Finite Group Databasebeta

← #14908076

Subgroups — #14908076

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622531C211yesmaximal, characteristic, complemented
2C2×#10622527C211yesmaximal, characteristic
3D11×#495C211yesmaximal, characteristic, complemented
4C4×#66972C211yesmaximal, characteristic, complemented
5#13070680C211yesmaximal, characteristic, complemented
6#13070678C211yesmaximal, characteristic, complemented
7#13070676C211yesmaximal, characteristic, complemented
8#13070674C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070670C211yesmaximal, characteristic, complemented
11#13070668C211yesmaximal, characteristic, complemented
12#13070370C211yesmaximal, characteristic, complemented
13#13070334C211yesmaximal, characteristic, complemented
14#13070330C211yesmaximal, characteristic, complemented
15C11×#2211C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic
18C2×SD16×D11—21no—
19C2×D8×D11C2211yescharacteristic
20D11×#124—21no—
21C4×#4343—21no—
22C2×C11×Q32C2211yescharacteristic, complemented
23C2×C11×SD32C2211yescharacteristic
24C11×#495C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic, complemented
26#10622804C2211yescharacteristic
27Q16×Dic11C2211yescharacteristic, complemented
28C2×#66893C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic, complemented
31#10622781—21no—
32#10622768C2211yescharacteristic
33C2×#66890C2211yescharacteristic
34#10622672—21no—
35C4×#4325—21no—
36#10622531—24no—
37#10622527—24no—
38C2×#66864C2211yescharacteristic, complemented
39C2×D176C2211yescharacteristic
40C2×#66862C2211yescharacteristic
41C2×#66862C2211yescharacteristic
42#10622493C2211yescharacteristic
43#10622485C2211yescharacteristic, complemented
44#10622417—21no—
45#10622401—21no—
46#10622309C2211yescharacteristic
47C4×D88C2211yescharacteristic, complemented
48C4×C8×D11C2211yescharacteristic
49C11×C4⋊C16C2211yescharacteristic, complemented
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic
52#10622202C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic
54#10622147C2211yescharacteristic
55#10622141C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×Q8×D11—21no—
63C2×D4×D11—21no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C11×#124—21no—
69C4×Q8×C11—21no—
70#67000—21no—
71Q8×Dic11—21no—
72C2×#4326—21no—
73C2×#4325—21no—
74C2×#4325—21no—
75#66989—21no—
76C2×#4324—21no—
77C2×#4323—21no—
78#66972—22no—
79#66972D414yes—
80Q16×D11—22no—
81Q16×D11—22no—
82SD16×D11—44no—
83D8×D11—22no—
84D8×D11—22no—
85C2×Dic44C2311yescharacteristic
86C2×D88C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×#4314—21no—
89C2×C8×D11D411yescharacteristic
90C2×C8×D11C2311yescharacteristic
91#66946—21no—
92#66946—41no—
93#66945—21no—
94#66945—41no—
95#66938—41no—
96#66938—41no—
97C22⋊C4×D11—41no—
98C22⋊C4×D11—41no—
99#66928—21no—
100C4×D44—21no—
101C4×D44—41no—
102C42×D11—41no—
103C42×D11D411yescharacteristic
104C11×Q32—22no—
105C11×SD32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66893—22no—
113#66892—22no—
114#66892—22no—
115#66890—22no—
116#66885—21no—
117#66882C2311yescharacteristic
118C8×Dic11D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66873—21no—
123#66872—21no—
124C4×C11⋊C8D411yescharacteristic
125#66864—22no—
126D176—22no—
127#66862—22no—
128#66862—22no—
129#33584—111nomaximal, Sylow
130C23×D11—41no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×D4×C11—21no—
134C2×C22⋊D11—41no—
135#4343—24no—
136#4343—42no—
137Q8×D11—42no—
138Q8×D11—42no—
139D4×D11—42no—
140D4×D11—42no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—41no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11D811yescharacteristic
149C2×C4×D11D811yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×Dic22—21no—
152C2×Dic22—41no—
153C11×Q16—21no—
154C11×Q16—21no—
155C11×Q16—21no—
156C11×Q16C2×D412yes—
157C11×SD16—42no—
158C11×D8—21no—
159C11×D8—21no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C4⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C42×C11—41no—
167C42×C11C2×D411yescharacteristic
