Finite Group Databasebeta

← #14910262

Subgroups — #14910262

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C22×#66892C211yesmaximal, characteristic, complemented
3#13080303C211yesmaximal, characteristic
4#13070885C211yesmaximal, characteristic, complemented
5#13070731C211yesmaximal, characteristic, complemented
6#13070705C211yesmaximal, characteristic, complemented
7#13070678C211yesmaximal, characteristic, complemented
8#13070658C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070550C211yesmaximal, characteristic, complemented
11#13070544C211yesmaximal, characteristic, complemented
12#13070533C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15D4×C11×Q16C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic, complemented
18D4×Q8×C11—21no—
19C2×#66957C2211yescharacteristic
20C22×D88C2211yescharacteristic
21#10623081—21no—
22C11×#494C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic, complemented
25C11×#462—21no—
26C11×#451—21no—
27C11×#451—21no—
28C4×C11×Q16C2211yescharacteristic, complemented
29C8×D4×C11C2211yescharacteristic
30C2×#66893C2211yescharacteristic, complemented
31C2×#66893C2211yescharacteristic, complemented
32C2×#66893C2211yescharacteristic, complemented
33#10622792—24no—
34C2×#66892—24no—
35C2×#66892C2211yescharacteristic
36C2×#66892C2211yescharacteristic
37C2×#66892C2211yescharacteristic
38C2×#66892C2211yescharacteristic
39C2×#66892C2211yescharacteristic
40C2×#66892C2211yescharacteristic
41#10622729C2211yescharacteristic
42#10622728C2211yescharacteristic
43C2×#66876C2211yescharacteristic, complemented
44C22×C11⋊C16C2211yescharacteristic
45#10622457—21no—
46#10622347—21no—
47#10622344—21no—
48#10622309C2211yescharacteristic
49C4×D88C2211yescharacteristic
50#10622202C2211yescharacteristic, complemented
51#10622202C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic, complemented
59C4⋊(C11⋊C16)C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C22×Q8×C11—21no—
62C22×Q8×C11—21no—
63C2×#4339—21no—
64C22×D44—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—41no—
71C2×C11×Q16—41no—
72C2×C11×Q16C2311yescharacteristic
73C2×C11×Q16C2311yescharacteristic
74C2×C11×Q16C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—41no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—41no—
82C11×C22⋊Q8—41no—
83C4×Q8×C11—21no—
84C4×D4×C11—41no—
85C4×D4×C11D411yescharacteristic
86#66990—41no—
87#66983—21no—
88#66977—21no—
89C2×Dic44C2311yescharacteristic
90#66957—22no—
91#66957—41no—
92C2×D88—22no—
93C2×D88—21no—
94C2×D88—41no—
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66947—41no—
100#66937—41no—
101C22⋊C4×D11—41no—
102#66928—21no—
103C4×D44—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66893—22no—
114#66893—41no—
115#66892—22no—
116#66892—22no—
117#66892—22no—
118#66892—22no—
119#66892—41no—
120#66892D414yescomplemented
121#66885—21no—
122#66885—21no—
123#66882C2311yescharacteristic
124#66880—21no—
125#66876—22no—
126C2×C11⋊C16—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33832—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—81no—
141C2×Q8×C11—81no—
142C2×D4×C11D811yescharacteristic
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149#4339—42no—
150#4339—81no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—42no—
154C2×D44—41no—
155C2×D44—81no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×Dic22—21no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—21no—
164C11×Q16—42no—
165C11×Q16—42no—
166C11×Q16—81no—
167C11×Q16C2×D412yes—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4D811yescharacteristic
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4D811yescharacteristic
186C11×C22⋊C4D811yescharacteristic
187C42×C11—41no—
188C42×C11C2×D411yescharacteristic
189C22⋊Dic11—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—41no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic44—21no—
197Dic44—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203#4314—42no—
204#4314—81no—
205C11⋊C16—21no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#510—111no—
210C22×SD32—111no—
211D4×Q16D1111yescharacteristic, complemented
212#3280—111no—
213#2251—111no—
214#2220—111no—
215#2216—111no—
216#2211—111no—
217#2208—111no—
218#2189—111no—
219#2188—111no—
220#2187—111no—
221#2185—111no—
222#2175—111no—
223#2168—111no—
224C23×C11C2×D811yescharacteristic
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—161no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—82no—
238Q8×C11—82no—
239D4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—82no—
249C2×C4×C11—82no—
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C2×D811yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C22⋊D11—82no—
256C22⋊D11—161no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259D44—22no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—82no—
264C4×D11—82no—
265C4×D11—161no—
266Dic22—41no—
267Dic22—41no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11C22×D411yescharacteristic
272C8×C11H(5,𝔽2)11yescharacteristic
273C2×#135—111no—
274C22×Q16C2×D1111yescharacteristic
275C22×Q16C2×D1111yescharacteristic, complemented
276C22×D8—111no—
277D4×Q8—21no—
278#546—221no—
279#510—224no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—224no—
290C2×M32—111no—
291C22×C16—111no—
292#495—111no—
293#494C2×D1111yescharacteristic, complemented
294#467—111no—
295#467C2×D1111yescharacteristic
296#467C2×D1111yescharacteristic, complemented
