Finite Group Databasebeta

← #14910245

Subgroups — #14910245

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13080356C211yesmaximal, characteristic, complemented
4#13080291C211yesmaximal, characteristic, complemented
5#13070726C211yesmaximal, characteristic, complemented
6#13070699C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070653C211yesmaximal, characteristic, complemented
9#13070543C211yesmaximal, characteristic, complemented
10#13070536C211yesmaximal, characteristic, complemented
11#13070531C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070482C211yesmaximal, characteristic, complemented
14#13070443C211yesmaximal, characteristic, complemented
15C11×#2250C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic, complemented
17C2×#66965C2211yescharacteristic, complemented
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623248—21no—
21#10623208—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×SD32C2211yescharacteristic, complemented
24C2×C11×D16C2211yescharacteristic, complemented
25C2×C11×D16C2211yescharacteristic, complemented
26C11×#495C2211yescharacteristic, complemented
27C11×#493C2211yescharacteristic
28#10622801C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30#10622786—21no—
31#10622783—21no—
32#10622770C2211yescharacteristic
33#10622770C2211yescharacteristic
34#10622770C2211yescharacteristic, complemented
35#10622769—21no—
36#10622769—21no—
37C2×#66891C2211yescharacteristic, complemented
38C2×#66891C2211yescharacteristic, complemented
39C2×#66890C2211yescharacteristic
40#10622685—21no—
41#10622667—21no—
42D11×SD32—24no—
43#10622524—24no—
44C2×#66864C2211yescharacteristic
45C2×#66862C2211yescharacteristic, complemented
46C2×C16×D11C2211yescharacteristic, complemented
47C4×Dic44C2211yescharacteristic, complemented
48C4×D88C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×#346C2211yescharacteristic, complemented
51#10622202C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622200C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57(C2×D11)⋊C16C2211yescharacteristic, complemented
58#10622142C2211yescharacteristic, complemented
59#10622141C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×#4341—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C2×D4×D11—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×SD16—21no—
68C2×C11×D8—21no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C11×#127—21no—
73C11×#124—21no—
74#66999—21no—
75C2×#4326—21no—
76#66991—21no—
77#66991—21no—
78#66991—21no—
79#66991—41no—
80#66990—41no—
81#66990—41no—
82C2×#4324—21no—
83C2×#4323—21no—
84C2×#4323—21no—
85Q16×D11—22no—
86Q16×D11—41no—
87#66965—22no—
88#66965—41no—
89D8×D11—22no—
90D8×D11—22no—
91D8×D11—41no—
92D8×D11—41no—
93C2×Dic44C2311yescharacteristic
94C2×D88C2311yescharacteristic
95C2×C8×D11C2311yescharacteristic
96C2×C8×D11C2311yescharacteristic
97#66938—41no—
98#66937—41no—
99(C22⋊D11)⋊C4—41no—
100#66931—41no—
101C4×D44—21no—
102C4×D44D411yescharacteristic
103C4×Dic22—21no—
104C11×SD32—22no—
105C11×SD32—41no—
106C11×D16—22no—
107C11×D16—41no—
108C2×C11×C16C2311yescharacteristic
109C2×C11×C16C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115#66892—22no—
116#66891—22no—
117#66891—22no—
118#66890—22no—
119#66885—21no—
120(C2×D11)⋊C8D411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122#66882C2311yescharacteristic
123#66882C2311yescharacteristic
124#66880—21no—
125C2×C11⋊C16C2311yescharacteristic
126C2×C11⋊C16C2311yescharacteristic
127C4⋊(C11⋊C8)D411yescharacteristic
128#66864D414yescomplemented
129#66862—22no—
130C16×D11—22no—
131#33831—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C22×Dic11—41no—
147Q8×D11—42no—
148Q8×D11—81no—
149#4341—42no—
150#4341—81no—
151D4×D11—42no—
152D4×D11—42no—
153D4×D11—81no—
154D4×D11—81no—
155D4×D11—84no—
156C2×D44—21no—
157C2×D44D811yescharacteristic
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×Dic22—21no—
163C2×Dic22—41no—
164C11×Q16—21no—
165C11×Q16—21no—
166C11×SD16—81no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—21no—
171C11×D8—21no—
172C11×D8—21no—
