Finite Group Databasebeta

← #14780757

Subgroups — #14780757

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C212yesmaximal, complemented
2C2×#10623041C211yesmaximal, characteristic, complemented
3C2×#10622618C212yesmaximal, complemented
4#13069662C214yesmaximal, complemented
5#13069657C214yesmaximal, complemented
6C2×#10622168C211yesmaximal, characteristic, complemented
7C11×#2311C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2212yes—
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#67004—22no—
13#10623353—28no—
14#10623353—28no—
15C2×#67003—24no—
16C2×#67002—22no—
17C2×#66995C2214yescomplemented
18C2×#66985C2214yescomplemented
19C2×#66983—22no—
20C22×#4318C2212yes—
21#10623041—24no—
22#10623041—22no—
23#10623041C2214yes—
24C2×#66950—22no—
25C2×#66948—22no—
26C11×#391C2212yescomplemented
27C11×#390C2212yescomplemented
28C11×#386—22no—
29C11×#380—22no—
30#10622618—28no—
31C2×#66869C2218yescomplemented
32#10622168C2214yescomplemented
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—24no—
37C2×C11×#41D414yescomplemented
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—24no—
48C2×#4339—24no—
49C2×#4339—24no—
50C2×#4339—24no—
51C2×#4339D414yes—
52C2×#4339C2314yes—
53C22×D44—22no—
54C22×D44D412yes—
55C22×C4×D11—22no—
56C22×Dic22D412yes—
57C11×#117—24no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—24no—
65C2×C42×C11C2312yes—
66#67004—216no—
67#67003—232no—
68#67002—216no—
69C2×#4326—24no—
70#66995—28no—
71#66995—28no—
72C2×#4325—24no—
73C2×#4324—24no—
74#66985—28no—
75#66985—28no—
76C2×#4323—24no—
77#66983—28no—
78#66983—28no—
79C2×(C2×D11)⋊C4—24no—
80C2×C4⋊Dic11—22no—
81C2×#4318—22no—
82C2×#4318—24no—
83C2×#4318D418yescomplemented
84C2×#4318C2314yes—
85C22×C11⋊C8—22no—
86#66950—28no—
87#66950—28no—
88#66948—28no—
89#66948—28no—
90C11×#95—24no—
91#66869—216no—
92#23409—111nomaximal, Sylow
93C24×C11—21no—
94C24×C11C2×D411yescharacteristic
95C23×D11—22no—
96C11×#41—28no—
97C11×#41—28no—
98C11×#41—44no—
99C11×#41—44no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C2×D412yescomplemented
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11C2×D412yescomplemented
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D414yes—
126C22×C4×C11#4112yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C22×Dic11—22no—
133#4339—28no—
134#4339—28no—
135#4339—24no—
136#4339—24no—
137#4339—24no—
138#4339—24no—
139#4339—44no—
140#4339—44no—
141#4339—44no—
142#4339—44no—
143C2×D44—28no—
144C2×D44—22no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—84no—
148C2×D44C2×D414yes—
149C2×C4×D11—24no—
150C2×C4×D11—24no—
151C2×C4×D11—44no—
152C2×C4×D11—44no—
153C2×Dic22—24no—
154C2×Dic22—22no—
155C2×Dic22—24no—
156C2×Dic22C2×D414yes—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—42no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—84no—
162C42×C11—24no—
163#4326—216no—
164#4325—216no—
165#4324—216no—
166#4323—216no—
167(C2×D11)⋊C4—216no—
168C4⋊Dic11—28no—
169#4318—28no—
170#4318—24no—
171#4318C2×D418yescomplemented
172C2×C11⋊C8—28no—
173C2×C11⋊C8—24no—
174C2×#575—112no—
175C2×#537—111no—
176C2×#421—112no—
177#2311D1111yescharacteristic, complemented
178#2007—114no—
179#2006—114no—
180C2×#343—111no—
181C23×C11—22no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11#12011yescharacteristic
189C23×C11#12011yescharacteristic
190C23×C11#12112yes—
191C23×C11#12712yes—
192C23×C11C22×D411yescharacteristic
