Finite Group Databasebeta

← #15620286

Subgroups — #15620286

Order 2816.

4746 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C212yesmaximal, complemented
2C2×#10623356C211yesmaximal, characteristic, complemented
3#13077911C218yesmaximal, complemented
4#13077893C218yesmaximal, complemented
5#13077876C218yesmaximal, complemented
6#13077135C212yesmaximal, complemented
7#13077061C211yesmaximal, characteristic, complemented
8C2×C11×#585C211yesmaximal, characteristic
9C11×#585—216no—
10C2×C11×2−1+4—21no—
11C2×C11×2−1+4C2214yes—
12C2×C11×H(5,𝔽2)—22no—
13C2×C11×H(5,𝔽2)—21no—
14C2×C11×H(5,𝔽2)C2214yes—
15C22×C11×#41—24no—
16C22×C11×#41C2214yes—
17C22×C11×#41C2212yes—
18C22×C11×#41C2211yescharacteristic
19C23×Dic22C2211yescharacteristic, complemented
20#10623356—24no—
21#10623356C2218yescomplemented
22C2×#67004—216no—
23C2×#67004C2218yescomplemented
24C2×#67004C2218yescomplemented
25C2×#66997—21no—
26C22×#4326C2214yescomplemented
27C2×#66989—21no—
28C2×#66988—22no—
29C22×#4324C2214yescomplemented
30C2×#66979C2211yescharacteristic, complemented
31C2×#66977C2214yescomplemented
32C22×#4318C2212yescomplemented
33#10622852C22132yescomplemented
34#10622847C2218yescomplemented
35#10622846C2218yescomplemented
36#10622845C2218yescomplemented
37#10622841C22116yescomplemented
38#10622838C2214yescomplemented
39#10622831C22116yescomplemented
40#10622828C2214yescomplemented
41#10622820C2214yescomplemented
42C11×2−1+4—216no—
43C11×2−1+4—216no—
44C11×2−1+4—216no—
45C11×H(5,𝔽2)—216no—
46C11×H(5,𝔽2)—232no—
47C11×H(5,𝔽2)—216no—
48C11×H(5,𝔽2)—216no—
49C2×C11×#41—264no—
50C2×C11×#41—232no—
51C2×C11×#41—24no—
52C2×C11×#41—28no—
53C2×C11×#41—24no—
54C2×C11×#41—24no—
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—22no—
58C2×C11×#41—28no—
59C2×C11×#41—28no—
60C2×C11×#41D4116yes—
61C2×C11×#41D414yes—
62C2×C11×#41C2318yes—
63C2×C11×#41C2314yes—
64C2×C11×#41C2314yes—
65C2×C11×#41C2314yes—
66C22×Q8×C11—24no—
67C22×Q8×C11D411yescharacteristic
68C22×Q8×C11C2314yes—
69C22×Q8×C11C2312yes—
70C22×D4×C11—24no—
71C22×D4×C11—22no—
72C22×D4×C11—28no—
73C22×D4×C11—24no—
74C22×D4×C11D412yes—
75C22×D4×C11D411yescharacteristic
76C22×D4×C11C2314yes—
77C22×D4×C11C2312yes—
78C23×C4×C11—24no—
79C23×C4×C11—22no—
80C23×C4×C11C2312yes—
81C23×C4×C11C2311yescharacteristic
82C23×Dic11—21no—
83C22×Dic22—28no—
84C22×Dic22—21no—
85C22×Dic22—22no—
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—21no—
90#67004—232no—
91#67004—232no—
92#66997—28no—
93C2×#4326—216no—
94C2×#4326C23116yes—
95#66989—28no—
96#66988—216no—
97C2×#4324—216no—
98C2×#4324C23116yes—
99#66979—22no—
100#66979C2314yes—
101C2×C4⋊Dic11C2312yes—
102#66977—28no—
103#66977C23116yes—
104C2×Dic11⋊C4—24no—
105C2×C4×Dic11—21no—
106C2×#4318—28no—
107C2×#4318C2314yes—
108C2×#4318C2314yes—
109C22×C11⋊C8C2314yes—
110#66899C23116yes—
111#66896C23116yes—
112C22⋊(C11⋊C8)C23116yes—
113#60370—111nomaximal, Sylow
114C24×C11—24no—
115C24×C11—22no—
116C24×C11C2×D412yes—
117C24×C11C2×D411yescharacteristic
