Finite Group Databasebeta

← #14735068

Subgroups — #14735068

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079806C211yesmaximal, characteristic, complemented
2#13079603C211yesmaximal, characteristic
3#13079019C211yesmaximal, characteristic, complemented
4#13067950C214yesmaximal, complemented
5#13067914C214yesmaximal, complemented
6#13067243C211yesmaximal, characteristic, complemented
7#13067218C211yesmaximal, characteristic, complemented
8#13067214C211yesmaximal, characteristic, complemented
9C2×C11×#563C211yesmaximal, characteristic, complemented
10C11×#563—22no—
11C11×#563—22no—
12C11×#563—22no—
13C11×#563C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×#126—21no—
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23#10623008C2211yescharacteristic
24#10622840—21no—
25#10622830—21no—
26#10622682C2212yescomplemented
27#10622681—22no—
28#10622680C2212yescomplemented
29#10622680C2212yescomplemented
30#10622679—22no—
31#10622678C2212yescomplemented
32#10622671C2212yes—
33#10622670—22no—
34#10622668C2212yes—
35#10622581—21no—
36#10622580—21no—
37#10622579—21no—
38#10622579—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622181C2214yescomplemented
43#10622181C2214yescomplemented
44#10622178C2214yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C2×#4339—21no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—24no—
52C11×#126—24no—
53C11×#126—24no—
54C11×#126—24no—
55C11×#126—24no—
56C11×#125—21no—
57C11×#125—21no—
58C11×#125—21no—
59C11×#125—21no—
60C11×#125D412yes—
61C11×#125D412yes—
62C11×#125C2312yes—
63C11×#125C2312yes—
64C11×#124—21no—
65C11×#124—21no—
66C11×#124D412yes—
67C11×#124C2312yes—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×#4325—22no—
92C2×#4323—22no—
93#66983—21no—
94#66983—21no—
95C2×#4318—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44—21no—
100#66922C2311yescharacteristic
101#66899—22no—
102#66896—22no—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—21no—
105#66874—22no—
106#66874—22no—
107#66873—22no—
108#66873—22no—
109#66873—22no—
110#66873—22no—
111#66872—22no—
112#66871—22no—
113C4⋊(C11⋊C8)—21no—
114C4⋊(C11⋊C8)—21no—
115#66867C2312yes—
116#66867C2312yes—
117#66867C2312yes—
118C4×C11⋊C8—21no—
119#19002—111nomaximal, Sylow
120C24×C11—21no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—81no—
124C2×Q8×C11—82no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—21no—
127C2×D4×C11—81no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—82no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C2×C22⋊D11—41no—
140#4339—44no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×C4×D11—41no—
145C2×Dic22—21no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2411yescharacteristic
176#4325—82no—
177#4323—82no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182#4318—42no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×#563D1111yescharacteristic, complemented
187#3234—111no—
188#3213—111no—
189#3142—111no—
190#1664—114no—
191#1657—114no—
192#1534—111no—
193#1528—111no—
194#1527—111no—
195C23×C11—22no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11#12011yescharacteristic
200C22×D11—41no—
201Q8×C11—42no—
202Q8×C11—81no—
203Q8×C11—84no—
204D4×C11—42no—
205D4×C11—81no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—84no—
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C22⋊D11—82no—
227C2×Dic11—41no—
228D44—42no—
229D44—42no—
230D44—42no—
231C4×D11—82no—
232Dic22—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C11⋊C8—42no—
236#563—22no—
237#563—22no—
238#563—22no—
239#563C2×D1114yes—
240#532—111no—
241C2×C4⋊Q8—21no—
242C2×#126—21no—
243C2×#126—21no—
244C2×#125C2×D1111yescharacteristic
245C2×#125C2×D1111yescharacteristic
246C2×#124C2×D1111yescharacteristic
247C2×#123—21no—
248C2×C22⋊Q8—21no—
249C2×C22⋊Q8—21no—
250#501—112no—
251#496—112no—
252#491—112no—
253#490—112no—
254#490—112no—
255#489—112no—
256#488—222no—
257#481—221no—
258#480—221no—
259#478—222no—
