no—
195#474—222no—
196#463—222no—
197#461—112no—
198#461—114no—
199#461—222no—
200#459—112no—
201C8×D4—22no—
202C8×D4C2×D1114yes—
203#431C2×D1111yescharacteristic
204#431C2×D1111yescharacteristic
205#423—111no—
206C2×C4⋊C8—111no—
207#417—221no—
208C2×#103—221no—
209C2×C22⋊C8—22no—
210#335—114no—
211#332—112no—
212#332—114no—
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#46612yes—
230C4×C11C22×D811yescharacteristic
231C4×C11C2×#13511yescharacteristic
232C4×C11#57712yes—
233Dic11—82no—
234Dic11—81no—
235C2×#41—221no—
236C22×Q8—221no—
237C22×D4D4411yescharacteristic
238C23×C4—21no—
239AGL(1,ℤ/8)—444no—
240C2×SD16—224no—
241C2×SD16—222no—
242C2×SD16—444no—
243C2×D8—222no—
244C2×M16—221no—
245C22×C8—24no—
246C22×C8—221no—
247C4⋊Q8—112no—
248C4⋊Q8—111no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
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×D4D4412yes—
261C4×D4C22×D1112yes—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4D4411yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—112no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272C4⋊C8C22⋊D1112yes—
273C4⋊C8C22×D1112yes—
274#103—224no—
275#103—222no—
276#102—224no—
277#102—222no—
278C22⋊C8—21no—
279C22⋊C8—24no—
280C22⋊C8C22⋊D1112yes—
281C4×C8—21no—
282C4×C8C22×D1112yes—
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—221no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—441no—
303C2×D4D8814yes—
304C2×D4C2×D4412yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4C2×D4411yescharacteristic
312C22×C4#433911yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—448no—
315SD16—444no—
316D8—444no—
317M16—442no—
318C2×C8—22no—
319C2×C8—84no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—442no—
323C2×C8C2×C22⋊D1114yes—
324C4⋊C4—21no—
325C4⋊C4—222no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—221no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4C2×D4412yes—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C42C2×D4411yescharacteristic
337C42#433911yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—22no—
342C23—24no—
343C23—81no—
344C23—81no—
345C23—441no—
346C23#6698311yescharacteristic
347Q8—442no—
348Q8—441no—
349Q8—442no—
350Q8—441no—
351Q8—882no—
352D4—24no—
353D4—22no—
354D4—441no—
355D4—441no—
356D4—442no—
357D4—881no—
358D4—882no—
359D4C2×D8814yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—82no—
365C2×C4—81no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—882no—
369C2×C4—882no—
370C2×C4C2×D8812yes—
371C2×C4#6695712yes—
372C2×C4#6698311yescharacteristic
373C2×C4#6698311yescharacteristic
374C2×C4#6698311yescharacteristic
375C2×C4C22×D4411yescharacteristic
376C2×C4C2×#433911yescharacteristic
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—24no—
379C8—42no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062272812yes—
392C22C2×#6698311yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—881no—
398C4—882no—
399C4#1062272812yes—
400C4C22×D8811yescharacteristic
401C4C2×#6695711yescharacteristic
402C4#1062336712yes—
403C2—22no—
404C2—44no—
405C2—1761no—
406C2#1307812811yescharacteristic
407C2C2×#1062272811yescharacteristic
408C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenter#2972D11
hypocenterC11#19392
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. #13079739C2semidirect
3. C2×#10622632C2semidirect
4. #13068053C2semidirect
5. #13068005C2semidirect
6. #13067391C2semidirect
7. #13067287C2semidirect
8. #13067263C2semidirect
9. C11×#2972C2semidirect
31. #10622307C22semidirect
32. #10622295C22semidirect
33. #10622124C22semidirect
34. #10622124C22semidirect
35. #10622123C22semidirect
36. #10622096C22semidirect
140. #2972D11semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130780802
C2×#106226322
#130680532
#130680052
#130673912
#130672872
#130672632
C11×#29722
#1939211