Finite Group Databasebeta

← #14737216

Subgroups — #14737216

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079942C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068142C211yesmaximal, characteristic, complemented
5#13068137C211yesmaximal, characteristic, complemented
6#13068098C211yesmaximal, characteristic, complemented
7#13068093C211yesmaximal, characteristic, complemented
8#13068034C211yesmaximal, characteristic, complemented
9#13068030C211yesmaximal, characteristic, complemented
10#13068027C211yesmaximal, characteristic, complemented
11#13068023C211yesmaximal, characteristic, complemented
12C2×#10622118C211yesmaximal, characteristic, complemented
13#13067311C211yesmaximal, characteristic, complemented
14#13067309C211yesmaximal, characteristic, complemented
15C11×#3247C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#478—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#466—21no—
23C11×#465—21no—
24C11×#463—21no—
25C11×#460C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622691C2211yescharacteristic
30#10622686C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622679—21no—
33#10622670—21no—
34#10622661—21no—
35#10622651—21no—
36#10622651—21no—
37#10622651—21no—
38#10622640C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44C4×#4323—21no—
45#10622625C2211yescharacteristic
46#10622624—21no—
47D4×C11⋊C8—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622118C2211yescharacteristic
66#10622118C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339—21no—
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C22×C8×C11—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4325—21no—
91C2×#4323—21no—
92C2×#4323—21no—
93C2×#4323—21no—
94#66983—21no—
95#66983—21no—
96C2×#4318—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8D411yescharacteristic
100C22×C11⋊C8D411yescharacteristic
101#66928—21no—
102#66927C2311yescharacteristic
103C4×D44—21no—
104C4×D44—21no—
105#66922C2311yescharacteristic
106C11×#107—21no—
107C11×#106—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—21no—
114C11×#102—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66872—21no—
127#66871—21no—
128#66871—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#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19227—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C2×C22⋊D11—41no—
160#4339—82no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C11×SD16—81no—
167C11×D8—81no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—81no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4325—81no—
192#4323—42no—
193#4323—42no—
194#4323—81no—
195(C2×D11)⋊C4—41no—
196(C2×D11)⋊C4—41no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199#4318—42no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—41no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#3247—111no—
213#3247D1111yescharacteristic, complemented
214#3169—111no—
215#2966—111no—
216#1696—111no—
217#1695—111no—
218#1688—111no—
219#1687—111no—
220#1678—111no—
221#1678—111no—
222#1677—111no—
223#1677—111no—
224C2×#334—111no—
225#1551—111no—
226#1551—111no—
227C23×C11—21no—
228C23×C11—41no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—81no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—82no—
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—82no—
262C2×Dic11—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—81no—
268C4×D11—82no—
269Dic22—81no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8#13512yes—
280#532—111no—
281#532C2×D1111yescharacteristic
282#529C2×D1111yescharacteristic
283#500—111no—
284#493—111no—
285#486—111no—
286#486—111no—
287#478—21no—
288#478—221no—
289#477—111no—
290#477C2×D1111yescharacteristic
291#476—111no—
292#476C2×D1111yescharacteristic
293#466—21no—
294#466—221no—
295#466—221no—
296#466—221no—
297#465—21no—
298#465—221no—
299#463—21no—
300#463—221no—
301#460—111no—
302#460C2×D1111yescharacteristic
303#459—111no—
304#459C2×D1111yescharacteristic
305#446—111no—
306C8×Q8—111no—
307C4×D8—221no—
308C4×D8—221no—
309#436—111no—
310#435—221no—
311C8×D4—111no—
312C8×D4—221no—
313#433—221no—
314#432—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317#405—221no—
318C2×C4×C8—111no—
319#334—111no—
320#334—111no—
321#334—111no—
322#334—111no—
323#333—111no—
324#333—111no—
325#333—111no—
326#333—111no—
327#331—111no—
