Finite Group Databasebeta

← #14726688

Subgroups — #14726688

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2C2×#10622840C212yesmaximal, complemented
3#13067584C214yesmaximal, complemented
4#13067567C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#2409C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic, complemented
9C2×#67037—21no—
10C2×C11×C22⋊Q8—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C22×#4325—22no—
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623086—22no—
16#10623085—24no—
17D4×D44—22no—
18#10623041C2212yes—
19#10623024—21no—
20#10623024C2212yes—
21#10623008—21no—
22C11×#395C2212yescomplemented
23C11×#393C2212yescomplemented
24C11×#391—21no—
25C11×#386—21no—
26C11×#385—21no—
27C11×#380C2211yescharacteristic, complemented
28#10622840—24no—
29#10622840C2218yescomplemented
30C2×#66899—22no—
31C2×C22⋊(C11⋊C8)C2212yescomplemented
32#10622166C2212yescomplemented
33#10622163C2212yescomplemented
34#10622089C2218yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—44no—
39C22×Q8×C11C2312yes—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46#67037—44no—
47#67037—44no—
48C2×#4341—24no—
49C2×D4×D11—24no—
50C2×#4339—22no—
51C22×D44—21no—
52C22×D44D412yes—
53C11×C22⋊Q8—44no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D411yescharacteristic
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×#4325—28no—
65C2×#4325—48no—
66#66983—22no—
67#66983—22no—
68#66983—22no—
69#66983—22no—
70#66983—22no—
71#66983—22no—
72#66983D414yes—
73#66983C2314yes—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D412yes—
78C22×C11⋊C8—22no—
79#66950—24no—
80#66948—24no—
81#66939—24no—
82#66939—24no—
83#66935—24no—
84#66935—24no—
85#66928—22no—
86#66927—21no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—21no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95C2312yes—
93#66899—28no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)C2314yes—
96#18195—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C2×Q8×C11—24no—
102C2×Q8×C11—28no—
103C2×Q8×C11—24no—
104C2×Q8×C11—44no—
105C2×Q8×C11—44no—
106C2×Q8×C11—42no—
107C2×Q8×C11—48no—
108C2×Q8×C11—41no—
109C2×Q8×C11—41no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11SD1614yescomplemented
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—44no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137#4341—416no—
138D4×D11—416no—
139#4339—44no—
140#4339—44no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—44no—
146C2×D44—82no—
147C2×D44C2×D414yes—
148C2×C4×D11—24no—
149C2×Dic22—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—44no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—42no—
157C42×C11—21no—
158C42×C11—21no—
159#4325—416no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D414yes—
168C2×C11⋊C8—24no—
169C2×C11⋊C8—44no—
170#3496—111no—
171C2×#448—112no—
172#2409D1111yescharacteristic, complemented
173#1604—114no—
174#1601—114no—
175#1519—112no—
176#1459—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#12012yes—
184C23×C11C2×SD1612yes—
185C23×C11C2×SD1612yescomplemented
186C23×C11AGL(1,ℤ/8)12yes—
187C23×C11C22×D411yescharacteristic
188C22×D11—24no—
189C22×D11—44no—
190C22×D11—44no—
191C22×D11—82no—
192C22×D11—82no—
193C22×D11—82no—
194C22×D11—82no—
195Q8×C11—28no—
196Q8×C11—44no—
197Q8×C11—44no—
198Q8×C11—44no—
199D4×C11—28no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—48no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—81no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11C2×SD1612yescomplemented
222C2×C4×C11C22×D412yes—
223C22⋊D11—48no—
224C22⋊D11—44no—
225C22⋊D11—44no—
226C22⋊D11—48no—
227C2×Dic11—24no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230D44—44no—
231D44—44no—
232D44—44no—
233D44—82no—
234D44—82no—
235C4×D11—48no—
236Dic22—44no—
237C11⋊C8—44no—
238C2×H(5,𝔽2)—221no—
239C23×Q8C2×D1111yescharacteristic, complemented
240C22×SD16—222no—
241#547—222no—
242#546—224no—
243D42—222no—
244#537—112no—
245#534—112no—
246#534—221no—
247#532—221no—
248C2×C22⋊Q8—21no—
249C2×#121—112no—
250C2×#121—221no—
251C2×C4×D4C2×D1111yescharacteristic
252#448—118no—
253#448—224no—
254C2×#103—222no—
255C2×C22⋊C8—112no—
256#395C2×D1112yescomplemented
257#393C2×D1112yescomplemented
258#391—21no—
259#386—21no—
260#385—21no—
261#380C2×D1111yescharacteristic, complemented
262#327—118no—
263#324—112no—
264#323—112no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—21no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—81no—
276C22×C11#45014yes—
277C22×C11C2×#12011yescharacteristic
278C22×C11C22×SD1611yescharacteristic
279C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—164no—
284C2×D11—164no—
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—41no—
289C4×C11—44no—
290C4×C11—41no—
291C4×C11—82no—
292C4×C11B(4,𝔽2)12yes—
293Dic11—44no—
294H(5,𝔽2)—444no—
295H(5,𝔽2)—444no—
296C2×#41—224no—
297C2×#41—222no—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—44no—
