Finite Group Databasebeta

← #14787695

Subgroups — #14787695

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068939C212yesmaximal, complemented
9#13068813C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66989—21no—
17C22×#4324C2211yescharacteristic
18C2×#66979C2212yes—
19C2×#66977C2212yes—
20#10623073—24no—
21#10623073—24no—
22C2×#66940—21no—
23C2×#66932—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#10622620—24no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66871C2212yes—
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—
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C11×#121—24no—
53C11×#121—42no—
54C11×#121—44no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71#66989—28no—
72C2×#4324—22no—
73C2×#4324—22no—
74C2×#4324—22no—
75#66979—24no—
76#66979—24no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2312yes—
80#66977—24no—
81#66977—24no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—22no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89#66940—28no—
90#66932—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—22no—
103#66871—24no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24119—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—82no—
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—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C2×Dic22—24no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C2×Dic22C2×D412yes—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—81no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—42no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C22⋊Dic11—28no—
162C22⋊Dic11—28no—
163#4324—28no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D414yes—
168C4⋊Dic11C2×D412yes—
169Dic11⋊C4—28no—
170Dic11⋊C4—24no—
171C4×Dic11—28no—
172C4×Dic11—24no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8#4112yes—
182C2×#556—111no—
183C2×#474—111no—
184C2×C4×SD16—111no—
185#2537D1111yescharacteristic
186#2036—112no—
187#2000—112no—
188#1990—111no—
189#1954—111no—
190#1875—112no—
191#1854—112no—
192#1803—111no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C22×D411yescharacteristic
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—44no—
213D4×C11—88no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12012yes—
232C2×C4×C11#13512yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249Dic22—22no—
250Dic22—22no—
251Dic22—41no—
252Dic22—41no—
253Dic22—48no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—42no—
257C22×SD16—111no—
258#556—224no—
259#556—224no—
260C2×C4⋊Q8—111no—
261C2×#126—222no—
262C2×#124—221no—
263C2×C22⋊Q8—112no—
264C2×#121—21no—
265C2×#121C2×D1112yes—
266C2×C4×Q8—111no—
267C2×C4×Q8—221no—
268C2×C4×D4C2×D1111yescharacteristic
269C2×C4×D4C2×D1111yescharacteristic
270C2×#117—112no—
271#474—224no—
272C4×SD16—224no—
273C2×#107—112no—
274C2×#106—111no—
275C2×C4⋊C8—111no—
276C2×#103—111no—
277C2×#103—112no—
278C2×#102—111no—
279C2×#102—112no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#394—22no—
284#384C2×D1111yescharacteristic
285#380—21no—
286#380C2×D1112yes—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11C2×#12011yescharacteristic
305C22×C11#54611yescharacteristic
306C22×C11#54711yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11#57711yescharacteristic
310C22×C11#57811yescharacteristic
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—81no—
314C4×C11—82no—
315C4×C11#44914yes—
316C4×C11#52511yescharacteristic
317C4×C11#53711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—42no—
321Dic11—44no—
322Dic11—42no—
323C22×Q8—111no—
324C22×Q8—221no—
325C22×D4—22no—
326C22×D4C22⋊D1111yescharacteristic
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4C22×D1112yes—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8—112no—
336C4⋊Q8—114no—
337C4⋊Q8—222no—
338#126—2216no—
339#124—228no—
340C22⋊Q8—224no—
341C22⋊Q8—224no—
342#121—24no—
343#121—42no—
344#121—44no—
345C4×Q8—114no—
346C4×Q8—228no—
347C4×Q8—222no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—224no—
353#117—224no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4C22⋊D1112yes—
370C2×C42—222no—
371C2×C42—221no—
372C2×C42C22×D1111yescharacteristic
373#107—224no—
374#106—222no—
375C4⋊C8—222no—
376#103—222no—
377#103—442no—
378#102—222no—
379#102—224no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—222no—
383#95—22no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11#240711yescharacteristic
387C2×C11C2×#44911yescharacteristic
388C2×C11#301311yescharacteristic
389C2×C11#330211yescharacteristic
390C2×C11#332411yescharacteristic
391C2×C11#334011yescharacteristic
392C2×C11#335311yescharacteristic
393C24—21no—
394C24C2×C22⋊D1112yes—
395C2×Q8—112no—
396C2×Q8—224no—
397C2×Q8—221no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—442no—
403C2×Q8—442no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—82no—
415C2×D4#434112yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—221no—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434SD16—228no—
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—222no—
440C2×C8—221no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—221no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—81no—
451C4⋊C4—112no—
452C4⋊C4—114no—
453C4⋊C4—228no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—221no—
457C4⋊C4—222no—
458C22⋊C4—24no—
459C22⋊C4—44no—
460C22⋊C4—44no—
461C22⋊C4—42no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C42—228no—
465C42—224no—
466C42D4×D1112yes—
467C42D4×D1112yes—
468C11#2411911yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23C22×C22⋊D1111yescharacteristic
484Q8—222no—
485Q8—222no—
486Q8—441no—
487Q8—441no—
488Q8—448no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—44no—
494D4—88no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4#6698512yes—
521C2×C4#6699012yes—
522C2×C4#6699012yes—
523C2×C4#6700312yes—
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×#434111yescharacteristic
527C2×C4#6703711yescharacteristic
528C2×C4#41×D1111yescharacteristic
529C2×C4#6704311yescharacteristic
530C8—222no—
531C8—442no—
532C8—441no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×#6698511yescharacteristic
548C22C2×#6699011yescharacteristic
549C22#1062333711yescharacteristic
550C22C2×#6700311yescharacteristic
551C22#1062335511yescharacteristic
552C22#1062336711yescharacteristic
553C22#1062336911yescharacteristic
554C4—22no—
555C4—42no—
556C4—82no—
557C4—81no—
558C4—444no—
559C4—442no—
560C4—442no—
561C4#1062265014yes—
562C4#1062312911yescharacteristic
563C4#1062313011yescharacteristic
564C4#1062313711yescharacteristic
565C4#1062313911yescharacteristic
566C2—82no—
567C2—82no—
568C2#1307195711yescharacteristic
569C2C2×#1062265011yescharacteristic
570C2#1307792811yescharacteristic
571C2#1308053311yescharacteristic
572C2#1308084711yescharacteristic
573C2#1308102911yescharacteristic
574C2#1308120011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#24119
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×#10623073C2semidirect
2. C2×#10622620C2semidirect
3. C2×C4×#4324C2semidirect
4. #13069819C2semidirect
5. #13069619C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068939C2semidirect
9. #13068813C2semidirect
10. #13068618C2semidirect
92. #66922D4semidirect
94. C4×Dic22D4semidirect
468. C11#24119semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106226202
C2×C4×#43242
#130698192
#130696192
#130695762
#130694112
#130689392
#130688132
#130686182
C11×#25372
#2411911