Finite Group Databasebeta

← #14780758

Subgroups — #14780758

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×#10622849C212yesmaximal, complemented
3#13071209C211yesmaximal, characteristic, complemented
4#13069663C214yesmaximal, complemented
5#13069658C214yesmaximal, complemented
6C2×#10622168C211yesmaximal, characteristic, complemented
7C2×C11×#537C211yesmaximal, characteristic, complemented
8C22×C11×#41C2212yes—
9C22×#4339C2211yescharacteristic
10C11×#537—24no—
11C11×#537—22no—
12C11×#537C2214yes—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#121—22no—
15C2×C11×#121—22no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#67004C2214yescomplemented
18#10623353—28no—
19#10623353—28no—
20C2×#67003—24no—
21C2×#67002C2214yescomplemented
22C2×#66995—22no—
23C2×#66985—22no—
24C2×#66979C2211yescharacteristic
25C22×#4318C2212yes—
26#10622849—28no—
27C2×#66901C2218yescomplemented
28#10622826—22no—
29#10622601C2212yescomplemented
30#10622600—22no—
31#10622587C2212yescomplemented
32#10622168C2214yescomplemented
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—24no—
36C2×C11×#41—24no—
37C2×C11×#41—24no—
38C2×C11×#41—24no—
39C2×C11×#41D414yes—
40C2×C11×#41C2314yes—
41C22×Q8×C11D412yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11D412yes—
45C23×C4×C11—22no—
46C23×C4×C11D412yes—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—24no—
53C2×#4339D414yescomplemented
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22C2311yescharacteristic
57C11×C22⋊Q8—28no—
58C11×C22⋊Q8—28no—
59C11×#121—28no—
60C11×#121—28no—
61C11×#121—28no—
62C11×#121—28no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—24no—
69C2×C22⋊Dic11—21no—
70#67004—28no—
71#67004—28no—
72#67003—232no—
73#67002—28no—
74#67002—28no—
75C2×#4326—24no—
76#66995—216no—
77C2×#4325—24no—
78C2×#4324—24no—
79#66985—216no—
80C2×#4323—24no—
81C2×(C2×D11)⋊C4—24no—
82#66979—24no—
83C2×C4⋊Dic11—21no—
84C2×C4×Dic11C2312yes—
85C2×#4318—22no—
86C2×#4318—24no—
87C2×#4318D418yescomplemented
88C2×#4318C2314yes—
89C22×C11⋊C8—22no—
90#66901—216no—
91C11⋊#95—24no—
92#23409—111nomaximal, Sylow
93C24×C11—22no—
94C24×C11C2×D411yescharacteristic
95C23×D11—21no—
96C11×#41—28no—
97C11×#41—28no—
98C11×#41—24no—
99C11×#41—24no—
100C11×#41—24no—
101C11×#41—24no—
102C11×#41—44no—
103C11×#41—44no—
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—22no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11C2×D414yes—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—84no—
119C2×D4×C11C2×D414yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D414yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—42no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142#4339—28no—
143#4339—28no—
144#4339—44no—
145#4339—44no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—21no—
149C2×D44C2×D412yescomplemented
150C2×C4×D11—24no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—21no—
156C2×Dic22C2×D412yescomplemented
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C22⋊C4—216no—
161C22⋊Dic11—42no—
162#4326—216no—
163#4325—216no—
164#4324—216no—
165#4323—216no—
166(C2×D11)⋊C4—84no—
167C4⋊Dic11—42no—
168C4×Dic11—24no—
169#4318—28no—
170#4318—24no—
171#4318C2×D418yescomplemented
172C2×C11⋊C8—28no—
173C2×C11⋊C8—24no—
174C2×#575—112no—
175C2×#537D1111yescharacteristic, complemented
176C2×#421—112no—
177#2311—111no—
178#2007—114no—
179#2006—114no—
180C2×#343—111no—
181C23×C11—24no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11#12011yescharacteristic
188C23×C11#12011yescharacteristic
189C23×C11#12112yes—
190C23×C11#12712yes—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—41no—
196C22×D11—41no—
197Q8×C11—24no—
198Q8×C11—24no—
199Q8×C11—44no—
200D4×C11—24no—
201D4×C11—24no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—48no—
205D4×C11—44no—
206D4×C11—88no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—48no—
214C2×C4×C11—44no—
215C2×C4×C11—82no—
216C2×C4×C11#12014yes—
217C2×C4×C11#12014yes—
218C2×C4×C11#12012yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#12114yes—
221C2×C4×C11#12114yes—
222C2×C4×C11#12712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4111yescharacteristic
227C22⋊D11—44no—
228C22⋊D11—44no—
229C2×Dic11—22no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235D44—24no—
236D44—42no—
237C4×D11—48no—
238Dic22—24no—
239Dic22—42no—
240C11⋊C8—28no—
241C22×#41—111no—
242C22×#41C2×D1112yes—
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—24no—
252#537—22no—
253#537C2×D1114yes—
254C2×C22⋊Q8—22no—
255C2×#121—22no—
256C2×#121—22no—
257C2×#117—111no—
258C22×C4⋊C4C2×D1111yescharacteristic
259#421—228no—
260C2×#104—118no—
261#391—112no—
262#390—112no—
263#386—222no—
264#380—222no—
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—44no—
276C22×C11—44no—
277C22×C11—88no—
278C22×C11#39212yes—
279C22×C11#39212yes—
280C22×C11C2×#12011yescharacteristic
