Finite Group Databasebeta

← #14726914

Subgroups — #14726914

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078620C211yesmaximal, characteristic, complemented
2#13078612C211yesmaximal, characteristic, complemented
3#13073513C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067562C214yesmaximal, complemented
6#13067180C211yesmaximal, characteristic, complemented
7#13067176C211yesmaximal, characteristic, complemented
8#13066937C211yesmaximal, characteristic, complemented
9C11×#3506C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538C2214yes—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525—22no—
21C11×#520—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66991—21no—
24C2×C4×D44C2211yescharacteristic
25#10622826—22no—
26#10622700—21no—
27#10622697—21no—
28#10622696—21no—
29#10622685—21no—
30#10622659C2212yes—
31#10622656C2212yes—
32#10622649C2212yes—
33#10622646C2212yes—
34C4×#4325—22no—
35C4×#4323—22no—
36#10622600—21no—
37#10622573C2212yes—
38#10622566C2212yes—
39#10622549C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622176C2214yes—
43#10622175C2214yes—
44#10622163C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11D412yes—
49C22×C22⋊D11—22no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C11×C4⋊Q8D411yescharacteristic, complemented
53C11×C4⋊Q8D411yescharacteristic, complemented
54C11×C4⋊Q8D411yescharacteristic, complemented
55C11×#127—22no—
56C11×#127D411yescharacteristic, complemented
57C11×#126—24no—
58C11×#125—21no—
59C11×#124—22no—
60C11×#124—24no—
61C11×#124—21no—
62C11×#123—24no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2312yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—21no—
72C11×#121C2312yes—
73C11×#120—24no—
74C4×Q8×C11—22no—
75C4×Q8×C11—21no—
76C4×Q8×C11D412yescomplemented
77C4×D4×C11—22no—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11D412yescomplemented
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C22⋊C4C2312yes—
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—22no—
94C2×#4325—22no—
95#66991—44no—
96C2×#4323—22no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103C4×D44—21no—
104C4×D44—21no—
105#66899—22no—
106#66896—22no—
107C11⋊#95—21no—
108C11⋊#95—22no—
109C11⋊#95C2312yes—
110C22⋊(C11⋊C8)C2312yes—
111C22⋊(C11⋊C8)C2312yes—
112#66873—22no—
113#66873—22no—
114#66872—22no—
115#66871—22no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—21no—
120#18222—111nomaximal, Sylow
121C24×C11C2×D412yes—
122C23×D11—21no—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—84no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11C2×D412yes—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—82no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—44no—
149C2×C22⋊D11—44no—
150C2×C22⋊D11—82no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—42no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C22⋊Dic11—44no—
186#4325—44no—
187#4323—44no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—82no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196#3506D1111yescharacteristic, complemented
197#3101—111no—
198#3100—111no—
199#2535—111no—
200#1612—114no—
201#1600—114no—
202#1518—111no—
203#1517—111no—
204#1460—111no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219Q8×C11—42no—
220Q8×C11—42no—
221Q8×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—84no—
230D4×C11—84no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—82no—
241C2×C4×C11—84no—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#13512yes—
247C2×C4×C11AGL(1,ℤ/8)12yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—88no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257D44—22no—
258D44—22no—
259D44—41no—
260D44—41no—
261C4×D11—82no—
262C4×D11—82no—
263C11⋊C8—42no—
264C11⋊C8—42no—
265#559—22no—
266#556—21no—
267#555—21no—
268#553—22no—
269#550—21no—
270#547—21no—
271#538C2×D1114yes—
272#535—21no—
273#533C2×D1111yescharacteristic
274#532C2×D1111yescharacteristic
275#525—22no—
276C2×#121—221no—
277#520—21no—
278C2×C4×D4—111no—
279C2×C4×D4C2×D1111yescharacteristic
280#483—112no—
281#480—112no—
282#476—221no—
283#474—221no—
284#461—221no—
285#459—221no—
286#450—112no—
287#447—112no—
288C4×SD16—222no—
289C4×D8—222no—
290#431—111no—
291#431—111no—
292#397—112no—
293#392—112no—
294#386—222no—
295#382—111no—
296#380—221no—
297#328—114no—
298#327—114no—
299#323—114no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—82no—
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C2×D11—81no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11#44912yes—
