Finite Group Databasebeta

← #14908247

Subgroups — #14908247

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C211yesmaximal, characteristic, complemented
2C22×#66862C211yesmaximal, characteristic, complemented
3#13078199C211yesmaximal, characteristic, complemented
4D11×#466C211yesmaximal, characteristic, complemented
5#13070732C211yesmaximal, characteristic, complemented
6#13070726C211yesmaximal, characteristic, complemented
7#13070720C211yesmaximal, characteristic, complemented
8#13070718C211yesmaximal, characteristic, complemented
9#13070714C211yesmaximal, characteristic, complemented
10#13070702C211yesmaximal, characteristic, complemented
11#13070700C211yesmaximal, characteristic, complemented
12#13070403C211yesmaximal, characteristic, complemented
13#13070330C211yesmaximal, characteristic, complemented
14#13070327C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623158—21no—
20D11×#121—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C22×C11×C16C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622801C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic
28C2×#66890C2211yescharacteristic, complemented
29#10622728C2211yescharacteristic
30#10622728C2211yescharacteristic, complemented
31C22×C11⋊C16C2211yescharacteristic, complemented
32#10622661—21no—
33#10622651—21no—
34#10622527—24no—
35C2×D176C2211yescharacteristic, complemented
36C2×#66862—24no—
37C2×#66862C2211yescharacteristic
38C2×#66862C2211yescharacteristic
39C2×#66862C2211yescharacteristic, complemented
40C2×#66862C2211yescharacteristic, complemented
41#10622496C2211yescharacteristic
42#10622496C2211yescharacteristic, complemented
43#10622493C2211yescharacteristic
44D11×#107C2211yescharacteristic
45#10622420—21no—
46#10622417—21no—
47#10622388—21no—
48D11×#102—21no—
49C11×#367C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56#10622142C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622128C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×D4×D11—21no—
63C2×D4×D11—41no—
64C22×C4×D11D411yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70#66999—21no—
71C2×#4325—21no—
72#66992—41no—
73#66991—21no—
74C2×#4323—21no—
75#66983—21no—
76#66983—21no—
77C22×C11⋊C8D411yescharacteristic
78#66972—22no—
79#66972—22no—
80D8×D11—22no—
81D8×D11—22no—
82C2×D88C2311yescharacteristic
83C2×D88C2311yescharacteristic
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11D411yescharacteristic
87C2×C8×D11D411yescharacteristic
88C2×C8×D11C2311yescharacteristic
89C2×C8×D11C2311yescharacteristic
90#66948—21no—
91#66948—21no—
92#66947—41no—
93#66946—41no—
94#66945—21no—
95C4⋊C4×D11—21no—
96#66937—41no—
97#66935—41no—
98(C22⋊D11)⋊C4—41no—
99C22⋊C4×D11—41no—
100C11×SD32—22no—
101C2×C11×C16—22no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#107C2311yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108#66899—21no—
109#66896—21no—
110#66892—22no—
111#66890—22no—
112#66885—21no—
113#66885—21no—
114#66882C2311yescharacteristic
115#66882C2311yescharacteristic
116C2×C11⋊C16—22no—
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66873—21no—
120#66873—21no—
121#66872—21no—
122#66871—21no—
123D176—22no—
124#66862—22no—
125#66862—22no—
126#66862—22no—
127#66862D414yescomplemented
128#33605—111nomaximal, Sylow
129C23×D11—41no—
130C23×D11D811yescharacteristic
131C2×Q8×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C22×Dic11D811yescharacteristic
140#4343—42no—
141#4343—42no—
142D4×D11—42no—
143D4×D11—42no—
144D4×D11—84no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—41no—
148C2×D44—41no—
149C2×D44—41no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11D811yescharacteristic
155C2×C4×D11D811yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C11×Q16—21no—
159C11×Q16—21no—
160C11×D8—21no—
161C11×D8—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—41no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C22⋊Dic11—41no—
172#4325—42no—