281C22×C11C2×#12111yescharacteristic
282C22×C11C2×#12711yescharacteristic
283C2×D11—44no—
284C2×D11—42no—
285C2×D11—82no—
286C2×D11—81no—
287C2×D11—81no—
288C4×C11—44no—
289C4×C11—44no—
290C4×C11#39214yes—
291C4×C11C2×#12012yes—
292C4×C11C2×#12112yes—
293Dic11—42no—
294Dic11—82no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—24no—
298C2×#41—24no—
299C2×#41—24no—
300C2×#41—24no—
301C2×#41—114no—
302C2×#41—222no—
303C2×#41—224no—
304C2×#41—222no—
305C2×#41—222no—
306C2×#41C22⋊D1114yes—
307C2×#41C22×D1114yes—
308C22×Q8—111no—
309C22×Q8C22⋊D1112yes—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—111no—
313C22×D4—221no—
314C22×D4C22⋊D1112yes—
315C23×C4—22no—
316C23×C4—221no—
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—28no—
336C22⋊Q8—28no—
337#121—28no—
338#121—28no—
339#121—28no—
340#121—28no—
341#117—224no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C22⋊D1112yes—
347C2×C4⋊C4C22×D1112yes—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—224no—
351C2×C42—112no—
352#104—2216no—
353#95—224no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—22no—
357C2×C11—22no—
358C2×C11—84no—
359C2×C11C2×#39211yescharacteristic
360C2×C11#301911yescharacteristic
361C2×C11#302011yescharacteristic
362D11—82no—
363C24—22no—
364C24—221no—
365C24C2×C22⋊D1111yescharacteristic
366#41—28no—
367#41—28no—
368#41—24no—
369#41—24no—
370#41—24no—
371#41—24no—
372#41—44no—
373#41—44no—
374#41—44no—
375#41—44no—
376#41—228no—
377#41—228no—
378#41—444no—
379#41—444no—
380C2×Q8—22no—
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—112no—
384C2×Q8—221no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8C2×C22⋊D1114yes—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—28no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—22no—
394C2×D4—44no—
395C2×D4—44no—
396C2×D4—84no—
397C2×D4—112no—
398C2×D4—224no—
399C2×D4—222no—
400C2×D4—221no—
401C2×D4—222no—
402C2×D4—442no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4C2×C22⋊D1114yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—82no—
414C22×C4—221no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4D4×D1112yes—
420C22×C4D4×D1114yes—
421C22×C4#434112yes—
422C22×C4C2×C22⋊D1114yes—
423C22×C4C2×C22⋊D1112yes—
424C22×C4C2×C22⋊D1112yes—
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—28no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—442no—
440C22⋊C4—216no—
441C22⋊C4—442no—
442C22⋊C4—884no—
443C42—224no—
444C11#2340911yescharacteristic, complemented, Sylow
445C23—24no—
446C23—41no—
447C23—41no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—222no—
452C23—442no—
453C23—442no—
454C23—441no—
455C23—441no—
456C23#6699112yes—
457C23#6699312yes—
458C23#6700611yescharacteristic
459C23#6700611yescharacteristic
460C23C22×C22⋊D1111yescharacteristic
461Q8—24no—
462Q8—24no—
463Q8—44no—
464Q8—224no—
465Q8—442no—
466D4—24no—
467D4—24no—
468D4—44no—
469D4—44no—
470D4—48no—
471D4—44no—
472D4—88no—
473D4—224no—
474D4—444no—
475D4—444no—
476D4—442no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—44no—
485C2×C4—82no—
486C2×C4—222no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—448no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4#6699014yes—
494C2×C4#6699014yes—
495C2×C4#6699112yes—
496C2×C4#6699214yes—
497C2×C4#6699214yes—
498C2×C4#6699312yes—
499C2×C4#6700612yes—
500C2×C4C2×D4×D1111yescharacteristic
501C2×C4C2×D4×D1112yes—
502C2×C4C2×#434111yescharacteristic
503C2×C4C22×C22⋊D1112yes—
504C8—228no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—44no—
514C22—44no—
515C22—44no—
516C22—88no—
517C22—444no—
518C22—442no—
519C22—882no—
520C22—881no—
521C22—881no—
522C22#1062283612yes—
523C22#1062283612yes—
524C22C2×#6699111yescharacteristic
525C22C2×#6699311yescharacteristic
526C22C2×#6700611yescharacteristic
527C4—44no—
528C4—44no—
529C4—442no—
530C4—882no—
531C4#1062283614yes—
532C4C2×#6699012yes—
533C4C2×#6699212yes—
534C2—21no—
535C2—22no—
536C2—21no—
537C2—22no—
538C2—84no—
539C2—882no—
540C2C2×#1062283611yescharacteristic
541C2#1307797311yescharacteristic
542C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#537C2
socleC22×C11C2×#120
hypercenterC2×#537D11
hypocenterC11#23409
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C2×#10622849C2semidirect
3. #13071209C2semidirect
4. #13069663C2semidirect
5. #13069658C2semidirect
6. C2×#10622168C2semidirect
7. C2×C11×#537C2semidirect
17. C2×#67004C22semidirect
21. C2×#67002C22semidirect
27. C2×#66901C22semidirect
29. #10622601C22semidirect
31. #10622587C22semidirect
32. #10622168C22semidirect
53. C2×#4339D4semidirect
87. C2×#4318D4semidirect
149. C2×D44C2×D4semidirect
156. C2×Dic22C2×D4semidirect
171. #4318C2×D4semidirect
175. C2×#537D11semidirect
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×#106228492
#130712092
#130696632
#130696582
C2×#106221682
C2×C11×#5372
#2340911