Finite Group Databasebeta

← #14780932

Subgroups — #14780932

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×#67002C211yesmaximal, characteristic
2C22×#67000C211yesmaximal, characteristic, complemented
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622744C211yesmaximal, characteristic, complemented
5#13071107C211yesmaximal, characteristic, complemented
6#13069707C214yesmaximal, complemented
7#13069690C214yesmaximal, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C23×D44C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—24no—
16C22×C11×Q16C2212yescomplemented
17C22×C11×SD16C2212yescomplemented
18C22×C11×M16C2211yescharacteristic
19C2×#67002—24no—
20C2×#67002—24no—
21C2×#67002—24no—
22C2×#67000—24no—
23C2×#67000—24no—
24C2×#67000—22no—
25C2×#67000C2214yes—
26C22×#4325C2212yes—
27C22×#4323C2212yes—
28C22×(C2×D11)⋊C4—22no—
29C2×#66979C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622843C2212yescomplemented
33#10622838—24no—
34C2×#66899C2214yescomplemented
35#10622834C2212yescomplemented
36#10622833—22no—
37C4×C22⋊Dic11—22no—
38#10622744—24no—
39C2×#66885C2214yes—
40#10622188C2214yescomplemented
41C24×D11—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D414yes—
48C22×Q8×C11—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—22no—
54C22×Q8×C11D414yes—
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11D412yes—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44D414yes—
70C22×D44C2312yes—
71C11×#137—232no—
72C2×C11×Q16—24no—
73C2×C11×Q16—24no—
74C2×C11×Q16—24no—
75C2×C11×SD16—24no—
76C2×C11×SD16—24no—
77C2×C11×SD16—24no—
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16D414yes—
81C22×C8×C11C2312yes—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—24no—
84#67002—232no—
85#67000—216no—
86#67000—28no—
87#67000—28no—
88C2×#4325—24no—
89C2×#4325—24no—
90C2×#4325—24no—
91C2×#4323—24no—
92C2×#4323—24no—
93C2×#4323—24no—
94C2×(C2×D11)⋊C4—216no—
95C2×(C2×D11)⋊C4—28no—
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2312yes—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D412yes—
103C2×C4×Dic11C2312yes—
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318D414yes—
107C22×C11⋊C8C2312yes—
108#66899—28no—
109C11⋊#95—24no—
110#66885—28no—
111#23431—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11C2×D411yescharacteristic
114C23×D11—24no—
115C23×D11—22no—
116C23×D11—48no—
117C23×D11—42no—
118C23×D11—42no—
119C11×#41—28no—
120C11×#41—28no—
121C11×#41—44no—
122C11×#41—44no—
123C2×Q8×C11—24no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—28no—
127C2×Q8×C11—28no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—44no—
137C2×Q8×C11—42no—
138C2×Q8×C11—44no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11C2×D414yes—
142C2×D4×C11—24no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—44no—
170C22×Dic11C2×D414yes—
171C2×D44—24no—
172C2×D44—28no—
173C2×D44—28no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—44no—
180C2×D44—44no—
181C2×D44—42no—
182C2×D44—42no—
183C2×D44C2×D414yes—
184C11×Q16—216no—
185C11×SD16—216no—
186C11×M16—28no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11C2×D414yes—
190C22⋊Dic11—48no—
191C22⋊Dic11—42no—
192#4325—216no—
193#4323—216no—
194(C2×D11)⋊C4—232no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4×Dic11—24no—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—42no—
201#4318—28no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8C2×D414yes—
205C22×#137D1111yescharacteristic, complemented
206C22×AGL(1,ℤ/8)—111no—
207C22×#124—111no—
208C2×#419—111no—
209C2×#418—111no—
210#2297—111no—
211#2015—114no—
212#2012—114no—
213#1728—111no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—44no—
219C23×C11#12012yes—
220C23×C11#12112yes—
221C23×C11#12712yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—416no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11—88no—
230C22×D11—88no—
231Q8×C11—22no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—24no—
235Q8×C11—42no—
236Q8×C11—42no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—48no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—48no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—48no—
252C2×C4×C11—48no—
253C2×C4×C11#12014yes—
254C2×C4×C11#12012yes—
255C2×C4×C11#12014yes—
256C2×C4×C11#12114yes—
257C2×C4×C11#12114yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12712yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—48no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272D44—24no—
273D44—24no—
274D44—42no—
275D44—42no—
276D44—48no—
277C8×C11—24no—
278C11⋊C8—24no—
279C22×#41C2×D1111yescharacteristic
280C23×Q8C2×D1111yescharacteristic
281C23×D4—111no—
282C2×#137—24no—
283C2×#137—24no—
284C2×#137—24no—
285C2×AGL(1,ℤ/8)—224no—
286C2×AGL(1,ℤ/8)—224no—
287C2×AGL(1,ℤ/8)—224no—
288C22×Q16C2×D1112yescomplemented
289C22×SD16—112no—
290C22×SD16C2×D1112yescomplemented
291C22×D8—112no—
292C22×M16—111no—
293C22×M16C2×D1111yescharacteristic
294C2×#124—114no—
295C2×#124—222no—
296C2×#124—224no—
297C2×#124—224no—
298C2×#117—111no—
299C22×C22⋊C4—222no—
300C22×C42—111no—
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—42no—
314C22×C11—44no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11#39214yes—
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11C2×#12711yescharacteristic
321C22×C11#57514yes—