260#463—222no—
261#448—221no—
262#447—221no—
263#432—111no—
264#432—111no—
265#417—221no—
266#417—221no—
267C4×M16—111no—
268#330—114no—
269#330—114no—
270#329—114no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—84no—
277C22×C11#45412yes—
278C22×C11C2×#12011yescharacteristic
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293Dic11—81no—
294C2×#41—221no—
295C22×Q8—21no—
296C22×Q8C22⋊D1111yescharacteristic
297C22×D4C22⋊D1111yescharacteristic
298C23×C4—21no—
299C2×SD16—222no—
300C2×D8—222no—
301C2×M16—221no—
302C4⋊Q8—24no—
303C4⋊Q8—24no—
304C4⋊Q8—111no—
305#127—111no—
306#126—24no—
307#126—24no—
308#126—24no—
309#126—24no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125C22⋊D1112yes—
315#125C22⋊D1112yes—
316#125C22×D1112yes—
317#125C22×D1112yes—
318#124—21no—
319#124—21no—
320#124—221no—
321#124C22⋊D1112yes—
322#124C22×D1112yes—
323#123—24no—
324#123—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329#121—221no—
330#121—221no—
331C4×D4—221no—
332C4×D4—221no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C22⋊D1111yescharacteristic
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C4⋊C4C22⋊D1111yescharacteristic
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42—21no—
349C2×C42C22×D1111yescharacteristic
350#107—222no—
351#106—222no—
352C4⋊C8—221no—
353C4⋊C8—221no—
354#103—222no—
355#103—222no—
356#103—222no—
357#102—222no—
358#102—222no—
359#102—222no—
360#102—222no—
361#102—222no—
362C22⋊C8—221no—
363C22⋊C8—221no—
364#97—112no—
365#97—112no—
366#97—112no—
367C4×C8—221no—
368C2×C11—22no—
369C2×C11—82no—
370C2×C11C2×#45411yescharacteristic
371C2×C11#301911yescharacteristic
372C2×C11#302011yescharacteristic
373D11—161no—
374C24—21no—
375#41—444no—
376C2×Q8—24no—
377C2×Q8—21no—
378C2×Q8—81no—
379C2×Q8—82no—
380C2×Q8—221no—
381C2×Q8C2×C22⋊D1112yes—
382C2×D4—21no—
383C2×D4—81no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—441no—
388C2×D4C2×C22⋊D1112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—82no—
396C22×C4—441no—
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400SD16—882no—
401D8—882no—
402M16—442no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4C2×C22⋊D1112yes—
423C4⋊C4C2×C22⋊D1112yes—
424C4⋊C4C2×C22⋊D1112yes—
425C4⋊C4C2×C22⋊D1112yes—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C42—24no—
436C42C2×C22⋊D1111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1900211yescharacteristic, complemented, Sylow
441C23—22no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—441no—
446C23#6700611yescharacteristic
447Q8—42no—
448Q8—81no—
449Q8—84no—
450Q8—442no—
451D4—42no—
452D4—81no—
453D4—442no—
454D4—442no—
455D4—442no—
456D4—882no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4—441no—
472C2×C4—882no—
473C2×C4#6700611yescharacteristic
474C2×C4#6700611yescharacteristic
475C2×C4#6700611yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C2×C4C22×C22⋊D1111yescharacteristic
479C8—442no—
480C8—442no—
481C8—442no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22#1062285812yes—
492C22C2×#6700611yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—881no—
505C2—22no—
506C2—82no—
507C2—1761no—
508C2C2×#1062285811yescharacteristic
509C2#1307797311yescharacteristic
510C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#563C2
socleC22×C11C2×#120
prime radical#13079603C2
hypercenterC2×#563D11
hypocenterC11#19002
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
3. #13079019C2semidirect
4. #13067950C2semidirect
5. #13067914C2semidirect
6. #13067243C2semidirect
7. #13067218C2semidirect
8. #13067214C2semidirect
9. C2×C11×#563C2semidirect
26. #10622682C22semidirect
28. #10622680C22semidirect
29. #10622680C22semidirect
31. #10622678C22semidirect
42. #10622181C22semidirect
43. #10622181C22semidirect
186. C2×#563D11semidirect
440. C11#19002semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130796032
#130790192
#130679502
#130679142
#130672432
#130672182
#130672142
C2×C11×#5632
#1900211