Finite Group Databasebeta

← #14739066

Subgroups — #14739066

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic
2#13078090C211yesmaximal, characteristic, complemented
3C2×#10622688C211yesmaximal, characteristic, complemented
4#13077696C211yesmaximal, characteristic, complemented
5#13068059C214yesmaximal, complemented
6#13067975C214yesmaximal, complemented
7#13067392C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C22×#4324—21no—
12C2×#66962—21no—
13#10623008C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17#10622830—22no—
18C2×#66896—21no—
19#10622746—21no—
20#10622688—22no—
21#10622688C2214yes—
22#10622686C2212yes—
23#10622685—22no—
24#10622683C2212yes—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622462C2212yescomplemented
28#10622461C2212yescomplemented
29#10622458—22no—
30#10622443C2214yescomplemented
31#10622331—22no—
32C8×Dic22—22no—
33C11×#331C2214yes—
34#10622124C2212yescomplemented
35#10622123C2212yescomplemented
36#10622117C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C2×#4339—21no—
41C22×Dic22D411yescharacteristic
42C2×C11×M16—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127C2312yes—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—24no—
49C2×#4324—44no—
50C2×#4323—24no—
51#66983—21no—
52#66983—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×C4×Dic11—21no—
56C22×C11⋊C8—21no—
57#66962—44no—
58C2×Dic44—22no—
59C2×#4314—22no—
60#66928—21no—
61#66927C2311yescharacteristic
62C4×D44—21no—
63C4×D44—21no—
64#66922C2311yescharacteristic
65C4×Dic22—21no—
66C4×Dic22—21no—
67C4×Dic22D412yes—
68C4×Dic22C2312yes—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8—21no—
73C4×C8×C11—21no—
74#66896—24no—
75#66896—24no—
76C22⋊(C11⋊C8)D412yes—
77#66885—22no—
78#66880—22no—
79Dic11⋊C8—24no—
80C8×Dic11—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8C2312yes—
85#19398—111nomaximal, Sylow
86C24×C11—41no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—82no—
96C2×D4×C11—82no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—41no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103#4339—42no—
104#4339—42no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×C4×D11—41no—
109C2×Dic22—21no—
110C2×Dic22—22no—
111C2×Dic22—21no—
112C2×Dic22D814yescomplemented
113C2×Dic22C2×D412yes—
114C11×M16—42no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11C2411yescharacteristic
121#4324—48no—
122#4323—84no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129Dic11⋊C4—22no—
130Dic11⋊C4—22no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—42no—
135C2×C11⋊C8C2×D414yes—
136Dic44—44no—
137#4314—44no—
138#3205—111no—
139#3037—111no—
140C2×#460—111no—
141#2982—111no—
142#1682—114no—
143#1668—114no—
144#1571—111no—
145#1545D1111yescharacteristic, complemented
146#1540—111no—
147C23×C11—42no—
148C23×C11—82no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152C22×D11—41no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—44no—
156D4×C11—82no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×D812yes—
166C2×C4×C11#13512yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C22⋊D11—82no—
171C2×Dic11—22no—
172C2×Dic11—24no—
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—81no—
176D44—41no—
177D44—41no—
178D44—42no—
179D44—81no—
180C4×D11—82no—
181Dic22—22no—
182Dic22—24no—
183Dic22—41no—
184Dic22—41no—
185Dic22C2×D814yes—
186C8×C11—42no—
187C8×C11—42no—
188C11⋊C8—24no—
189C11⋊C8—42no—
190C2×#137—221no—
191C22×SD16—221no—
192#532—111no—
193C2×#127C2×D1111yescharacteristic
194C2×C4×Q8—111no—
195#493—112no—
196#486—112no—
197#464—222no—
198#462—112no—
199#460—114no—
200#460—112no—
201#460—222no—
202#459—222no—
203#447—222no—
204C8×Q8—114no—
205C8×Q8—222no—
206#431—111no—
207#431—222no—
208#431C2×D1111yescharacteristic
209#423C2×D1111yescharacteristic
210C2×C4⋊C8—111no—
211#417—221no—
212C2×#102—221no—
213#335—114no—
214#332—112no—
215#331—112no—
