Finite Group Databasebeta

← #14737805

Subgroups — #14737805

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic, complemented
3#13078707C211yesmaximal, characteristic
4#13068191C212yesmaximal, complemented
5#13068177C212yesmaximal, complemented
6#13068115C212yesmaximal, complemented
7#13068081C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067314C211yesmaximal, characteristic, complemented
10#13067309C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#436—21no—
17C11×#436—21no—
18C11×#436C2212yes—
19C11×#436C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622831—21no—
24#10622830—21no—
25#10622727—21no—
26#10622727—21no—
27#10622632C2212yes—
28#10622631—22no—
29#10622628C2212yes—
30#10622627—22no—
31#10622621C2212yes—
32#10622620C2212yes—
33#10622583—21no—
34#10622581—21no—
35#10622539C2211yescharacteristic
36#10622539C2211yescharacteristic
37#10622307C2211yescharacteristic, complemented
38#10622306C2211yescharacteristic, complemented
39C4×#4314—21no—
40C4×#4314—21no—
41#10622294C2211yescharacteristic, complemented
42#10622293C2211yescharacteristic, complemented
43#10622124C2212yescomplemented
44#10622123C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—44no—
55C22×C8×C11—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66C2×#4323—22no—
67#66983—21no—
68#66983—21no—
69#66979—21no—
70#66977—21no—
71#66977—21no—
72C2×#4314—21no—
73C2×#4314—21no—
74#66928—21no—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66923—21no—
79#66922C2311yescharacteristic
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66885—21no—
97#66885—21no—
98#66881—21no—
99#66881—21no—
100#66880—21no—
101#66880—21no—
102#66874—22no—
103#66873—22no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108#66867—21no—
109#66867—21no—
110#19282—111nomaximal, Sylow
111C24×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—42no—
114C2×D4×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C2×C22⋊D11—41no—
124#4339—82no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C11×M16—44no—
133C11×M16—44no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—41no—
137C2×C8×C11—42no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150C22⋊Dic11—41no—
151#4324—44no—
152#4323—44no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166#4314—42no—
167#4314—42no—
168#3167—111no—
169#3110—111no—
170#3109—111no—
171C2×#436D1111yescharacteristic, complemented
172#1703—112no—
173#1701—112no—
174#1691—112no—
175#1685—112no—
176#1568—111no—
177#1552—111no—
178#1551—111no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12111yescharacteristic
184C22×D11—41no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—42no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—44no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C22⋊D11—82no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207D44—41no—
208D44—41no—
209D44—42no—
210D44—81no—
211C4×D11—82no—
212Dic22—41no—
213Dic22—41no—
214Dic22—42no—
215Dic22—81no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—42no—
220C8×C11AGL(1,ℤ/8)12yes—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C22×M16—21no—
224#533—111no—
225#532—111no—
226C2×C4×D4C2×D1111yescharacteristic
227#498—111no—
228#492—111no—
229#487—111no—
230#486—111no—
231#484—221no—
232#481—221no—
233#476—112no—
234#474—112no—
235#465—221no—
236#465—221no—
237#461—112no—
238#459—112no—
239#450—221no—
240#447—221no—
241#442—222no—
242#440—222no—
243C4×SD16—221no—
244C4×SD16—221no—
245#436—21no—
246#436—21no—
247#436C2×D1112yes—
248#436C2×D1112yes—
249#432—111no—
250#432—111no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×C22⋊C8—21no—
253C2×C4×C8C2×D1111yescharacteristic
254#335—112no—
255#334—112no—
256#333—112no—
257#332—112no—
258#332—112no—
259#331—112no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—84no—
266C22×C11#47112yes—
267C22×C11C2×#12111yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11#57512yes—
278C4×C11#57511yescharacteristic
279Dic11—81no—
280Dic11—81no—
281Dic11—81no—
282C2×#41—221no—
283C22×D4D4411yescharacteristic
284C23×C4—21no—
285C2×SD16—222no—
286C2×SD16—221no—
287C2×SD16—221no—
288C2×D8—222no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—44no—
292C22×C8—21no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298#127—111no—
299#125—221no—
300#124—221no—
301C22⋊Q8—221no—
302C22⋊Q8—221no—
303#121—221no—
304#121—221no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—221no—
310C4×D4—221no—
311C4×D4D4412yes—
312C4×D4C22×D1112yes—
313#117—221no—
314C2×C4⋊C4D4411yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42C22×D1111yescharacteristic
317#107—222no—
318#106—221no—
319#106—221no—
320#106—222no—
321C4⋊C8—21no—
322C4⋊C8—112no—
323C4⋊C8—112no—
324C4⋊C8C22×D1112yes—
325#103—221no—
326#103—221no—
327#103—222no—
328#102—222no—
329#102—222no—
330#102—221no—
331#102—221no—
332#102—222no—
333C22⋊C8—22no—
334C22⋊C8—22no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337#97—221no—
338#97—221no—
339C4×C8C22⋊D1111yescharacteristic
340C4×C8C22⋊D1111yescharacteristic
341C4×C8C22×D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C2×C11—22no—
344C2×C11—82no—
345C2×C11#303611yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11C2×#47111yescharacteristic
348D11—161no—
349C24—21no—
350#41—882no—
351C2×Q8—221no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×D4—21no—
355C2×D4—42no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4C2×D4412yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—441no—
367C22×C4C2×D4411yescharacteristic
368C22×C4#433911yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—442no—
371SD16—444no—
372SD16—442no—
373D8—444no—
374M16—44no—
375M16—44no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—41no—
379C2×C8—42no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4C2×D4412yes—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C42—441no—
402C42C2×D4411yescharacteristic
403C42#433911yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1928211yescharacteristic, complemented, Sylow
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—441no—
412C23#6698311yescharacteristic
413Q8—442no—
414Q8—441no—
415Q8—441no—
416Q8—881no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—442no—
421D4—441no—
422D4—441no—
423D4—881no—
424D4—882no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—882no—
438C2×C4#6698311yescharacteristic
439C2×C4#6698311yescharacteristic
440C2×C4#6698311yescharacteristic
441C2×C4C22×D4411yescharacteristic
442C2×C4C2×#433911yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8—42no—
448C8—442no—
449C8—442no—
450C8#6698512yes—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22#1062275412yes—
461C22C2×#6698311yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—881no—
468C4—881no—
469C4—881no—
470C4#1062327912yes—
471C4C2×#6698511yescharacteristic
472C4#1062335311yescharacteristic
473C2—22no—
474C2—82no—
475C2—1761no—
476C2#1307808011yescharacteristic
477C2#1307822511yescharacteristic
478C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC22×C11C2×#121
prime radical#13078707C2
hypercenterC2×#436D11
hypocenterC11#19282
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #13079175C2semidirect
2. #13078715C2semidirect
4. #13068191C2semidirect
5. #13068177C2semidirect
6. #13068115C2semidirect
7. #13068081C2semidirect
8. #13067379C2semidirect
9. #13067314C2semidirect
10. #13067309C2semidirect
11. C2×C11×#436C2semidirect
37. #10622307C22semidirect
38. #10622306C22semidirect
41. #10622294C22semidirect
42. #10622293C22semidirect
43. #10622124C22semidirect
44. #10622123C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
171. C2×#436D11semidirect
406. C11#19282semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130787152
#130787072
#130681912
#130681772
#130681152
#130680812
#130673792
#130673142
#130673092
C2×C11×#4362
#1928211