329C4×C11#44912yes—
330Dic11—82no—
331Dic11—81no—
332C2×#41—22no—
333C2×#41—21no—
334C22×D4—111no—
335C22×D4—222no—
336C22×D4C22⋊D1111yescharacteristic
337C23×C4—221no—
338C23×C4C22⋊D1112yes—
339C2×SD16—222no—
340C2×D8—222no—
341C4⋊Q8C22⋊D1111yescharacteristic, complemented
342C4⋊Q8C22⋊D1111yescharacteristic, complemented
343C4⋊Q8C22⋊D1111yescharacteristic, complemented
344#127—22no—
345#127C22⋊D1111yescharacteristic, complemented
346#126—24no—
347#125—21no—
348#124—22no—
349#124—24no—
350#124—21no—
351#123—24no—
352#123—24no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8C22×D1112yes—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—24no—
360#121—21no—
361#121—444no—
362#121C22×D1112yes—
363#120—24no—
364C4×Q8—22no—
365C4×Q8—21no—
366C4×Q8C22⋊D1112yescomplemented
367C4×D4—22no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4C22⋊D1112yescomplemented
380#117—22no—
381#117—22no—
382#117—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C22⋊C4—222no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4C22×D1112yes—
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#106—222no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396#103—222no—
397#102—222no—
398#102—222no—
399#102—222no—
400C22⋊C8—112no—
401C22⋊C8—112no—
402C4×C8—221no—
403C4×C8—221no—
404#95—112no—
405#95—222no—
406#95—221no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—82no—
410C2×C11—82no—
411C2×C11C2×#44911yescharacteristic
412C2×C11#301911yescharacteristic
413C2×C11#302511yescharacteristic
414D11—82no—
415C24—221no—
416C24C2×C22⋊D1112yes—
417#41—42no—
418#41—42no—
419#41—84no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×C22⋊D1112yes—
423C2×D4—22no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—442no—
435C2×D4—444no—
436C2×D4—444no—
437C2×D4—882no—
438C2×D4C2×C22⋊D1112yes—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—82no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454SD16—444no—
455D8—444no—
456C2×C8—222no—
457C2×C8—222no—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—442no—
470C4⋊C4C2×C22⋊D1112yes—
471C4⋊C4C2×C22⋊D1112yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—444no—
481C22⋊C4—441no—
482C22⋊C4—441no—
483C22⋊C4—882no—
484C42—24no—
485C42—22no—
486C42C2×C22⋊D1111yescharacteristic
487C42C2×C22⋊D1111yescharacteristic
488C42C2×C22⋊D1111yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C11#1822211yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—42no—
496C23—42no—
497C23—222no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23C22×C22⋊D1111yescharacteristic
505Q8—42no—
506Q8—42no—
507Q8—42no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—84no—
516D4—84no—
517D4—222no—
518D4—222no—
519D4—441no—
520D4—441no—
521D4—888no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—84no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—441no—
536C2×C4—442no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—882no—
540C2×C4—882no—
541C2×C4#6700212yes—
542C2×C4#6700312yes—
543C2×C4#6700611yescharacteristic
544C2×C4#6700611yescharacteristic
545C2×C4#6700611yescharacteristic
546C2×C4#6700611yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—442no—
550C8—442no—
551C22—21no—
552C22—21no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—82no—
561C22—442no—
562C22—442no—
563C22—442no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6700211yescharacteristic
569C22C2×#6700311yescharacteristic
570C22C2×#6700611yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—882no—
580C4—881no—
581C4#1062285112yes—
582C4#1062285112yes—
583C2—21no—
584C2—21no—
585C2—82no—
586C2—82no—
587C2—882no—
588C2C2×#1062285111yescharacteristic
589C2#1307797311yescharacteristic
590C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#18222
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13078620C2semidirect
2. #13078612C2semidirect
3. #13073513C2semidirect
4. #13067630C2semidirect
5. #13067562C2semidirect
6. #13067180C2semidirect
7. #13067176C2semidirect
8. #13066937C2semidirect
9. C11×#3506C2semidirect
52. C11×C4⋊Q8D4semidirect
53. C11×C4⋊Q8D4semidirect
54. C11×C4⋊Q8D4semidirect
56. C11×#127D4semidirect
76. C4×Q8×C11D4semidirect
85. C4×D4×C11D4semidirect
196. #3506D11semidirect
341. C4⋊Q8C22⋊D11semidirect
342. C4⋊Q8C22⋊D11semidirect
343. C4⋊Q8C22⋊D11semidirect
345. #127C22⋊D11semidirect
366. C4×Q8C22⋊D11semidirect
379. C4×D4C22⋊D11semidirect
490. C11#18222semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130786122
#130735132
#130676302
#130675622
#130671802
#130671762
#130669372
C11×#35062
#1822211