Finite Group Databasebeta

← #14780935

Subgroups — #14780935

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C22×#66985C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5#13071106C211yesmaximal, characteristic, complemented
6#13069710C214yesmaximal, complemented
7#13069693C214yesmaximal, complemented
8#13068310C211yesmaximal, characteristic, complemented
9C22×C11×#124C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C2×C11×#124—24no—
14C2×C11×#124—24no—
15C2×C11×#124—22no—
16C2×C11×#124C2214yes—
17C22×C11×C22⋊C4—22no—
18C22×C42×C11C2211yescharacteristic
19C22×#4326C2212yescomplemented
20C2×#66995—24no—
21C2×#66995—24no—
22C2×#66995—24no—
23C22×#4325C2212yescomplemented
24C22×#4324C2212yes—
25C2×#66985—24no—
26C2×#66985—24no—
27C2×#66985—24no—
28C22×#4323C2212yes—
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622838—24no—
33C2×#66899C2214yescomplemented
34#10622828—24no—
35C2×#66896C2214yes—
36#10622826—22no—
37#10622552C2212yescomplemented
38C4×(C2×D11)⋊C4—22no—
39#10622542C2212yescomplemented
40#10622162C2214yescomplemented
41C25×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11D414yes—
49C22×Q8×C11C2312yes—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11D414yes—
57C22×D4×C11C2312yes—
58C23×C4×C11—21no—
59C23×C4×C11D412yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339D414yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C11×#124—216no—
72C11×#124—28no—
73C11×#124—28no—
74C2×C11×C22⋊C4—216no—
75C2×C11×C22⋊C4—28no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11D412yes—
79C2×C42×C11C2312yes—
80C2×C22⋊Dic11—21no—
81C2×#4326—24no—
82C2×#4326—24no—
83C2×#4326—24no—
84#66995—232no—
85C2×#4325—24no—
86C2×#4325—24no—
87C2×#4325—24no—
88C2×#4324—24no—
89C2×#4324—24no—
90C2×#4324—24no—
91#66985—232no—
92C2×#4323—24no—
93C2×#4323—24no—
94C2×#4323—24no—
95C2×(C2×D11)⋊C4—24no—
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2312yes—
99C2×C4×Dic11—21no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—22no—
104C2×#4318D414yes—
105C2×#4318D414yes—
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2312yes—
108#66899—28no—
109#66896—28no—
110C11⋊#95—24no—
111#23431—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—48no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11C2×D411yescharacteristic
118C23×D11—21no—
119C2×Q8×C11—24no—
120C2×Q8×C11—22no—
121C2×Q8×C11—28no—
122C2×Q8×C11—28no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11—42no—
129C2×Q8×C11—44no—
130C2×Q8×C11—42no—
131C2×Q8×C11C2×D414yes—
132C2×D4×C11—28no—
133C2×D4×C11—24no—
134C2×D4×C11—28no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—44no—
141C2×D4×C11—42no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—44no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165#4339—28no—
166#4339—28no—
167#4339—44no—
168#4339—44no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44C2×D412yes—
175C2×C4×D11—24no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22C2×D412yes—
184C11×C22⋊C4—232no—
185C42×C11—24no—
186C42×C11—22no—
187C42×C11—22no—
188C22⋊Dic11—42no—
189#4326—216no—
190#4325—216no—
191#4324—216no—
192#4323—216no—
193(C2×D11)⋊C4—48no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4×Dic11—42no—
197#4318—28no—
198#4318—28no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8C2×D414yes—
204C2×C11⋊C8C2×D414yes—
205C22×#137—111no—
206C22×AGL(1,ℤ/8)—111no—
207C22×#124D1111yescharacteristic, complemented
208C2×#419—111no—
209C2×#418—111no—
210#2297—111no—
211#2015—114no—