328#331—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11#47212yes—
340C22×C11C2×#12111yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11C2×#13511yescharacteristic
353C4×C11#57511yescharacteristic
354C4×C11#57711yescharacteristic
355C4×C11#57711yescharacteristic
356Dic11—81no—
357C2×#41—21no—
358C2×#41—221no—
359C2×SD16—21no—
360C2×SD16—221no—
361C2×D8—21no—
362C2×D8—221no—
363C2×D8—221no—
364C2×D8—221no—
365C2×M16—221no—
366C22×C8—21no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—221no—
370C22×C8—221no—
371C4⋊Q8—111no—
372C4⋊Q8C22×D1111yescharacteristic
373#127—111no—
374#127C22×D1111yescharacteristic
375#126—21no—
376#125C22⋊D1111yescharacteristic
377#124—21no—
378#124—221no—
379#124C22⋊D1111yescharacteristic
380#123—21no—
381C22⋊Q8C22⋊D1111yescharacteristic
382#121—21no—
383#121—21no—
384#121—221no—
385#121—221no—
386#121C22⋊D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—221no—
392C4×D4—221no—
393C4×D4C22×D1111yescharacteristic
394#117—21no—
395C2×C42C22×D1111yescharacteristic
396#107—21no—
397#107—221no—
398#107—221no—
399#107—221no—
400#106—21no—
401#106—221no—
402C4⋊C8—21no—
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—21no—
413#103—221no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—221no—
428#97—221no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C2×C11—22no—
435C2×C11—81no—
436C2×C11—161no—
437C2×C11#303511yescharacteristic
438C2×C11#306011yescharacteristic
439C2×C11C2×#47211yescharacteristic
440D11—161no—
441#41—82no—
442#41—882no—
443C2×Q8—21no—
444C2×Q8—221no—
445C2×Q8C2×C22⋊D1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4C2×C22⋊D1111yescharacteristic
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—441no—
459C22×C4D4×D1111yescharacteristic
460C22×C4#434111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462SD16—81no—
463SD16—881no—
464D8—81no—
465D8—442no—
466D8—442no—
467D8—881no—
468M16—442no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—222no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—441no—
482C2×C8—442no—
483C2×C8—881no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4C2×C22⋊D1111yescharacteristic
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C42—21no—
504C42D4×D1111yescharacteristic
505C42#434111yescharacteristic
506C42C2×C22⋊D1111yescharacteristic
507C42C23×D1111yescharacteristic
508C11#1922711yescharacteristic, complemented, Sylow
509C23—21no—
510C23—41no—
511C23—441no—
512C23#6699211yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—81no—
516Q8—881no—
517D4—21no—
518D4—21no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—441no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—881no—
531D4—882no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—441no—
545C2×C4—882no—
546C2×C4#6699211yescharacteristic
547C2×C4#6699211yescharacteristic
548C2×C4#6699211yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×#434111yescharacteristic
551C2×C4C22×C22⋊D1111yescharacteristic
552C8—41no—
553C8—41no—
554C8—112no—
555C8—221no—
556C8—221no—
557C8—221no—
558C8—441no—
559C8—441no—
560C8—441no—
561C8—441no—
562C22—21no—
563C22—21no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22#1062281212yes—
574C22C2×#6699211yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—881no—
584C4D11×#13511yescharacteristic
585C4#1062329911yescharacteristic
586C4#1062336711yescharacteristic
587C4#1062336811yescharacteristic
588C2—22no—
589C2—81no—
590C2—161no—
591C2—1761no—
592C2#1307806711yescharacteristic
593C2#1307827511yescharacteristic
594C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3247C2
socleC22×C11C2×#121
hypercenter#3247D11
hypocenterC11#19227
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #13079942C2semidirect
2. #13079191C2semidirect
3. #13077592C2semidirect
4. #13068142C2semidirect
5. #13068137C2semidirect
6. #13068098C2semidirect
7. #13068093C2semidirect
8. #13068034C2semidirect
9. #13068030C2semidirect
10. #13068027C2semidirect
11. #13068023C2semidirect
12. C2×#10622118C2semidirect
13. #13067311C2semidirect
14. #13067309C2semidirect
15. C11×#3247C2semidirect
213. #3247D11semidirect
508. C11#19227semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130791912
#130775922
#130681422
#130681372
#130680982
#130680932
#130680342
#130680302
#130680272
#130680232
C2×#106221182
#130673112
#130673092
C11×#32472
#1922711