118C11×#41—232no—
119C11×#41—264no—
120C11×#41—232no—
121C11×#41—232no—
122C11×#41—232no—
123C11×#41—216no—
124C11×#41—216no—
125C11×#41—216no—
126C11×#41—216no—
127C11×#41—216no—
128C11×#41—28no—
129C11×#41—28no—
130C11×#41—28no—
131C11×#41—28no—
132C11×#41C2×D4116yes—
133C11×#41C2×D4116yes—
134C2×Q8×C11—232no—
135C2×Q8×C11—216no—
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C2×Q8×C11—22no—
139C2×Q8×C11—24no—
140C2×Q8×C11C2×D418yes—
141C2×Q8×C11C2×D414yes—
142C2×Q8×C11C2414yes—
143C2×D4×C11—232no—
144C2×D4×C11—264no—
145C2×D4×C11—232no—
146C2×D4×C11—216no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—216no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—24no—
156C2×D4×C11C2×D418yes—
157C2×D4×C11C2×D414yes—
158C2×D4×C11C2×D418yes—
159C2×D4×C11C2414yes—
160C22×C4×C11—232no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—216no—
164C22×C4×C11—24no—
165C22×C4×C11—28no—
166C22×C4×C11—24no—
167C22×C4×C11—28no—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D418yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11—44no—
180C2×Dic22—28no—
181C2×Dic22—28no—
182C2×Dic22—28no—
183C2×Dic22—22no—
184C2×Dic22—24no—
185C2×Dic22—48no—
186C2×Dic22—44no—
187C2×Dic22C2414yes—
188C22⋊Dic11—216no—
189C22⋊Dic11—24no—
190#4326—232no—
191#4324—232no—
192C4⋊Dic11—22no—
193C4⋊Dic11C2414yes—
194Dic11⋊C4—216no—
195C4×Dic11—24no—
196#4318—28no—
197#4318—28no—
198C2×C11⋊C8—28no—
199C2×C11⋊C8C2418yes—
200C2×#585D1111yescharacteristic
201C22×#137—112no—
202C2×#536—111no—
203#3011—118no—
204#3009—118no—
205#3007—118no—
206#2896—112no—
207#2879—111no—
208C23×C11—216no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—28no—
212C23×C11—42no—
213C23×C11—44no—
214C23×C11—84no—
215C23×C11—88no—
216C23×C11#12014yes—
217C23×C11C22×D414yes—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—216no—
221Q8×C11—28no—
222Q8×C11—28no—
223Q8×C11—24no—
224Q8×C11C22×D418yes—
225D4×C11—232no—
226D4×C11—216no—
227D4×C11—216no—
228D4×C11—216no—
229D4×C11—216no—
230D4×C11—28no—
231D4×C11—28no—
232D4×C11—24no—
233D4×C11C22×D418yes—
234C2×C4×C11—216no—
235C2×C4×C11—232no—
236C2×C4×C11—28no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—216no—
240C2×C4×C11—28no—
241C2×C4×C11—216no—
242C2×C4×C11—28no—
243C2×C4×C11#12018yes—
244C2×C4×C11#12014yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D414yes—
251C2×C4×C11C2511yescharacteristic
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—44no—
255C2×Dic11—48no—
256C2×Dic11—44no—
257Dic22—28no—
258Dic22—44no—
259Dic22—48no—
260C11⋊C8—28no—
261#585—216no—
262C2×2−1+4—21no—
263C2×2−1+4C2×D1114yes—
264C2×H(5,𝔽2)—22no—
265C2×H(5,𝔽2)—21no—
266C2×H(5,𝔽2)C2×D1114yes—
267C22×#41—24no—
268C22×#41C2×D1114yes—
269C22×#41C2×D1112yes—
270C22×#41C2×D1111yescharacteristic
271C23×Q8—111no—
272C2×#137—118no—
273C2×#137—118no—
274C2×#137—2216no—
275C22×Q16—114no—
276C22×SD16—114no—
277C22×M16—112no—
278#536—118no—
279#536—224no—
280C2×C4⋊Q8—221no—
281C2×#124—221no—
282C2×#123—222no—
