Finite Group Databasebeta

← #14788554

Subgroups — #14788554

Order 2816.

1394 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic, complemented
3#13073986C211yesmaximal, characteristic, complemented
4#13069848C212yesmaximal, complemented
5#13069702C212yesmaximal, complemented
6#13069552C211yesmaximal, characteristic, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13068947C212yesmaximal, complemented
9#13068874C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66993C2212yes—
18C2×#66983—21no—
19#10623084—24no—
20#10623084—24no—
21C2×#66946C2212yes—
22C2×#66937—22no—
23C2×#66927C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30#10622843C2212yes—
31C2×#66896C2212yes—
32C2×#66885C2212yes—
33C2×#66885C2212yes—
34#10622640—24no—
35#10622597—22no—
36#10622586C2212yes—
37C2×#66873C2212yes—
38#10622548C2211yescharacteristic
39#10622542—21no—
40#10622541—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C2×#4339—28no—
51C2×#4339—44no—
52C2×#4339—44no—
53C22×D44—21no—
54C22×D44—21no—
55C22×D44C2312yes—
56C22×C4×D11—22no—
57C22×Dic22D411yescharacteristic
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×SD16—22no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11D414yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×#4325—24no—
74C2×#4325—24no—
75C2×#4325—42no—
76#66993—24no—
77#66993—24no—
78#66983—28no—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4D412yes—
86C2×C4×Dic11C2312yes—
87C22×C11⋊C8C2312yes—
88#66946—24no—
89#66946—24no—
90#66937—216no—
91#66927—22no—
92#66927D414yes—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C11×#106—22no—
96C11×#103—22no—
97C11×#102—22no—
98C4×C8×C11—22no—
99#66896—42no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103#66885—24no—
104#66885—42no—
105#66873—24no—
106C4⋊(C11⋊C8)—22no—
107#24188—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11#4112yescomplemented
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—28no—
132C2×C22⋊D11—28no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—82no—
136C2×C22⋊D11—82no—
137C22×Dic11—22no—
138C22×Dic11C2×D412yes—
139C22×Dic11C2×D412yes—
140#4339—432no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—81no—
151C2×D44—81no—
152C2×D44C2×D414yes—
153C2×C4×D11—28no—
154C2×C4×D11—44no—
155C2×C4×D11—44no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22SD1614yescomplemented
159C11×SD16—28no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11#4112yescomplemented
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C42×C11—42no—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175#4325—48no—
176(C2×D11)⋊C4—28no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—42no—
181C4⋊Dic11—81no—
182Dic11⋊C4—24no—
183Dic11⋊C4—82no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×#550—111no—
190C2×#460—111no—
191C2×C4×SD16D1111yescharacteristic, complemented
192#2582—111no—
193#2041—112no—
194#2014—112no—
195#1984—111no—
196#1957—111no—
197#1877—112no—
198#1864—112no—
199#1802—111no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—41no—
218Q8×C11—41no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C22⋊D11—416no—
246C22⋊D11—88no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11C2×SD1614yes—
256D44—24no—
257D44—24no—
258D44—42no—
259D44—42no—
260D44—48no—
261D44—84no—
262C4×D11—416no—
263Dic22—28no—
264C8×C11—22no—
265C8×C11—41no—
266C11⋊C8—42no—
267C22×#41—221no—
268C22×SD16—112no—
269C22×SD16C2×D1111yescharacteristic
270#550—224no—
271#550—224no—
272C2×#127—112no—
273C2×#127—111no—
274C2×#121—222no—
275C2×#121—221no—
276C2×C4×Q8—111no—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—112no—
279C2×C4×D4C2×D1111yescharacteristic
280#460—224no—
281C4×SD16—24no—
282C2×#106C2×D1111yescharacteristic
283C2×C4⋊C8—111no—
284C2×#103C2×D1111yescharacteristic
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×#102C2×D1111yescharacteristic
290C2×C4×C8C2×D1111yescharacteristic
291#398—222no—
292#391—112no—
293#391—221no—
294#389—112no—
295#389—221no—
296#384—111no—
297#340—112no—
298#336—112no—
299#336—112no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11C2×#12011yescharacteristic
308C22×C11#54811yescharacteristic
309C22×C11#55011yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—81no—
325C4×C11#45014yes—
326C4×C11#52511yescharacteristic
327C4×C11#53711yescharacteristic
328C4×C11#54611yescharacteristic
329C4×C11#54711yescharacteristic
330Dic11—24no—
331Dic11—42no—
332Dic11—82no—
333C2×#41—228no—
334C2×#41—444no—
335C2×#41—444no—
336C22×Q8—111no—
337C22×Q8C22×D1111yescharacteristic
