Finite Group Databasebeta

← #14910345

Subgroups — #14910345

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
2#13080332C211yesmaximal, characteristic, complemented
3D8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13070870C211yesmaximal, characteristic, complemented
5#13070729C211yesmaximal, characteristic, complemented
6#13070726C211yesmaximal, characteristic, complemented
7#13070659C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11#13070539C211yesmaximal, characteristic, complemented
12#13070536C211yesmaximal, characteristic, complemented
13D16×Dic11C211yesmaximal, characteristic, complemented
14#13070446C211yesmaximal, characteristic, complemented
15C2×C11×#509C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17C22×C11×D8C2211yescharacteristic
18#10623355—21no—
19D4×C22⋊D11—21no—
20C2×#66965C2211yescharacteristic, complemented
21C2×D8×D11C2211yescharacteristic
22C11×#509—24no—
23C2×C11×SD32C2211yescharacteristic
24C2×C11×SD32C2211yescharacteristic, complemented
25C2×C11×D16C2211yescharacteristic
26C2×C11×D16C2211yescharacteristic, complemented
27C2×C11×M32C2211yescharacteristic, complemented
28#10622852—21no—
29#10622830—21no—
30#10622801C2211yescharacteristic, complemented
31#10622794C2211yescharacteristic, complemented
32C2×#66892C2211yescharacteristic, complemented
33#10622786—21no—
34#10622775—21no—
35#10622770C2211yescharacteristic
36#10622769—21no—
37#10622764C2211yescharacteristic
38#10622763—21no—
39D8×Dic11C2211yescharacteristic
40D8×Dic11C2211yescharacteristic, complemented
41C2×#66891C2211yescharacteristic
42C2×#66891C2211yescharacteristic, complemented
43C2×#66890C2211yescharacteristic, complemented
44#10622729C2211yescharacteristic, complemented
45#10622728C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47#10622524—24no—
48C2×#66864C2211yescharacteristic, complemented
49C2×#66862C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622142C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59Dic11⋊C16C2211yescharacteristic, complemented
60C16×Dic11C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C22×D4×C11—21no—
63C22×C22⋊D11—41no—
64C2×#4341—21no—
65C2×D4×D11—21no—
66C11×#135—22no—
67C11×#135—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8—22no—
71C2×C11×D8—21no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77#67006—41no—
78#66999—21no—
79#66997—21no—
80C2×#4326—21no—
81#66993—21no—
82#66992—41no—
83#66992—41no—
84#66991—21no—
85#66990—41no—
86#66988—41no—
87D4×Dic11—21no—
88D4×Dic11—21no—
89C2×#4324—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92#66983—21no—
93#66982—41no—
94C4×C22⋊D11D411yescharacteristic
95#66977—21no—
96C2×Dic11⋊C4—41no—
97#66965—22no—
98#66965—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×Dic44C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C11×D16—22no—
107C11×D16D414yescomplemented
108C11×M32—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66892—41no—
117#66891—22no—
118#66891—41no—
119#66890—22no—
120#66885—21no—
121(C2×D11)⋊C8D411yescharacteristic
122#66882C2311yescharacteristic
123#66882C2311yescharacteristic
124#66880—21no—
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129#66864—22no—
130#66862—22no—
131#33838—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C11×#41—42no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11—84no—
153C2×C22⋊D11D811yescharacteristic
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11—41no—
157#4341—42no—
158#4341—81no—
159D4×D11—42no—
160D4×D11—81no—
161C2×D44—21no—
162C2×C4×D11C2×D411yescharacteristic
163C2×Dic22—21no—
164C11×Q16—21no—
165C11×Q16—21no—
166C11×SD16—42no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—21no—
171C11×D8—42no—
172C11×D8C2×D412yes—
173C11×D8C2×D412yescomplemented
