Finite Group Databasebeta

← #14737343

Subgroups — #14737343

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079933C211yesmaximal, characteristic, complemented
2#13079557C211yesmaximal, characteristic, complemented
3#13079066C211yesmaximal, characteristic
4#13077559C211yesmaximal, characteristic, complemented
5#13068099C212yesmaximal, complemented
6#13068087C212yesmaximal, complemented
7#13067975C212yesmaximal, complemented
8#13067963C212yesmaximal, complemented
9#13067366C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic, complemented
11C2×C11×#331C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×#66985—21no—
14C2×#66985—21no—
15#10623008C2211yescharacteristic
16#10623001C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19#10622831—22no—
20#10622727—22no—
21#10622715—21no—
22#10622714—21no—
23#10622689—21no—
24#10622689C2212yes—
25#10622688C2212yes—
26#10622688C2212yes—
27#10622687—22no—
28#10622686C2212yes—
29#10622683—21no—
30#10622538C2211yescharacteristic
31C4×#4318C2211yescharacteristic
32#10622464C2212yescomplemented
33#10622461C2212yescomplemented
34#10622455—21no—
35#10622454—21no—
36#10622444C2212yescomplemented
37#10622443C2212yescomplemented
38#10622441—22no—
39C11×#331C2212yes—
40C11×#331C2212yes—
41#10622123C2211yescharacteristic, complemented
42#10622123C2211yescharacteristic, complemented
43#10622120C2211yescharacteristic, complemented
44#10622120C2211yescharacteristic, complemented
45#10622118C2212yescomplemented
46#10622117C2212yescomplemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C2×#4339—21no—
51C22×C8×C11—21no—
52C22×C8×C11—21no—
53C11×#127—21no—
54C11×#127—21no—
55C11×#127—21no—
56C11×#127C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×#4324—22no—
59C2×#4324—22no—
60C2×#4324—22no—
61C2×#4324—22no—
62#66985—44no—
63#66985—44no—
64C2×#4323—22no—
65C2×#4323—22no—
66#66983—21no—
67#66983—21no—
68#66979—21no—
69#66977—21no—
70#66977D412yes—
71C2×#4318D411yescharacteristic
72C2×#4318D411yescharacteristic
73C2×#4314—22no—
74#66928—21no—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66923—21no—
79#66922D411yescharacteristic
80#66922D411yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22C2312yes—
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×C4⋊C8C2311yescharacteristic
88C11×C4⋊C8C2311yescharacteristic
89#66896—22no—
90#66896—22no—
91C22⋊(C11⋊C8)—21no—
92#66885—22no—
93#66881—22no—
94#66880—22no—
95#66879—22no—
96Dic11⋊C8—22no—
97Dic11⋊C8—22no—
98C8×Dic11—22no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867D412yes—
102C4×C11⋊C8—21no—
103C4×C11⋊C8C2312yes—
104#19238—111nomaximal, Sylow
105C24×C11—41no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—81no—
115C2×D4×C11—81no—
116C2×D4×C11—82no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—41no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22C2×D412yes—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—42no—
134C2×C8×C11—81no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—22no—
140#4324—44no—
141#4324—44no—
142#4324—82no—
143#4324—82no—
144#4323—44no—
145#4323—44no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11C2×D412yes—
154Dic11⋊C4—22no—
155Dic11⋊C4—22no—
156C4×Dic11—22no—
157#4318—22no—
158#4318SD1614yescomplemented
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8C2×D412yes—
162C2×C11⋊C8C2×D412yes—
163#4314—82no—
164#3246—111no—
165#3208—111no—
166#3151—111no—
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540—111no—
174C2×#331D1111yescharacteristic, complemented
175C23×C11—42no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11#12111yescharacteristic
180C22×D11—41no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—82no—
186D4×C11—82no—
187D4×C11—82no—
188D4×C11—82no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11C2×SD1612yes—
196C2×C4×C11AGL(1,ℤ/8)12yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—82no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204D44—41no—
205D44—41no—
206D44—41no—
207D44—41no—
208D44—81no—
209C4×D11—82no—
210Dic22—22no—
211Dic22—22no—
212Dic22—41no—
213Dic22—41no—
214Dic22—81no—
215C8×C11—41no—
216C8×C11—41no—
217C8×C11—42no—
218C11⋊C8—22no—
219C11⋊C8—41no—
220C11⋊C8—41no—
221C11⋊C8C2×SD1614yes—
222C2×AGL(1,ℤ/8)—221no—
223C2×AGL(1,ℤ/8)—221no—
224#533—111no—
225#532—111no—
226C2×#127C2×D1111yescharacteristic
227#496—222no—
228#493—112no—
229#492—112no—
230#492—221no—
231#486—221no—
232#476—221no—
233#475—112no—
234#465—222no—
235#461—221no—
236#460—112no—
237#460—112no—
238#460—112no—
239#450—222no—
240#446—112no—
241#446—222no—
242C8×Q8—112no—
243#431—111no—
244#424—221no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×C4⋊C8C2×D1111yescharacteristic
247#405—221no—
