Finite Group Databasebeta

← #14669567

Subgroups — #14669567

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070308C211yesmaximal, characteristic, complemented
2#13070270C211yesmaximal, characteristic, complemented
3#13070257C211yesmaximal, characteristic, complemented
4#13069169C211yesmaximal, characteristic, complemented
5#13069144C211yesmaximal, characteristic, complemented
6#13069035C211yesmaximal, characteristic, complemented
7C11×#3540C211yesmaximal, characteristic
8C11×H(3,𝔽4)—21no—
9C11×#560C412yescomplemented
10C11×#559C412yescomplemented
11C11×#556—21no—
12C11×#555—21no—
13C11×#551—21no—
14C11×#548—21no—
15C11×#546—21no—
16C11×#542—22no—
17C11×#542—21no—
18C11×#538—22no—
19C11×#536C2211yescharacteristic
20C11×#535C2211yescharacteristic
21C11×#525—21no—
22C11×#525C2211yescharacteristic
23#10623350C2211yescharacteristic
24#10622853C2211yescharacteristic
25#10622850C2211yescharacteristic
26#10622850C2211yescharacteristic
27C2×#66900—21no—
28#10622828—21no—
29#10622820—21no—
30#10622180—22no—
31#10622177—21no—
32#10622177—22no—
33#10622174—21no—
34#10622171—21no—
35#10622171—21no—
36#10622169—21no—
37C2×C11×#41—21no—
38C2×C11×#41C2311yescharacteristic
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×#127C2×C412yes—
45C11×#126—22no—
46C11×#126—22no—
47C11×#126—22no—
48C11×#124—22no—
49C11×#124—21no—
50C11×#124—22no—
51C11×#124—22no—
52C11×#124—21no—
53C11×#124—22no—
54C11×#124—22no—
55C11×#124D412yes—
56C11×#123—22no—
57C11×#123—22no—
58C11×#123—22no—
59C11×#123C2×C411yescharacteristic
60C11×#123C2×C412yes—
61C11×#123D411yescharacteristic
62C11×#123D412yes—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70C11×#121—22no—
71C11×#121—21no—
72C11×#121—22no—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121—22no—
76C11×#120—22no—
77C11×#120—22no—
78C11×#120—21no—
79C11×#120—21no—
80C11×#120C2×C411yescharacteristic
81C11×#120D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C11×#117—21no—
91C11×#117—22no—
92C11×#117D411yescharacteristic
93C11×#117D411yescharacteristic
94C11×#117D411yescharacteristic
95C2×C11×C22⋊C4—22no—
96#67001—42no—
97#66979—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—21no—
101C2×#4318—21no—
102C2×#4318—21no—
103#66900—21no—
104#66900—21no—
105#66900—42no—
106#66898—21no—
107#66898—21no—
108#66897—21no—
109#66897—21no—
110#66896—42no—
111C22⋊(C11⋊C8)—42no—
112#12758—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11C22⋊C411yescharacteristic
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—81no—
118C11×#41—81no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—41no—
123C2×Q8×C11—41no—
124C2×Q8×C11C2×D411yescharacteristic
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11C22⋊C412yes—
135C2×D4×C11C22×C411yescharacteristic
136C2×D4×C11C2×D411yescharacteristic
137C2×D4×C11C2×D411yescharacteristic
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C22⋊C411yescharacteristic
145C22×C4×C11C22⋊C412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4C22⋊C411yescharacteristic
175C11×C22⋊C4C22⋊C411yescharacteristic
176C11×C22⋊C4C22⋊C412yes—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C22⋊C412yes—
182C22⋊Dic11—41no—
183C4⋊Dic11—41no—
184C4×Dic11—41no—
185#4318—22no—
186#4318—41no—
187#4318—41no—
188#4318—41no—
189#4318—41no—
190#4318—41no—
191#4318—41no—
192#4318—41no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198#3540D1111yescharacteristic
199#2134—111no—
200#2123—111no—
201#2120—111no—
202#1915—111no—
203#1910—111no—
204#1891—111no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—81no—
209C23×C11—81no—
210C23×C11—82no—
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11#12011yescharacteristic
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—81no—
218Q8×C11—82no—
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—81no—
226D4×C11—82no—
227D4×C11—82no—
228D4×C11—82no—
229D4×C11—81no—
230D4×C11—82no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—81no—
248C2×C4×C11—82no—
249C2×C4×C11—82no—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×Dic11—81no—
255C11⋊C8—42no—
256C11⋊C8—81no—
257C11⋊C8—81no—
258#568—111no—
259H(3,𝔽4)—21no—
260#560Dic1112yescomplemented
261#559Dic1112yescomplemented
262#556—21no—
263#555—21no—
264#551—21no—
265#548—21no—
266#546—21no—
267#542—22no—
268#542—21no—
269#538—22no—
270#536C2×D1111yescharacteristic
271#535C2×D1111yescharacteristic
272#525—21no—
273#525C2×D1111yescharacteristic
274#418—221no—
275#413—111no—
276#413—111no—
277C2×#101—221no—
278#410—111no—
279#407—221no—
280#355—222no—
281#352—221no—
282#352—222no—
283AΣL(1,𝔽16)—221no—
284#344—221no—
285#344—221no—
286H(3,ℤ/4)—221no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—42no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—81no—