216#331C2×D1114yes—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—164no—
223C22×C11#46612yes—
224C22×C11C2×#12111yescharacteristic
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11#46612yes—
232C4×C11C22×D811yescharacteristic
233C4×C11C2×#13511yescharacteristic
234C4×C11#57712yes—
235Dic11—24no—
236Dic11—42no—
237Dic11—81no—
238C2×#41—221no—
239C22×Q8—111no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243#137—444no—
244C2×Q16—222no—
245C2×SD16—222no—
246C2×SD16—224no—
247C2×SD16—444no—
248C2×D8—224no—
249C2×M16—21no—
250C22×C8—221no—
251C4⋊Q8—111no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127—111no—
256#127C22×D1112yes—
257#124—221no—
258#121—221no—
259#121—221no—
260C4×Q8—112no—
261C4×Q8—112no—
262C4×Q8—221no—
263C4×Q8—221no—
264C4×D4—221no—
265C4×D4—221no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—112no—
272C4⋊C8—112no—
273C4⋊C8—224no—
274C4⋊C8—221no—
275C4⋊C8C22×D1112yes—
276C4⋊C8C22×D1112yes—
277#103—222no—
278#102—222no—
279#102—224no—
280#102—224no—
281C22⋊C8—21no—
282C22⋊C8—112no—
283C4×C8—21no—
284C4×C8—112no—
285C4×C8—224no—
286C2×C11—22no—
287C2×C11—162no—
288C2×C11#304311yescharacteristic
289C2×C11C2×#46611yescharacteristic
290C2×C11#306811yescharacteristic
291D11—161no—
292C24—41no—
293#41—442no—
294#41—442no—
295C2×Q8—114no—
296C2×Q8—112no—
297C2×Q8—221no—
298C2×Q8—222no—
299C2×Q8—221no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—82no—
309C2×D4—82no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—441no—
317C22×C4#433911yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320Q16—444no—
321SD16—444no—
322SD16—448no—
323D8—884no—
324M16—42no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—114no—
328C2×C8—222no—
329C2×C8—442no—
330C4⋊C4—112no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—222no—
339C42—222no—
340C42#433911yescharacteristic
341C42D4×D1111yescharacteristic
342C42D4×D1111yescharacteristic
343C42C23×D1111yescharacteristic
344C11#1939811yescharacteristic, complemented, Sylow
345C23—42no—
346C23—82no—
347C23—82no—
348C23—82no—
349C23—441no—
350C23#6693711yescharacteristic
351Q8—114no—
352Q8—222no—
353Q8—224no—
354Q8—441no—
355Q8—441no—
356D4—42no—
357D4—42no—
358D4—44no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—82no—
363D4—441no—
364D4—441no—
365D4—442no—
366D4—881no—
367D4—882no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—222no—
371C2×C4—224no—
372C2×C4—222no—
373C2×C4—441no—
374C2×C4—881no—
375C2×C4—882no—
376C2×C4#6693711yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4D8×D1112yes—
380C2×C4#6696912yes—
381C2×C4C2×#433911yescharacteristic
382C2×C4C2×D4×D1111yescharacteristic
383C2×C4C2×D4×D1111yescharacteristic
384C8—42no—
385C8—42no—
386C8—224no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—82no—
392C22—82no—
393C22—164no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22#1062238812yes—
398C22C2×#6693711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—224no—
403C4—442no—
404C4—881no—
405C4#1062238812yes—
406C4C2×D8×D1111yescharacteristic
407C4C2×#6696911yescharacteristic
408C4#1062330612yes—
409C2—22no—
410C2—162no—
411C2—1761no—
412C2#1307813611yescharacteristic
413C2C2×#1062238811yescharacteristic
414C2#1307834311yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenter#1545D11
hypocenterC11#19398
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13078090C2semidirect
3. C2×#10622688C2semidirect
4. #13077696C2semidirect
5. #13068059C2semidirect
6. #13067975C2semidirect
7. #13067392C2semidirect
8. #13067263C2semidirect
9. C11×#1545C2semidirect
27. #10622462C22semidirect
28. #10622461C22semidirect
30. #10622443C22semidirect
34. #10622124C22semidirect
35. #10622123C22semidirect
36. #10622117C22semidirect
112. C2×Dic22D8semidirect
145. #1545D11semidirect
344. C11#19398semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780902
C2×#106226882
#130776962
#130680592
#130679752
#130673922
#130672632
C11×#15452
#1939811