Finite Group Databasebeta

← #14732278

Subgroups — #14732278

Order 2816.

1040 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic, complemented
4#13067802C214yesmaximal, complemented
5#13067675C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067045C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#559C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#559—22no—
12C11×#559—22no—
13C11×#559C2214yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124—21no—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C2×#66995—21no—
23#10623008C2211yescharacteristic
24#10622840—21no—
25#10622830—22no—
26#10622686C2212yes—
27#10622685—22no—
28#10622683C2212yes—
29#10622644C2212yescomplemented
30#10622641—22no—
31#10622640C2212yescomplemented
32#10622640C2212yescomplemented
33C4×#4325—22no—
34#10622633C2212yescomplemented
35#10622581—21no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622182C2214yes—
41Q8⋊(C11⋊C8)C2214yescomplemented
42Q8⋊(C11⋊C8)C2214yescomplemented
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11D412yes—
48C23×C4×C11—22no—
49C2×#4339—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127D412yes—
53C11×#127C2312yes—
54C11×#124—24no—
55C11×#124—24no—
56C11×#124—24no—
57C11×#124—24no—
58C11×#123—28no—
59C11×#123—28no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D412yes—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×Q8×C11C2312yes—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83#66995—44no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4323—24no—
87#66983—21no—
88#66983—21no—
89C2×#4318—21no—
90#66928—21no—
91#66927C2311yescharacteristic
92C4×D44—21no—
93C4×D44—21no—
94#66922C2311yescharacteristic
95#66899—22no—
96#66896—24no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66872—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109#18750—111nomaximal, Sylow
110C24×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—44no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—82no—
127C2×D4×C11C2×D414yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—28no—
133C22×C4×C11—84no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—41no—
138#4339—42no—
139#4339—42no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×C4×D11—41no—
144C2×Dic22—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—28no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164#4326—44no—
165#4325—44no—
166#4325—44no—
167#4323—84no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172#4318—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×#559D1111yescharacteristic, complemented
177#3205—111no—
178#3103—111no—
179#3037—111no—
180#1640—114no—
181#1620—114no—
182#1545—111no—
183#1487—111no—
184#1479—111no—
185C23×C11—24no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11#12011yescharacteristic
190C22×D11—41no—
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—42no—
196Q8×C11—42no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—82no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—88no—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#13512yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C22⋊D11—82no—
224C2×Dic11—41no—
225D44—42no—
226D44—41no—
227D44—41no—
228D44—42no—
229C4×D11—82no—
230Dic22—41no—
231Dic22—41no—
232C11⋊C8—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C2×#137—221no—
236#559—22no—
237#559—22no—
238#559—22no—
239#559C2×D1114yes—
240#532—111no—
241C2×#127C2×D1111yescharacteristic
242C2×#124—21no—
243C2×#124—21no—
244C2×#123—22no—
245C2×C4×Q8C2×D1111yescharacteristic
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249#493—112no—
250#486—112no—
251#481—221no—
252#475—112no—
253#464—222no—
254#462—112no—
255#460—112no—
256#460—112no—
257#459—222no—
258#448—221no—
259#447—222no—
260C4×SD16—222no—
261#431—111no—
262#431—111no—
263#423—111no—
264#417—221no—
265#331—114no—
266Q8⋊C8—114no—
267Q8⋊C8—114no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—88no—
274C22×C11#44912yes—
275C22×C11C2×#12011yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11#44912yes—
287C4×C11C2×#13511yescharacteristic
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C11#57512yes—
