Finite Group Databasebeta

← #14788155

Subgroups — #14788155

Order 2816.

1114 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×#10623259C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×#10622703C211yesmaximal, characteristic, complemented
4C4×#66950C211yesmaximal, characteristic
5#13069811C212yesmaximal
6#13069625C212yesmaximal
7#13069568C211yesmaximal, characteristic, complemented
8#13068955C212yesmaximal, complemented
9#13068886C212yesmaximal, complemented
10#13068593C211yesmaximal, characteristic
11C11×#1981C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×Q8×Dic11C2212yes—
15C22×#4326C2212yes—
16#10623259—24no—
17#10623259—24no—
18C2×#66950—21no—
19C2×#66950C2211yescharacteristic
20C2×#66945—21no—
21C2×#66943—21no—
22C2×#66940—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66881C2212yes—
33C2×#66880C2212yes—
34#10622703—24no—
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622587C2211yescharacteristic
38C4×(C2×D11)⋊C4—21no—
39C4×C4⋊Dic11—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622464—24no—
42#10622281—21no—
43#10622266—21no—
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2312yes—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#66999—24no—
63#66999—24no—
64Q8×Dic11—24no—
65Q8×Dic11—24no—
66C2×#4326—24no—
67C2×#4326—24no—
68C2×#4326—42no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66950—28no—
87#66950—22no—
88#66950—22no—
89#66945—28no—
90#66943—28no—
91#66940—28no—
92C42×D11—22no—
93C42×D11—22no—
94#66922—22no—
95#66922D414yes—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×C4⋊C8—22no—
99C11×#103—24no—
100C11×#103—42no—
101C11×#95—21no—
102#66899—24no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107(C2×D11)⋊C8—42no—
108#66881—24no—
109#66880—24no—
110C4⋊(C11⋊C8)—22no—
111#24157—111nomaximal, Sylow
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D414yes—
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×Dic11—21no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×Dic22—24no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—42no—
150C2×Dic22—42no—
151C2×Dic22#4112yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4#4112yes—
161C42×C11—42no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4326—48no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—28no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11C2×D414yes—
176Dic11⋊C4—28no—
177Dic11⋊C4—42no—
178C4×Dic11—28no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#533—111no—
188C2×#475—111no—
189C2×#462—111no—
190C4×C22⋊Q8—111no—
191#2035—112no—
192#2001—112no—
193#1988—111no—
194#1981D1111yescharacteristic, complemented
195#1878—112no—
196#1865—112no—
197#1797—111no—
198C23×C11C22×D411yescharacteristic
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11#13712yes—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11#12012yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#13512yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—24no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11#13712yes—
249C4×D11—28no—
250C4×D11—41no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—41no—
254C4×D11—44no—
255Dic22—22no—
256Dic22—22no—
257Dic22—41no—
258Dic22—41no—
259Dic22—48no—
260C8×C11—42no—
261C11⋊C8—42no—
262C22×Q16—112no—
263#533—224no—
264#533—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#125—221no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—111no—
270C2×C22⋊Q8—221no—
271C2×C4×Q8—112no—
272C2×C4×Q8—111no—
273C2×C4×Q8—221no—
274C2×#117—221no—
275C22×C42—111no—
276#475—224no—
277#462—224no—
278C2×#106—112no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—112no—
282C2×#103—112no—
283C2×#103C2×D1112yes—
284C2×#103C2×D1112yes—
285C2×C22⋊C8—112no—
286#391—111no—
287#389—111no—
288#387—221no—
289#385—221no—
290#380—111no—
291C4×C4⋊C4—221no—
292C4×C4⋊C4C2×D1111yescharacteristic
293C4×C22⋊C4—221no—
294#340—112no—
295#340—112no—
296#336—112no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#52511yescharacteristic
299C22×C11#53711yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11C2×#13711yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—41no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—81no—
