Finite Group Databasebeta

← #14926495

Subgroups — #14926495

Order 2816.

4346 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
1C22×#67006C211yesmaximal, characteristic
2#13076908C214yesmaximal, complemented
3#13074389C214yesmaximal, complemented
4#13072894C214yesmaximal, complemented
5#13072012C218yesmaximal, complemented
6#13071943C214yesmaximal, complemented
7#13071228C212yesmaximal, complemented
8#13071191C212yesmaximal, complemented
9C2×#10622860C211yesmaximal, characteristic, complemented
10C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
11C26×C11C2211yescharacteristic
12C24×C4×C11C2212yescomplemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C22×C11×C22⋊C4—28no—
16C22×C11×C22⋊C4C2214yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2214yescomplemented
19C22×C11×C22⋊C4C2212yescomplemented
20C2×#67006—28no—
21C2×#67006C2214yes—
22C2×#67006C2212yes—
23C2×#67006C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2214yescomplemented
28C2×#66982C2218yescomplemented
29#10622860C2214yes—
30#10622860C2212yescomplemented
31#10622860C2212yescomplemented
32#10622826C2218yescomplemented
33#10622826C2218yescomplemented
34#10622824C2218yescomplemented
35#10622823C2218yescomplemented
36#10622823C2218yescomplemented
37#10622572C22116yescomplemented
38#10622571C2218yescomplemented
39#10622568C2214yescomplemented
40#10622565C22116yescomplemented
41#10622559C2218yescomplemented
42#10622556C2214yescomplemented
43#10622555C2218yescomplemented
44C25×C11—28no—
45C25×C11—48no—
46C25×C11D418yes—
47C25×C11C2311yescharacteristic
48C25×C11C2312yes—
49C25×C11C2312yes—
50C25×C11C2311yescharacteristic
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11—28no—
54C23×C4×C11—48no—
55C23×C4×C11C2314yes—
56C23×C4×C11C2314yes—
57C23×C4×C11C2314yes—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—48no—
62C22×C22⋊D11C2314yes—
63C22×C22⋊D11C2312yes—
64C22×C22⋊D11C2312yes—
65C22×C22⋊D11C2314yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2314yes—
68C23×Dic11C2312yes—
69C2×C11×C22⋊C4—216no—
70C2×C11×C22⋊C4—28no—
71C2×C11×C22⋊C4—216no—
72C2×C11×C22⋊C4—28no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2314yes—
75C2×C11×C22⋊C4C2318yes—
76#67006—28no—
77#67006—216no—
78#67006—28no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—48no—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2312yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2312yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91#66982—416no—
92C2×(C2×D11)⋊C4C23116yescomplemented
93C2×Dic11⋊C4C23116yescomplemented
94C11⋊#95C23116yescomplemented
95C11⋊#95C23116yescomplemented
96#34992—111nomaximal, Sylow
97C24×C11—24no—
98C24×C11—28no—
99C24×C11—232no—
100C24×C11—28no—
101C24×C11—28no—
102C24×C11—24no—
103C24×C11—28no—
104C24×C11—28no—
105C24×C11—432no—
106C24×C11—44no—
107C24×C11—44no—
108C24×C11—44no—
109C24×C11—44no—
110C24×C11—464no—
111C24×C11C2×D414yes—
112C24×C11C2×D418yes—
113C24×C11C2×D418yes—
114C24×C11C2×D414yes—
115C24×C11C2×D414yes—