283C2×C22⋊Q8—114no—
284C2×#117—111no—
285#452—1132no—
286#451—1116no—
287#450—1116no—
288#419—114no—
289#418—114no—
290#417—118no—
291#416—118no—
292#408—118no—
293#407—114no—
294C22×C11—22no—
295C22×C11—24no—
296C22×C11—28no—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—84no—
302C22×C11—88no—
303C22×C11—816no—
304C22×C11C2×#12014yes—
305C22×C11C2×#12012yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—28no—
308C4×C11—24no—
309C4×C11C2×#12012yes—
310C4×C11C2×#12014yes—
311C4×C11C23×D412yes—
312Dic11—44no—
313Dic11—44no—
3142−1+4—216no—
3152−1+4—216no—
3162−1+4—216no—
317H(5,𝔽2)—216no—
318H(5,𝔽2)—232no—
319H(5,𝔽2)—216no—
320H(5,𝔽2)—216no—
321C2×#41—264no—
322C2×#41—232no—
323C2×#41—24no—
324C2×#41—28no—
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—22no—
328C2×#41—24no—
329C2×#41—22no—
330C2×#41—28no—
331C2×#41—28no—
332C2×#41C22⋊D11116yes—
333C2×#41C22⋊D1114yes—
334C2×#41C22×D1118yes—
335C2×#41C22×D1114yes—
336C2×#41C22×D1114yes—
337C2×#41C22×D1114yes—
338C22×Q8—24no—
339C22×Q8—112no—
340C22×Q8—114no—
341C22×Q8—221no—
342C22×Q8—222no—
343C22×Q8—228no—
344C22×Q8C22⋊D1111yescharacteristic
345C22×Q8C22×D1114yes—
346C22×Q8C22×D1112yes—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—28no—
350C22×D4—24no—
351C22×D4C22⋊D1112yes—
352C22×D4C22⋊D1111yescharacteristic
353C22×D4C22×D1114yes—
354C22×D4C22×D1112yes—
355C23×C4—24no—
356C23×C4—22no—
357C23×C4—221no—
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360#137—2232no—
361#137—2232no—
362C2×Q16—1116no—
363C2×Q16—2216no—
364C2×SD16—1116no—
365C2×SD16—2216no—
366C2×M16—114no—
367C2×M16—114no—
368C2×M16—228no—
369C22×C8—114no—
370C4⋊Q8—228no—
371#124—228no—
372#123—2216no—
373C22⋊Q8—1116no—
374C22⋊Q8—228no—
375#117—114no—
376#117—222no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—224no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—224no—
381C2×C42—221no—
382#103—1116no—
383#102—1116no—
384C22⋊C8—1116no—
385C2×C11—22no—
386C2×C11—24no—
387C2×C11—44no—
388C2×C11—48no—
389C2×C11C22×#12011yescharacteristic
390C2×C11#358612yes—
391C24—24no—
392C24—22no—
393C24C2×C22⋊D1112yes—
394C24C2×C22⋊D1111yescharacteristic
395#41—232no—
396#41—264no—
397#41—232no—
398#41—232no—
399#41—232no—
400#41—216no—
401#41—216no—
402#41—216no—
403#41—216no—
404#41—216no—
405#41—28no—
406#41—28no—
407#41—28no—
408#41—28no—
409#41C2×C22⋊D11116yes—
410#41C2×C22⋊D11116yes—
411C2×Q8—232no—
412C2×Q8—216no—
413C2×Q8—24no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—24no—
417C2×Q8—114no—
418C2×Q8—222no—
419C2×Q8—224no—
420C2×Q8—228no—
421C2×Q8—228no—
422C2×Q8—228no—
423C2×Q8—448no—
424C2×Q8—444no—
425C2×Q8C2×C22⋊D1118yes—
426C2×Q8C2×C22⋊D1114yes—
427C2×Q8C23×D1114yes—
428C2×D4—232no—
429C2×D4—264no—
430C2×D4—232no—
431C2×D4—216no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—216no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4C2×C22⋊D1118yes—
442C2×D4C2×C22⋊D1114yes—
443C2×D4C2×C22⋊D1118yes—
444C2×D4C23×D1114yes—
