Finite Group Databasebeta

← #14787690

Subgroups — #14787690

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13069814C212yesmaximal, complemented
5#13069620C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069409C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal, complemented
9#13068807C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66999—22no—
15C2×#66991C2212yes—
16C22×#4324C2211yescharacteristic
17C2×#66983—21no—
18#10623261—24no—
19#10623261—24no—
20C2×#66950C2212yes—
21C2×#66946—21no—
22C2×C4⋊C4×D11C2212yes—
23C2×#66943—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#476—24no—
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66880C2212yes—
35C4×#4324—24no—
36#10622600C2212yes—
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622574—22no—
40#10622548C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C22×D44D411yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11C2312yes—
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yescomplemented
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64#66999—216no—
65#66991—24no—
66#66991—42no—
67C2×#4324—22no—
68C2×#4324—22no—
69C2×#4324—22no—
70#66983—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66950—24no—
86#66950—24no—
87#66946—28no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—24no—
90#66943—28no—
91C4×D44—22no—
92C4×D44—22no—
93C4×Dic22—22no—
94C4×Dic22D414yescomplemented
95C11×#106—24no—
96C11×C4⋊C8—22no—
97C11×#102—24no—
98#66896—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—42no—
102#66880—42no—
103#66874—22no—
104#66872—22no—
105C4×C11⋊C8—22no—
106#24118—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—81no—
111C2×Q8×C11—81no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11#4112yes—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C2×C22⋊D11—82no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11C2×D412yes—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44SD1614yescomplemented
136C2×C4×D11—28no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—82no—
144C2×C4×D11—82no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22C2×D412yes—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C2×D414yes—
159C11×C22⋊C4—42no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—44no—
163#4324—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—44no—
167C4⋊Dic11—28no—
168C4⋊Dic11—22no—
169C4⋊Dic11—21no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—42no—
173C4⋊Dic11—81no—
174C4⋊Dic11C2×D412yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—24no—
177C4×Dic11—24no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8#4112yes—
184C2×#554—111no—
185C2×#476D1111yescharacteristic, complemented
186C2×C4×SD16—111no—
187#2537—111no—
188#2035—112no—
189#2000—112no—
190#1990—111no—
191#1954—111no—
192#1874—112no—
193#1853—112no—
194#1803—111no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11C2×SD1614yes—
210Q8×C11—84no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—84no—
224C2×C4×C11#12012yes—
225C2×C4×C11#12012yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13712yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C22⋊D11—88no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—28no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—88no—
253Dic22—22no—
254Dic22—22no—
255Dic22—41no—
256Dic22—41no—
257C8×C11—42no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C22×SD16—111no—
261#554—224no—
262#554—224no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#125—221no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—222no—
267C2×#121—112no—
268C2×#121—221no—
269C2×C4×Q8—111no—
270C2×C4×D4—111no—
271C2×C4×D4—221no—
272C2×C4×D4C2×D1111yescharacteristic
273C22×C4⋊C4—112no—
274#476—24no—
275C4×SD16—224no—
276C2×#106—111no—
277C2×#106C2×D1112yes—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—111no—
280C2×#103—112no—
281C2×#102—111no—
282C2×#102C2×D1112yes—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C4×C8—111no—
286#394—222no—
287#384—111no—
288#380—112no—
289#380—221no—
290#340—112no—
291#340—112no—
292#340—112no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54611yescharacteristic
302C22×C11#54711yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C4×C11—22no—
315C4×C11—44no—
316C4×C11—81no—
317C4×C11#44814yes—
318C4×C11#52511yescharacteristic
319C4×C11#53711yescharacteristic