338C22×D4—112no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—221no—
342C22×D4—221no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—21no—
345C23×C4—222no—
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×SD16—442no—
352C22×C8—112no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355#127—114no—
356#127—224no—
357#127—224no—
358#127—222no—
359#121—2216no—
360#121—228no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—222no—
364C4×Q8—222no—
365C4×D4—22no—
366C4×D4—224no—
367C4×D4—224no—
368C4×D4C22⋊D1114yes—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—222no—
380C2×C42—21no—
381C2×C42—112no—
382C2×C42C22×D1111yescharacteristic
383#106—22no—
384C4⋊C8—222no—
385#103—22no—
386#102—22no—
387#102—224no—
388#102—224no—
389#102—442no—
390#102—442no—
391C4×C8—22no—
392#95—222no—
393#95—222no—
394#95—222no—
395C2×C11—82no—
396C2×C11#240711yescharacteristic
397C2×C11C2×#45011yescharacteristic
398C2×C11#301211yescharacteristic
399C2×C11#336211yescharacteristic
400C2×C11#336811yescharacteristic
401C2×C11#339211yescharacteristic
402C2×C11#339911yescharacteristic
403D11—84no—
404C24—21no—
405C24—222no—
406#41—4432no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—114no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8#433912yescomplemented
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—114no—
422C2×D4—228no—
423C2×D4—228no—
424C2×D4—224no—
425C2×D4—224no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—444no—
432C2×D4—444no—
433C2×D4—442no—
434C2×D4—442no—
435C2×D4—881no—
436C2×D4—881no—
437C2×D4—882no—
438C2×D4—882no—
439C2×D4C2×C22⋊D1112yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—228no—
449C22×C4—222no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455SD16—28no—
456SD16—448no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8#433912yescomplemented
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—224no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4—882no—
477C4⋊C4C2×C22⋊D1112yes—
478C22⋊C4—24no—
479C22⋊C4—228no—
480C42—42no—
481C42—222no—
482C42—222no—
483C42D4×D1112yes—
484C42C2×C22⋊D1112yes—
485C11#2418811yescharacteristic, complemented, Sylow
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—224no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23C2×D4×D1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505Q8—228no—
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510D4—224no—
511D4—224no—
512D4—4416no—
513D4—448no—
514D4—442no—
515D4—442no—
516D4—884no—
517D4—888no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—114no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—4416no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4SD16×D1112yes—
541C2×C4#6696712yes—
542C2×C4#6699012yes—
543C2×C4#6699012yes—
544C2×C4C2×#433911yescharacteristic
545C2×C4C2×#433911yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C2×C4#6704211yescharacteristic
548C2×C4#6704311yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C8—22no—
551C8—41no—
552C8—442no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—882no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22#1062308311yescharacteristic
568C22#1062308411yescharacteristic
569C22C2×SD16×D1111yescharacteristic
570C22C2×#6696711yescharacteristic
571C22#1062330011yescharacteristic
572C22#1062330111yescharacteristic
573C22C2×#6699011yescharacteristic
574C4—22no—
575C4—42no—
576C4—42no—
577C4—81no—
578C4—224no—
579C4—442no—
580C4—882no—
581C4#1062278214yes—
582C4#1062308111yescharacteristic
583C4#1062308211yescharacteristic
584C4#1062332211yescharacteristic
585C4#1062336411yescharacteristic
586C2—82no—
587C2—884no—
588C2#1307196111yescharacteristic
589C2C2×#1062278211yescharacteristic
590C2#1307791611yescharacteristic
591C2#1308128511yescharacteristic
592C2#1308134311yescharacteristic
593C2#1308159511yescharacteristic
594C2#1308165611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×C4×SD16D11
hypocenterC11#24188
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. #13073986C2semidirect
4. #13069848C2semidirect
5. #13069702C2semidirect
6. #13069552C2semidirect
7. #13069422C2semidirect
8. #13068947C2semidirect
9. #13068874C2semidirect
10. #13068616C2semidirect
11. C2×C4×C11×SD16C2semidirect
115. C2×Q8×C11#41semidirect
158. C2×Dic22SD16semidirect
165. C2×C8×C11#41semidirect
191. C2×C4×SD16D11semidirect
415. C2×Q8#4339semidirect
465. C2×C8#4339semidirect
485. C11#24188semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106226402
#130739862
#130698482
#130697022
#130695522
#130694222
#130689472
#130688742
#130686162
C2×C4×C11×SD162
#2418811