Finite Group Databasebeta

← #14743645

Subgroups — #14743645

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081491C211yesmaximal, characteristic, complemented
2#13081395C211yesmaximal, characteristic, complemented
3#13080440C211yesmaximal, characteristic
4#13068277C211yesmaximal, characteristic, complemented
5#13068153C211yesmaximal, characteristic, complemented
6#13068067C211yesmaximal, characteristic, complemented
7#13068030C211yesmaximal, characteristic, complemented
8#13067993C211yesmaximal, characteristic, complemented
9#13067795C211yesmaximal, characteristic
10#13067750C211yesmaximal, characteristic, complemented
11#13067748C211yesmaximal, characteristic, complemented
12#13067710C211yesmaximal, characteristic, complemented
13#13067452C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3295C211yesmaximal, characteristic
16C11×#554C2211yescharacteristic
17D42×C11C2211yescharacteristic
18#10623098C2211yescharacteristic, complemented
19#10623074C2211yescharacteristic
20C11×#486C2211yescharacteristic
21C11×#481—21no—
22C11×#476C2211yescharacteristic
23C11×#465—21no—
24C11×#460C2211yescharacteristic
25C11×#450—21no—
26C4×C11×SD16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×C11×#102—21no—
29#10622831—21no—
30C2×#66896—21no—
31#10622775—21no—
32#10622705C2211yescharacteristic, complemented
33#10622704C2211yescharacteristic, complemented
34#10622692C2211yescharacteristic, complemented
35#10622688C2211yescharacteristic
36#10622683C2211yescharacteristic
37#10622683C2211yescharacteristic
38#10622677—21no—
39#10622676—21no—
40#10622654—21no—
41#10622647—21no—
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622634C2211yescharacteristic, complemented
44#10622632C2211yescharacteristic
45C4×#4324—21no—
46C4×#4324C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622622—21no—
49#10622621C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622470—21no—
52#10622410—21no—
53#10622370—21no—
54#10622294C2211yescharacteristic, complemented
55#10622292C2211yescharacteristic, complemented
56#10622184C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622122C2211yescharacteristic, complemented
62#10622120C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16D411yescharacteristic
71C22×C8×C11—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#120—41no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C2×C11×C4⋊C4—21no—
85#66997—21no—
86C2×#4326—41no—
87D4×Dic11—21no—
88C2×#4324—21no—
89C2×#4324—21no—
90C2×#4324D411yescharacteristic
91C2×C4⋊Dic11—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94#66943—21no—
95#66942—41no—
96#66940—21no—
97#66931—41no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22C2311yescharacteristic
103C11×#106—21no—
104C11×#106D411yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103D411yescharacteristic
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×#102D411yescharacteristic
112C11×C22⋊C8—21no—
113C4×C8×C11C2311yescharacteristic
114#66899—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119#66896—21no—
120#66896—41no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123#66880—21no—
124#66880—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127#66874—21no—
128#66874—21no—
129#66874D411yescharacteristic
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66872D411yescharacteristic
134#66871—21no—
135#66871—21no—
136#66871—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19790—111nomaximal, Sylow
145C24×C11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—41no—
152C2×D4×C11—41no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11—81no—
156C2×D4×C11—81no—
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×Dic11—41no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D411yescharacteristic
166C11×SD16—22no—
167C11×SD16—81no—
168C2×C8×C11—21no—
169C2×C8×C11—81no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4326—82no—
188#4324—22no—
189#4324—42no—
190#4324—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—41no—
196C4⋊Dic11C2×D411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202C4×Dic11—21no—
203C4×Dic11—41no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#3381—111no—
212#3372—111no—
213#3295—111no—
214#3295D1111yescharacteristic
215#1720—111no—
216#1698—111no—
217#1683—111no—
218#1678—111no—
219#1671—111no—
220#1639—111no—
221#1632—111no—
222#1632—111no—
223#1626—111no—
224#1582—111no—
225SD16⋊C8—111no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—41no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—161no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—81no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—82no—
243D4×C11—82no—
244D4×C11#13512yes—
245D4×C11#13712yes—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—161no—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—161no—
264Dic22—21no—
265Dic22—21no—
266Dic22—41no—
267Dic22—41no—
268Dic22—81no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278#557—111no—
279#554—111no—
280#554C2×D1111yescharacteristic
281D42C2×D1111yescharacteristic
282#499—221no—
283#498—111no—
284#494—111no—
285#491—221no—
286#487—111no—
287#486—111no—
288#486—111no—
289#486C2×D1111yescharacteristic
