Finite Group Databasebeta

← #14739010

Subgroups — #14739010

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#13078082C211yesmaximal, characteristic
3C2×#10622454C211yesmaximal, characteristic, complemented
4#13077639C211yesmaximal, characteristic, complemented
5#13068054C214yesmaximal, complemented
6#13068006C214yesmaximal, complemented
7#13067289C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C2×#66961—21no—
11C22×#4314—21no—
12#10623008C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622746—21no—
19C2×#66880—21no—
20#10622538C2211yescharacteristic
21#10622459—22no—
22#10622457—22no—
23#10622456C2212yes—
24#10622454—22no—
25#10622454C2214yes—
26#10622454C2212yes—
27#10622447—22no—
28#10622349—22no—
29D11×C22⋊C8—22no—
30#10622307C2212yescomplemented
31C8×D44C2214yes—
32#10622295C2212yescomplemented
33C11×#335C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622120C2214yescomplemented
37C2×#4339—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#66983—21no—
45#66983—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50#66961—44no—
51C2×D88—22no—
52C2×#4314—24no—
53C2×#4314—22no—
54C2×#4314—44no—
55C2×C8×D11—24no—
56#66928—21no—
57#66927C2311yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44D412yes—
63C4×D44C2312yes—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68#66922C2311yescharacteristic
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8D412yes—
75C4×C8×C11C2312yes—
76C22⋊(C11⋊C8)—21no—
77#66885—24no—
78#66885—22no—
79(C2×D11)⋊C8—24no—
80#66882—24no—
81#66880—22no—
82#66880—24no—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8—21no—
85#19392—111nomaximal, Sylow
86C23×D11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91C22×Dic11—21no—
92C22×Dic11—41no—
93#4339—42no—
94#4339—42no—
95C2×D44—21no—
96C2×D44—22no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44D814yes—
101C2×D44C2×D412yes—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—41no—
105C2×C4×D11—82no—
106C2×Dic22—22no—
107C2×Dic22—21no—
108C2×Dic22—41no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C11×M16—42no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—42no—
115C2×C8×C11C2×D414yes—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D412yes—
132C2×C11⋊C8—22no—
133D88—44no—
134#4314—48no—
135#4314—44no—
136C8×D11—84no—
137#3226—111no—
138#3036—111no—
139C2×#461—111no—
140#2972—111no—
141#1681—114no—
142#1673—114no—
143#1571D1111yescharacteristic, complemented
144#1546—111no—
145#1540—111no—
146C23×C11#12111yescharacteristic
147C22×D11—22no—
148C22×D11—24no—
149C22×D11—41no—
150C22×D11—81no—
151C22×D11—81no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×D812yes—
158C2×C4×C11#13512yes—
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C22⋊D11—82no—
163C2×Dic11—22no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—82no—
168D44—22no—
169D44—24no—
170D44—41no—
171D44—41no—
172D44—42no—
173D44—81no—
174D44C2×D814yes—
175C4×D11—44no—
176C4×D11—82no—
177C4×D11—82no—
178Dic22—42no—
179Dic22—41no—
180Dic22—42no—
181Dic22—41no—
182Dic22—82no—
183C8×C11—24no—
184C8×C11—42no—
185C8×C11—42no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—221no—
188C22×SD16—221no—
189#532—111no—
190C2×C4⋊Q8—111no—
191C2×C4×D4—111no—
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—114no—
202C8×D4—222no—
203#431—111no—
204#431C2×D1111yescharacteristic
205#423C2×D1111yescharacteristic
206C2×C4⋊C8C2×D1111yescharacteristic
207#417—221no—
208C2×#103—221no—
209C2×C22⋊C8—222no—
210#335C2×D1114yescomplemented
211#332—112no—
212#332—114no—
213#331—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11#46612yes—
217C22×C11C2×#12111yescharacteristic
