Finite Group Databasebeta

← #14809945

Subgroups — #14809945

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622405C212yesmaximal, complemented
3#13076967C211yesmaximal, characteristic
4#13069863C211yesmaximal, characteristic, complemented
5#13069862C211yesmaximal, characteristic, complemented
6#13069859C211yesmaximal, characteristic, complemented
7#13069416C212yesmaximal, complemented
8#13068549C212yesmaximal
9#13068549C212yesmaximal
10#13068373C211yesmaximal, characteristic
11C11×#2043C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66997C2212yes—
15D11×C4⋊Q8—28no—
16C2×#66949—21no—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11—21no—
19C2×#66941—21no—
20C2×#66941—21no—
21C2×#66941C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C11×#389C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×#66880C2212yes—
32C2×C8×Dic11C2212yes—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622589C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39#10622541C2211yescharacteristic
40#10622405—28no—
41#10622280—21no—
42#10622259—21no—
43C11×#336C2211yescharacteristic
44#10622162C2211yescharacteristic
45C22×Q8×C11C2312yes—
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—24no—
50C2×Q8×D11—42no—
51C2×Q8×D11—42no—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—22no—
57C22×Dic22—21no—
58C22×Dic22C2312yes—
59C22×C8×C11C2312yes—
60C11×C4⋊Q8—24no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#66997—24no—
68#66997D418yes—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66949—44no—
86C4⋊C4×D11—28no—
87C4⋊C4×D11—28no—
88#66941—28no—
89#66941—28no—
90#66941—24no—
91C42×D11—24no—
92#66922—24no—
93C11×#103—24no—
94C11×#103—42no—
95C11×#95—21no—
96#66899—24no—
97#66899—42no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101(C2×D11)⋊C8—24no—
102#66880—24no—
103#66880—42no—
104C8×Dic11—24no—
105#66874—24no—
106#66874—42no—
107#25856—111nomaximal, Sylow
108C23×D11C2×D411yescharacteristic
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127Q8×D11—48no—
128Q8×D11—48no—
129Q8×D11—48no—
130Q8×D11—48no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—28no—
136C2×C4×D11—22no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11SD1614yes—
142C2×C4×D11Q1614yes—
143C2×C4×D11#4114yes—
144C2×Dic22—28no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—44no—
151C2×Dic22—44no—
152C2×Dic22—42no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22C2×D414yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C42×C11—22no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—24no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175Dic11⋊C4—42no—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11C2×D414yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C22×C4⋊Q8—111no—
186C2×#487—112no—
187#2857—111no—
188#2043—111no—
189#2043—111no—
190#2043—111no—
191#2043D1111yescharacteristic, complemented
192#1956—112no—
193#1787—112no—
194#1787—112no—
195C4×C22⋊C8—111no—
196C23×C11C22×D411yescharacteristic
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11#12412yes—
202C22×D11C2×SD1612yes—
203C22×D11C2×Q1612yes—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—42no—
207Q8×C11—42no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11C2×SD1612yes—
222C2×C4×C11C2×Q1612yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2×#4112yes—
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11#12012yes—
239C2×Dic11#12012yes—
240C2×Dic11#12412yes—
241C2×Dic11C2×SD1612yes—
242C2×Dic11C2×Q1612yes—
243C2×Dic11#13712yes—
244C2×Dic11#13712yes—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—28no—
248C4×D11—28no—
249C4×D11—416no—
250Dic22—24no—
251Dic22—24no—
252Dic22—416no—
253Dic22—42no—
254Dic22—42no—
255Dic22—84no—
256C8×C11—42no—
257C11⋊C8—42no—
258C23×Q8—112no—
259C2×C4⋊Q8—111no—
260C2×C4⋊Q8—112no—
261C2×C4⋊Q8—111no—
262C2×C4⋊Q8—221no—
263C2×C4⋊Q8—221no—
264C2×C4⋊Q8—228no—
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×C22⋊Q8—221no—
267C22×C4⋊C4—221no—
268C22×C4⋊C4—221no—
269C22×C42—111no—
270#487—228no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103C2×D1112yes—
278C2×#103C2×D1112yes—
279C2×C22⋊C8—112no—
280C2×C4×C8—112no—
281#391—221no—
282#389—111no—
283#389—221no—
284#389C2×D1111yescharacteristic
285#384—111no—
286#380—111no—
