Finite Group Databasebeta

← #14738871

Subgroups — #14738871

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068182C211yesmaximal, characteristic, complemented
5#13068175C211yesmaximal, characteristic, complemented
6#13068154C211yesmaximal, characteristic, complemented
7#13068147C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068051C211yesmaximal, characteristic, complemented
10#13068030C211yesmaximal, characteristic, complemented
11#13068023C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067284C211yesmaximal, characteristic, complemented
15C11×#3217C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#496—21no—
20C11×#490—21no—
21C11×#460C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#459C2211yescharacteristic
25C11×#450—21no—
26C11×#447—21no—
27C11×#432C2211yescharacteristic
28#10622828—21no—
29#10622828—21no—
30#10622684—21no—
31#10622684—21no—
32#10622683C2211yescharacteristic
33#10622683C2211yescharacteristic
34#10622683C2211yescharacteristic
35#10622683C2211yescharacteristic
36#10622676—21no—
37#10622667—21no—
38#10622665—21no—
39#10622655—21no—
40#10622644C2211yescharacteristic, complemented
41#10622637C2211yescharacteristic, complemented
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622634C2211yescharacteristic, complemented
44#10622632C2211yescharacteristic, complemented
45#10622625—21no—
46#10622625C2211yescharacteristic, complemented
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic, complemented
49#10622621C2211yescharacteristic, complemented
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622182C2211yescharacteristic
56#10622182C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622120C2211yescharacteristic, complemented
60#10622120C2211yescharacteristic, complemented
61#10622119C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622118C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622117C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×D8—21no—
73C2×C11×D8—21no—
74C11×#127—21no—
75C11×#127—21no—
76C11×#127—21no—
77C11×#127C2311yescharacteristic
78C11×#127C2311yescharacteristic
79C11×#126—21no—
80C11×#125D411yescharacteristic
81C11×#124D411yescharacteristic
82C11×#123—21no—
83C11×C22⋊Q8D411yescharacteristic
84C11×#121D411yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4324—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113#66899—21no—
114#66896—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66874—21no—
127#66874—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19380—111nomaximal, Sylow
145C24×C11—41no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11—82no—
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C2×Dic22—21no—
168C2×Dic22—21no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×D8—81no—
172C11×D8—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191C22⋊Dic11—41no—
192#4326—81no—
193#4324—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201#4318—41no—
202#4318—41no—
203#4318—42no—
204#4318—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3252—111no—
215#3217D1111yescharacteristic
216#3138—111no—
217#2969—111no—
218#1702—111no—
219#1701—111no—
220#1698—111no—
221#1697—111no—
222#1682—111no—
223#1681—111no—
224#1678—111no—
225#1677—111no—
226#1569—111no—
227#1554—111no—
228#1545—111no—
229C23×C11—21no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—82no—
233C23×C11—82no—
234C23×C11—82no—
235C23×C11#12111yescharacteristic
236Q8×C11—21no—
237Q8×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—81no—
249D4×C11—81no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11—82no—
253D4×C11—81no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11#12111yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×Dic11—41no—
271C2×Dic11—41no—
272Dic22—41no—
273Dic22—41no—
274Dic22—81no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#533—111no—
286C2×#127C2×D1111yescharacteristic
287#529C2×D1111yescharacteristic
288#496—21no—
289#490—21no—
290#490—221no—
291#490—221no—
292#486—111no—
293#486—111no—
294#486—111no—
295#486—111no—
296#479—221no—
297#477—111no—
298#476—111no—
299#470—221no—
300#468—221no—
301#464—221no—
302#462—111no—
303#461—111no—
304#460C2×D1111yescharacteristic
305#460C2×D1111yescharacteristic
306#459C2×D1111yescharacteristic
307#459C2×D1111yescharacteristic
308#450—21no—
309#447—21no—
310#446—111no—
311C8×Q8—111no—
312#436—111no—
313#436—221no—
