Finite Group Databasebeta

← #14770236

Subgroups — #14770236

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C4⋊C4×D44C211yesmaximal, characteristic, complemented
4#13069578C211yesmaximal, characteristic, complemented
5#13069053C212yesmaximal, complemented
6#13068932C212yesmaximal, complemented
7#13068709C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9C4×#66873C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C11×#1987C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000—22no—
14C22×#4313C2212yes—
15#10623265—24no—
16#10623265C418yescomplemented
17C2×#66948—21no—
18C2×#66948C2212yes—
19C2×#66945—21no—
20C2×#66945C2212yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66885C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29#10622600C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32#10622548C2211yescharacteristic
33#10622541—21no—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622451—24no—
36#10622281—22no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×D44—22no—
46C22×D44D411yescharacteristic
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C4×D11C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yescomplemented
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60#67000—216no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4D412yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C2×#4313—24no—
76C2×#4313—24no—
77C2×#4313—42no—
78#66948—28no—
79#66948—24no—
80#66948C2×C418yescomplemented
81#66945—24no—
82#66945—28no—
83#66945C2×C418yescomplemented
84C4⋊C4×D11—24no—
85C4⋊C4×D11—42no—
86C4×D44—22no—
87C4×D44—44no—
88C4×D44C2×C414yes—
89C4×D44C2×C414yescomplemented
90C4×D44D414yes—
91C11×C4⋊C8—22no—
92C11×#95—21no—
93C11⋊#95—22no—
94#66885—42no—
95(C2×D11)⋊C8—24no—
96#66873—22no—
97#66873—22no—
98C4×C11⋊C8—22no—
99#22503—111nomaximal, Sylow
100C23×D11—21no—
101C23×D11C2×D412yes—
102C2×Q8×C11—24no—
103C2×Q8×C11—81no—
104C2×Q8×C11—81no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C2×D44—28no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—82no—
123C2×D44—82no—
124C2×D44C22⋊C414yes—
125C2×D44C22×C412yes—
126C2×C4×D11—24no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×C4×D11—82no—
136C2×C4×D11C22×C414yes—
137C2×C4×D11C2×D414yes—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C22×C414yes—
147C11×C4⋊C4#4112yes—
148C42×C11—42no—
149C42×C11C22×C412yes—
150C42×C11C2×D412yes—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4C22⋊C418yes—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—42no—
160C4⋊Dic11—81no—
161C4⋊Dic11C22⋊C414yes—
162C4⋊Dic11C22×C412yes—
163Dic11⋊C4—44no—
164C4×Dic11—28no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8#4112yes—
171#4313—48no—
172C2×#555—111no—
173C2×#436—111no—
174D4×C4⋊C4—111no—
175#1990—111no—
176#1987D1111yescharacteristic, complemented
177#1895—112no—
178#1874—112no—
179#1825—112no—
180#1802—111no—
181C4×#102—111no—
182#1736—112no—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11C2×C22⋊C414yes—
198Q8×C11—84no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11#13712yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11C2×C22⋊C414yes—
229D44—22no—
230D44—22no—
231D44—28no—
232D44—41no—
233D44—41no—
234D44—88no—
235C4×D11—24no—
236C4×D11—24no—
237C4×D11—24no—
238C4×D11—24no—
239C4×D11—48no—
240C4×D11—88no—
241C8×C11—42no—
242C11⋊C8—22no—
243C11⋊C8—41no—
244C22×M16—112no—
245#555—118no—
246#555—224no—
247C2×C4⋊Q8C2×D1111yescharacteristic
248C2×#124—222no—
249C2×#121—112no—
250C2×#121—221no—
251C2×C4×D4—111no—
252C2×C4×D4—111no—
253C2×C4×D4—221no—
254C2×#117—112no—
255C2×#117—221no—
256C22×C4⋊C4—112no—
257#436—224no—
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×#102—111no—
260C2×#102—111no—
261C2×#102—112no—
262C2×C22⋊C8—112no—
263C2×C4×C8—111no—
264#389—221no—
265#385—222no—
266#384—111no—
267#380—112no—
268C4×C4⋊C4C2×D1111yescharacteristic
269#340—112no—
270#340—111no—
271#340—112no—
272#340—112no—
273#340—111no—
274#340C2×D1112yes—
275#340C2×D1112yes—
276C22×C11C22×C22⋊C411yescharacteristic
277C22×C11#54611yescharacteristic
278C22×C11#54711yescharacteristic
279C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C11C2×#13711yescharacteristic
281C22×C11#57611yescharacteristic
282C22×C11#57711yescharacteristic
283C2×D11—24no—
284C2×D11—24no—
285C2×D11—24no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C4×C11—22no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11#41714yes—
302C4×C11C4×#4111yescharacteristic
303C4×C11#52011yescharacteristic
304C4×C11#54611yescharacteristic
305C4×C11#54711yescharacteristic
306Dic11—24no—
307Dic11—42no—
308Dic11—82no—
309C22×Q8—21no—
310C22×D4—111no—
311C22×D4—111no—
312C22×D4—222no—
313C23×C4—112no—