287#380—111no—
288#380—221no—
289#336—111no—
290#336C2×D1111yescharacteristic
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×#12411yescharacteristic
293C22×C11#53511yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C22×Q1611yescharacteristic
296C22×C11C2×#13711yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—22no—
304C2×D11#48714yescomplemented
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—44no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#54612yes—
311C4×C11#54612yes—
312Dic11—22no—
313Dic11—44no—
314Dic11—81no—
315Dic11—81no—
316Dic11#44814yes—
317Dic11#45114yes—
318C22×Q8—112no—
319C22×Q8—222no—
320C22×Q8—221no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×Q8—224no—
324C22×Q8—224no—
325C22×Q8—442no—
326C22×Q8—442no—
327C22×Q8C22×D1112yes—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—222no—
332C22×C8—112no—
333C22×C8C22×D1112yes—
334C4⋊Q8—24no—
335C4⋊Q8—118no—
336C4⋊Q8—224no—
337C4⋊Q8—224no—
338C4⋊Q8—224no—
339C4⋊Q8—228no—
340C4⋊Q8—228no—
341C22⋊Q8—444no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—224no—
365C2×C42C22×D1111yescharacteristic
366#103—24no—
367#103—42no—
368#103—224no—
369#103—224no—
370#103—224no—
371#103—442no—
372#103—442no—
373#103—442no—
374C22⋊C8—224no—
375C4×C8—224no—
376#95—21no—
377#95—221no—
378#95—221no—
379#95—221no—
380C2×C11#243511yescharacteristic
381C2×C11C2×#44811yescharacteristic
382C2×C11C2×#45111yescharacteristic
383C2×C11C2×#48711yescharacteristic
384C2×C11#313911yescharacteristic
385C2×C11#320611yescharacteristic
386C2×C11#320911yescharacteristic
387D11—24no—
388C24—111no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—114no—
395C2×Q8—228no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—444no—
402C2×Q8—442no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×Q8—444no—
406C2×Q8—448no—
407C2×Q8—448no—
408C2×Q8—448no—
409C2×Q8—448no—
410C2×Q8D4×D1114yes—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—228no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—444no—
432C22×C4—444no—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—42no—
448C4⋊C4—228no—
449C4⋊C4—228no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—442no—
456C4⋊C4—442no—
457C4⋊C4—442no—
458C4⋊C4—442no—
459C22⋊C4—442no—
460C22⋊C4—442no—
461C42—22no—
462C42—114no—
463C42—222no—
464C42—222no—
465C11#2585611yescharacteristic, complemented, Sylow
466C23—112no—
467C23—112no—
468C23—112no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23C2×D4×D1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—42no—
477Q8—42no—
478Q8—224no—
479Q8—224no—
480Q8—4416no—
481Q8—442no—
482Q8—442no—
483Q8—884no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—228no—
505C2×C4—228no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—4416no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4SD16×D1112yes—
521C2×C4Q16×D1112yes—
522C2×C4C2×D4×D1112yes—
523C2×C4#6703711yescharacteristic
524C2×C4#41×D1112yes—
525C2×C4#6704211yescharacteristic
526C8—42no—
527C8—442no—
528C22—114no—
529C22—222no—
530C22—222no—
531C22—222no—
532C22—222no—
533C22—222no—
534C22—222no—
535C22D11×#12011yescharacteristic
536C22#1062313811yescharacteristic
537C22D11×#12411yescharacteristic
538C22C2×SD16×D1111yescharacteristic
539C22C2×Q16×D1111yescharacteristic
540C22D11×#13711yescharacteristic
541C22D11×#13711yescharacteristic
542C4—22no—
543C4—22no—
544C4—44no—
545C4—81no—
546C4—81no—
547C4—114no—
548C4—114no—
549C4—222no—
550C4—444no—
551C4—881no—
552C4—881no—
553C4#1062314112yes—
554C4#1062318512yes—
555C2—224no—
556C2#1307226211yescharacteristic
557C2D11×#44811yescharacteristic
558C2D11×#45111yescharacteristic
559C2D11×#48711yescharacteristic
560C2#1307899511yescharacteristic
561C2#1307954011yescharacteristic
562C2#1307956311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2043D11
hypocenterC11#25856
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. C2×#10622405C2semidirect
4. #13069863C2semidirect
5. #13069862C2semidirect
6. #13069859C2semidirect
7. #13069416C2semidirect
11. C11×#2043C2semidirect
191. #2043D11semidirect
304. C2×D11#487semidirect
465. C11#25856semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106224052
#130769672
#130698632
#130698622
#130698592
#130694162
#130685492
#130683732
C11×#20432
#2585611