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170#4326—42no—
171#4325—24no—
172#4325—42no—
173#4324—42no—
174#4323—42no—
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—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182C4⋊Dic11—21no—
183C4⋊Dic11—41no—
184C4×Dic11—41no—
185C4×Dic11—41no—
186C4×Dic11D811yescharacteristic
187C4×Dic11D811yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191Dic44—21no—
192Dic44—21no—
193D88—21no—
194D88—21no—
195D88—21no—
196D88C2×D412yes—
197#4314—42no—
198C8×D11—22no—
199C8×D11C2×D412yes—
200C8×D11#4112yes—
201C11×C16—21no—
202C11×C16—21no—
203C11⋊C16—21no—
204C11⋊C16—21no—
205C2×#510—111no—
206C2×#509—111no—
207C2×#495—111no—
208C4×#135—111no—
209#2211—111no—
210#2211—111no—
211#2211—111no—
212#2211D1111yescharacteristic, complemented
213#2210—111no—
214#2210—111no—
215#2210—111no—
216#2210—111no—
217#2150—111no—
218#2141—111no—
219#2140—111no—
220C23×C11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—82no—
224C22×D11—82no—
225C22×D11—82no—
226C22×D11C2×D811yescharacteristic
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C2×D811yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—82no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11C2×D811yescharacteristic
243C2×Dic11C2×D811yescharacteristic
244C2×Dic11C2×D811yescharacteristic
245D44—22no—
246D44—44no—
247D44—41no—
248D44—41no—
249D44—41no—
250C4×D11—41no—
251C4×D11—41no—
252C4×D11—44no—
253C4×D11—82no—
254C4×D11—82no—
255C4×D11—82no—
256C4×D11#12112yes—
257C4×D11AGL(1,ℤ/8)12yes—
258Dic22—41no—
259Dic22—41no—
260Dic22—82no—
261C8×C11—21no—
262C8×C11C22×D411yescharacteristic
263C8×C11C2×#4111yescharacteristic
264C11⋊C8—21no—
265C11⋊C8#12112yes—
266C2×#135—111no—
267C22×Q16—111no—
268C22×SD16—221no—
269C22×D8—111no—
270C2×#124—221no—
271C4×#41—221no—
272#510—224no—
273#509—224no—
274C2×Q32—111no—
275C2×Q32C2×D1111yescharacteristic, complemented
276C2×SD32—111no—
277C2×SD32—111no—
278C2×SD32—111no—
279C2×SD32C2×D1111yescharacteristic
280C2×D16—111no—
281C2×D16—111no—
282C2×M32—111no—
283C2×M32—111no—
284#495—111no—
285#495—111no—
286#495—111no—
287#495—221no—
288#495—221no—
289#495C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×Q16C2×D1111yescharacteristic, complemented
292C4×SD16—221no—
293C4×SD16—221no—
294C4×D8—111no—
295C4×D8—111no—
296#427—111no—
297#416—221no—
298C2×C4×C8—111no—
299C4⋊C16—111no—
300C4⋊C16—111no—
301C4⋊C16—111no—
302C4⋊C16C2×D1111yescharacteristic, complemented
303#358—111no—
304#358—111no—
305#358—111no—
306#358C2×D1111yescharacteristic, complemented
307#357—111no—
308#357—111no—
309#357—111no—
310#357C2×D1111yescharacteristic
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C22×D811yescharacteristic
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—42no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—164no—
324C2×D11#45912yes—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
332Dic11—21no—
333Dic11—21no—
334Dic11—81no—
335Dic11—81no—
336Dic11#45912yes—
337C2×#41—221no—
338C22×Q8—221no—
339C22×D4—221no—
340#135—114no—
341#135—222no—
342C2×Q16—111no—
343C2×Q16—222no—
344C2×Q16—222no—
345C2×Q16—221no—
346C2×Q16C22×D1111yescharacteristic
347C2×Q16C22×D1111yescharacteristic
348C2×SD16—21no—
349C2×SD16—221no—
350C2×SD16—221no—
351C2×SD16—221no—
352C2×SD16—221no—
353C2×SD16—444no—
354C2×D8—111no—
355C2×D8—111no—
356C2×D8—222no—
357C2×D8—222no—
358C2×D8—221no—
359C2×D8C22×D1111yescharacteristic
360C22×C8—111no—
361C22×C8—111no—
362#124—21no—
363#124—221no—
364#124—221no—
365#124—221no—
366#124—441no—
367#124—441no—
368C4×Q8—21no—
369C4×Q8—221no—
370C4×D4—221no—
371C4×D4—221no—
372C4×D4—441no—
373C4×D4—441no—
374#117—221no—
375#117—441no—
376C2×C22⋊C4—441no—
377C2×C22⋊C4—441no—
378C2×C42—111no—
379C2×C42—441no—
380Q32—22no—
381Q32—222no—
382SD32—22no—
383SD32—222no—
384SD32—222no—
385SD32—222no—
386D16—222no—
387D16—222no—
388M32—222no—
389M32—222no—
390C2×C16—111no—
391C2×C16—111no—
392C2×C16C22×D1111yescharacteristic
393C2×C16C22×D1111yescharacteristic
394#107—111no—
395#107C22×D1111yescharacteristic
396#106—221no—
