Finite Group Databasebeta

← #14781769

Subgroups — #14781769

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3C2×#10622615C211yesmaximal, characteristic
4C22×#66899C211yesmaximal, characteristic, complemented
5#13071204C211yesmaximal, characteristic
6#13069938C214yesmaximal, complemented
7#13069931C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C11×#2310C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×#4326C2212yes—
15C2×#66995—24no—
16C2×#66995—24no—
17C2×#66995—24no—
18C22×#4325C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#391—22no—
23C11×#391C2214yes—
24C11×#381—22no—
25C2×#66899—24no—
26C2×#66899C2214yes—
27#10622615—24no—
28#10622612—24no—
29#10622600—22no—
30C2×#66874C2212yes—
31C2×#66873C2212yes—
32#10622571—22no—
33#10622552C2212yes—
34#10622542C2212yes—
35C2×C4⋊(C11⋊C8)C2214yes—
36#10622167C2214yes—
37C22×Q8×C11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11D414yes—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339D414yes—
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C22×Dic22C2311yescharacteristic
58C11×#117—22no—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117—22no—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4D412yes—
66C2×C42×C11—21no—
67C2×C42×C11C2312yes—
68C2×#4326—24no—
69C2×#4326—24no—
70C2×#4326—24no—
71#66995—232no—
72C2×#4325—24no—
73C2×#4325—24no—
74C2×#4325—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×#4318—22no—
81C2×#4318—22no—
82C2×#4318D414yes—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2312yes—
88C11×#95—28no—
89#66899—28no—
90C11⋊#95—24no—
91#66874—24no—
92#66873—24no—
93C4⋊(C11⋊C8)—28no—
94#23545—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C23×D11—21no—
97C2×Q8×C11—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11—28no—
100C2×Q8×C11—28no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×Q8×C11—44no—
108C2×Q8×C11—44no—
109C2×Q8×C11C2×D414yes—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D414yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11—82no—
131#4339—28no—
132#4339—28no—
133#4339—44no—
134#4339—44no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×D412yes—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22C2×D412yes—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—42no—
158#4326—216no—
159#4325—216no—
160(C2×D11)⋊C4—84no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—42no—
164#4318—28no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—44no—
171C2×C11⋊C8C2×D414yes—
172C22×#137—111no—
173C2×#424—111no—
174C2×#416—111no—
175C22×#103—111no—
176#2311—111no—
177#2310D1111yescharacteristic, complemented
178#2056—114no—
179#2055—114no—
180#1736—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11#12112yes—
184C23×C11#12112yes—
185C23×C11#12112yes—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—42no—
191C22×D11—42no—
192Q8×C11—24no—
193Q8×C11—24no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—48no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#12014yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#12314yes—
212C2×C4×C11#12314yes—
213C2×C4×C11#12414yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C22⋊D11—48no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—84no—
227D44—22no—
228D44—22no—
229D44—41no—
230D44—41no—
231C4×D11—48no—
232Dic22—22no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236C11⋊C8—24no—
237C11⋊C8—42no—
238C22×#41—111no—
239C23×Q8C2×D1111yescharacteristic
240C2×#137—224no—
241C2×#137—224no—
242C2×#137—224no—
243C22×Q16—112no—
244C22×SD16—112no—
245C22×M16—111no—
246C23×C8—111no—
247C2×#117C2×D1111yescharacteristic
248C2×#117C2×D1111yescharacteristic
249C22×C4⋊C4—111no—
250#424—224no—
251C2×C4⋊C8—114no—
252#416—224no—
253C2×#103—114no—
254C2×#103—112no—
255C2×#103—224no—
256C2×#102—112no—
257#391—22no—
258#391—112no—
259#391C2×D1114yes—
260#390—112no—
261#386—222no—
262#381—22no—
263#380—222no—
264#340—114no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11#39414yes—
270C22×C11C2×#12111yescharacteristic
271C22×C11C2×#12111yescharacteristic
272C22×C11C2×#12111yescharacteristic
273C22×C11#57712yes—
274C22×C11#57812yes—
275C2×D11—42no—
276C2×D11—44no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—82no—
280C4×C11—44no—
281C4×C11—44no—
282C4×C11—82no—
283C4×C11#39414yes—
284C4×C11C2×#12011yescharacteristic