301C22×C11—162no—
302C22×C11#37911yescharacteristic
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—41no—
311C4×C11—42no—
312C4×C11B(4,𝔽2)11yescharacteristic
313C4×C11#45811yescharacteristic
314Dic11—161no—
315C2×#41—21no—
316C2×#41C22×D1111yescharacteristic
317C22×Q8C22⋊D1111yescharacteristic
318C22×D4C22⋊D1111yescharacteristic
319C23×C4C22⋊D1111yescharacteristic
320#131—442no—
321C2×M16—221no—
322C2×M16—221no—
323C2×M16—221no—
324C2×M16—221no—
325C2×M16—221no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328#127C2×Dic1112yes—
329#126—22no—
330#126—22no—
331#126—22no—
332#124—22no—
333#124—21no—
334#124—22no—
335#124—22no—
336#124—21no—
337#124—22no—
338#124—22no—
339#124C22⋊D1112yes—
340#123—22no—
341#123—22no—
342#123—22no—
343#123C2×Dic1111yescharacteristic
344#123C2×Dic1112yes—
345#123C22⋊D1111yescharacteristic
346#123C22⋊D1112yes—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353#121—21no—
354#121—22no—
355#121—21no—
356#121—22no—
357#121—21no—
358#121—21no—
359#121—22no—
360#120—22no—
361#120—22no—
362#120—21no—
363#120—21no—
364#120C2×Dic1111yescharacteristic
365#120C22⋊D1111yescharacteristic
366C4×Q8—21no—
367C4×Q8—22no—
368C4×D4—22no—
369C4×D4—21no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—21no—
374#117—21no—
375#117—22no—
376#117—221no—
377#117C22⋊D1111yescharacteristic
378#117C22⋊D1111yescharacteristic
379#117C22⋊D1111yescharacteristic
380C2×C22⋊C4—22no—
381#102—442no—
382#101—221no—
383#101—221no—
384#101—442no—
385#100—221no—
386#100—221no—
387#99—221no—
388#99—221no—
389C22⋊C8—442no—
390C2×C11—21no—
391C2×C11—41no—
392C2×C11—41no—
393C2×C11—41no—
394C2×C11—81no—
395C2×C11—82no—
396C2×C11#179011yescharacteristic
397C24—21no—
398C24C22⋊Dic1111yescharacteristic
399#41—41no—
400#41—41no—
401#41—81no—
402#41—81no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8C2×C22⋊D1111yescharacteristic
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4C22⋊Dic1112yes—
419C2×D4C22×Dic1111yescharacteristic
420C2×D4C2×C22⋊D1111yescharacteristic
421C2×D4C2×C22⋊D1111yescharacteristic
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C22⋊Dic1111yescharacteristic
429C22×C4C22⋊Dic1112yes—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433M16—222no—
434M16—441no—
435M16—441no—
436M16—441no—
437M16—441no—
438M16—441no—
439M16—441no—
440M16—441no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—441no—
444C2×C8—441no—
445C2×C8—441no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—441no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—21no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—22no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—441no—
473C22⋊C4C22⋊Dic1111yescharacteristic
474C22⋊C4C22⋊Dic1111yescharacteristic
475C22⋊C4C22⋊Dic1112yes—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—441no—
481C42C22⋊Dic1112yes—
482C11#1275811yescharacteristic, complemented, Sylow
483C23—21no—
484C23—22no—
485C23—41no—
486C23—81no—
487C23—81no—
488C23—82no—
489C23C2×C22⋊Dic1111yescharacteristic
490C23C2×C22⋊Dic1111yescharacteristic
491C23#6700611yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—81no—
496Q8—82no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—41no—
502D4—41no—
503D4—81no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—81no—
508D4—82no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—881no—
529C2×C4C2×C22⋊Dic1111yescharacteristic
530C2×C4#6700611yescharacteristic
531C2×C4#6700611yescharacteristic
532C2×C4#6700611yescharacteristic
533C8—442no—
534C8—881no—
535C8—881no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—41no—
545C22—42no—
546C22—42no—
547C22—41no—
548C22—42no—
549C22—81no—
550C22—162no—
551C22#1062286011yescharacteristic
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—1761no—
562C4#1062285611yescharacteristic
563C4#1062285711yescharacteristic
564C2—21no—
565C2—41no—
566C2—41no—
567C2—41no—
568C2—81no—
569C2—82no—
570C2#1306856411yescharacteristic
subgroupG/H
centerC2#13068564
commutatorC2×D4×C11C22×C4
FrattiniC2×#41C22×D11
Fitting, prime radicalC11×#3540C2
socleC2×C11#1790
cosocleC2×C11×#41C23
hypercenter#3540D11
hypocenterC11#12758
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3540

Complements

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

NH ≅ G/Ntype
1. #13070308C2semidirect
2. #13070270C2semidirect
3. #13070257C2semidirect
4. #13069169C2semidirect
5. #13069144C2semidirect
6. #13069035C2semidirect
9. C11×#560C4semidirect
10. C11×#559C4semidirect
260. #560Dic11semidirect
261. #559Dic11semidirect
482. C11#12758semidirect

Maximal subgroups

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

subgroupindex
#130703082
#130702702
#130702572
#130691692
#130691442
#130690352
C11×#35402
#1275811