Finite Group Databasebeta

← #14730933

Subgroups — #14730933

Order 2816.

1152 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic, complemented
4#13067681C214yesmaximal, complemented
5#13067675C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic, complemented
10C11×#559—21no—
11C11×#559C2212yescomplemented
12C11×#550—21no—
13C11×#550C2212yescomplemented
14C11×#546—22no—
15C11×#546—22no—
16C11×#540—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532—21no—
20C11×#532—21no—
21C2×C11×#127C2211yescharacteristic
22C11×#518—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67002—21no—
25C22×#4323—22no—
26C2×#66927C2211yescharacteristic
27#10622701—21no—
28#10622698—21no—
29#10622686—22no—
30#10622686C2214yes—
31#10622659—22no—
32#10622640—21no—
33#10622640C2214yescomplemented
34#10622640C2212yescomplemented
35#10622628—21no—
36#10622628C2212yescomplemented
37#10622614—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622182C2214yescomplemented
42Q8⋊(C11⋊C8)C2214yescomplemented
43Q8⋊(C11⋊C8)C2212yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D412yes—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×#127—22no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127D412yes—
60C11×#127C2312yes—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8D412yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—22no—
75C11×#120—24no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×Q8×C11C2312yes—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11D411yescharacteristic
89C4×D4×C11C2311yescharacteristic
90C11×#117—21no—
91C11×#117—21no—
92C11×#117D411yescharacteristic
93C2×C11×C22⋊C4—24no—
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96#67002—44no—
97C2×#4325—22no—
98C2×#4325—24no—
99C2×#4323—28no—
100C2×#4323—22no—
101C2×#4323—48no—
102C2×#4318—21no—
103C22×C11⋊C8—21no—
104#66927—21no—
105#66927—21no—
106#66927—21no—
107#66927C2312yes—
108C22⋊(C11⋊C8)—21no—
109#66873—22no—
110#66873—22no—
111#66873—24no—
112C4⋊(C11⋊C8)—21no—
113C4⋊(C11⋊C8)C2312yes—
114C4⋊(C11⋊C8)C2312yes—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117C4×C11⋊C8C2312yes—
118#18624—111nomaximal, Sylow
119C24×C11—22no—
120C23×D11—41no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—84no—
124C11×#41—84no—
125C2×Q8×C11—21no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—21no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—44no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—82no—
140C2×D4×C11C2×D411yescharacteristic
141C2×D4×C11C2×D414yes—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—44no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—82no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—22no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2411yescharacteristic
186#4325—44no—
187#4325—84no—
188#4323—44no—
189#4323—416no—
190#4318—42no—
191C2×C11⋊C8—24no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195#3508D1111yescharacteristic, complemented
196#3208—111no—
197C2×#493—111no—
198#3038—111no—
199#1621—114no—
200#1620—114no—
201#1545—111no—
202#1493—111no—
203#1476—111no—
204C23×C11—24no—
205C23×C11—21no—
206C23×C11—44no—
207C23×C11—82no—
208C23×C11—82no—
209C23×C11#12011yescharacteristic
210C22×D11—42no—
211C22×D11—82no—
212C22×D11—82no—
213C22×D11—82no—
214Q8×C11—21no—
215Q8×C11—21no—
216Q8×C11—24no—
217Q8×C11—42no—
218D4×C11—21no—
219D4×C11—21no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—44no—
225D4×C11—44no—
226D4×C11—44no—
227D4×C11—82no—
228D4×C11—84no—
229D4×C11—84no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—84no—
241C2×C4×C11—84no—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#13512yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250D44—44no—
251D44—42no—
252D44—42no—
253D44—44no—
254D44—82no—
255D44—82no—
256D44—82no—
257C11⋊C8—24no—
258C11⋊C8—42no—
259C11⋊C8—42no—
260C2×AGL(1,ℤ/8)—221no—
261C22×D8—222no—
262#559—21no—
263#559C2×D1112yescomplemented
264#550—21no—
265#550C2×D1112yescomplemented
266#546—22no—
267#546—22no—
268#540—22no—
269#535—21no—
270#533C2×D1111yescharacteristic
271#532—21no—
272#532—21no—
273C2×#127—111no—
274C2×#127C2×D1111yescharacteristic
275#518—21no—
276C4×#41C2×D1111yescharacteristic
277#493—114no—
278#493—222no—
279#492—221no—
280#486—221no—
281#460—112no—
282#460—114no—
283#460—221no—
284#459—112no—
285#459—221no—
286#450—222no—
287#431—111no—
288#423—111no—
289#418—221no—
290C2×C4×C8—111no—
291#331—114no—
292Q8⋊C8—112no—
293Q8⋊C8—114no—
294D4⋊C8—112no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—41no—
298C22×C11—44no—
299C22×C11—41no—
300C22×C11—44no—
301C22×C11—41no—
302C22×C11—44no—
303C22×C11—164no—
304C22×C11#44912yes—
305C22×C11C2×#12011yescharacteristic
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C2×D11—164no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11#44912yes—
318C4×C11#45312yes—