116C24×C11#4118yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C24×C11C2411yescharacteristic
120C24×C11C2411yescharacteristic
121C24×C11C2412yes—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—44no—
125C23×D11C2412yes—
126C22×C4×C11—28no—
127C22×C4×C11—28no—
128C22×C4×C11—28no—
129C22×C4×C11—216no—
130C22×C4×C11—48no—
131C22×C4×C11—48no—
132C22×C4×C11—432no—
133C22×C4×C11C2418yes—
134C2×C22⋊D11—28no—
135C2×C22⋊D11—24no—
136C2×C22⋊D11—24no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—216no—
141C2×C22⋊D11—48no—
142C2×C22⋊D11—432no—
143C2×C22⋊D11—416no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—28no—
148C22×Dic11—44no—
149C22×Dic11—48no—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2418yes—
153C11×C22⋊C4—216no—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—28no—
156C22⋊Dic11—28no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159C22⋊Dic11—28no—
160C22⋊Dic11—28no—
161C22⋊Dic11—28no—
162C22⋊Dic11—216no—
163C22⋊Dic11—48no—
164(C2×D11)⋊C4—416no—
165Dic11⋊C4—416no—
166C22×#120—111no—
167C23×C22⋊C4D1111yescharacteristic, complemented
168#2849—114no—
169#2622—114no—
170#2483—114no—
171#2412—118no—
172#2405—114no—
173#2315—112no—
174#2308—112no—
175C2×#379—111no—
176C23×C11—232no—
177C23×C11—28no—
178C23×C11—216no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—216no—
185C23×C11—216no—
186C23×C11—28no—
187C23×C11—216no—
188C23×C11—216no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—48no—
195C23×C11—48no—
196C23×C11—416no—
197C23×C11—432no—
198C23×C11—432no—
199C23×C11—4128no—
200C23×C11—416no—
201C23×C11#123116yescomplemented
202C23×C11C22×D414yes—
203C23×C11C22×D412yes—
204C23×C11C22×D412yes—
205C23×C11C22×D412yes—
206C23×C11C22×D414yes—
207C23×C11C2×#4114yes—
208C23×C11C2×#4114yes—
209C23×C11C2×#4114yes—
210C23×C11H(5,𝔽2)18yes—
211C23×C11C2511yescharacteristic
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—28no—
215C22×D11—48no—
216C22×D11—44no—
217C22×D11—88no—
218C2×C4×C11—28no—
219C2×C4×C11—216no—
220C2×C4×C11—416no—
221C2×C4×C11—416no—
222C2×C4×C11—416no—
223C22⋊D11—416no—
224C22⋊D11—48no—
225C22⋊D11—48no—
226C22⋊D11—416no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—28no—
230C2×Dic11—24no—
231C2×Dic11—28no—
232C2×Dic11—216no—
233C2×Dic11—48no—
234C2×Dic11—44no—
235C2×Dic11—88no—
236C26C2×D1111yescharacteristic
237C23×D4—111no—
238C23×D4—112no—
239C24×C4C2×D1112yescomplemented
240C2×#123—118no—
241C2×#120—112no—
242C2×#120—112no—
243C2×#120—114no—
244C2×#120—228no—
245C22×C22⋊C4—28no—
246C22×C22⋊C4—112no—
247C22×C22⋊C4—111no—
248C22×C22⋊C4—112no—
249C22×C22⋊C4—114no—
250C22×C22⋊C4C2×D1112yes—
251C22×C22⋊C4C2×D1114yes—
252C22×C22⋊C4C2×D1112yescomplemented
253C22×C22⋊C4C2×D1114yescomplemented
254#397—1116no—
255#394—1116no—
256#386—118no—
257#386—118no—
258#386—118no—
259#385—118no—
260#385—118no—
261#385—118no—
262#381—118no—
263#381—114no—
264#380—118no—
265#379—112no—
266#379—112no—
267#379—114no—
268#379—114no—
269C22×C11—232no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—28no—
276C22×C11—28no—
277C22×C11—216no—
