Finite Group Databasebeta

← #14787712

Subgroups — #14787712

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069807C212yesmaximal, complemented
5#13069618C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069409C211yesmaximal, characteristic, complemented
8#13068920C212yesmaximal, complemented
9#13068807C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16C2×#66999C2212yes—
17C22×#4325C2211yescharacteristic
18#10623257—24no—
19#10623257—24no—
20C2×#66948C2212yes—
21C2×#66947—22no—
22C2×C4⋊C4×D11C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C11×#475—24no—
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×#66899C2211yescharacteristic
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C4×#4325—24no—
34#10622607—22no—
35#10622600C2212yes—
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38#10622552—21no—
39#10622548C2211yescharacteristic
40#10622541—21no—
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C2×#4343—28no—
48C2×#4343—44no—
49C2×#4343—44no—
50C22×D44—22no—
51C22×D44D411yescharacteristic
52C22×D44C2311yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—21no—
55C22×C4×D11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yes—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#66999—28no—
68#66999—24no—
69#66999—42no—
70C2×#4325—22no—
71C2×#4325—22no—
72C2×#4325—22no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4D412yes—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87#66948—24no—
88#66948—24no—
89#66947—216no—
90C4⋊C4×D11—24no—
91C4⋊C4×D11—24no—
92C4×D44—22no—
93C4×D44—22no—
94C4×D44—22no—
95C4×D44D414yes—
96C11×#106—24no—
97C11×C4⋊C8—22no—
98C11×#103—24no—
99#66899—22no—
100C11⋊#95—22no—
101#66885—42no—
102(C2×D11)⋊C8—24no—
103(C2×D11)⋊C8—42no—
104#66873—22no—
105#66872—22no—
106C4×C11⋊C8—22no—
107#24120—111nomaximal, Sylow
108C23×D11—21no—
109C23×D11C2×D412yes—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11#4112yescomplemented
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—22no—
127C22×Dic11C2×D412yes—
128#4343—432no—
129C2×D44—28no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—44no—
138C2×D44—44no—
139C2×D44SD1614yescomplemented
140C2×D44C2×D412yes—
141C2×C4×D11—28no—
142C2×C4×D11—24no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—44no—
150C2×C4×D11—44no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4C2×D414yes—
162C42×C11—42no—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165#4325—28no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—44no—
170(C2×D11)⋊C4—82no—
171C4⋊Dic11—22no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177C4⋊Dic11C2×D412yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—44no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8#4112yescomplemented
186C2×#547—111no—
187C2×#475D1111yescharacteristic, complemented
188C2×C4×SD16—111no—
189#2538—111no—
190#2034—112no—
191#2000—112no—
192#1990—111no—
193#1954—111no—
194#1872—112no—
195#1853—112no—
196#1802—111no—
197C23×C11C22×D411yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11C2×SD1614yes—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—48no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12012yes—
230C2×C4×C11C2×SD1612yes—
231C2×C4×C11AGL(1,ℤ/8)12yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—22no—
248D44—22no—
249D44—28no—
250D44—416no—
251D44—41no—
252D44—41no—
253C4×D11—416no—
254C4×D11—42no—
255C4×D11—42no—
256C4×D11—42no—
257C4×D11—42no—
258C4×D11—48no—
259C8×C11—42no—
260C11⋊C8—22no—
261C11⋊C8—41no—
262C22×#41—221no—
263C22×SD16—111no—
264#547—224no—
265#547—224no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#123—222no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—221no—
270C2×#121—112no—
271C2×C4×Q8C2×D1111yescharacteristic
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C22×C4⋊C4—112no—
275#475—24no—
276C4×SD16—224no—
277C2×#106—111no—
278C2×#106C2×D1112yes—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#103—111no—
281C2×#103C2×D1112yes—
282C2×#102—111no—
283C2×#102—112no—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C4×C8—111no—
287#396—222no—
288#390—221no—
289#389—221no—
290#384—111no—
291#380—112no—
292#340—112no—
293#340—112no—
294#340—112no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#54611yescharacteristic
297C22×C11#54711yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57811yescharacteristic
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—81no—
320C4×C11#45014yes—
321C4×C11#52511yescharacteristic
322C4×C11#53711yescharacteristic