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2411yescharacteristic
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11D811yescharacteristic
183#4326—81no—
184#4324—42no—
185#4323—42no—
186#4323—81no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196Dic11⋊C4D811yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200Dic44—21no—
201Dic44—21no—
202D88—21no—
203D88—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C2×#509—111no—
211C2×#509D1111yescharacteristic, complemented
212#3283—111no—
213D4×D8—111no—
214#2248—111no—
215#2220—111no—
216#2220—111no—
217#2208—111no—
218#2206—111no—
219#2187—111no—
220#2187—111no—
221#2186—111no—
222#2186—111no—
223C4×D16—111no—
224#2169—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—161no—
231C23×C11C2×D811yescharacteristic
232C22×D11—41no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—161no—
236C22×D11C2×D811yescharacteristic
237Q8×C11—41no—
238Q8×C11—41no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—82no—
246D4×C11—82no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—22no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—82no—
259C22⋊D11—161no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—82no—
264C2×Dic11—82no—
265C2×Dic11—82no—
266C2×Dic11C2×D811yescharacteristic
267C2×Dic11C2×D811yescharacteristic
268C2×Dic11C2×D811yescharacteristic
269D44—41no—
270D44—41no—
271C4×D11—21no—
272C4×D11—21no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—21no—
276C8×C11C22×D411yescharacteristic
277C8×C11H(5,𝔽2)11yescharacteristic
278C11⋊C8—21no—
279C11⋊C8—21no—
280C2×#135—111no—
281C2×#135C2×D1111yescharacteristic, complemented
282C22×D8—111no—
283C22×D8C2×D1111yescharacteristic
284#547—221no—
285D42—221no—
286#509—24no—
287#509—224no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32C2×D1111yescharacteristic
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16C2×D1111yescharacteristic
296C2×D16C2×D1111yescharacteristic, complemented
297C2×M32—111no—
298C2×M32C2×D1111yescharacteristic, complemented
299#494—111no—
300#493—111no—
301#467—111no—
302#467—111no—
303#466—111no—
304#466—111no—
305#461—221no—
306#459—221no—
307#452—221no—
308#452—221no—
309#447—221no—
310#447—221no—
311C4×D8—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—
324C4×C16—111no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—164no—
338C22×C11C22×D811yescharacteristic
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—164no—
346C4×C11—21no—
347C4×C11—81no—
348C4×C11D4211yescharacteristic
349C4×C11#57611yescharacteristic
350Dic11—21no—
351Dic11—21no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11#50912yescomplemented
356C2×#41—21no—
357C2×#41—221no—
358C22×D4—21no—
359C22×D4—221no—
360C22×D4—441no—
361#135—22no—
362#135—41no—
363#135—222no—
364#135—441no—
365C2×Q16—111no—
366C2×Q16—221no—
367C2×Q16C22×D1111yescharacteristic
368C2×SD16—21no—
369C2×SD16—221no—
370C2×D8—22no—
371C2×D8—21no—
372C2×D8—41no—
373C2×D8—111no—
374C2×D8—221no—
375C2×D8—221no—
376C2×D8—222no—
377C2×D8—441no—
378C2×D8C22×D1111yescharacteristic
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383C4⋊Q8—221no—
384#127—221no—
385#123—441no—
386#123—441no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389#121—221no—
390#121—221no—
391#121—441no—
392#121—441no—
393#120—441no—
394#120—441no—
395C4×D4—111no—
396C4×D4—221no—
397C4×D4—221no—
398C2×C4⋊C4—441no—
399SD32—22no—
400SD32—22no—
401SD32—222no—
402SD32—222no—
403SD32—441no—
404SD32—441no—
405D16—22no—
406D16—222no—
407D16C22⋊D1114yescomplemented
408M32—22no—
409M32—222no—
410C2×C16—111no—
411C2×C16—111no—
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×C8—111no—
426C2×C11—41no—
427C2×C11—82no—
428C2×C11—82no—
429C2×C11—161no—
430C2×C11D4×D811yescharacteristic