193C22×D11—24no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—44no—
197Q8×C11—24no—
198Q8×C11—42no—
199D4×C11—24no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—42no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—48no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—82no—
214C2×C4×C11#12014yes—
215C2×C4×C11#12014yes—
216C2×C4×C11#12012yes—
217C2×C4×C11#12114yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#12712yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D412yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2×#4111yescharacteristic
225C22⋊D11—44no—
226C22⋊D11—44no—
227C22⋊D11—48no—
228C2×Dic11—24no—
229C2×Dic11—44no—
230D44—24no—
231D44—24no—
232D44—44no—
233D44—88no—
234C4×D11—44no—
235C4×D11—44no—
236C4×D11—48no—
237Dic22—24no—
238Dic22—24no—
239Dic22—44no—
240C11⋊C8—28no—
241C22×#41—112no—
242C22×#41C2×D1111yescharacteristic
243#575—228no—
244#575—228no—
245C2×#137—114no—
246C2×#137—222no—
247C2×AGL(1,ℤ/8)—114no—
248C2×AGL(1,ℤ/8)—222no—
249C2×#135—224no—
250C22×M16—112no—
251#537—114no—
252#537—224no—
253#537—222no—
254C2×C22⋊Q8—222no—
255C2×#121—222no—
256C2×#121—222no—
257C2×#117C2×D1111yescharacteristic
258C22×C4⋊C4C2×D1111yescharacteristic
259#421—228no—
260C2×#104—118no—
261#391C2×D1112yescomplemented
262#390C2×D1112yescomplemented
263#386—22no—
264#380—22no—
265#343—114no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11#39212yes—
280C22×C11#39212yes—
281C22×C11C2×#12011yescharacteristic
282C22×C11C2×#12111yescharacteristic
283C22×C11C2×#12711yescharacteristic
284C2×D11—44no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—88no—
288C4×C11—42no—
289C4×C11—44no—
290C4×C11—82no—
291C4×C11#39214yes—
292C4×C11C2×#12012yes—
293C4×C11C2×#12112yes—
294Dic11—44no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—24no—
299C2×#41—114no—
300C2×#41—114no—
301C2×#41—222no—
302C2×#41—222no—
303C2×#41—224no—
304C2×#41—224no—
305C2×#41—224no—
306C2×#41—224no—
307C2×#41D4414yescomplemented
308C22×Q8—112no—
309C22×Q8C22×D1111yescharacteristic
310C22×D4—21no—
311C22×D4—112no—
312C22×D4—222no—
313C22×D4—222no—
314C22×D4C22×D1111yescharacteristic
315C23×C4—21no—
316C23×C4—222no—
317C23×C4C22⋊D1112yes—
318C23×C4C22×D1111yescharacteristic
319#137—228no—
320#137—2216no—
321#137—228no—
322AGL(1,ℤ/8)—228no—
323AGL(1,ℤ/8)—2216no—
324AGL(1,ℤ/8)—228no—
325#135—2232no—
326C2×Q16—224no—
327C2×SD16—224no—
328C2×SD16—224no—
329C2×D8—224no—
330C2×M16—118no—
331C2×M16—114no—
332C2×M16—224no—
333C2×M16—222no—
334C22×C8—222no—
335C22⋊Q8—228no—
336C22⋊Q8—228no—
337#121—228no—
338#121—228no—
339#121—228no—
340#121—228no—
341#117—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4C22⋊D1112yes—
347C2×C4⋊C4C22×D1112yes—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—224no—
351C2×C42C22×D1112yes—
352#104—2216no—
353#95—24no—
354C2×C11—21no—
355C2×C11—22no—
356C2×C11—21no—
357C2×C11—22no—
358C2×C11—82no—
359C2×C11C2×#39211yescharacteristic
360C2×C11#301911yescharacteristic
361C2×C11#302011yescharacteristic
362D11—84no—
363C24—21no—
364C24—222no—
365C24C2×C22⋊D1111yescharacteristic
366#41—28no—
367#41—28no—
368#41—44no—
369#41—44no—
370#41—228no—
371#41—228no—
372#41—224no—
373#41—224no—
374#41—224no—
375#41—224no—
376#41—444no—
377#41—444no—
378#41—444no—
379#41—444no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—114no—
384C2×Q8—222no—
385C2×Q8—224no—
386C2×Q8—224no—
387C2×Q8C2×D4412yescomplemented
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—114no—