173#4323—42no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184C4×Dic11—41no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2×D411yescharacteristic
187C2×C11⋊C8C2×D411yescharacteristic
188D88—21no—
189D88—21no—
190D88—21no—
191D88—21no—
192C8×D11—22no—
193C8×D11—21no—
194C8×D11—21no—
195C8×D11—22no—
196C8×D11C2×D412yes—
197C8×D11#4112yes—
198C11×C16—21no—
199C11×C16C2×D412yescomplemented
200C11⋊C16—21no—
201C11⋊C16C2×D412yescomplemented
202C2×#509—111no—
203C22×M32—111no—
204#3050—111no—
205C2×#466—111no—
206#2220—111no—
207#2220—111no—
208#2218—111no—
209#2218—111no—
210#2217—111no—
211#2217D1111yescharacteristic, complemented
212#2215—111no—
213#2215—111no—
214#2159—111no—
215#2140—111no—
216#2139—111no—
217C23×C11—41no—
218C23×C11C2×D811yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—82no—
225C22×D11—82no—
226C22×D11—82no—
227C22×D11C2×D811yescharacteristic
228C22×D11C2×D811yescharacteristic
229Q8×C11—41no—
230Q8×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—82no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C22⋊D11—82no—
242C22⋊D11—82no—
243C22⋊D11—82no—
244C22⋊D11—82no—
245C2×Dic11—22no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250D44—41no—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—82no—
255D44—82no—
256D44—82no—
257C4×D11—22no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—22no—
261C4×D11—82no—
262C4×D11—82no—
263C4×D11#12112yes—
264C4×D11#13512yes—
265C8×C11—21no—
266C8×C11C22×D411yescharacteristic
267C8×C11C2×#4111yescharacteristic
268C11⋊C8—21no—
269C11⋊C8#12112yes—
270C2×#135—111no—
271C22×D8—111no—
272C23×C8—111no—
273#525—221no—
274C2×#121—221no—
275#509—224no—
276C2×SD32—111no—
277C2×SD32C2×D1111yescharacteristic, complemented
278C2×D16—111no—
279C2×D16—111no—
280C2×M32—111no—
281C2×M32—111no—
282C2×M32—111no—
283C2×M32—111no—
284C2×M32—224no—
285C22×C16—111no—
286C22×C16C2×D1111yescharacteristic, complemented
287#467—111no—
288#467C2×D1111yescharacteristic, complemented
289#466—111no—
290#466—111no—
291#466—111no—
292#466—111no—
293#466—111no—
294#466—221no—
295#466—221no—
296#466C2×D1111yescharacteristic
297#465—221no—
298#465—221no—
299#427—111no—
300C2×#107—111no—
301#416—221no—
302C2×#102—221no—
303#367—111no—
304#367C2×D1111yescharacteristic, complemented
305#366—111no—
306#366—111no—
307#358—111no—
308#358C2×D1111yescharacteristic, complemented
309#357—111no—
310#357—111no—
311#357—111no—
312#357—111no—
313#357—111no—
314#357C2×D1111yescharacteristic, complemented
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11#50912yescomplemented
321C22×C11C22×D811yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—44no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—164no—
335C2×D11#46612yes—
336C4×C11—21no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11C2×#12111yescharacteristic
341C4×C11C2×#13511yescharacteristic
342Dic11—21no—
343Dic11—81no—
344Dic11—81no—
345Dic11#46612yes—
346C2×#41—221no—
347C22×D4—221no—
348C22×D4—441no—
349C23×C4—111no—
350#135—222no—
351#135—222no—
352C2×Q16C22×D1111yescharacteristic
353C2×SD16—221no—
354C2×D8—111no—
355C2×D8—111no—
356C2×D8—222no—
357C2×D8—222no—
358C2×D8—221no—
359C2×D8C22×D1111yescharacteristic
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—222no—
366C22×C8—222no—
367C22×C8C22×D1111yescharacteristic
368#123—441no—
369C22⋊Q8—21no—
370C22⋊Q8—221no—
371#121—21no—
372#121—221no—
373#121—221no—
374#121—221no—
375#121—221no—
376#121—221no—
377#121—441no—
378#121—441no—
379#120—441no—
380C4×D4—441no—
381C4×D4—441no—
382#117—221no—
383C2×C4⋊C4—221no—
384C2×C22⋊C4—441no—
385SD32—22no—
386SD32—222no—
387D16—222no—
388D16—222no—
389M32—114no—
390M32—222no—
391M32—222no—
392M32—222no—
393C2×C16—22no—
394C2×C16—111no—
395C2×C16—111no—
396C2×C16—222no—
397C2×C16C22×D1111yescharacteristic
398C2×C16C22×D1111yescharacteristic
399#107—111no—
400#107—111no—
401#107—221no—
402#107C22×D1111yescharacteristic
403#107C22×D1111yescharacteristic
404#106—221no—
405#103—21no—
406#103—221no—