297#466—111no—
298#463—221no—
299#462—21no—
300#451—21no—
301#451—21no—
302#450—221no—
303#449—221no—
304C4×Q16C2×D1111yescharacteristic, complemented
305C4×D8—111no—
306C8×D4C2×D1111yescharacteristic
307#366—111no—
308C4⋊C16—111no—
309#358—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315C22⋊C16—111no—
316C22⋊C16—111no—
317#346—111no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11#51012yescomplemented
324C22×C11C22×D811yescharacteristic
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—164no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—42no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11D4211yescharacteristic
341C4×C11#57611yescharacteristic
342Dic11—81no—
343Dic11—81no—
344C2×#41—221no—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×D4—221no—
348#135—222no—
349#135—441no—
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16—41no—
356C2×Q16—41no—
357C2×Q16—111no—
358C2×Q16C22×D1111yescharacteristic
359C2×Q16C22×D1111yescharacteristic
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—111no—
364C2×D8—111no—
365C2×D8—222no—
366C2×D8—221no—
367C2×D8—441no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4⋊Q8—21no—
371C4⋊Q8—41no—
372#124—221no—
373#123—441no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—41no—
377C22⋊Q8—41no—
378C22⋊Q8—221no—
379#121—221no—
380#121—441no—
381#120—441no—
382C4×Q8—21no—
383C4×D4—41no—
384C4×D4—221no—
385C4×D4C22⋊D1111yescharacteristic
386C2×C22⋊C4—441no—
387Q32—222no—
388Q32—222no—
389Q32—441no—
390SD32—114no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—441no—
396M32—222no—
397C2×C16—111no—
398C2×C16—111no—
399C2×C16—111no—
400C2×C16—111no—
401C2×C16—222no—
402#107—111no—
403#107C22×D1111yescharacteristic
404C4⋊C8C22⋊D1111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—221no—
409#102—221no—
410#102—221no—
411C22⋊C8C22⋊D1111yescharacteristic
412C22⋊C8C22⋊D1111yescharacteristic
413C4×C8C22×D1111yescharacteristic
414C2×C11—22no—
415C2×C11—41no—
416C2×C11D4×D811yescharacteristic
417C2×C11C2×#51011yescharacteristic
418C2×C11#341611yescharacteristic
419D11—82no—
420D11—161no—
421C24—441no—
422#41—442no—
423#41—881no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—442no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—881no—
441C2×D4#432311yescharacteristic
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448Q16—21no—
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—21no—
453Q16—42no—
454Q16—42no—
455Q16—81no—
456Q16—221no—
457Q16—221no—
458Q16D4×D1112yes—
459SD16—442no—
460SD16—881no—
461D8—112no—
462D8—221no—
463D8—221no—
464D8—221no—
465D8—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4#432311yescharacteristic
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4#432311yescharacteristic
491C22⋊C4#432311yescharacteristic
492C42—41no—
493C42C2×C22⋊D1111yescharacteristic
494C16—112no—
495C16—221no—
496C16—221no—
497C16—221no—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—441no—
500C23—441no—
501C23—882no—
502C23—882no—
503C23—1761no—
504C23C2×#432311yescharacteristic
505C23C2×#432311yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—82no—
513Q8—82no—
514Q8—441no—
515Q8—441no—
516D4—22no—
517D4—222no—
518D4—441no—
519D4—441no—
520D4—441no—
521D4—882no—
522D4—882no—
523D4—1761no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—882no—
537C2×C4—1761no—
538C2×C4C2×#432311yescharacteristic
539C2×C4C2×#432311yescharacteristic
540C2×C4C2×#432311yescharacteristic
541C2×C4C2×#432311yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8C2×D4×D1111yescharacteristic
547C8#6703711yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—442no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—1764no—
560C22#1062279212yescomplemented
561C22C22×#432311yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—881no—
571C4—881no—
572C4D4×C22⋊D1111yescharacteristic
573C4#1062336611yescharacteristic
574C2—22no—
575C2—41no—
576C2—882no—
577C2—1761no—
578C2D4×#432311yescharacteristic
579C2C2×#1062279211yescharacteristic
580C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenterD4×Q16D11
hypocenterC11#33832
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C22×#66892C2semidirect
4. #13070885C2semidirect
5. #13070731C2semidirect
6. #13070705C2semidirect
7. #13070678C2semidirect
8. #13070658C2semidirect
9. #13070554C2semidirect
10. #13070550C2semidirect
11. #13070544C2semidirect
12. #13070533C2semidirect
13. #13070478C2semidirect
14. #13070442C2semidirect
15. D4×C11×Q16C2semidirect
17. C22×C11×Q16C22semidirect
22. C11×#494C22semidirect
24. C11×#467C22semidirect
28. C4×C11×Q16C22semidirect
30. C2×#66893C22semidirect
31. C2×#66893C22semidirect
32. C2×#66893C22semidirect
43. C2×#66876C22semidirect
50. #10622202C22semidirect
51. #10622202C22semidirect
52. #10622202C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622130C22semidirect
58. #10622127C22semidirect
59. C4⋊(C11⋊C16)C22semidirect
60. #10622099C22semidirect
120. #66892D4semidirect
211. D4×Q16D11semidirect
275. C22×Q16C2×D11semidirect
293. #494C2×D11semidirect
296. #467C2×D11semidirect
304. C4×Q16C2×D11semidirect
323. C22×C11#510semidirect
498. C11#33832semidirect
560. C22#10622792semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C22×#668922
#130803032
#130708852
#130707312
#130707052
#130706782
#130706582
#130705542
#130705502
#130705442
#130705332
#130704782
#130704422
D4×C11×Q162
#3383211