322C2×D11—44no—
323C2×D11—48no—
324C2×D11—816no—
325C2×D11—84no—
326C2×D11—84no—
327C4×C11—42no—
328C4×C11—44no—
329C4×C11#39214yes—
330C4×C11C2×#12011yescharacteristic
331C4×C11C2×#12011yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12111yescharacteristic
334Dic11—44no—
335Dic11—82no—
336C25—221no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41C22⋊D1114yes—
343C22×Q8—22no—
344C22×Q8—21no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8C22⋊D1114yes—
350C22×Q8C22×D1112yes—
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4—114no—
354C22×D4—112no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—222no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—112no—
365C23×C4C22×D1111yescharacteristic
366#137—232no—
367AGL(1,ℤ/8)—2232no—
368C2×Q16—24no—
369C2×Q16—24no—
370C2×Q16—24no—
371C2×SD16—24no—
372C2×SD16—24no—
373C2×SD16—24no—
374C2×SD16—224no—
375C2×SD16—224no—
376C2×SD16—224no—
377C2×D8—224no—
378C2×D8—224no—
379C2×D8—224no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—114no—
383C2×M16—222no—
384C2×M16—222no—
385C2×M16C22⋊D1114yes—
386C22×C8—112no—
387C22×C8C22×D1112yes—
388#124—228no—
389#124—2216no—
390#124—228no—
391#117—222no—
392#117—222no—
393C2×C4⋊C4—112no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—2216no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—221no—
398C2×C42—112no—
399C2×C42—112no—
400C2×C42—222no—
401C2×C42—222no—
402C2×C42—221no—
403#103—228no—
404#102—228no—
405#95—224no—
406C2×C11—24no—
407C2×C11—82no—
408C2×C11C2×#39211yescharacteristic
409C2×C11#300512yes—
410C2×C11#304012yes—
411C2×C11#315312yes—
412D11—84no—
413C24—21no—
414C24—224no—
415C24—222no—
416C24—448no—
417C24—442no—
418C24—442no—
419C24D4×D1111yescharacteristic
420#41—28no—
421#41—28no—
422#41—44no—
423#41—44no—
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—28no—
428C2×Q8—28no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8C2×C22⋊D1114yes—
442C2×Q8C2×C22⋊D1112yes—
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—114no—
452C2×D4—228no—
453C2×D4—224no—
454C2×D4—228no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—444no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4—444no—
464C2×D4C2×C22⋊D1112yes—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—114no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—444no—
477C22×C4D4×D1112yes—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1112yes—
480C22×C4#434112yes—
481C22×C4C2×C22⋊D1112yes—
482C22×C4C2×C22⋊D1112yes—
483C22×C4C2×C22⋊D1112yes—
484C22×C4C23×D1111yescharacteristic
485Q16—216no—
486SD16—216no—
487SD16—2216no—
488D8—2216no—
489M16—28no—
490M16—228no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—114no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8C2×C22⋊D1114yes—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C22⋊C4—2232no—
500C22⋊C4—448no—
501C22⋊C4—442no—
502C42—224no—
503C42—222no—
504C42—222no—
505C42—442no—
506C11#2343111yescharacteristic, complemented, Sylow
507C23—24no—
508C23—22no—
509C23—44no—
510C23—41no—
511C23—41no—
512C23—224no—
513C23—4416no—
514C23—448no—
515C23—442no—
516C23—442no—
517C23—448no—
518C23—888no—
519C23—888no—
520C23#6699012yes—
521C23#6699212yes—
522C23#6699312yes—
523C23C2×D4×D1111yescharacteristic
524Q8—22no—
525Q8—24no—
526Q8—24no—
527Q8—22no—
528Q8—42no—
529Q8—42no—
530Q8—41no—
531Q8—41no—
532Q8—48no—
533D4—22no—
534D4—22no—
535D4—48no—
536D4—41no—
537D4—41no—
538D4—224no—
539D4—224no—
540D4—442no—
541D4—448no—
542D4—442no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—48no—
550C2×C4—48no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—448no—
555C2×C4—444no—
556C2×C4—442no—
557C2×C4#6699014yes—
558C2×C4#6699012yes—
559C2×C4#6699114yes—
560C2×C4#6699214yes—
561C2×C4#6699212yes—
562C2×C4#6699312yes—
563C2×C4#6700614yes—
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C8—24no—
571C8—224no—
572C22—24no—
573C22—24no—
574C22—24no—
575C22—44no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—448no—
580C22—444no—
581C22—8816no—
582C22—884no—
583C22—884no—
584C22#1062283614yes—
585C22#1062330814yes—
586C22C2×#6699011yescharacteristic
587C22C2×#6699211yescharacteristic
588C22C2×#6699311yescharacteristic
589C4—42no—
590C4—44no—
591C4—444no—
592C4—882no—
593C4#1062283614yes—
594C4C2×#6699011yescharacteristic
595C4C2×#6699111yescharacteristic
596C4C2×#6699211yescharacteristic
597C4C2×#6700611yescharacteristic
598C2—24no—
599C2—82no—
600C2—884no—
601C2C2×#1062283611yescharacteristic
602C2#1307785712yes—
603C2#1307811212yes—
604C2#1307908312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
hypercenterC22×#137D11
hypocenterC11#23431
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#67000C2semidirect
3. C2×#10622838C2semidirect
4. C2×#10622744C2semidirect
5. #13071107C2semidirect
6. #13069707C2semidirect
7. #13069690C2semidirect
8. #13068309C2semidirect
9. C22×C11×#137C2semidirect
16. C22×C11×Q16C22semidirect
17. C22×C11×SD16C22semidirect
32. #10622843C22semidirect
34. C2×#66899C22semidirect
35. #10622834C22semidirect
40. #10622188C22semidirect
205. C22×#137D11semidirect
288. C22×Q16C2×D11semidirect
290. C22×SD16C2×D11semidirect
506. C11#23431semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#670002
C2×#106228382
C2×#106227442
#130711072
#130697072
#130696902
#130683092
C22×C11×#1372
#2343111