314C23×C4—222no—
315C23×C4—221no—
316C2×M16—224no—
317C2×M16—224no—
318C2×M16—442no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8C22×D1112yes—
322C4⋊Q8—22no—
323C4⋊Q8C4×D1114yescomplemented
324#124—2216no—
325#121—118no—
326#121—224no—
327#121—228no—
328C4×D4—114no—
329C4×D4—114no—
330C4×D4—114no—
331C4×D4—222no—
332C4×D4—444no—
333#117—118no—
334#117—228no—
335#117—224no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—442no—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C4⋊C4C22×D1112yes—
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—112no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—222no—
353C2×C42—21no—
354C2×C42—222no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—22no—
357#102—222no—
358#102—222no—
359#102—442no—
360C22⋊C8—224no—
361C4×C8—222no—
362#95—21no—
363#95—222no—
364C2×C11#233911yescharacteristic
365C2×C11C2×#41711yescharacteristic
366C2×C11#289711yescharacteristic
367C2×C11#332511yescharacteristic
368C2×C11#332911yescharacteristic
369C2×C11#335411yescharacteristic
370C2×C11#335711yescharacteristic
371D11—44no—
372D11—82no—
373C24—112no—
374C24—221no—
375C2×Q8—24no—
376C2×Q8—81no—
377C2×Q8—81no—
378C2×D4—114no—
379C2×D4—112no—
380C2×D4—228no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—882no—
389C2×D4—882no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—112no—
394C22×C4—114no—
395C22×C4—114no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—221no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4—444no—
404C22×C4—444no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4—882no—
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4C23×D1111yescharacteristic
411M16—448no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—112no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8—221no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—114no—
427C4⋊C4—112no—
428C4⋊C4—221no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—444no—
432C4⋊C4—442no—
433C4⋊C4—881no—
434C4⋊C4C2×C4×D1114yes—
435C4⋊C4#434312yes—
436C22⋊C4—118no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C22⋊C4—224no—
440C22⋊C4—444no—
441C42—42no—
442C42—228no—
443C42C2×C4×D1112yes—
444C42D4×D1112yes—
445C11#2250311yescharacteristic, complemented, Sylow
446C23—114no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23—222no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23C2×D4×D1111yescharacteristic
461Q8—84no—
462D4—222no—
463D4—222no—
464D4—228no—
465D4—441no—
466D4—441no—
467D4—888no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—114no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—448no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—888no—
494C2×C4C22⋊C4×D1112yes—
495C2×C4C22⋊C4×D1112yes—
496C2×C4#6696712yes—
497C2×C4#6697112yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4C2×#434311yescharacteristic
501C2×C4#6704011yescharacteristic
502C2×C4#41×D1111yescharacteristic
503C2×C4#6704211yescharacteristic
504C8—42no—
505C8—222no—
506C8—441no—
507C22—224no—
508C22—224no—
509C22—224no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—442no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—881no—
518C22—881no—
519C22—881no—
520C22—881no—
521C22C2×C22⋊C4×D1111yescharacteristic
522C22#1062316111yescharacteristic
523C22#1062316211yescharacteristic
524C22C2×#6696711yescharacteristic
525C22C2×#6697111yescharacteristic
526C22#1062330511yescharacteristic
527C22#1062330611yescharacteristic
528C4—22no—
529C4—42no—
530C4—44no—
531C4—81no—
532C4—224no—
533C4—442no—
534C4—882no—
535C4#1062241614yes—
536C4C4×#434311yescharacteristic
537C4#1062310511yescharacteristic
538C4#1062320711yescharacteristic
539C4#1062325711yescharacteristic
540C2—444no—
541C2—882no—
542C2#1307144511yescharacteristic
543C2C2×#1062241611yescharacteristic
544C2#1307714111yescharacteristic
545C2#1308085511yescharacteristic
546C2#1308090711yescharacteristic
547C2#1308120811yescharacteristic
548C2#1308123911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC2×#10623265C2
cosocleC22×C4×C11C24
hypercenter#1987D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C4⋊C4×D44C2semidirect
4. #13069578C2semidirect
5. #13069053C2semidirect
6. #13068932C2semidirect
7. #13068709C2semidirect
8. #13068617C2semidirect
9. C4×#66873C2semidirect
10. #13068334C2semidirect
11. C11×#1987C2semidirect
16. #10623265C4semidirect
53. C11×C4⋊Q8C2×C4semidirect
80. #66948C2×C4semidirect
83. #66945C2×C4semidirect
89. C4×D44C2×C4semidirect
176. #1987D11semidirect
323. C4⋊Q8C4×D11semidirect
445. C11#22503semidirect

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106224512
C4⋊C4×D442
#130695782
#130690532
#130689322
#130687092
#130686172
C4×#668732
#130683342
C11×#19872
#2250311