Finite Group Databasebeta

← #14727645

Subgroups — #14727645

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079388C211yesmaximal, characteristic, complemented
2#13079373C211yesmaximal, characteristic
3#13074429C211yesmaximal, characteristic, complemented
4#13067647C214yesmaximal, complemented
5#13067579C214yesmaximal, complemented
6#13067188C211yesmaximal, characteristic, complemented
7#13067184C211yesmaximal, characteristic
8C2×#10622166C211yesmaximal, characteristic, complemented
9C2×C11×#539C211yesmaximal, characteristic
10C11×#539—22no—
11C11×#539—22no—
12C11×#539—22no—
13C11×#539C2214yes—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24#10622841—21no—
25#10622831—21no—
26#10622825C2211yescharacteristic
27#10622824—21no—
28#10622823—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622664—22no—
32#10622663C2212yescomplemented
33#10622657C2212yescomplemented
34#10622654—22no—
35#10622653C2212yes—
36#10622647C2212yes—
37#10622599C2212yescomplemented
38#10622597—22no—
39#10622592C2212yescomplemented
40#10622584—21no—
41#10622583—21no—
42#10622176C2214yescomplemented
43#10622175C2214yes—
44#10622166C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×Dic22C2311yescharacteristic
53C11×#126—24no—
54C11×#126—24no—
55C11×#125—24no—
56C11×#125—24no—
57C11×#123—24no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8D412yes—
66C11×C22⋊Q8C2312yes—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121D412yes—
70C11×#121C2312yes—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4326—22no—
94C2×#4324—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97#66977—21no—
98#66977—21no—
99#66977—21no—
100#66977—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—22no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105#66899—22no—
106#66896—22no—
107C11⋊#95—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95C2312yes—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2312yes—
114C22⋊(C11⋊C8)C2312yes—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66871—22no—
119#18289—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—81no—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—81no—
131C2×D4×C11C2×D412yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—21no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11—82no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—81no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C42×C11—24no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11—42no—
183#4326—82no—
184#4324—82no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—81no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—82no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—81no—
194C2×C11⋊C8—81no—
195C2×#539D1111yescharacteristic
196#3189—111no—
197#3187—111no—
198#2627—111no—
199#1615—114no—
200#1603—114no—
201#1520—111no—
202#1519—111no—
203C2×#324—111no—
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11#12011yescharacteristic
211C23×C11#12011yescharacteristic
212C23×C11#13512yes—
213C23×C11#13712yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—42no—
216Q8×C11—81no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—44no—
221D4×C11—81no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—81no—
243C2×C4×C11—84no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255Dic22—42no—
256Dic22—42no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259#539—22no—
260#539—22no—
261#539—22no—
262#539C2×D1114yes—
263C2×#126—21no—
264C2×#125—21no—
265C2×#123—21no—
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8—111no—
269C2×C22⋊Q8C2×D1111yescharacteristic
270C2×#121C2×D1111yescharacteristic
271C2×C4×D4—21no—
272C22×C4⋊C4C2×D1111yescharacteristic
273#484—112no—
274#484—221no—
275#483—221no—
276#481—112no—
277#467—222no—
278#465—222no—
279#451—112no—
280#451—221no—
281#450—221no—
282#448—112no—
283C2×C22⋊C8—111no—
284C2×C22⋊C8—111no—
285#400—112no—
286#398—222no—
287#395—112no—
288#385—221no—
289#381—221no—
290#380—111no—
291#328—114no—
292#327—114no—
293#324—114no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—84no—
306C22×C11#45212yes—
307C22×C11#45212yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#13511yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320Dic11—82no—
321Dic11—81no—
322Dic11—81no—
323C22×Q8—111no—
324C22×Q8C22⋊D1111yescharacteristic
325C22×D4—21no—
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—21no—
328C23×C4C22⋊D1111yescharacteristic
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×Q16—222no—
332C2×SD16—222no—
333C22×C8—221no—
334C22×C8—221no—
335#126—24no—
336#126—24no—
337#125—24no—
338#125—24no—
339#123—24no—
340#123—24no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—221no—
348C22⋊Q8—221no—
349C22⋊Q8—221no—
350C22⋊Q8—221no—
351C22⋊Q8C22⋊D1112yes—
352C22⋊Q8C22×D1112yes—
353#121—21no—
354#121—21no—
355#121C22⋊D1112yes—
356#121C22×D1112yes—
357C4×D4—24no—
358C4×D4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4C22⋊D1112yes—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1112yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—21no—
383#107—222no—
384#106—222no—
385#103—222no—
386#103—222no—
387#103—222no—
388#102—222no—
389C22⋊C8—112no—
390C22⋊C8—112no—
391C22⋊C8—221no—
392C22⋊C8—221no—
393#95—112no—
394#95—222no—
395#95—222no—
396#95—222no—
397C2×C11—21no—
398C2×C11—22no—
399C2×C11—21no—
400C2×C11—22no—
401C2×C11—82no—
402C2×C11C2×#45211yescharacteristic
403C2×C11#302011yescharacteristic
404C2×C11#302611yescharacteristic
405C24—21no—
406C24C2×C22⋊D1111yescharacteristic
407C2×Q8—21no—
408C2×Q8—81no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×Q8—881no—
412C2×Q8C2×C22⋊D1112yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—81no—
419C2×D4C2×C22⋊D1112yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4—82no—
433C22×C4—222no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444Q16—882no—
445SD16—882no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—881no—
449C2×C8—881no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—882no—
466C4⋊C4—881no—
467C4⋊C4C2×C22⋊D1112yes—
468C4⋊C4C2×C22⋊D1112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—442no—
477C22⋊C4—441no—
478C22⋊C4—441no—
479C42—24no—
480C11#1828911yescharacteristic, complemented, Sylow
481C23—22no—
482C23—41no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#6700312yes—
488C23#6700412yes—
489C23#6700611yescharacteristic
490C23#6700611yescharacteristic
491C23C22×C22⋊D1111yescharacteristic
492Q8—42no—
493Q8—81no—
494Q8—442no—
495Q8—442no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—44no—
500D4—81no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—81no—
522C2×C4—84no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4#6700611yescharacteristic
531C2×C4#6700611yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C8—442no—
535C8—442no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—84no—
548C22#1062285212yes—
549C22#1062285212yes—
550C22C2×#6700311yescharacteristic
551C22C2×#6700411yescharacteristic
552C22C2×#6700611yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—882no—
563C4—881no—
564C4—881no—
565C2—21no—
566C2—22no—
567C2—21no—
568C2—22no—
569C2—82no—
570C2C2×#1062285211yescharacteristic
571C2#1307798011yescharacteristic
572C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC22×C11C2×#120
prime radicalC2×C11×#121C22
hypercenterC2×#539D11
hypocenterC11#18289
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #13079388C2semidirect
3. #13074429C2semidirect
4. #13067647C2semidirect
5. #13067579C2semidirect
6. #13067188C2semidirect
8. C2×#10622166C2semidirect
32. #10622663C22semidirect
33. #10622657C22semidirect
37. #10622599C22semidirect
39. #10622592C22semidirect
42. #10622176C22semidirect
44. #10622166C22semidirect
480. C11#18289semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130793732
#130744292
#130676472
#130675792
#130671882
#130671842
C2×#106221662
C2×C11×#5392
#1828911