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12311yescharacteristic
287C4×C11C2×#12411yescharacteristic
288Dic11—42no—
289Dic11—82no—
290C2×#41—114no—
291C2×#41—222no—
292C2×#41—222no—
293C2×#41—222no—
294C2×#41—222no—
295C2×#41—222no—
296C22×Q8—22no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—111no—
303C22×Q8D4414yes—
304C22×Q8C22×D1112yes—
305C22×D4—111no—
306C22×D4—221no—
307C23×C4—21no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311#137—2232no—
312C2×Q16—224no—
313C2×Q16—224no—
314C2×Q16—224no—
315C2×SD16—224no—
316C2×SD16—224no—
317C2×SD16—224no—
318C2×M16—114no—
319C2×M16—222no—
320C2×M16—222no—
321C22×C8—112no—
322C22×C8—112no—
323C22×C8—222no—
324C22×C8—222no—
325C22×C8—222no—
326#117—22no—
327#117—22no—
328#117—22no—
329#117—22no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22⋊D1112yes—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—224no—
338C2×C22⋊C4C22⋊D1112yes—
339C2×C42—21no—
340C2×C42C22×D1112yes—
341C4⋊C8—228no—
342#103—224no—
343#103—228no—
344#102—224no—
345#95—28no—
346#95—224no—
347C2×C11—24no—
348C2×C11C2×#39411yescharacteristic
349C2×C11#304311yescharacteristic
350C2×C11#304411yescharacteristic
351C2×C11#304612yes—
352C2×C11#306312yes—
353D11—82no—
354C24—221no—
355C24C2×C22⋊D1111yescharacteristic
356#41—228no—
357#41—228no—
358#41—444no—
359#41—444no—
360C2×Q8—24no—
361C2×Q8—22no—
362C2×Q8—28no—
363C2×Q8—28no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—44no—
369C2×Q8—44no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—112no—
373C2×Q8—221no—
374C2×Q8—221no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8—221no—
378C2×Q8C2×D4414yes—
379C2×D4—112no—
380C2×D4—224no—
381C2×D4—221no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—442no—
387C2×D4—442no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—221no—
394C22×C4—224no—
395C22×C4—222no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—882no—
400C22×C4C2×D4412yes—
401C22×C4#433912yes—
402C22×C4D4×D1112yes—
403C22×C4D4×D1112yes—
404C22×C4#434112yes—
405C22×C4#434112yes—
406C22×C4C2×C22⋊D1114yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—2216no—
410SD16—2216no—
411M16—228no—
412C2×C8—114no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—444no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—442no—
425C22⋊C4—24no—
426C22⋊C4—42no—
427C22⋊C4—884no—
428C42—22no—
429C42—22no—
430C42—42no—
431C11#2354511yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—442no—
438C23—442no—
439C23#6698312yes—
440C23#6699112yes—
441C23#6699212yes—
442C23C22×C22⋊D1111yescharacteristic
443Q8—24no—
444Q8—24no—
445Q8—42no—
446Q8—42no—
447Q8—48no—
448Q8—222no—
449Q8—222no—
450Q8—441no—
451Q8—441no—
452D4—222no—
453D4—222no—
454D4—448no—
455D4—441no—
456D4—441no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—222no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—448no—
471C2×C4—442no—
472C2×C4—444no—
473C2×C4—884no—
474C2×C4#6693514yes—
475C2×C4#6693614yes—
476C2×C4#6693814yes—
477C2×C4#6693914yes—
478C2×C4#6698312yes—
479C2×C4#6699112yes—
480C2×C4#6699212yes—
481C2×C4C22×D4411yescharacteristic
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C8—224no—
488C8—442no—
489C22—24no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—444no—
494C22—442no—
495C22—882no—
496C22—881no—
497C22—881no—
498C22#1062257414yes—
499C22C2×#6698311yescharacteristic
500C22C2×#6699111yescharacteristic
501C22C2×#6699211yescharacteristic
502C22#1062336812yes—
503C22#1062336912yes—
504C4—44no—
505C4—44no—
506C4—82no—
507C4—442no—
508C4—882no—
509C4#1062257414yes—
510C4C2×#6693511yescharacteristic
511C4C2×#6693611yescharacteristic
512C4C2×#6693811yescharacteristic
513C4C2×#6693911yescharacteristic
514C2—24no—
515C2—882no—
516C2C2×#1062257411yescharacteristic
517C2#1307813711yescharacteristic
518C2#1307814611yescharacteristic
519C2#1307816212yes—
520C2#1307830312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2310C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#2310D11
hypocenterC11#23545
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
4. C22×#66899C2semidirect
6. #13069938C2semidirect
7. #13069931C2semidirect
8. #13068337C2semidirect
9. C11×#2310C2semidirect
177. #2310D11semidirect
431. C11#23545semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106226122
C2×#106226152
C22×#668992
#130712042
#130699382
#130699312
#130683372
C11×#23102
#2354511