397#103—21no—
398#103—221no—
399#102—221no—
400#102—221no—
401C4×C8—111no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8C22×D1111yescharacteristic
405C2×C11—161no—
406C2×C11C2×#45911yescharacteristic
407C2×C11#341411yescharacteristic
408C2×C11#341411yescharacteristic
409D11—22no—
410D11—82no—
411D11—161no—
412C24—441no—
413#41—224no—
414#41—442no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—221no—
418C2×Q8—441no—
419C2×Q8—442no—
420C2×Q8—442no—
421C2×D4—21no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—441no—
425C2×D4—442no—
426C2×D4—442no—
427C2×D4—441no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4—441no—
434C22×C4—441no—
435Q16—21no—
436Q16—21no—
437Q16—21no—
438Q16—221no—
439Q16—221no—
440Q16—442no—
441Q16D4×D1112yes—
442SD16—42no—
443SD16—224no—
444SD16—442no—
445SD16—442no—
446SD16—442no—
447D8—21no—
448D8—21no—
449D8—112no—
450D8—221no—
451D8—221no—
452D8—221no—
453D8—442no—
454C2×C8—111no—
455C2×C8—112no—
456C2×C8—112no—
457C2×C8—111no—
458C2×C8—222no—
459C2×C8D4×D1111yescharacteristic
460C2×C8C23×D1111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—221no—
464C4⋊C4—441no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C42—41no—
477C42—111no—
478C42—111no—
479C42—111no—
480C42—441no—
481C42—441no—
482C42D4×D1111yescharacteristic
483C16—21no—
484C16—21no—
485C16—221no—
486C16—221no—
487C11#3358411yescharacteristic, complemented, Sylow
488C23—41no—
489C23—111no—
490C23—441no—
491C23—441no—
492C23—882no—
493C23—882no—
494C23—882no—
495Q8—22no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—441no—
500Q8—441no—
501Q8—882no—
502D4—41no—
503D4—41no—
504D4—222no—
505D4—444no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—882no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—111no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—444no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—882no—
524C2×C4—882no—
525C2×C4—882no—
526C2×C4D8×D1111yescharacteristic
527C2×C4D8×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C8—21no—
530C8—112no—
531C8—221no—
532C8C2×D4×D1111yescharacteristic
533C8#41×D1111yescharacteristic
534C22—81no—
535C22—81no—
536C22—81no—
537C22—112no—
538C22—221no—
539C22—221no—
540C22—442no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—1764no—
547C22C2×D8×D1111yescharacteristic
548C4—21no—
549C4—21no—
550C4—42no—
551C4—81no—
552C4—81no—
553C4—112no—
554C4—221no—
555C4—221no—
556C4—881no—
557C4—881no—
558C4D11×#12111yescharacteristic
559C4D11×AGL(1,ℤ/8)11yescharacteristic
560C2—161no—
561C2—222no—
562C2—882no—
563C2—1761no—
564C2D11×#45911yescharacteristic
565C2#1308174911yescharacteristic
566C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radicalC2×#10622527C2
hypercenter#2211D11
hypocenterC11#33584
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. C2×#10622531C2semidirect
3. D11×#495C2semidirect
4. C4×#66972C2semidirect
5. #13070680C2semidirect
6. #13070678C2semidirect
7. #13070676C2semidirect
8. #13070674C2semidirect
9. #13070672C2semidirect
10. #13070670C2semidirect
11. #13070668C2semidirect
12. #13070370C2semidirect
13. #13070334C2semidirect
14. #13070330C2semidirect
15. C11×#2211C2semidirect
22. C2×C11×Q32C22semidirect
25. C4×C11×Q16C22semidirect
27. Q16×Dic11C22semidirect
28. C2×#66893C22semidirect
30. C2×#66892C22semidirect
38. C2×#66864C22semidirect
43. #10622485C22semidirect
47. C4×D88C22semidirect
49. C11×C4⋊C16C22semidirect
50. C11×#358C22semidirect
52. #10622202C22semidirect
55. #10622141C22semidirect
56. Dic11⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. #10622130C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
212. #2211D11semidirect
275. C2×Q32C2×D11semidirect
291. C4×Q16C2×D11semidirect
302. C4⋊C16C2×D11semidirect
306. #358C2×D11semidirect
487. C11#33584semidirect

Maximal subgroups

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

subgroupindex
C2×#106225312
C2×#106225272
D11×#4952
C4×#669722
#130706802
#130706782
#130706762
#130706742
#130706722
#130706702
#130706682
#130703702
#130703342
#130703302
C11×#22112
#3358411