212#2012—114no—
213#1728—111no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—416no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11—88no—
222C23×C11—88no—
223C23×C11#12012yes—
224C23×C11#12112yes—
225C23×C11#12712yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—44no—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—42no—
234Q8×C11—42no—
235Q8×C11—48no—
236D4×C11—24no—
237D4×C11—24no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—48no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—48no—
249C2×C4×C11#12014yes—
250C2×C4×C11#12014yes—
251C2×C4×C11#12012yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#12114yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12712yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C22⋊D11—48no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—42no—
267C2×Dic11—44no—
268D44—22no—
269D44—22no—
270D44—41no—
271D44—41no—
272C4×D11—48no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C11⋊C8—24no—
278C11⋊C8—24no—
279C22×#41—111no—
280C23×Q8C2×D1111yescharacteristic
281C23×D4C2×D1111yescharacteristic
282C2×#137—224no—
283C2×#137—224no—
284C2×#137—224no—
285C2×AGL(1,ℤ/8)—224no—
286C2×AGL(1,ℤ/8)—224no—
287C2×AGL(1,ℤ/8)—224no—
288C22×Q16—112no—
289C22×SD16—112no—
290C22×SD16—112no—
291C22×D8—112no—
292C22×M16—111no—
293C22×M16—111no—
294C2×#124—24no—
295C2×#124—24no—
296C2×#124—22no—
297C2×#124C2×D1114yes—
298C2×#117—111no—
299C22×C22⋊C4—22no—
300C22×C42C2×D1111yescharacteristic
301#419—224no—
302#418—224no—
303C2×#103—114no—
304C2×#102—114no—
305#391—112no—
306#390—112no—
307#386—222no—
308C4×C22⋊C4—222no—
309#336—114no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—44no—
314C22×C11—48no—
315C22×C11—816no—
316C22×C11—84no—
317C22×C11—84no—
318C22×C11#39214yes—
319C22×C11C2×#12011yescharacteristic
320C22×C11C2×#12111yescharacteristic
321C22×C11C2×#12711yescharacteristic
322C22×C11#57514yes—
323C2×D11—42no—
324C2×D11—44no—
325C2×D11—82no—
326C2×D11—82no—
327C4×C11—44no—
328C4×C11—44no—
329C4×C11#39214yes—
330C4×C11C2×#12011yescharacteristic
331C4×C11C2×#12011yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12111yescharacteristic
334Dic11—42no—
335Dic11—82no—
336C25—21no—
337C2×#41—114no—
338C2×#41—222no—
339C2×#41—222no—
340C2×#41—222no—
341C2×#41—222no—
342C2×#41—222no—
343C22×Q8—22no—
344C22×Q8—21no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—111no—
350C22×Q8C22⋊D1114yes—
351C22×Q8C22×D1112yes—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—111no—
359C22×D4—221no—
360C22×D4C22⋊D1114yes—
361C22×D4C22×D1112yes—
362C23×C4—21no—
363C23×C4—221no—
364C23×C4C22⋊D1112yes—
365C23×C4C22×D1111yescharacteristic
366#137—2232no—
367AGL(1,ℤ/8)—2232no—
368C2×Q16—224no—
369C2×Q16—224no—
370C2×Q16—224no—
371C2×SD16—224no—
372C2×SD16—224no—
373C2×SD16—224no—
374C2×SD16—224no—
375C2×SD16—224no—
376C2×SD16—224no—
377C2×D8—224no—
378C2×D8—224no—
379C2×D8—224no—
380C2×M16—114no—
381C2×M16—114no—
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—222no—
385C2×M16—222no—
386C22×C8—112no—
387C22×C8—112no—
388#124—216no—
389#124—28no—
390#124—28no—
391#117—222no—
392#117—222no—
393C2×C4⋊C4—112no—
394C2×C22⋊C4—216no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—224no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—221no—
401C2×C42C22⋊D1112yes—
402C2×C42C22×D1112yes—
403#103—228no—
404#102—228no—
405#95—224no—
406C2×C11—24no—
407C2×C11—84no—
408C2×C11C2×#39211yescharacteristic
409C2×C11#300512yes—
410C2×C11#304012yes—
411C2×C11#315312yes—
