Finite Group Databasebeta

← #14726142

Subgroups — #14726142

Order 2816.

1654 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1654 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2#13077868C212yesmaximal, complemented
3#13067567C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067144C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C11×#2404C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic, complemented
9C23×C22⋊D11—21no—
10C2×C11×#120—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C2×#67002—22no—
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623024—22no—
16#10623024—24no—
17#10623024C2214yes—
18C2×#66939—22no—
19C2×#66935—22no—
20C11×#393C2212yescomplemented
21C11×#392C2212yescomplemented
22C11×#386—21no—
23C11×#386—22no—
24C11×#381C2211yescharacteristic, complemented
25#10622851—24no—
26#10622845—22no—
27#10622840C2214yescomplemented
28#10622830C2214yescomplemented
29#10622820C2212yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C25×C11D411yescharacteristic
33C24×D11—21no—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—44no—
37C22×Q8×C11C2311yescharacteristic, complemented
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11C2311yescharacteristic, complemented
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—48no—
49C23×Dic11—21no—
50C22×D44—21no—
51C22×D44D412yescomplemented
52C11×#120—44no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4D412yes—
59C2×C11×C22⋊C4C2312yes—
60#67002—48no—
61C2×#4325—24no—
62C2×#4323—24no—
63#66983—24no—
64#66983—22no—
65#66983—22no—
66#66983—24no—
67#66983D414yescomplemented
68#66983C2314yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11D412yescomplemented
73C2×#4318—22no—
74#66939—28no—
75#66939—28no—
76#66935—28no—
77#66935—28no—
78C11×#95—21no—
79C11×#95—22no—
80C11×#95C2312yescomplemented
81#66899—24no—
82#66896—24no—
83C22⋊(C11⋊C8)—22no—
84C22⋊(C11⋊C8)C2314yescomplemented
85#18132—111nomaximal, Sylow
86C24×C11—21no—
87C24×C11—21no—
88C24×C11—24no—
89C24×C11—21no—
90C24×C11—42no—
91C24×C11—81no—
92C24×C11C2×D411yescharacteristic
93C24×C11C2×D412yes—
94C23×D11—22no—
95C23×D11—24no—
96C23×D11—44no—
97C23×D11—82no—
98C23×D11—82no—
99C11×#41—28no—
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—44no—
103C2×Q8×C11—22no—
104C2×Q8×C11—42no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—82no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—81no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—28no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—48no—
132C2×C22⋊D11—416no—
133C2×C22⋊D11—48no—
134C2×C22⋊D11—48no—
135C2×C22⋊D11—48no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—44no—
139C2×D44—24no—
140C2×D44—22no—
141C2×D44—44no—
142C2×D44—82no—
143C2×D44C2×D414yes—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—82no—
149#4325—48no—
150#4323—48no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154C4⋊Dic11—24no—
155C4⋊Dic11—22no—
156C4⋊Dic11C2×D414yes—
157#4318—44no—
158C2×C11⋊C8—24no—
159C2×#534—111no—
160#3006—112no—
161#2404D1111yescharacteristic, complemented
162#1601—114no—
163#1595—114no—
164#1510—112no—
165#1462—111no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—42no—
182C23×C11—81no—
183C23×C11—81no—
184C23×C11—88no—
185C23×C11#12011yescharacteristic
186C23×C11#12011yescharacteristic
187C23×C11AGL(1,ℤ/8)14yescomplemented
188C23×C11C22×D411yescharacteristic
189C22×D11—24no—
190C22×D11—44no—
191C22×D11—44no—
192C22×D11—48no—
193C22×D11—44no—
194C22×D11—84no—
195C22×D11—84no—
196C22×D11—816no—
197Q8×C11—24no—
198Q8×C11—42no—
199D4×C11—24no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—88no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—48no—
211C2×C4×C11—42no—
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—81no—
219C2×C4×C11#12012yes—
220C2×C4×C11C22×D412yes—
221C22⋊D11—416no—
222C22⋊D11—48no—
223C22⋊D11—48no—
224C2×Dic11—24no—
225C2×Dic11—44no—
226C2×Dic11—48no—
227D44—44no—
228D44—82no—
229D44—84no—
230C11⋊C8—44no—
231C22×#41C2×D1111yescharacteristic, complemented
232C23×D4—221no—
233C2×AGL(1,ℤ/8)—222no—
234#534—114no—
235#534—224no—
236#534—222no—
237C2×#123—222no—
238C2×#121—112no—
239C2×#121—221no—
240C2×#120—21no—
241C2×#120—222no—
242C22×C22⋊C4C2×D1111yescharacteristic
243#449—224no—
244#448—114no—
245#447—114no—
246#417—222no—
247#407—112no—
248#393C2×D1112yescomplemented
249#392C2×D1112yescomplemented
250#386—21no—
251#386—22no—
252#381C2×D1111yescharacteristic, complemented
253#327—118no—
254#323—114no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—24no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—48no—
266C22×C11—44no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—84no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11B(4,𝔽2)12yes—
276C22×C11C2×#12011yescharacteristic
277C22×C11C2×AGL(1,ℤ/8)12yes—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—88no—