290#481—21no—
291#481—221no—
292#479—221no—
293#479—221no—
294#478—221no—
295#477—111no—
296#477—111no—
297#476—111no—
298#476C2×D1111yescharacteristic
299#474—111no—
300#465—21no—
301#465—221no—
302#461—111no—
303#461—221no—
304#460—111no—
305#460C2×D1111yescharacteristic
306#450—21no—
307#450—221no—
308#446—111no—
309C8×Q8—111no—
310#440—221no—
311C4×SD16—111no—
312C4×SD16—221no—
313C4×SD16C2×D1111yescharacteristic
314C8×D4—111no—
315C8×D4C2×D1111yescharacteristic
316C2×#102—21no—
317C2×#102—221no—
318#335—111no—
319#334—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#331—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328#322—111no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—164no—
339C22×C11D4211yescharacteristic
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×#13711yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57711yescharacteristic
350Dic11—41no—
351Dic11—41no—
352Dic11—81no—
353Dic11—81no—
354C22×D4—21no—
355C22×D4—21no—
356C2×Q16—441no—
357C2×SD16—21no—
358C2×SD16—111no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16C22⋊D1111yescharacteristic
362C22×C8—21no—
363C22×C8—221no—
364C4⋊Q8—111no—
365C4⋊Q8—111no—
366C4⋊Q8—221no—
367C4⋊Q8C22×D1111yescharacteristic
368#127C22×D1111yescharacteristic
369#125—21no—
370#125—221no—
371#125—221no—
372#125—441no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—221no—
376C22⋊Q8—441no—
377#121—21no—
378#121—21no—
379#120—41no—
380C4×Q8—111no—
381C4×Q8—221no—
382C4×Q8—221no—
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—221no—
386C4×D4C22×D1111yescharacteristic
387C4×D4C22×D1111yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—221no—
390#107—221no—
391#107—221no—
392#107—221no—
393#106—21no—
394#106—111no—
395#106—221no—
396#106—221no—
397#106—221no—
398#106C22⋊D1111yescharacteristic
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405#103—111no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103C22⋊D1111yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—111no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—441no—
423#102C22⋊D1111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—221no—
426#97—221no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C2×C11—42no—
432C2×C11—42no—
433C2×C11—161no—
434C2×C11#326611yescharacteristic
435C2×C11#328211yescharacteristic
436C2×C11#328811yescharacteristic
437C24—41no—
438C2×Q8—21no—
439C2×Q8—111no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8C2×C22⋊D1111yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4D4×D1111yescharacteristic
453C2×D4C2×C22⋊D1111yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—441no—
458Q16—882no—
459SD16—22no—
460SD16—81no—
461SD16—222no—
462SD16—442no—
463SD16—881no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—881no—
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—111no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4—441no—
491C4⋊C4D4×D1111yescharacteristic
492C4⋊C4C2×C22⋊D1111yescharacteristic
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—441no—
499C42—21no—
500C42—221no—
501C42—441no—
502C42C23×D1111yescharacteristic
503C11#1979011yescharacteristic, complemented, Sylow
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—81no—
513Q8—221no—
514Q8—221no—
515Q8—441no—
516Q8—441no—
517Q8—881no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—82no—
527D4#6696812yes—
528D4#6700312yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—1761no—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—221no—
551C8—221no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8—441no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D4×C22⋊D1111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—441no—
574C4—441no—
575C4—881no—
576C4—881no—
577C4C2×#6696811yescharacteristic
578C4#1062329311yescharacteristic
579C4C2×#6700311yescharacteristic
580C4#1062336711yescharacteristic
581C2—42no—
582C2—42no—
583C2—161no—
584C2#1308012611yescharacteristic
585C2#1308031911yescharacteristic
586C2#1308038011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3295C2
socleC22×C11D42
prime radicalD42×C11C22
hypercenter#3295D11
hypocenterC11#19790
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #13081491C2semidirect
2. #13081395C2semidirect
4. #13068277C2semidirect
5. #13068153C2semidirect
6. #13068067C2semidirect
7. #13068030C2semidirect
8. #13067993C2semidirect
10. #13067750C2semidirect
11. #13067748C2semidirect
12. #13067710C2semidirect
13. #13067452C2semidirect
14. SD16⋊(C11⋊C8)C2semidirect
18. #10623098C22semidirect
32. #10622705C22semidirect
33. #10622704C22semidirect
34. #10622692C22semidirect
42. Q8×C11⋊C8C22semidirect
43. #10622634C22semidirect
54. #10622294C22semidirect
55. #10622292C22semidirect
56. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
61. #10622122C22semidirect
62. #10622120C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622093C22semidirect
503. C11#19790semidirect

Maximal subgroups

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

subgroupindex
#130814912
#130813952
#130804402
#130682772
#130681532
#130680672
#130680302
#130679932
#130677952
#130677502
#130677482
#130677102
#130674522
SD16⋊(C11⋊C8)2
C11×#32952
#1979011