412D11—82no—
413C24—24no—
414C24—22no—
415C24—48no—
416C24—42no—
417C24—42no—
418C24—221no—
419C24C2×C22⋊D1111yescharacteristic
420#41—228no—
421#41—228no—
422#41—444no—
423#41—444no—
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—28no—
427C2×Q8—28no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—44no—
433C2×Q8—42no—
434C2×Q8—44no—
435C2×Q8—42no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8C2×C22⋊D1114yes—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—44no—
454C2×D4—42no—
455C2×D4—112no—
456C2×D4—224no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4C2×C22⋊D1114yes—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—221no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4D4×D1112yes—
477C22×C4D4×D1112yes—
478C22×C4D4×D1112yes—
479C22×C4#434112yes—
480C22×C4C2×C22⋊D1114yes—
481C22×C4C2×C22⋊D1112yes—
482C22×C4C2×C22⋊D1112yes—
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—2216no—
486SD16—2216no—
487SD16—2216no—
488D8—2216no—
489M16—228no—
490M16—228no—
491C2×C8—114no—
492C2×C8—114no—
493C2×C8—222no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C22⋊C4—232no—
500C22⋊C4—448no—
501C22⋊C4—442no—
502C42—24no—
503C42—22no—
504C42—22no—
505C42—442no—
506C11#2343111yescharacteristic, complemented, Sylow
507C23—24no—
508C23—24no—
509C23—416no—
510C23—42no—
511C23—42no—
512C23—48no—
513C23—48no—
514C23—88no—
515C23—88no—
516C23—222no—
517C23—441no—
518C23—444no—
519C23—441no—
520C23#6699112yes—
521C23#6699312yes—
522C23#6700612yes—
523C23C22×C22⋊D1111yescharacteristic
524Q8—24no—
525Q8—24no—
526Q8—42no—
527Q8—42no—
528Q8—48no—
529Q8—222no—
530Q8—222no—
531Q8—441no—
532Q8—441no—
533D4—24no—
534D4—24no—
535D4—42no—
536D4—42no—
537D4—48no—
538D4—222no—
539D4—222no—
540D4—448no—
541D4—441no—
542D4—441no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—448no—
555C2×C4—442no—
556C2×C4—444no—
557C2×C4#6699014yes—
558C2×C4#6699014yes—
559C2×C4#6699112yes—
560C2×C4#6699214yes—
561C2×C4#6699214yes—
562C2×C4#6699312yes—
563C2×C4#6700612yes—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—224no—
571C8—224no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—48no—
576C22—44no—
577C22—816no—
578C22—84no—
579C22—84no—
580C22—444no—
581C22—442no—
582C22—882no—
583C22—882no—
584C22#1062283614yes—
585C22C2×#6699111yescharacteristic
586C22C2×#6699311yescharacteristic
587C22#1062335314yes—
588C22C2×#6700611yescharacteristic
589C4—44no—
590C4—44no—
591C4—442no—
592C4—882no—
593C4#1062283614yes—
594C4C2×#6699011yescharacteristic
595C4C2×#6699011yescharacteristic
596C4C2×#6699211yescharacteristic
597C4C2×#6699211yescharacteristic
598C2—24no—
599C2—84no—
600C2—882no—
601C2C2×#1062283611yescharacteristic
602C2#1307785812yes—
603C2#1307810612yes—
604C2#1307908012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#124C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
hypercenterC22×#124D11
hypocenterC11#23431
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C2×#10622838C2semidirect
4. C2×#10622828C2semidirect
5. #13071106C2semidirect
6. #13069710C2semidirect
7. #13069693C2semidirect
8. #13068310C2semidirect
9. C22×C11×#124C2semidirect
19. C22×#4326C22semidirect
23. C22×#4325C22semidirect
33. C2×#66899C22semidirect
37. #10622552C22semidirect
39. #10622542C22semidirect
40. #10622162C22semidirect
207. C22×#124D11semidirect
506. C11#23431semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C22×#669852
C2×#106228382
C2×#106228282
#130711062
#130697102
#130696932
#130683102
C22×C11×#1242
#2343111