315C4×C11#45214yes—
316C4×C11#54611yescharacteristic
317C4×C11#54711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—22no—
321Dic11—42no—
322Dic11—41no—
323Dic11—44no—
324Dic11—41no—
325Dic11—81no—
326C22×Q8—111no—
327C22×Q8—221no—
328C22×Q8C22×D1112yes—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—111no—
332C2×Q16—224no—
333C2×Q16—224no—
334C2×Q16—442no—
335C22×C8—112no—
336C22×C8C22×D1112yes—
337C4⋊Q8—22no—
338C4⋊Q8—114no—
339C4⋊Q8—222no—
340C4⋊Q8D4414yes—
341#125—228no—
342C22⋊Q8—222no—
343C22⋊Q8—228no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346C22⋊Q8—222no—
347C4×Q8—228no—
348C4×Q8—224no—
349C4×Q8—224no—
350C4×Q8—222no—
351C4×Q8—222no—
352#117—228no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C42—21no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—222no—
373C2×C42—222no—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#106—224no—
378C4⋊C8—22no—
379C4⋊C8—222no—
380#103—24no—
381#103—42no—
382#103—224no—
383#103—224no—
384C22⋊C8—442no—
385#95—21no—
386#95—221no—
387#95—221no—
388#95—221no—
389#95—221no—
390C2×C11#240711yescharacteristic
391C2×C11C2×#45211yescharacteristic
392C2×C11#300411yescharacteristic
393C2×C11#310711yescharacteristic
394C2×C11#311311yescharacteristic
395C2×C11#324811yescharacteristic
396C2×C11#325511yescharacteristic
397D11—42no—
398C24—111no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—112no—
405C2×Q8—224no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×Q8—442no—
412C2×Q8—442no—
413C2×Q8C2×D4414yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—114no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—222no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—442no—
459C4⋊C4—442no—
460C4⋊C4#434112yes—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C22⋊C4—442no—
464C42—42no—
465C42—228no—
466C42—222no—
467C42—222no—
468C42—221no—
469C42—221no—
470C42—442no—
471C42C2×D4412yes—
472C42D4×D1112yes—
473C11#2415711yescharacteristic, complemented, Sylow
474C23—112no—
475C23—221no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23—221no—
480C23—221no—
481C23C2×D4×D1111yescharacteristic
482Q8—24no—
483Q8—24no—
484Q8—42no—
485Q8—42no—
486Q8—222no—
487Q8—222no—
488Q8—441no—
489Q8—441no—
490Q8—448no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—112no—
503C2×C4—228no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—224no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—444no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4#6693512yes—
527C2×C4#6693512yes—
528C2×C4#6696912yes—
529C2×C4#6697112yes—
530C2×C4C22×D4411yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×#434111yescharacteristic
533C2×C4#6703711yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—42no—
537C8—442no—
538C22—222no—
539C22—222no—
540C22—222no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22—441no—
545C22C2×#6693511yescharacteristic
546C22#1062313711yescharacteristic
547C22#1062313911yescharacteristic
548C22C2×#6696911yescharacteristic
549C22C2×#6697111yescharacteristic
550C22D11×#13711yescharacteristic
551C22D11×#13711yescharacteristic
552C4—22no—
553C4—44no—
554C4—42no—
555C4—81no—
556C4—222no—
557C4—441no—
558C4—444no—
559C4—441no—
560C4—442no—
561C4—881no—
562C4#1062242314yes—
563C4#1062308511yescharacteristic
564C4#1062308611yescharacteristic
565C4#1062320811yescharacteristic
566C4#1062324911yescharacteristic
567C2—442no—
568C2#1307195911yescharacteristic
569C2C2×#1062242311yescharacteristic
570C2#1307785211yescharacteristic
571C2#1307868411yescharacteristic
572C2#1307874511yescharacteristic
573C2#1307994911yescharacteristic
574C2#1308000811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1981D11
hypocenterC11#24157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×#10622703C2semidirect
7. #13069568C2semidirect
8. #13068955C2semidirect
9. #13068886C2semidirect
11. C11×#1981C2semidirect
194. #1981D11semidirect
473. C11#24157semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224642
C2×#106227032
C4×#669502
#130698112
#130696252
#130695682
#130689552
#130688862
#130685932
C11×#19812
#2415711