323C4×C11#54811yescharacteristic
324C4×C11#55011yescharacteristic
325Dic11—42no—
326Dic11—42no—
327Dic11—82no—
328C2×#41—228no—
329C2×#41—444no—
330C2×#41—444no—
331C22×Q8—21no—
332C22×Q8C22×D1111yescharacteristic
333C22×D4—111no—
334C22×D4—111no—
335C22×D4—222no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4—221no—
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—222no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8C22×D1112yes—
345C4⋊Q8—22no—
346C4⋊Q8C22⋊D1114yes—
347#123—2216no—
348C22⋊Q8—228no—
349C22⋊Q8—224no—
350C22⋊Q8—442no—
351#121—224no—
352#121—224no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—114no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—222no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1112yes—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—21no—
378C2×C42C22×D1111yescharacteristic
379#106—24no—
380#106—222no—
381C4⋊C8—22no—
382#103—24no—
383#103—222no—
384#102—222no—
385#102—442no—
386C22⋊C8—224no—
387C22⋊C8—442no—
388C4×C8—222no—
389#95—222no—
390C2×C11#240711yescharacteristic
391C2×C11C2×#45011yescharacteristic
392C2×C11#301311yescharacteristic
393C2×C11#329811yescharacteristic
394C2×C11#333211yescharacteristic
395C2×C11#333511yescharacteristic
396C2×C11#335311yescharacteristic
397D11—44no—
398D11—82no—
399C24—112no—
400C24—221no—
401#41—4432no—
402C2×Q8—24no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8#434312yescomplemented
411C2×D4—114no—
412C2×D4—112no—
413C2×D4—228no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—444no—
422C2×D4—444no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—112no—
427C22×C4—228no—
428C22×C4—221no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—444no—
438C22×C4—444no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444SD16—228no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—112no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—112no—
460C4⋊C4—228no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—444no—
466C4⋊C4—442no—
467C4⋊C4—881no—
468C4⋊C4C2×C22⋊D1114yes—
469C22⋊C4—228no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—444no—
473C22⋊C4—882no—
474C42—42no—
475C42D4×D1112yes—
476C42C2×C22⋊D1112yes—
477C11#2412011yescharacteristic, complemented, Sylow
478C23—114no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23C2×D4×D1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—48no—
496Q8—41no—
497Q8—41no—
498D4—228no—
499D4—222no—
500D4—222no—
501D4—4416no—
502D4—441no—
503D4—441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—4416no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—448no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4SD16×D1112yes—
531C2×C4#6696712yes—
532C2×C4#6699012yes—
533C2×C4#6699012yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434311yescharacteristic
536C2×C4#6704011yescharacteristic
537C2×C4#41×D1111yescharacteristic
538C2×C4#6704211yescharacteristic
539C2×C4C22×C22⋊D1111yescharacteristic
540C8—42no—
541C8—222no—
542C8—441no—
543C22—224no—
544C22—224no—
545C22—224no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062316111yescharacteristic
558C22#1062316211yescharacteristic
559C22C2×SD16×D1111yescharacteristic
560C22C2×#6696711yescharacteristic
561C22#1062330911yescharacteristic
562C22#1062331011yescharacteristic
563C22C2×#6699011yescharacteristic
564C4—22no—
565C4—44no—
566C4—42no—
567C4—81no—
568C4—442no—
569C4—442no—
570C4—882no—
571C4#1062278214yes—
572C4#1062315811yescharacteristic
573C4#1062316011yescharacteristic
574C4#1062334811yescharacteristic
575C4#1062336511yescharacteristic
576C2—444no—
577C2—882no—
578C2#1307196311yescharacteristic
579C2C2×#1062278211yescharacteristic
580C2#1307793011yescharacteristic
581C2#1308047811yescharacteristic
582C2#1308094011yescharacteristic
583C2#1308097611yescharacteristic
584C2#1308120311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#475D11
hypocenterC11#24120
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. #13073534C2semidirect
4. #13069807C2semidirect
5. #13069618C2semidirect
6. #13069578C2semidirect
7. #13069409C2semidirect
8. #13068920C2semidirect
9. #13068807C2semidirect
10. #13068617C2semidirect
11. C2×C11×#475C2semidirect
118. C2×Q8×C11#41semidirect
139. C2×D44SD16semidirect
185. C2×C11⋊C8#41semidirect
187. C2×#475D11semidirect
410. C2×Q8#4343semidirect
477. C11#24120semidirect

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×C4×#43252
#130735342
#130698072
#130696182
#130695782
#130694092
#130689202
#130688072
#130686172
C2×C11×#4752
#2412011