407#102—21no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C2×C11—22no—
414C2×C11—161no—
415C2×C11C2×#46611yescharacteristic
416C2×C11C2×#50911yescharacteristic
417C2×C11#341411yescharacteristic
418D11—22no—
419D11—41no—
420D11—161no—
421D11—161no—
422C24—111no—
423C24—441no—
424#41—442no—
425#41—442no—
426C2×Q8—21no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—884no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4D4×D1111yescharacteristic
451Q16—21no—
452Q16—21no—
453SD16—442no—
454D8—21no—
455D8—21no—
456D8—221no—
457D8—221no—
458D8—221no—
459D8—221no—
460D8—442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—111no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—111no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8D4×D1111yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—441no—
491C16—21no—
492C16—112no—
493C16—221no—
494C16D4×D1112yescomplemented
495C11#3360511yescharacteristic, complemented, Sylow
496C23—41no—
497C23—111no—
498C23—111no—
499C23—222no—
500C23—222no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—882no—
505C23—882no—
506C23—882no—
507C23D8×D1111yescharacteristic
508Q8—41no—
509Q8—41no—
510D4—41no—
511D4—41no—
512D4—82no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—882no—
518D4—882no—
519D4—882no—
520D4—882no—
521D4—882no—
522D4—882no—
523D4—882no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—111no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—111no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—882no—
541C2×C4—882no—
542C2×C4D8×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C8—21no—
545C8—112no—
546C8—221no—
547C8C2×D4×D1111yescharacteristic
548C8#41×D1111yescharacteristic
549C22—21no—
550C22—21no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—112no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22—444no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—1764no—
568C22#1062252712yescomplemented
569C22C2×D8×D1111yescharacteristic
570C4—21no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—112no—
575C4—221no—
576C4—881no—
577C4—881no—
578C4D11×#12111yescharacteristic
579C4D11×#13511yescharacteristic
580C2—22no—
581C2—161no—
582C2—222no—
583C2—441no—
584C2—1761no—
585C2—1761no—
586C2D11×#46611yescharacteristic
587C2C2×#1062252711yescharacteristic
588C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
hypercenter#2217D11
hypocenterC11#33605
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C22×#66862C2semidirect
3. #13078199C2semidirect
4. D11×#466C2semidirect
5. #13070732C2semidirect
6. #13070726C2semidirect
7. #13070720C2semidirect
8. #13070718C2semidirect
9. #13070714C2semidirect
10. #13070702C2semidirect
11. #13070700C2semidirect
12. #13070403C2semidirect
13. #13070330C2semidirect
14. #13070327C2semidirect
15. C11×#2217C2semidirect
21. C2×C11×SD32C22semidirect
22. C22×C11×C16C22semidirect
23. C11×#467C22semidirect
25. #10622801C22semidirect
26. C2×#66892C22semidirect
28. C2×#66890C22semidirect
30. #10622728C22semidirect
31. C22×C11⋊C16C22semidirect
35. C2×D176C22semidirect
39. C2×#66862C22semidirect
40. C2×#66862C22semidirect
42. #10622496C22semidirect
49. C11×#367C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. #10622202C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. #10622142C22semidirect
57. #10622129C22semidirect
58. #10622129C22semidirect
59. #10622128C22semidirect
60. #10622127C22semidirect
127. #66862D4semidirect
199. C11×C16C2×D4semidirect
201. C11⋊C16C2×D4semidirect
211. #2217D11semidirect
277. C2×SD32C2×D11semidirect
286. C22×C16C2×D11semidirect
288. #467C2×D11semidirect
304. #367C2×D11semidirect
308. #358C2×D11semidirect
314. #357C2×D11semidirect
320. C22×C11#509semidirect
494. C16D4×D11semidirect
495. C11#33605semidirect
568. C22#10622527semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
C22×#668622
#130781992
D11×#4662
#130707322
#130707262
#130707202
#130707182
#130707142
#130707022
#130707002
#130704032
#130703302
#130703272
C11×#22172
#3360511