314#435—221no—
315C8×D4—111no—
316#433—221no—
317#432C2×D1111yescharacteristic
318#431—111no—
319#423—111no—
320#418—221no—
321#418—221no—
322#405—221no—
323C4×M16—111no—
324#335—111no—
325#335—111no—
326#334—111no—
327#334—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—164no—
349C22×C11C2×#12111yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#57511yescharacteristic
358C4×C11#57511yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361Dic11—81no—
362Dic11—81no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C2×Q16—221no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—221no—
370C2×D8—21no—
371C2×D8—21no—
372C2×M16—111no—
373C2×M16—111no—
374C2×M16—221no—
375C2×M16—221no—
376C22×C8—221no—
377C4⋊Q8—111no—
378C4⋊Q8—111no—
379#127—21no—
380#127—21no—
381#127—21no—
382#127C22×D1111yescharacteristic
383#127C22×D1111yescharacteristic
384#126—21no—
385#125—221no—
386#125C22⋊D1111yescharacteristic
387#124C22⋊D1111yescharacteristic
388#123—21no—
389C22⋊Q8—221no—
390C22⋊Q8—221no—
391C22⋊Q8C22⋊D1111yescharacteristic
392#121C22⋊D1111yescharacteristic
393C4×Q8—221no—
394C4×Q8—221no—
395C4×Q8C22×D1111yescharacteristic
396C4×D4—21no—
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399#117—221no—
400C2×C42C22×D1111yescharacteristic
401#107—221no—
402#106—221no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—221no—
413#103—221no—
414#103—221no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—21no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—21no—
433#97—111no—
434#97—111no—
435#97—221no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C2×C11—41no—
441C2×C11—81no—
442C2×C11—161no—
443C2×C11—161no—
444C2×C11#304011yescharacteristic
445C2×C11#306211yescharacteristic
446C2×C11#306811yescharacteristic
447C24—41no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8C2×C22⋊D1111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—82no—
466C2×D4C2×C22⋊D1111yescharacteristic
467C22×C4—21no—
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471Q16—881no—
472SD16—81no—
473SD16—81no—
474SD16—881no—
475D8—81no—
476D8—81no—
477M16—441no—
478M16—441no—
479M16—442no—
480M16—881no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4C2×C22⋊D1111yescharacteristic
503C4⋊C4C2×C22⋊D1111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—441no—
510C42—21no—
511C42—441no—
512C42D4×D1111yescharacteristic
513C42#434111yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1938011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—41no—
519C23—41no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23#6699211yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—441no—
527Q8—441no—
528Q8—881no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6699211yescharacteristic
558C2×C4#6699211yescharacteristic
559C2×C4#6699211yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—41no—
564C8—41no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22C2×#6699211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—881no—
595C4—881no—
596C4#1062330411yescharacteristic
597C4#1062330411yescharacteristic
598C4#1062336611yescharacteristic
599C4#1062336711yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2#1307810811yescharacteristic
605C2#1307829211yescharacteristic
606C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19380
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #13079989C2semidirect
2. #13078990C2semidirect
3. #13077621C2semidirect
4. #13068182C2semidirect
5. #13068175C2semidirect
6. #13068154C2semidirect
7. #13068147C2semidirect
8. #13068058C2semidirect
9. #13068051C2semidirect
10. #13068030C2semidirect
11. #13068023C2semidirect
12. #13067384C2semidirect
13. #13067327C2semidirect
14. #13067284C2semidirect
40. #10622644C22semidirect
41. #10622637C22semidirect
42. Q8×C11⋊C8C22semidirect
43. #10622634C22semidirect
44. #10622632C22semidirect
46. #10622625C22semidirect
48. D4×C11⋊C8C22semidirect
49. #10622621C22semidirect
59. #10622120C22semidirect
60. #10622120C22semidirect
61. #10622119C22semidirect
62. #10622119C22semidirect
63. #10622118C22semidirect
64. #10622118C22semidirect
65. #10622117C22semidirect
66. #10622117C22semidirect
516. C11#19380semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130789902
#130776212
#130681822
#130681752
#130681542
#130681472
#130680582
#130680512
#130680302
#130680232
#130673842
#130673272
#130672842
C11×#32172
#1938011