218C2×D11—24no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—84no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11#46612yes—
229C4×C11C22×D811yescharacteristic
230C4×C11C2×#13511yescharacteristic
231C4×C11#57712yes—
232Dic11—42no—
233Dic11—82no—
234Dic11—81no—
235C2×#41—221no—
236C22×Q8—221no—
237C22×D4—111no—
238C23×C4—221no—
239AGL(1,ℤ/8)—444no—
240C2×SD16—224no—
241C2×SD16—222no—
242C2×SD16—444no—
243C2×D8—222no—
244C2×M16—21no—
245C22×C8—21no—
246C22×C8—224no—
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—112no—
257C4×D4—112no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—112no—
271C4⋊C8D4412yes—
272C4⋊C8C22×D1112yes—
273C4⋊C8C22×D1112yes—
274#103—224no—
275#103—222no—
276#102—222no—
277#102—224no—
278C22⋊C8—221no—
279C22⋊C8—224no—
280C22⋊C8D4412yes—
281C4×C8—221no—
282C4×C8C22×D1112yes—
283C2×C11—22no—
284C2×C11#304211yescharacteristic
285C2×C11C2×#46611yescharacteristic
286C2×C11#306911yescharacteristic
287D11—44no—
288D11—161no—
289C24—221no—
290#41—442no—
291#41—442no—
292C2×Q8—221no—
293C2×Q8—222no—
294C2×Q8—441no—
295C2×Q8—442no—
296C2×Q8—442no—
297C2×D4—114no—
298C2×D4—112no—
299C2×D4—221no—
300C2×D4—222no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—441no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—882no—
311C22×C4C2×D4411yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4#434311yescharacteristic
314SD16—448no—
315SD16—444no—
316D8—444no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—222no—
322C2×C8—884no—
323C2×C8C2×D4414yes—
324C4⋊C4—112no—
325C4⋊C4—221no—
326C4⋊C4—222no—
327C4⋊C4—221no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—222no—
333C22⋊C4—222no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C42C2×D4411yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434311yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—222no—
342C23—224no—
343C23—441no—
344C23—881no—
345C23—881no—
346C23#6694811yescharacteristic
347Q8—442no—
348Q8—441no—
349Q8—442no—
350Q8—441no—
351Q8—882no—
352D4—114no—
353D4—224no—
354D4—222no—
355D4—442no—
356D4—441no—
357D4—441no—
358D4—881no—
359D4—882no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—222no—
363C2×C4—444no—
364C2×C4—441no—
365C2×C4—442no—
366C2×C4—882no—
367C2×C4—881no—
368C2×C4—882no—
369C2×C4—882no—
370C2×C4#6694811yescharacteristic
371C2×C4#6694811yescharacteristic
372C2×C4#6694811yescharacteristic
373C2×C4D8×D1112yes—
374C2×C4#6697212yes—
375C2×C4C22×D4411yescharacteristic
376C2×C4C2×D4×D1111yescharacteristic
377C2×C4C2×#434311yescharacteristic
378C8—24no—
379C8—42no—
380C8—42no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—224no—
385C22—442no—
386C22—442no—
387C22—884no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22#1062249612yes—
392C22C2×#6694811yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—442no—
397C4—881no—
398C4—882no—
399C4#1062249612yes—
400C4#1062328212yes—
401C4C2×D8×D1111yescharacteristic
402C4C2×#6697211yescharacteristic
403C2—22no—
404C2—444no—
405C2—1761no—
406C2#1307812911yescharacteristic
407C2C2×#1062249611yescharacteristic
408C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×#121
prime radical#13078082C2
hypercenter#1571D11
hypocenterC11#19392
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
1. #13079739C2semidirect
3. C2×#10622454C2semidirect
4. #13077639C2semidirect
5. #13068054C2semidirect
6. #13068006C2semidirect
7. #13067289C2semidirect
8. #13067266C2semidirect
9. C11×#1571C2semidirect
30. #10622307C22semidirect
32. #10622295C22semidirect
33. C11×#335C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622120C22semidirect
143. #1571D11semidirect
210. #335C2×D11semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130780822
C2×#106224542
#130776392
#130680542
#130680062
#130672892
#130672662
C11×#15712
#1939211