278C22×C11—28no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—416no—
283C22×C11—432no—
284C22×C11—432no—
285C22×C11—416no—
286C22×C11—48no—
287C22×C11C2×#12314yes—
288C22×C11C2×#12314yes—
289C22×C11C2×#12314yes—
290C22×C11#53418yes—
291C22×C11C23×D411yescharacteristic
292C22×C11C22×#4112yes—
293C22×C11C2×H(5,𝔽2)14yes—
294C2×D11—42no—
295C2×D11—44no—
296C2×D11—48no—
297C2×D11—88no—
298C4×C11—48no—
299Dic11—42no—
300Dic11—44no—
301Dic11—48no—
302C25—28no—
303C25—48no—
304C25—111no—
305C25C22⋊D1118yes—
306C25C22×D1111yescharacteristic
307C25C22×D1112yes—
308C25C22×D1112yes—
309C25C22×D1111yescharacteristic
310C25C22×D1111yescharacteristic
311C22×D4—114no—
312C22×D4—112no—
313C22×D4—112no—
314C22×D4—114no—
315C22×D4—228no—
316C22×D4—228no—
317C22×D4—224no—
318C22×D4—448no—
319C23×C4—28no—
320C23×C4—48no—
321C23×C4—111no—
322C23×C4—114no—
323C23×C4—112no—
324C23×C4C22×D1114yes—
325C23×C4C22×D1114yes—
326C23×C4C22×D1114yes—
327#123—4416no—
328#120—228no—
329#120—2216no—
330#120—228no—
331C2×C4⋊C4—1116no—
332C2×C22⋊C4—216no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—216no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—112no—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—114no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—118no—
344C2×C22⋊C4—1116no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—228no—
347C2×C22⋊C4—224no—
348C2×C22⋊C4—448no—
349C2×C22⋊C4C22×D1114yes—
350C2×C22⋊C4C22×D1114yes—
351C2×C22⋊C4C22×D1118yes—
352#95—1116no—
353#95—1116no—
354C2×C11—24no—
355C2×C11—24no—
356C2×C11—28no—
357C2×C11—24no—
358C2×C11—44no—
359C2×C11C22×#12311yescharacteristic
360C2×C11C2×#53412yes—
361C2×C11#349014yes—
362D11—82no—
363C24—24no—
364C24—28no—
365C24—232no—
366C24—28no—
367C24—28no—
368C24—24no—
369C24—28no—
370C24—28no—
371C24—44no—
372C24—44no—
373C24—44no—
374C24—44no—
375C24—432no—
376C24—464no—
377C24—112no—
378C24—222no—
379C24—224no—
380C24—444no—
381C24#433918yes—
382C24C2×C22⋊D1114yes—
383C24C2×C22⋊D1118yes—
384C24C2×C22⋊D1118yes—
385C24C2×C22⋊D1114yes—
386C24C2×C22⋊D1114yes—
387C24C23×D1112yes—
388C24C23×D1111yescharacteristic
389C24C23×D1111yescharacteristic
390C24C23×D1111yescharacteristic
391C24C23×D1112yes—
392C2×D4—228no—
393C2×D4—228no—
394C2×D4—2216no—
395C2×D4—228no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—228no—
399C2×D4—448no—
400C2×D4—4432no—
401C2×D4—4416no—
402C22×C4—216no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—48no—
407C22×C4—48no—
408C22×C4—432no—
409C22×C4—112no—
410C22×C4—118no—
411C22×C4—114no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—228no—
416C22×C4—444no—
417C22×C4—448no—
418C22×C4C23×D1118yes—
419C4⋊C4—4416no—
420C22⋊C4—216no—
421C22⋊C4—28no—
422C22⋊C4—28no—
423C22⋊C4—228no—
424C22⋊C4—228no—
425C22⋊C4—2216no—
426C22⋊C4—228no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—228no—
430C22⋊C4—4416no—
431C22⋊C4—448no—
432C11#3499211yescharacteristic, complemented, Sylow
433C23—232no—
434C23—28no—
435C23—216no—
436C23—24no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—216no—