445C22×C4—232no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—216no—
449C22×C4—24no—
450C22×C4—28no—
451C22×C4—24no—
452C22×C4—28no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—224no—
456C22×C4—444no—
457C22×C4C2×C22⋊D1112yes—
458C22×C4C2×C22⋊D1114yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1112yes—
461C22×C4C2×C22⋊D1118yes—
462C22×C4C23×D1114yes—
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1112yes—
465Q16—2232no—
466SD16—2232no—
467M16—228no—
468M16—228no—
469C2×C8—118no—
470C2×C8—228no—
471C4⋊C4—114no—
472C4⋊C4—222no—
473C4⋊C4—2216no—
474C22⋊C4—224no—
475C22⋊C4—2216no—
476C42—224no—
477C11#6037011yescharacteristic, complemented, Sylow
478C23—216no—
479C23—24no—
480C23—24no—
481C23—28no—
482C23—42no—
483C23—44no—
484C23—84no—
485C23—88no—
486C23#6700614yes—
487C23C22×C22⋊D1114yes—
488C23C22×C22⋊D1112yes—
489C23C22×C22⋊D1111yescharacteristic
490Q8—216no—
491Q8—28no—
492Q8—28no—
493Q8—24no—
494Q8—228no—
495Q8—444no—
496Q8—448no—
497Q8C22×C22⋊D1118yes—
498D4—232no—
499D4—216no—
500D4—216no—
501D4—216no—
502D4—216no—
503D4—28no—
504D4—28no—
505D4—24no—
506D4C22×C22⋊D1118yes—
507C2×C4—216no—
508C2×C4—232no—
509C2×C4—28no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—216no—
513C2×C4—28no—
514C2×C4—216no—
515C2×C4—28no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—444no—
519C2×C4—444no—
520C2×C4—448no—
521C2×C4#6700618yes—
522C2×C4#6700614yes—
523C2×C4C22×C22⋊D1114yes—
524C2×C4C22×C22⋊D1112yes—
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1114yes—
528C2×C4C22×C22⋊D1114yes—
529C2×C4C24×D1111yescharacteristic
530C8—228no—
531C22—22no—
532C22—24no—
533C22—28no—
534C22—24no—
535C22—28no—
536C22—44no—
537C22—48no—
538C22—84no—
539C22—88no—
540C22—816no—
541C22C2×#6700614yes—
542C22C2×#6700612yes—
543C22C23×C22⋊D1111yescharacteristic
544C4—28no—
545C4—24no—
546C4—444no—
547C4—444no—
548C4C2×#6700612yes—
549C4C2×#6700614yes—
550C4C23×C22⋊D1112yes—
551C2—22no—
552C2—24no—
553C2—44no—
554C2—48no—
555C2C22×#6700611yescharacteristic
556C2#1308340212yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#585C2
socleC22×C11C23×D4
hypercenterC2×#585D11
hypocenterC11#60370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C2×#10623356C2semidirect
3. #13077911C2semidirect
4. #13077893C2semidirect
5. #13077876C2semidirect
6. #13077135C2semidirect
7. #13077061C2semidirect
19. C23×Dic22C22semidirect
21. #10623356C22semidirect
23. C2×#67004C22semidirect
24. C2×#67004C22semidirect
26. C22×#4326C22semidirect
29. C22×#4324C22semidirect
30. C2×#66979C22semidirect
31. C2×#66977C22semidirect
32. C22×#4318C22semidirect
33. #10622852C22semidirect
34. #10622847C22semidirect
35. #10622846C22semidirect
36. #10622845C22semidirect
37. #10622841C22semidirect
38. #10622838C22semidirect
39. #10622831C22semidirect
40. #10622828C22semidirect
41. #10622820C22semidirect
477. C11#60370semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106233562
#130779112
#130778932
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