302C22×Q8C22×D1112yes—
303C22×D4—112no—
304C22×D4—221no—
305C22×D4—224no—
306C22×D4—222no—
307C22×D4—222no—
308C22×D4C22⋊D1111yescharacteristic
309C23×C4—21no—
310C23×C4C22⋊D1111yescharacteristic
311C23×C4C22×D1111yescharacteristic
312C2×SD16—228no—
313C2×SD16—448no—
314C22×C8—222no—
315C4⋊Q8—221no—
316#127—221no—
317#124—222no—
318#123—224no—
319#123—224no—
320C22⋊Q8—44no—
321C22⋊Q8—224no—
322#121—114no—
323#121—114no—
324#121—224no—
325#121—222no—
326#121—222no—
327#121—222no—
328#121—222no—
329#121—222no—
330#121—222no—
331#120—224no—
332#120—224no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—222no—
336C4×D4—222no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4C22×D1111yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C22⋊C4C22⋊D1111yescharacteristic
347C2×C22⋊C4C22×D1111yescharacteristic
348C2×C42C22⋊D1111yescharacteristic
349#103—228no—
350C22⋊C8—114no—
351C22⋊C8—222no—
352#95—22no—
353#95—22no—
354#95C22×D1112yes—
355C2×C11—21no—
356C2×C11—24no—
357C2×C11—21no—
358C2×C11—42no—
359C2×C11C2×#45011yescharacteristic
360C2×C11#302211yescharacteristic
361C2×C11C2×B(4,𝔽2)11yescharacteristic
362D11—84no—
363C24—222no—
364C24—222no—
365C24C2×C22⋊D1111yescharacteristic
366C24C2×C22⋊D1111yescharacteristic
367#41—444no—
368#41—4416no—
369#41—444no—
370C2×Q8—24no—
371C2×Q8—28no—
372C2×Q8—24no—
373C2×Q8—44no—
374C2×Q8—42no—
375C2×Q8—44no—
376C2×Q8—48no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—222no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—114no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—222no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—224no—
389C2×D4—222no—
390C2×D4—444no—
391C2×D4—4416no—
392C2×D4—444no—
393C2×D4—444no—
394C2×D4—444no—
395C2×D4—444no—
396C2×D4—882no—
397C2×D4#432514yescomplemented
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—42no—
403C22×C4—44no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4D4×D1112yes—
410C22×C4D4×D1112yes—
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416SD16—4416no—
417C2×C8—224no—
418C2×C8—444no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—44no—
422C4⋊C4—114no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—44no—
429C22⋊C4—42no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—224no—
433C22⋊C4—224no—
434C42—21no—
435C42—21no—
436C11#1819511yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—224no—
444C23—444no—
445C23—444no—
446C23—882no—
447C23—882no—
448C23—882no—
449C23—882no—
450C23#6699012yes—
451C23C2×#432512yes—
452C23C2×#432512yescomplemented
453C23#6700212yes—
454C23C22×C22⋊D1111yescharacteristic
455Q8—28no—
456Q8—44no—
457Q8—44no—
458Q8—44no—
459Q8—444no—
460D4—28no—
461D4—444no—
462D4—444no—
463D4—448no—
464D4—444no—
465D4—444no—
466D4—448no—
467D4—444no—
468D4—882no—
469D4—882no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—48no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—81no—
489C2×C4—224no—
490C2×C4—448no—
491C2×C4—444no—
492C2×C4—444no—
493C2×C4#6699011yescharacteristic
494C2×C4#6699011yescharacteristic
495C2×C4C2×#432512yescomplemented
496C2×C4C2×D4×D1112yes—
497C8—444no—
498C22—21no—
499C22—22no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—81no—
509C22—444no—
510C22—444no—
511C22—444no—
512C22—1764no—
513C22—1764no—
514C22#1062265914yes—
515C22C2×#6699011yescharacteristic
516C22C22×#432511yescharacteristic
517C22C2×#6700211yescharacteristic
518C4—22no—
519C4—22no—
520C4—21no—
521C4—41no—
522C4—44no—
523C4—41no—
524C4—82no—
525C4—444no—
526C4#1062264512yes—
527C2—21no—
528C2—21no—
529C2—24no—
530C2—42no—
531C2—884no—
532C2C2×#1062265911yescharacteristic
533C2#1307799411yescharacteristic
534C2C2×#1062264511yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2409C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2409D11
hypocenterC11#18195
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2409

Complements

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

NH ≅ G/Ntype
2. C2×#10622840C2semidirect
3. #13067584C2semidirect
4. #13067567C2semidirect
5. #13067183C2semidirect
6. #13066934C2semidirect
7. C11×#2409C2semidirect
8. C23×Q8×C11C22semidirect
22. C11×#395C22semidirect
23. C11×#393C22semidirect
27. C11×#380C22semidirect
29. #10622840C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
32. #10622166C22semidirect
33. #10622163C22semidirect
34. #10622089C22semidirect
112. C2×D4×C11SD16semidirect
172. #2409D11semidirect
185. C23×C11C2×SD16semidirect
221. C2×C4×C11C2×SD16semidirect
239. C23×Q8C2×D11semidirect
256. #395C2×D11semidirect
257. #393C2×D11semidirect
261. #380C2×D11semidirect
397. C2×D4#4325semidirect
436. C11#18195semidirect
452. C23C2×#4325semidirect
495. C2×C4C2×#4325semidirect

Maximal subgroups

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

subgroupindex
#130823802
C2×#106228402
#130675842
#130675672
#130671832
#130669342
C11×#24092
#1819511