173C11×D8—81no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2411yescharacteristic
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C42×C11C2×D411yescharacteristic
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182#4326—42no—
183#4324—42no—
184#4323—42no—
185#4323—42no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4D811yescharacteristic
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11D811yescharacteristic
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198Dic44—21no—
199Dic44C2×D412yescomplemented
200D88—21no—
201D88C2×D412yes—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C2×#509—111no—
211C22×SD32—111no—
212#3285—111no—
213D4×D8—111no—
214#2250D1111yescharacteristic, complemented
215#2220—111no—
216#2215—111no—
217#2210—111no—
218#2207—111no—
219#2187—111no—
220#2186—111no—
221#2185—111no—
222#2184—111no—
223#2175—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C22×D11—41no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—161no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236C22×D11C2×D811yescharacteristic
237Q8×C11—41no—
238Q8×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—82no—
246D4×C11—161no—
247C2×C4×C11—41no—
248C2×C4×C11C2×D811yescharacteristic
249C2×C4×C11C2×D811yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C22⋊D11—82no—
252C22⋊D11—82no—
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—82no—
261C2×Dic11C2×D811yescharacteristic
262C2×Dic11C2×D811yescharacteristic
263D44—22no—
264D44—22no—
265D44—41no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—82no—
271C4×D11—82no—
272Dic22—22no—
273Dic22—41no—
274Dic22—82no—
275C8×C11—21no—
276C8×C11C22×D411yescharacteristic
277C8×C11H(5,𝔽2)11yescharacteristic
278C11⋊C8—21no—
279C11⋊C8—21no—
280C2×#135—111no—
281C22×Q16—111no—
282C22×D8—111no—
283C22×D8—111no—
284#548—221no—
285D42—221no—
286#509—224no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—224no—
292C2×SD32C2×D1111yescharacteristic, complemented
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16C2×D1111yescharacteristic, complemented
296C2×D16C2×D1111yescharacteristic, complemented
297C2×M32—111no—
298C22×C16—111no—
299#495C2×D1111yescharacteristic, complemented
300#493C2×D1111yescharacteristic
301#467—111no—
302#466—111no—
303#466—111no—
304#466—111no—
305#464—221no—
306#459—221no—
307#452—221no—
308#448—221no—
309#447—221no—
310#447—221no—
311C4×Q16—111no—
312C4×D8—111no—
313C8×D4—111no—
314#366—111no—
315C4⋊C16—111no—
316#358—111no—
317#358—111no—
318#357—111no—
319#357—111no—
320#357—111no—
321#357—111no—
322C22⋊C16—111no—
323C22⋊C16—111no—
324#346C2×D1111yescharacteristic, complemented
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—42no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—164no—
344C2×D11—164no—
345C2×D11#50912yescomplemented
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—81no—
349C4×C11D4211yescharacteristic
350C4×C11#57611yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356C2×#41—221no—
357C22×Q8—221no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—441no—
361#135—222no—
362#135—441no—
363C2×Q16—111no—
364C2×Q16—221no—
365C2×Q16—222no—
366C2×Q16—441no—
367C2×Q16C22×D1111yescharacteristic
368C2×SD16—21no—
369C2×SD16—221no—
370C2×D8—21no—
371C2×D8—111no—
372C2×D8—221no—
373C2×D8—221no—
374C2×D8—222no—
375C2×D8—222no—
376C2×D8—441no—
377C2×D8—441no—
378C2×D8C22×D1111yescharacteristic
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#127—21no—
384#124—21no—
385#124—441no—
386C22⋊Q8—221no—
387C22⋊Q8—441no—
388#121—221no—
389#121—221no—
390#121—221no—
391#121—441no—
392#121—441no—
393#120—441no—
394#120—441no—
395C4×Q8—221no—
396C4×D4—111no—
397C4×D4—221no—
398C4×D4—441no—
399SD32—22no—
400SD32—41no—
401SD32—114no—
402SD32—222no—
403SD32—222no—
404SD32—222no—
405D16—22no—
406D16—41no—
407D16—222no—
408M32—222no—
409C2×C16—111no—
410C2×C16—111no—
411C2×C16—222no—
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107—111no—
415#107—111no—
416C4⋊C8—111no—
417#103—221no—
418#103—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C4×C8C22×D1111yescharacteristic
426C2×C11—161no—
427C2×C11—161no—
428C2×C11—161no—
