Finite Group Databasebeta

← #14787684

Subgroups — #14787684

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×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4#13069812C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068808C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×D4×Dic11—21no—
17C22×#4324C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C2×#66977C2212yes—
20#10623074—24no—
21#10623074—24no—
22C2×#66943—21no—
23C2×#66931—22no—
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#394—22no—
27C11×#384C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4324—24no—
35#10622621—24no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66872C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C23×Dic11—22no—
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C11×#121—24no—
54C11×#121—42no—
55C11×#121—44no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71D4×Dic11—28no—
72C2×#4324—22no—
73C2×#4324—22no—
74C2×#4324—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2312yes—
81#66977—24no—
82#66977—24no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89#66943—28no—
90#66931—216no—
91#66922—22no—
92#66922D414yescomplemented
93C4×Dic22—22no—
94C4×Dic22D414yescomplemented
95C11×#95—22no—
96#66896—24no—
97#66896—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66874—22no—
101#66874—42no—
102#66872—24no—
103#66872—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24118—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—82no—
119C2×D4×C11SD1614yescomplemented
120C2×D4×C11#4112yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—28no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—82no—
141C22×Dic11—82no—
142C2×Dic22—24no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—81no—
149C2×Dic22—81no—
150C2×Dic22C2×D412yes—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—81no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—28no—
165#4324—28no—
166C4⋊Dic11—28no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11C2×D412yes—
171C4⋊Dic11C2×D414yes—
172Dic11⋊C4—28no—
173Dic11⋊C4—24no—
174C4×Dic11—24no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8#4112yes—
184C2×#554—111no—
185C2×#476—111no—
186C2×C4×SD16—111no—
187#2537D1111yescharacteristic
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—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11C2×SD1614yes—
209C23×C11C22×D411yescharacteristic
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—28no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—88no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—84no—
232C2×C4×C11#12012yes—
233C2×C4×C11#12012yes—
234C2×C4×C11C2×SD1612yes—
235C2×C4×C11#13712yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—88no—
252Dic22—22no—
253Dic22—22no—
254Dic22—41no—
255Dic22—41no—
256Dic22—84no—
257C11⋊C8—22no—
258C11⋊C8—41no—
259C11⋊C8—42no—
260C22×SD16—111no—
261#554—224no—
262#554—224no—
263C2×C4⋊Q8—111no—
264C2×#125—221no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—222no—
267C2×#121—21no—
268C2×#121C2×D1112yes—
269C2×C4×Q8—111no—
270C2×C4×D4—221no—
271C2×C4×D4C2×D1111yescharacteristic
272C2×C4×D4C2×D1111yescharacteristic
273C22×C4⋊C4—112no—
274#476—224no—
275C4×SD16—224no—
276C2×#106—111no—
277C2×#106—112no—
278C2×C4⋊C8—111no—
279C2×#103—111no—
280C2×#103—112no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C4×C8—111no—
286#394—22no—
287#384C2×D1111yescharacteristic
288#380—21no—
289#380C2×D1112yes—
290#340—112no—
291#340—112no—
292#340—112no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
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#54611yescharacteristic
309C22×C11#54711yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13711yescharacteristic
312C22×C11#57611yescharacteristic
313C22×C11#57711yescharacteristic
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—81no—
317C4×C11—82no—
318C4×C11#44814yes—
319C4×C11#52511yescharacteristic
320C4×C11#53711yescharacteristic
321C4×C11#54811yescharacteristic
322C4×C11#55011yescharacteristic
323Dic11—42no—
324Dic11—44no—
325Dic11—42no—
326C22×Q8—111no—
327C22×Q8—221no—
328C22×D4—22no—
329C22×D4C22⋊D1111yescharacteristic
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—222no—
333C23×C4C22×D1112yes—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—112no—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342#125—228no—
343C22⋊Q8—2216no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346#121—24no—
347#121—42no—
348#121—44no—
349C4×Q8—114no—
350C4×Q8—222no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—228no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4C22⋊D1112yes—
374C2×C42—221no—
375C2×C42C22×D1111yescharacteristic
376#106—222no—
377#106—224no—
378C4⋊C8—222no—
379#103—222no—
380#103—442no—
381#102—222no—
382#102—224no—
383C22⋊C8—224no—
384C22⋊C8—442no—
385C4×C8—222no—
386#95—22no—
387C2×C11—44no—
388C2×C11—82no—
389C2×C11#240711yescharacteristic
390C2×C11C2×#44811yescharacteristic
391C2×C11#301211yescharacteristic
392C2×C11#329511yescharacteristic
393C2×C11#333111yescharacteristic
394C2×C11#333511yescharacteristic
395C2×C11#335711yescharacteristic
396C24—21no—
397C24C2×C22⋊D1112yes—
398C2×Q8—112no—
399C2×Q8—224no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—881no—
406C2×Q8—881no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—82no—
417C2×D4#432414yescomplemented
418C2×D4#434112yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—228no—
434C22×C4—882no—
435C22×C4—882no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—228no—
441C2×C8—112no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—222no—
446C2×C8—221no—
447C2×C8—222no—
448C2×C8—222no—
449C2×C8—221no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—114no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4—221no—
464C4⋊C4—222no—
465C22⋊C4—24no—
466C22⋊C4—44no—
467C22⋊C4—44no—
468C22⋊C4—42no—
469C22⋊C4—228no—
470C42—224no—
471C42D4×D1112yes—
472C42D4×D1112yes—
473C11#2411811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×#432414yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—222no—
490Q8—222no—
491Q8—441no—
492Q8—441no—
493Q8—884no—
494D4—22no—
495D4—22no—
496D4—28no—
497D4—41no—
498D4—41no—
499D4—88no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—224no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—888no—
526C2×C4C2×#432412yes—
527C2×C4#6699012yes—
528C2×C4#6699012yes—
529C2×C4#6700412yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×#434111yescharacteristic
533C2×C4#6703711yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—222no—
537C8—442no—
538C8—441no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C22×#432411yescharacteristic
554C22C2×#6699011yescharacteristic
555C22#1062333711yescharacteristic
556C22C2×#6700411yescharacteristic
557C22#1062335511yescharacteristic
558C22#1062336611yescharacteristic
559C22#1062336811yescharacteristic
560C4—22no—
561C4—42no—
562C4—81no—
563C4—82no—
564C4—442no—
565C4—442no—
566C4—444no—
567C4#1062265314yes—
568C4#1062312911yescharacteristic
569C4#1062313011yescharacteristic
570C4#1062313711yescharacteristic
571C4#1062313911yescharacteristic
572C2—44no—
573C2—82no—
574C2#1307195711yescharacteristic
575C2C2×#1062265311yescharacteristic
576C2#1307791711yescharacteristic
577C2#1308044011yescharacteristic
578C2#1308093211yescharacteristic
579C2#1308097311yescharacteristic
580C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#24118
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622621C2semidirect
3. C2×C4×#4324C2semidirect
4. #13069812C2semidirect
5. #13069619C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068934C2semidirect
9. #13068808C2semidirect
10. #13068618C2semidirect
92. #66922D4semidirect
94. C4×Dic22D4semidirect
119. C2×D4×C11SD16semidirect
417. C2×D4#4324semidirect
473. C11#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226212
C2×C4×#43242
#130698122
#130696192
#130695762
#130694112
#130689342
#130688082
#130686182
C11×#25372
#2411811