442C23—216no—
443C23—28no—
444C23—216no—
445C23—216no—
446C23—24no—
447C23—24no—
448C23—24no—
449C23—416no—
450C23—48no—
451C23—48no—
452C23—48no—
453C23—48no—
454C23—432no—
455C23—432no—
456C23—4128no—
457C23—416no—
458C23—224no—
459C23—228no—
460C23—222no—
461C23—448no—
462C23—444no—
463C23—888no—
464C23#66982116yescomplemented
465C23C2×#433914yes—
466C23C2×#433914yes—
467C23C2×#433914yes—
468C23#6703718yes—
469C23C22×C22⋊D1114yes—
470C23C22×C22⋊D1112yes—
471C23C22×C22⋊D1112yes—
472C23C22×C22⋊D1112yes—
473C23C22×C22⋊D1114yes—
474C23C24×D1111yescharacteristic
475D4—4416no—
476D4—448no—
477D4—448no—
478D4—4416no—
479C2×C4—216no—
480C2×C4—28no—
481C2×C4—416no—
482C2×C4—416no—
483C2×C4—416no—
484C2×C4—228no—
485C2×C4—224no—
486C2×C4—2216no—
487C2×C4—228no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—448no—
491C2×C4—444no—
492C2×C4—888no—
493C22—232no—
494C22—24no—
495C22—24no—
496C22—24no—
497C22—24no—
498C22—28no—
499C22—28no—
500C22—216no—
501C22—28no—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—24no—
506C22—416no—
507C22—432no—
508C22—432no—
509C22—416no—
510C22—48no—
511C22—444no—
512C22—448no—
513C22—442no—
514C22—888no—
515C22C2×#6698214yes—
516C22C2×#6698214yes—
517C22C2×#6698214yes—
518C22#1062333518yes—
519C22C22×#433912yes—
520C22C2×#6703714yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—48no—
523C4—444no—
524C4—448no—
525C4—442no—
526C2—24no—
527C2—28no—
528C2—24no—
529C2—24no—
530C2—44no—
531C2—882no—
532C2C22×#6698211yescharacteristic
533C2C2×#1062333512yes—
534C2#1308230514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC23×C11×C22⋊C4C2
prime radicalC22×#67006C2
hypercenterC23×C22⋊C4D11
hypocenterC11#34992
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13076908C2semidirect
3. #13074389C2semidirect
4. #13072894C2semidirect
5. #13072012C2semidirect
6. #13071943C2semidirect
7. #13071228C2semidirect
8. #13071191C2semidirect
9. C2×#10622860C2semidirect
10. C23×C11×C22⋊C4C2semidirect
12. C24×C4×C11C22semidirect
18. C22×C11×C22⋊C4C22semidirect
19. C22×C11×C22⋊C4C22semidirect
27. C22×C22⋊Dic11C22semidirect
28. C2×#66982C22semidirect
30. #10622860C22semidirect
31. #10622860C22semidirect
32. #10622826C22semidirect
33. #10622826C22semidirect
34. #10622824C22semidirect
35. #10622823C22semidirect
36. #10622823C22semidirect
37. #10622572C22semidirect
38. #10622571C22semidirect
39. #10622568C22semidirect
40. #10622565C22semidirect
41. #10622559C22semidirect
42. #10622556C22semidirect
43. #10622555C22semidirect
92. C2×(C2×D11)⋊C4C23semidirect
93. C2×Dic11⋊C4C23semidirect
94. C11⋊#95C23semidirect
95. C11⋊#95C23semidirect
167. C23×C22⋊C4D11semidirect
201. C23×C11#123semidirect
239. C24×C4C2×D11semidirect
252. C22×C22⋊C4C2×D11semidirect
253. C22×C22⋊C4C2×D11semidirect
432. C11#34992semidirect
464. C23#66982semidirect

Maximal subgroups

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

subgroupindex
C22×#670062
#130769082
#130743892
#130728942
#130720122
#130719432
#130712282
#130711912
C2×#106228602
C23×C11×C22⋊C42
#3499211