429C2×C11D4×D811yescharacteristic
430C2×C11C2×#50911yescharacteristic
431C2×C11#341611yescharacteristic
432D11—22no—
433D11—41no—
434D11—82no—
435C24—441no—
436C24—441no—
437#41—442no—
438#41—881no—
439C2×Q8—21no—
440C2×Q8—221no—
441C2×Q8—441no—
442C2×Q8—442no—
443C2×Q8—881no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—442no—
454C2×D4—442no—
455C2×D4—441no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—881no—
460C2×D4—881no—
461C2×D4—884no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4—441no—
467Q16—21no—
468Q16—21no—
469Q16—112no—
470Q16—221no—
471Q16—442no—
472SD16—81no—
473SD16—442no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—21no—
479D8—21no—
480D8—81no—
481D8—112no—
482D8—221no—
483D8—442no—
484D8—442no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8D4×D1111yescharacteristic
492C2×C8C23×D1111yescharacteristic
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—111no—
501C22⋊C4—111no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C42—441no—
508C42D4×D1111yescharacteristic
509C16—21no—
510C16—221no—
511C16—221no—
512C16D4×D1112yescomplemented
513C11#3383111yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—41no—
517C23—111no—
518C23—111no—
519C23—441no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23—882no—
524C23—1761no—
525C23—1761no—
526Q8—41no—
527Q8—41no—
528Q8—222no—
529Q8—441no—
530Q8—882no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—82no—
538D4—161no—
539D4—222no—
540D4—222no—
541D4—441no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—882no—
547D4—882no—
548C2×C4—41no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—882no—
559C2×C4—882no—
560C2×C4—882no—
561C2×C4D8×D1111yescharacteristic
562C2×C4D8×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C8—21no—
565C8—221no—
566C8—221no—
567C8C2×D4×D1111yescharacteristic
568C8#6703711yescharacteristic
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—112no—
579C22—221no—
580C22—221no—
581C22—221no—
582C22—221no—
583C22—221no—
584C22—442no—
585C22—881no—
586C22—881no—
587C22—1764no—
588C22—1764no—
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—21no—
592C4—81no—
593C4—221no—
594C4—221no—
595C4—442no—
596C4—881no—
597C4—881no—
598C4#1062324811yescharacteristic
599C4#1062328811yescharacteristic
600C2—161no—
601C2—161no—
602C2—161no—
603C2—222no—
604C2—441no—
605C2—882no—
606C2#1308029111yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2250C2
socleC22×C11C22×D8
hypercenter#2250D11
hypocenterC11#33831
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080356C2semidirect
4. #13080291C2semidirect
5. #13070726C2semidirect
6. #13070699C2semidirect
7. #13070668C2semidirect
8. #13070653C2semidirect
9. #13070543C2semidirect
10. #13070536C2semidirect
11. #13070531C2semidirect
12. #13070526C2semidirect
13. #13070482C2semidirect
14. #13070443C2semidirect
15. C11×#2250C2semidirect
16. C2×Q16×D11C22semidirect
17. C2×#66965C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×SD32C22semidirect
24. C2×C11×D16C22semidirect
25. C2×C11×D16C22semidirect
26. C11×#495C22semidirect
28. #10622801C22semidirect
34. #10622770C22semidirect
37. C2×#66891C22semidirect
38. C2×#66891C22semidirect
45. C2×#66862C22semidirect
46. C2×C16×D11C22semidirect
47. C4×Dic44C22semidirect
50. C11×#346C22semidirect
51. #10622202C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. #10622200C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. (C2×D11)⋊C16C22semidirect
58. #10622142C22semidirect
59. #10622141C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
128. #66864D4semidirect
199. Dic44C2×D4semidirect
207. C11×C16C2×D4semidirect
214. #2250D11semidirect
292. C2×SD32C2×D11semidirect
293. C2×SD32C2×D11semidirect
295. C2×D16C2×D11semidirect
296. C2×D16C2×D11semidirect
299. #495C2×D11semidirect
324. #346C2×D11semidirect
345. C2×D11#509semidirect
512. C16D4×D11semidirect
513. C11#33831semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×D11×SD322
#130803562
#130802912
#130707262
#130706992
#130706682
#130706532
#130705432
#130705362
#130705312
#130705262
#130704822
#130704432
C11×#22502
#3383111