Finite Group Databasebeta

← #14780881

Subgroups — #14780881

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C23×#4326C211yesmaximal, characteristic, complemented
3C2×#10623057C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5C2×#10622615C211yesmaximal, characteristic
6#13069715C214yesmaximal, complemented
7#13069709C214yesmaximal, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C11×#2310C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4326—24no—
16C22×#4326—24no—
17C22×#4326—24no—
18C22×#4326C2214yes—
19C22×#4326C2212yes—
20C2×#66995—24no—
21C2×#66995—24no—
22C2×#66995—24no—
23C22×#4325C2212yes—
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26#10623057—24no—
27#10623057—24no—
28C2×#66950—22no—
29C2×#66939—22no—
30C2×#66928C2212yes—
31C2×#66922C2212yes—
32C11×#391—22no—
33C11×#391C2214yes—
34C11×#381—22no—
35#10622617—24no—
36#10622615—24no—
37C2×#66874C2212yes—
38C2×#66874C2214yes—
39C2×#66873C2212yes—
40#10622162C2214yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11D414yes—
48C22×Q8×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C23×Dic11—21no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339D414yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—21no—
66C22×Dic22—22no—
67C22×Dic22D414yes—
68C22×Dic22C2311yescharacteristic
69C22×Dic22C2312yes—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11C2312yes—
80C2×#4326—232no—
81C2×#4326—24no—
82C2×#4326—28no—
83C2×#4326—24no—
84C2×#4326—28no—
85C2×#4326—24no—
86C2×#4326—28no—
87#66995—232no—
88C2×#4325—24no—
89C2×#4325—24no—
90C2×#4325—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×C4⋊Dic11—24no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318D414yes—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8D414yes—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66950—216no—
102#66939—216no—
103#66928—24no—
104#66928—24no—
105#66922—24no—
106#66922—24no—
107C11×#95—28no—
108#66874—24no—
109#66874—28no—
110#66873—24no—
111#23425—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C2×Q8×C11—24no—
115C2×Q8×C11—22no—
116C2×Q8×C11—28no—
117C2×Q8×C11—28no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—42no—
123C2×Q8×C11—44no—
124C2×Q8×C11—44no—
125C2×Q8×C11—42no—
126C2×Q8×C11C2×D414yes—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—42no—
144C22×Dic11—24no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149#4339—28no—
150#4339—28no—
151#4339—44no—
152#4339—44no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C2×D412yes—
159C2×C4×D11—24no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×Dic22—28no—
163C2×Dic22—24no—
164C2×Dic22—28no—
165C2×Dic22—22no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—21no—
175C2×Dic22—44no—
176C2×Dic22—44no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22C2×D412yes—
180C2×Dic22C2×D414yes—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—42no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—42no—
189#4326—216no—
190#4326—232no—
191#4325—216no—
192(C2×D11)⋊C4—216no—
193C4⋊Dic11—216no—
194#4318—28no—
195C2×C11⋊C8—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8C2×D414yes—
201C2×C11⋊C8C2×D414yes—
202C22×#137—111no—
203C23×Q16—111no—
204C2×#536—111no—
205C2×#419—111no—
206C2×#416—111no—
207#2310D1111yescharacteristic, complemented
208#2016—114no—
209#2015—114no—
210#1729—111no—
211C23×C11—24no—
212C23×C11#12012yes—
213C23×C11#12112yes—
214C23×C11#12712yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—44no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—42no—
223Q8×C11—42no—
224Q8×C11—48no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—28no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11#12014yes—
234C2×C4×C11#12014yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12114yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12712yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—48no—
254D44—22no—
255D44—22no—
256D44—41no—
257D44—41no—
258C4×D11—48no—
259Dic22—24no—
260Dic22—22no—
261Dic22—24no—
262Dic22—22no—
263Dic22—42no—
264Dic22—41no—
265Dic22—42no—
266Dic22—41no—
267Dic22—48no—
268C11⋊C8—24no—
269C11⋊C8—24no—
270C22×#41—111no—
271C23×Q8—111no—
272C23×Q8C2×D1111yescharacteristic
273C2×#137—224no—
274C2×#137—224no—
275C2×#137—224no—
276C22×Q16—114no—
277C22×Q16—112no—
278C22×Q16—224no—
279C22×Q16—224no—
280C22×Q16—224no—
281C22×SD16—112no—
282C22×M16—111no—
283C23×C8—111no—
284#536—224no—
285#536—224no—
286C2×C4⋊Q8—112no—
287C2×#124—112no—
288C2×#123—222no—
289C2×C22⋊Q8—222no—
290C2×#117C2×D1111yescharacteristic
291C2×#117C2×D1111yescharacteristic
292#419—224no—
293#416—224no—
294C2×#103—112no—
295C2×#103—114no—
296C2×#102—112no—
297#391—22no—
298#391C2×D1114yes—
299#381—22no—
300#336—114no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11#39214yes—
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×#12711yescharacteristic
308C22×C11#57814yes—