319C4×C11C2×#13511yescharacteristic
320C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C4×C11#57612yes—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41C22⋊D1111yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—221no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4C22⋊D1112yes—
331AGL(1,ℤ/8)—444no—
332C2×SD16—222no—
333C2×SD16—224no—
334C2×D8—228no—
335C2×D8—222no—
336C2×D8—448no—
337C2×M16—221no—
338C22×C8—221no—
339C4⋊Q8C22⋊D1111yescharacteristic
340C4⋊Q8C22⋊D1111yescharacteristic
341#127—22no—
342#127—21no—
343#127—21no—
344#127—112no—
345#127—221no—
346#127—221no—
347#127—221no—
348#127C22⋊D1112yes—
349#127C22×D1112yes—
350#125—21no—
351#124—22no—
352#124—22no—
353#124—22no—
354#123—24no—
355#123—24no—
356C22⋊Q8—21no—
357C22⋊Q8C22⋊D1112yes—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—24no—
362#121—24no—
363#121—22no—
364#120—24no—
365C4×Q8—21no—
366C4×Q8C22⋊D1111yescharacteristic
367C4×Q8C22×D1111yescharacteristic
368C4×Q8C22×D1112yes—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4C22⋊D1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379#117—21no—
380#117—21no—
381#117C22⋊D1111yescharacteristic
382C2×C22⋊C4—24no—
383C2×C42—21no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—112no—
386C4⋊C8—112no—
387C4⋊C8—221no—
388#102—222no—
389#102—222no—
390#102—224no—
391C22⋊C8—221no—
392C4×C8—112no—
393C4×C8—221no—
394C4×C8—221no—
395C2×C11—22no—
396C2×C11—81no—
397C2×C11—84no—
398C2×C11C2×#44911yescharacteristic
399C2×C11#300811yescharacteristic
400C2×C11C2×#45311yescharacteristic
401D11—162no—
402C24—22no—
403C24—441no—
404#41—22no—
405#41—22no—
406#41—84no—
407#41—84no—
408C2×Q8—21no—
409C2×Q8C2×C22⋊D1111yescharacteristic
410C2×Q8C2×C22⋊D1112yes—
411C2×D4—21no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—44no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—82no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—444no—
427C2×D4—442no—
428C2×D4—442no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—441no—
432C2×D4—882no—
433C2×D4C2×C22⋊D1111yescharacteristic
434C2×D4C2×C22⋊D1114yes—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443SD16—444no—
444SD16—884no—
445D8—4416no—
446D8—444no—
447M16—442no—
448C2×C8—224no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—222no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4C2×C22⋊D1111yescharacteristic
460C4⋊C4C2×C22⋊D1111yescharacteristic
461C4⋊C4C2×C22⋊D1112yes—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—21no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—22no—
474C42C2×C22⋊D1111yescharacteristic
475C42C2×C22⋊D1111yescharacteristic
476C42C2×C22⋊D1111yescharacteristic
477C42C23×D1111yescharacteristic
478C11#1862411yescharacteristic, complemented, Sylow
479C23—24no—
480C23—21no—
481C23—44no—
482C23—82no—
483C23—82no—
484C23—442no—
485C23—882no—
486C23—882no—
487C23—882no—
488C23#6700611yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—24no—
492Q8—42no—
493D4—21no—
494D4—21no—
495D4—44no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—44no—
500D4—44no—
501D4—44no—
502D4—82no—
503D4—84no—
504D4—84no—
505D4—444no—
506D4—442no—
507D4—442no—
508D4—444no—
509D4—882no—
510D4—882no—
511D4—882no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—84no—
523C2×C4—84no—
524C2×C4#6700212yes—
525C2×C4#6700312yes—
526C2×C4#6700611yescharacteristic
527C2×C4#6700611yescharacteristic
528C2×C4#6700611yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C2×C4C22×C22⋊D1111yescharacteristic
532C8—224no—
533C8—442no—
534C8—442no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—44no—
539C22—41no—
540C22—44no—
541C22—41no—
542C22—44no—
543C22—164no—
544C22—882no—
545C22—882no—
546C22—882no—
547C22—1764no—
548C22#1062285112yes—
549C22C2×#6700611yescharacteristic
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4#1062285112yes—
558C4#1062285412yes—
559C4C2×#6700211yescharacteristic
560C4C2×#6700311yescharacteristic
561C4#1062336612yes—
562C2—22no—
563C2—84no—
564C2—81no—
565C2—1762no—
566C2C2×#1062285111yescharacteristic
567C2#1307788411yescharacteristic
568C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#18624
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
2. C2×#10622686C2semidirect
3. #13078096C2semidirect
4. #13067681C2semidirect
5. #13067675C2semidirect
6. #13067284C2semidirect
7. #13067071C2semidirect
8. #13066998C2semidirect
9. C11×#3508C2semidirect
11. C11×#559C22semidirect
13. C11×#550C22semidirect
33. #10622640C22semidirect
34. #10622640C22semidirect
36. #10622628C22semidirect
41. #10622182C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
195. #3508D11semidirect
263. #559C2×D11semidirect
265. #550C2×D11semidirect
478. C11#18624semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226862
#130780962
#130676812
#130676752
#130672842
#130670712
#130669982
C11×#35082
#1862411