290Dic11—81no—
291C2×#41—221no—
292C22×Q8C22⋊D1111yescharacteristic
293C22×Q8C22⋊D1111yescharacteristic
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C22⋊D1112yes—
297C23×C4—22no—
298#137—444no—
299C2×Q16—222no—
300C2×SD16—222no—
301C2×SD16—222no—
302C2×D8—224no—
303C2×M16—221no—
304C4⋊Q8—111no—
305#127—21no—
306#127—21no—
307#127—111no—
308#127C22⋊D1112yes—
309#127C22×D1112yes—
310#124—24no—
311#124—24no—
312#124—24no—
313#124—24no—
314#124—221no—
315#123—28no—
316#123—28no—
317#121—221no—
318#121—221no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8C22⋊D1112yes—
324C4×Q8C22⋊D1112yes—
325C4×Q8C22×D1112yes—
326C4×Q8C22×D1112yes—
327C4×D4—24no—
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—221no—
332C4×D4—221no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C22⋊D1111yescharacteristic
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42C22×D1111yescharacteristic
343#106—222no—
344C4⋊C8—112no—
345C4⋊C8—112no—
346C4⋊C8—221no—
347C4⋊C8—221no—
348#103—222no—
349#103—222no—
350#102—224no—
351#102—222no—
352#102—222no—
353C22⋊C8—221no—
354C22⋊C8—221no—
355C4×C8—112no—
356C4×C8—221no—
357C2×C11—22no—
358C2×C11—84no—
359C2×C11C2×#44911yescharacteristic
360C2×C11#300511yescharacteristic
361C2×C11#301911yescharacteristic
362D11—161no—
363C24—22no—
364#41—442no—
365#41—442no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—42no—
371C2×Q8—221no—
372C2×Q8C2×C22⋊D1112yes—
373C2×Q8C2×C22⋊D1112yes—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—44no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—82no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—441no—
387C2×D4C2×C22⋊D1114yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—28no—
393C22×C4—84no—
394C22×C4—441no—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398Q16—444no—
399SD16—444no—
400SD16—444no—
401D8—884no—
402M16—442no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4C2×C22⋊D1112yes—
415C4⋊C4C2×C22⋊D1112yes—
416C22⋊C4—28no—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C42—22no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42C2×C22⋊D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C23×D1111yescharacteristic
429C11#1875011yescharacteristic, complemented, Sylow
430C23—24no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—441no—
435C23#6700611yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—22no—
439Q8—22no—
440Q8—42no—
441Q8—42no—
442Q8—441no—
443Q8—441no—
444D4—44no—
445D4—44no—
446D4—42no—
447D4—42no—
448D4—44no—
449D4—44no—
450D4—82no—
451D4—442no—
452D4—441no—
453D4—441no—
454D4—442no—
455D4—882no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—88no—
467C2×C4—441no—
468C2×C4—882no—
469C2×C4#6700212yes—
470C2×C4#6700312yes—
471C2×C4#6700611yescharacteristic
472C2×C4#6700611yescharacteristic
473C2×C4#6700611yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—442no—
478C8—442no—
479C8—442no—
480C22—21no—
481C22—21no—
482C22—44no—
483C22—44no—
484C22—44no—
485C22—88no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22#1062285112yes—
490C22C2×#6700611yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—881no—
499C4#1062285112yes—
500C4C2×#6700211yescharacteristic
501C4C2×#6700311yescharacteristic
502C4#1062335312yes—
503C2—22no—
504C2—84no—
505C2—1761no—
506C2C2×#1062285111yescharacteristic
507C2#1307785811yescharacteristic
508C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#559C2
socleC22×C11C2×#120
prime radical#13079534C2
hypercenterC2×#559D11
hypocenterC11#18750
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. #13078647C2semidirect
3. #13078088C2semidirect
4. #13067802C2semidirect
5. #13067675C2semidirect
6. #13067284C2semidirect
7. #13067045C2semidirect
8. #13067011C2semidirect
9. C2×C11×#559C2semidirect
29. #10622644C22semidirect
31. #10622640C22semidirect
32. #10622640C22semidirect
34. #10622633C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
176. C2×#559D11semidirect
429. C11#18750semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130786472
#130780882
#130678022
#130676752
#130672842
#130670452
#130670112
C2×C11×#5592
#1875011