309C2×D11—42no—
310C2×D11—44no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—44no—
314C4×C11—44no—
315C4×C11—82no—
316C4×C11#39214yes—
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12011yescharacteristic
319C4×C11C2×#12111yescharacteristic
320C4×C11C2×#12111yescharacteristic
321Dic11—44no—
322Dic11—42no—
323C2×#41—114no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C22×Q8—22no—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—114no—
336C22×Q8—112no—
337C22×Q8—111no—
338C22×Q8—222no—
339C22×Q8—221no—
340C22×Q8—222no—
341C22×Q8—222no—
342C22×Q8—222no—
343C22×Q8—222no—
344C22×Q8D4414yes—
345C22×Q8C22×D1112yes—
346C22×D4—111no—
347C22×D4—221no—
348C23×C4—21no—
349C23×C4—221no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352#137—2232no—
353C2×Q16—228no—
354C2×Q16—224no—
355C2×Q16—228no—
356C2×Q16—224no—
357C2×Q16—2232no—
358C2×Q16—228no—
359C2×Q16—224no—
360C2×SD16—224no—
361C2×SD16—224no—
362C2×SD16—224no—
363C2×M16—114no—
364C2×M16—222no—
365C2×M16—222no—
366C22×C8—114no—
367C22×C8—112no—
368C22×C8—112no—
369C22×C8—222no—
370C22×C8—222no—
371C4⋊Q8—224no—
372C4⋊Q8—224no—
373#124—224no—
374#124—224no—
375#123—2216no—
376C22⋊Q8—2216no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4C22⋊D1112yes—
383C2×C4⋊C4C22×D1112yes—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4C22⋊D1112yes—
387C2×C42—21no—
388C2×C42C22×D1112yes—
389#103—224no—
390#103—228no—
391#102—224no—
392#95—28no—
393C2×C11—24no—
394C2×C11C2×#39211yescharacteristic
395C2×C11#301112yes—
396C2×C11#304412yes—
397C2×C11#315612yes—
398D11—82no—
399C24—221no—
400C24C2×C22⋊D1111yescharacteristic
401#41—228no—
402#41—228no—
403#41—444no—
404#41—444no—
405C2×Q8—24no—
406C2×Q8—22no—
407C2×Q8—28no—
408C2×Q8—28no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—42no—
416C2×Q8—42no—
417C2×Q8—114no—
418C2×Q8—112no—
419C2×Q8—224no—
420C2×Q8—222no—
421C2×Q8—221no—
422C2×Q8—228no—
423C2×Q8—228no—
424C2×Q8—222no—
425C2×Q8—221no—
426C2×Q8—222no—
427C2×Q8—221no—
428C2×Q8—222no—
429C2×Q8—221no—
430C2×Q8—222no—
431C2×Q8—221no—
432C2×Q8—444no—
433C2×Q8—444no—
434C2×Q8—442no—
435C2×Q8—442no—
436C2×Q8C2×D4414yes—
437C2×D4—112no—
438C2×D4—224no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—442no—
445C2×D4—442no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—224no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4C2×D4412yes—
460C22×C4#433912yes—
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4D4×D1112yes—
464C22×C4D4×D1112yes—
465C22×C4C2×C22⋊D1114yes—
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468Q16—2232no—
469Q16—2216no—
470SD16—2216no—
471M16—228no—
472C2×C8—114no—
473C2×C8—114no—
474C2×C8—228no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—2216no—
483C22⋊C4—24no—
484C22⋊C4—42no—
485C22⋊C4—2216no—
486C42—22no—
487C42—22no—
488C42—42no—
489C11#2342511yescharacteristic, complemented, Sylow
490C23—24no—
491C23—222no—
492C23—441no—
493C23—441no—
494C23—444no—
495C23#6698312yes—
496C23#6699012yes—
497C23#6699312yes—
498C23C22×C22⋊D1111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—42no—
502Q8—42no—
503Q8—48no—
504Q8—224no—
505Q8—222no—
506Q8—224no—
507Q8—222no—
508Q8—442no—
509Q8—441no—
510Q8—442no—
511Q8—441no—
512Q8—448no—
513D4—222no—
514D4—222no—
515D4—448no—
516D4—441no—
517D4—441no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—28no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—441no—
529C2×C4—442no—
530C2×C4—441no—
531C2×C4—442no—
532C2×C4—448no—
533C2×C4—448no—
534C2×C4#6693514yes—
535C2×C4#6693514yes—
536C2×C4#6693714yes—
537C2×C4#6693714yes—
538C2×C4#6698312yes—
539C2×C4#6699012yes—
540C2×C4#6699312yes—
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C2×D4×D1111yescharacteristic
547C8—224no—
548C8—224no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—444no—
553C22—442no—
554C22—882no—
555C22—882no—
556C22#1062257314yes—
557C22C2×#6698311yescharacteristic
558C22C2×#6699011yescharacteristic
559C22C2×#6699311yescharacteristic
560C22#1062336914yes—
561C4—44no—
562C4—44no—
563C4—82no—
564C4—442no—
565C4—444no—
566C4#1062257314yes—
567C4C2×#6693511yescharacteristic
568C4C2×#6693511yescharacteristic
569C4C2×#6693711yescharacteristic
570C4C2×#6693711yescharacteristic
571C2—24no—
572C2—882no—
573C2C2×#1062257311yescharacteristic
574C2#1307790912yes—
575C2#1307814612yes—
576C2#1307910712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2310C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#2310D11
hypocenterC11#23425
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. C23×#4326C2semidirect
4. C2×#10622617C2semidirect
6. #13069715C2semidirect
7. #13069709C2semidirect
8. #13068313C2semidirect
9. C11×#2310C2semidirect
207. #2310D11semidirect
489. C11#23425semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C23×#43262
C2×#106230572
C2×#106226172
C2×#106226152
#130697152
#130697092
#130683132
C11×#23102
#2342511