248C4×M16—111no—
249#335—112no—
250#334—112no—
251#332—111no—
252#332—111no—
253#331—111no—
254#331—111no—
255#331C2×D1112yes—
256#331C2×D1112yes—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—164no—
263C22×C11#46012yes—
264C22×C11C2×#12111yescharacteristic
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11#46012yes—
272C4×C11C22×SD1611yescharacteristic
273C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C4×C11#57611yescharacteristic
275C4×C11#57711yescharacteristic
276Dic11—42no—
277Dic11—42no—
278Dic11—81no—
279C2×#41—221no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283AGL(1,ℤ/8)—444no—
284AGL(1,ℤ/8)—444no—
285C2×SD16—222no—
286C2×SD16—222no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×D8—222no—
292C2×M16—111no—
293C2×M16—111no—
294C22×C8—21no—
295C22×C8—21no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298C4⋊Q8—111no—
299#127—21no—
300#127—21no—
301#127—21no—
302#127—111no—
303#127C22×D1112yes—
304#125—221no—
305#124—221no—
306C22⋊Q8—112no—
307C22⋊Q8—221no—
308#121—221no—
309#121—221no—
310C4×Q8—112no—
311C4×Q8—221no—
312C4×D4—221no—
313C4×D4—221no—
314#117—221no—
315C2×C42C22×D1111yescharacteristic
316#106—222no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—111no—
320C4⋊C8—111no—
321C4⋊C8—222no—
322C4⋊C8—222no—
323C4⋊C8C22×D1111yescharacteristic
324C4⋊C8C22×D1111yescharacteristic
325C4⋊C8C22×D1112yes—
326#103—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330C22⋊C8—221no—
331#97—112no—
332#97—222no—
333C4×C8—112no—
334C4×C8—222no—
335C4×C8—221no—
336C2×C11—22no—
337C2×C11—162no—
338C2×C11C2×#46011yescharacteristic
339C2×C11#306211yescharacteristic
340C2×C11#306811yescharacteristic
341D11—161no—
342C24—41no—
343#41—442no—
344#41—442no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—81no—
357C2×D4—81no—
358C2×D4—82no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—441no—
363C22×C4—441no—
364C22×C4#433911yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367SD16—444no—
368SD16—444no—
369SD16—882no—
370SD16—882no—
371SD16—882no—
372D8—444no—
373D8—444no—
374M16—114no—
375M16—222no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—42no—
380C2×C8—81no—
381C2×C8—112no—
382C2×C8—112no—
383C2×C8—221no—
384C2×C8—221no—
385C4⋊C4—112no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C22⋊C4—222no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C42—222no—
397C42#433911yescharacteristic
398C42D4×D1111yescharacteristic
399C42D4×D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—42no—
403C23—82no—
404C23—82no—
405C23—82no—
406C23—441no—
407C23#6693711yescharacteristic
408Q8—222no—
409Q8—222no—
410Q8—441no—
411Q8—441no—
412Q8—881no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—82no—
418D4—82no—
419D4—82no—
420D4—82no—
421D4—441no—
422D4—441no—
423D4—441no—
424D4—441no—
425D4—881no—
426D4—882no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—441no—
433C2×C4—882no—
434C2×C4#6693711yescharacteristic
435C2×C4#6693711yescharacteristic
436C2×C4#6693711yescharacteristic
437C2×C4#6696412yes—
438C2×C4SD16×D1112yes—
439C2×C4C2×#433911yescharacteristic
440C2×C4C2×D4×D1111yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C8—41no—
443C8—41no—
444C8—42no—
445C8—114no—
446C8—222no—
447C8—441no—
448C8—441no—
449C22—21no—
450C22—21no—
451C22—82no—
452C22—82no—
453C22—82no—
454C22—164no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062237512yes—
459C22C2×#6693711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—442no—
464C4—442no—
465C4—881no—
466C4#1062237512yes—
467C4C2×#6696411yescharacteristic
468C4#1062328811yescharacteristic
469C4C2×SD16×D1111yescharacteristic
470C4#1062329311yescharacteristic
471C2—22no—
472C2—162no—
473C2—1761no—
474C2C2×#1062237511yescharacteristic
475C2#1307829411yescharacteristic
476C2#1307834311yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#331C2
socleC22×C11C2×#121
prime radical#13079066C2
hypercenterC2×#331D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. #13079933C2semidirect
2. #13079557C2semidirect
4. #13077559C2semidirect
5. #13068099C2semidirect
6. #13068087C2semidirect
7. #13067975C2semidirect
8. #13067963C2semidirect
9. #13067366C2semidirect
10. #13067266C2semidirect
11. C2×C11×#331C2semidirect
32. #10622464C22semidirect
33. #10622461C22semidirect
36. #10622444C22semidirect
37. #10622443C22semidirect
41. #10622123C22semidirect
42. #10622123C22semidirect
43. #10622120C22semidirect
44. #10622120C22semidirect
45. #10622118C22semidirect
46. #10622117C22semidirect
158. #4318SD16semidirect
174. C2×#331D11semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130795572
#130790662
#130775592
#130680992
#130680872
#130679752
#130679632
#130673662
#130672662
C2×C11×#3312
#1923811