282C2×D11—816no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—82no—
288Dic11—44no—
289C25—221no—
290C25C22⋊D1111yescharacteristic
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—44no—
294C22×Q8C22×D1111yescharacteristic, complemented
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—112no—
298C22×D4—221no—
299C22×D4—222no—
300C22×D4—224no—
301C22×D4—222no—
302C22×D4—224no—
303C22×D4—448no—
304C22×D4C22×D1111yescharacteristic, complemented
305C23×C4—21no—
306C23×C4—221no—
307C23×C4C22⋊D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309AGL(1,ℤ/8)—448no—
310C2×SD16—224no—
311C2×D8—224no—
312C2×M16—222no—
313#123—228no—
314#123—228no—
315#121—114no—
316#121—114no—
317#121—224no—
318#121—222no—
319#121—222no—
320#121—224no—
321#120—44no—
322#120—228no—
323#120—228no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—221no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4C22⋊D1112yes—
334C2×C22⋊C4C22×D1112yes—
335#103—224no—
336#102—224no—
337C22⋊C8—114no—
338C22⋊C8—222no—
339#95—21no—
340#95—22no—
341#95C22×D1112yescomplemented
342C2×C11—22no—
343C2×C11—22no—
344C2×C11—44no—
345C2×C11—41no—
346C2×C11—82no—
347C2×C11#300311yescharacteristic
348C2×C11#301911yescharacteristic
349C2×C11C2×B(4,𝔽2)11yescharacteristic
350D11—84no—
351C24—21no—
352C24—21no—
353C24—24no—
354C24—21no—
355C24—42no—
356C24—81no—
357C24—224no—
358C24—222no—
359C24—444no—
360C24—882no—
361C24—882no—
362C24C2×C22⋊D1111yescharacteristic
363C24C2×C22⋊D1112yes—
364#41—28no—
365#41—44no—
366#41—44no—
367#41—44no—
368C2×Q8—22no—
369C2×Q8—42no—
370C2×D4—24no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—82no—
379C2×D4—114no—
380C2×D4—224no—
381C2×D4—228no—
382C2×D4—224no—
383C2×D4—224no—
384C2×D4—222no—
385C2×D4—444no—
386C2×D4—448no—
387C2×D4—4416no—
388C2×D4—448no—
389C2×D4—448no—
390C2×D4—448no—
391C2×D4—882no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—81no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—444no—
404C22×C4D4×D1112yes—
405C22×C4D4×D1112yes—
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409SD16—448no—
410D8—448no—
411M16—444no—
412C2×C8—224no—
413C4⋊C4—114no—
414C4⋊C4—224no—
415C4⋊C4—222no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C22⋊C4—82no—
421C22⋊C4—228no—
422C22⋊C4—224no—
423C22⋊C4—224no—
424C11#1813211yescharacteristic, complemented, Sylow
425C23—24no—
426C23—24no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—41no—
438C23—42no—
439C23—41no—
440C23—42no—
441C23—81no—
442C23—81no—
443C23—88no—
444C23—224no—
445C23—444no—
446C23—448no—
447C23—444no—
448C23—444no—
449C23—884no—
450C23—884no—
451C23—8816no—
452C23#6699011yescharacteristic
453C23#6699011yescharacteristic
454C23#6700214yescomplemented
455C23C22×C22⋊D1111yescharacteristic
456Q8—24no—
457Q8—42no—
458D4—24no—
459D4—42no—
460D4—44no—
461D4—44no—
462D4—88no—
463D4—444no—
464D4—4416no—
465D4—448no—
466D4—448no—
467D4—882no—
468D4—884no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—48no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—81no—
484C2×C4—224no—
485C2×C4—444no—
486C2×C4—448no—
487C2×C4#6699012yes—
488C2×C4C2×D4×D1112yes—
489C8—444no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—24no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—44no—
499C22—44no—
500C22—48no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—82no—
506C22—82no—
507C22—84no—
508C22—81no—
509C22—81no—
510C22—444no—
511C22—444no—
512C22—444no—
513C22—888no—
514C22—8816no—
515C22#1062264512yes—
516C22C2×#6699011yescharacteristic
517C22C2×#6700212yes—
518C4—22no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—82no—
523C4—444no—
524C2—22no—
525C2—22no—
526C2—41no—
527C2—44no—
528C2—82no—
529C2—884no—
530C2#1307784211yescharacteristic
531C2#1307797211yescharacteristic
532C2C2×#1062264511yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2404C2
socleC22×C11C2×#120
hypercenter#2404D11
hypocenterC11#18132
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. #13077868C2semidirect
3. #13067567C2semidirect
4. #13067533C2semidirect
5. #13067144C2semidirect
6. #13066943C2semidirect
7. C11×#2404C2semidirect
8. C22×C11×#41C22semidirect
20. C11×#393C22semidirect
21. C11×#392C22semidirect
24. C11×#381C22semidirect
27. #10622840C22semidirect
28. #10622830C22semidirect
29. #10622820C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
37. C22×Q8×C11C23semidirect
40. C22×D4×C11C23semidirect
51. C22×D44D4semidirect
67. #66983D4semidirect
72. C2×C4⋊Dic11D4semidirect
80. C11×#95C23semidirect
84. C22⋊(C11⋊C8)C23semidirect
161. #2404D11semidirect
187. C23×C11AGL(1,ℤ/8)semidirect
231. C22×#41C2×D11semidirect
248. #393C2×D11semidirect
249. #392C2×D11semidirect
252. #381C2×D11semidirect
294. C22×Q8C22×D11semidirect
304. C22×D4C22×D11semidirect
341. #95C22×D11semidirect
424. C11#18132semidirect
454. C23#67002semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
#130778682
#130675672
#130675332
#130671442
#130669432
C11×#24042
#1813211