320C4×C11#54811yescharacteristic
321C4×C11#55011yescharacteristic
322Dic11—42no—
323Dic11—42no—
324Dic11—42no—
325Dic11—82no—
326C22×Q8—21no—
327C22×Q8—111no—
328C22×D4—111no—
329C22×D4—222no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—112no—
333C23×C4—222no—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8C22×D1112yes—
340C4⋊Q8—22no—
341C4⋊Q8C22⋊D1114yescomplemented
342#125—228no—
343C22⋊Q8—224no—
344C22⋊Q8—2216no—
345C22⋊Q8—224no—
346#121—224no—
347#121—442no—
348#121—444no—
349C4×Q8—114no—
350C4×Q8—222no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—228no—
354C4×D4—222no—
355C4×D4—222no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—221no—
375C2×C42C22×D1111yescharacteristic
376#106—24no—
377#106—222no—
378C4⋊C8—22no—
379#103—222no—
380#103—442no—
381#102—24no—
382#102—222no—
383C22⋊C8—224no—
384C22⋊C8—442no—
385C4×C8—222no—
386#95—222no—
387C2×C11—82no—
388C2×C11#240711yescharacteristic
389C2×C11C2×#44811yescharacteristic
390C2×C11#301211yescharacteristic
391C2×C11#329511yescharacteristic
392C2×C11#333111yescharacteristic
393C2×C11#333511yescharacteristic
394C2×C11#335711yescharacteristic
395D11—44no—
396C24—21no—
397C24—112no—
398C2×Q8—24no—
399C2×Q8—81no—
400C2×Q8—81no—
401C2×Q8—112no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—114no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—882no—
418C2×D4#434312yes—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—112no—
425C22×C4—228no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—882no—
436C22×C4—882no—
437C22×C4D4×D1111yescharacteristic
438C22×C4D4×D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—228no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—112no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—112no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—222no—
458C4⋊C4—224no—
459C4⋊C4—221no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—442no—
463C4⋊C4—881no—
464C4⋊C4C2×C22⋊D1114yes—
465C22⋊C4—42no—
466C22⋊C4—228no—
467C22⋊C4—224no—
468C22⋊C4—444no—
469C22⋊C4—444no—
470C42—224no—
471C42D4×D1112yes—
472C42C2×C22⋊D1112yes—
473C11#2411811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—114no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—222no—
488C23C2×D4×D1111yescharacteristic
489Q8—84no—
490Q8—222no—
491Q8—222no—
492Q8—441no—
493Q8—441no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498D4—228no—
499D4—888no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—84no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—888no—
526C2×C4SD16×D1112yes—
527C2×C4#6696812yes—
528C2×C4#6699012yes—
529C2×C4#6699012yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×#434311yescharacteristic
532C2×C4#6704011yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—42no—
537C8—222no—
538C8—441no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—224no—
547C22—224no—
548C22—224no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22#1062316111yescharacteristic
554C22#1062316211yescharacteristic
555C22C2×SD16×D1111yescharacteristic
556C22C2×#6696811yescharacteristic
557C22#1062330511yescharacteristic
558C22#1062330611yescharacteristic
559C22C2×#6699011yescharacteristic
560C4—22no—
561C4—44no—
562C4—81no—
563C4—442no—
564C4—442no—
565C4—442no—
566C4—882no—
567C4#1062278314yes—
568C4#1062315811yescharacteristic
569C4#1062316011yescharacteristic
570C4#1062334811yescharacteristic
571C4#1062336511yescharacteristic
572C2—82no—
573C2—444no—
574C2#1307196311yescharacteristic
575C2C2×#1062278311yescharacteristic
576C2#1307791911yescharacteristic
577C2#1308043711yescharacteristic
578C2#1308092911yescharacteristic
579C2#1308097011yescharacteristic
580C2#1308124511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#476D11
hypocenterC11#24118
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
2. C2×C4×#4324C2semidirect
4. #13069814C2semidirect
5. #13069620C2semidirect
6. #13069578C2semidirect
7. #13069409C2semidirect
8. #13068930C2semidirect
9. #13068807C2semidirect
10. #13068622C2semidirect
11. C2×C11×#476C2semidirect
55. C11×C4⋊Q8D4semidirect
94. C4×Dic22D4semidirect
135. C2×D44SD16semidirect
185. C2×#476D11semidirect
341. C4⋊Q8C22⋊D11semidirect
473. C11#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×C4×#43242
#130735292
#130698142
#130696202
#130695782
#130694092
#130689302
#130688072
#130686222
C2×C11×#4762
#2411811