396C2×D4—228no—
397C2×D4—224no—
398C2×D4—224no—
399C2×D4—224no—
400C2×D4—224no—
401C2×D4—222no—
402C2×D4—444no—
403C2×D4—444no—
404C2×D4—884no—
405C2×D4C2×D4412yescomplemented
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—82no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—444no—
418C22×C4—444no—
419C22×C4C2×D4412yes—
420C22×C4#433912yes—
421C22×C4D4×D1112yes—
422C22×C4D4×D1112yes—
423C22×C4D4×D1114yes—
424C22×C4C2×C22⋊D1114yes—
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C23×D1111yescharacteristic
427Q16—2216no—
428SD16—2216no—
429SD16—2216no—
430D8—2216no—
431M16—118no—
432M16—228no—
433M16—224no—
434C2×C8—228no—
435C2×C8—224no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—42no—
439C4⋊C4—228no—
440C22⋊C4—42no—
441C22⋊C4—84no—
442C22⋊C4—2216no—
443C42—24no—
444C11#2340911yescharacteristic, complemented, Sylow
445C23—22no—
446C23—41no—
447C23—41no—
448C23—42no—
449C23—42no—
450C23—41no—
451C23—41no—
452C23—224no—
453C23—444no—
454C23—444no—
455C23—444no—
456C23#6698312yes—
457C23#6699011yescharacteristic
458C23#6699011yescharacteristic
459C23#6699312yes—
460C23C22×C22⋊D1111yescharacteristic
461Q8—24no—
462Q8—42no—
463Q8—224no—
464Q8—224no—
465Q8—444no—
466D4—24no—
467D4—44no—
468D4—44no—
469D4—42no—
470D4—224no—
471D4—224no—
472D4—444no—
473D4—444no—
474D4—448no—
475D4—444no—
476D4—888no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—44no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—48no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—82no—
488C2×C4—224no—
489C2×C4—444no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—448no—
493C2×C4#6693514yes—
494C2×C4#6693514yes—
495C2×C4#6693714yes—
496C2×C4#6693714yes—
497C2×C4#6698312yes—
498C2×C4#6699012yes—
499C2×C4#6699312yes—
500C2×C4C22×D4411yescharacteristic
501C2×C4C2×#433911yescharacteristic
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1112yes—
504C8—228no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—44no—
514C22—42no—
515C22—82no—
516C22—81no—
517C22—81no—
518C22—444no—
519C22—444no—
520C22—444no—
521C22—888no—
522C22#1062257312yes—
523C22#1062257312yes—
524C22C2×#6698311yescharacteristic
525C22C2×#6699011yescharacteristic
526C22C2×#6699311yescharacteristic
527C4—42no—
528C4—44no—
529C4—82no—
530C4—444no—
531C4#1062257314yes—
532C4C2×#6693512yes—
533C4C2×#6693712yes—
534C2—21no—
535C2—21no—
536C2—22no—
537C2—22no—
538C2—82no—
539C2—884no—
540C2C2×#1062257311yescharacteristic
541C2#1307797211yescharacteristic
542C2#1307797911yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC22×C11C2×#120
hypercenter#2311D11
hypocenterC11#23409
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C2×#10623041C2semidirect
3. C2×#10622618C2semidirect
4. #13069662C2semidirect
5. #13069657C2semidirect
6. C2×#10622168C2semidirect
7. C11×#2311C2semidirect
17. C2×#66995C22semidirect
18. C2×#66985C22semidirect
26. C11×#391C22semidirect
27. C11×#390C22semidirect
31. C2×#66869C22semidirect
32. #10622168C22semidirect
37. C2×C11×#41D4semidirect
83. C2×#4318D4semidirect
103. C2×Q8×C11C2×D4semidirect
111. C2×D4×C11C2×D4semidirect
171. #4318C2×D4semidirect
177. #2311D11semidirect
261. #391C2×D11semidirect
262. #390C2×D11semidirect
307. C2×#41D44semidirect
387. C2×Q8C2×D44semidirect
405. C2×D4C2×D44semidirect
444. C11#23409semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106230412
C2×#106226182
#130696622
#130696572
C2×#106221682
C11×#23112
#2340911