431C2×C11C2×#50911yescharacteristic
432C2×C11#341611yescharacteristic
433D11—41no—
434D11—161no—
435C24—41no—
436C24—441no—
437#41—42no—
438#41—81no—
439#41—442no—
440#41—881no—
441C2×Q8—21no—
442C2×Q8—221no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—42no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—81no—
450C2×D4—111no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—442no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—881no—
460C2×D4—884no—
461C22×C4—41no—
462C22×C4—111no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4D4×D1111yescharacteristic
467Q16—21no—
468Q16—21no—
469Q16—221no—
470Q16—221no—
471Q16—881no—
472SD16—42no—
473SD16—442no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—42no—
479D8—221no—
480D8—221no—
481D8—442no—
482D8—881no—
483D8C2×C22⋊D1112yes—
484D8C2×C22⋊D1112yescomplemented
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—111no—
488C2×C8—111no—
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—
498C4⋊C4—441no—
499C4⋊C4—441no—
500C22⋊C4—111no—
501C22⋊C4—111no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—111no—
509C16—21no—
510C16—221no—
511C16—221no—
512C16C2×C22⋊D1112yescomplemented
513C11#3383811yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—41no—
517C23—82no—
518C23—82no—
519C23—111no—
520C23—161no—
521C23—441no—
522C23—882no—
523C23—882no—
524C23—1761no—
525C23D8×D1111yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—441no—
529Q8—441no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—82no—
538D4—222no—
539D4—441no—
540D4—441no—
541D4—882no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—1761no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—111no—
552C2×C4—111no—
553C2×C4—111no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—882no—
560C2×C4—882no—
561C2×C4—882no—
562C2×C4D8×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C8—21no—
565C8—221no—
566C8—221no—
567C8#6703711yescharacteristic
568C8C22×C22⋊D1111yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—42no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—164no—
582C22—221no—
583C22—221no—
584C22—221no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22—1764no—
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—81no—
592C4—112no—
593C4—221no—
594C4—221no—
595C4—881no—
596C4—881no—
597C4—881no—
598C4#1062328811yescharacteristic
599C4D4×C22⋊D1111yescharacteristic
600C2—41no—
601C2—82no—
602C2—82no—
603C2—161no—
604C2—441no—
605C2—1761no—
606C2D8×C22⋊D1111yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33838
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. #13080332C2semidirect
3. D8×C22⋊D11C2semidirect
4. #13070870C2semidirect
5. #13070729C2semidirect
6. #13070726C2semidirect
7. #13070659C2semidirect
8. #13070649C2semidirect
9. #13070545C2semidirect
10. #13070543C2semidirect
11. #13070539C2semidirect
12. #13070536C2semidirect
13. D16×Dic11C2semidirect
14. #13070446C2semidirect
15. C2×C11×#509C2semidirect
16. C2×C11×#135C22semidirect
20. C2×#66965C22semidirect
24. C2×C11×SD32C22semidirect
26. C2×C11×D16C22semidirect
27. C2×C11×M32C22semidirect
30. #10622801C22semidirect
31. #10622794C22semidirect
32. C2×#66892C22semidirect
40. D8×Dic11C22semidirect
42. C2×#66891C22semidirect
43. C2×#66890C22semidirect
44. #10622729C22semidirect
48. C2×#66864C22semidirect
49. C2×#66862C22semidirect
50. #10622202C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622142C22semidirect
58. #10622141C22semidirect
59. Dic11⋊C16C22semidirect
60. C16×Dic11C22semidirect
107. C11×D16D4semidirect
173. C11×D8C2×D4semidirect
207. C11×C16C2×D4semidirect
211. C2×#509D11semidirect
281. C2×#135C2×D11semidirect
293. C2×SD32C2×D11semidirect
296. C2×D16C2×D11semidirect
298. C2×M32C2×D11semidirect
355. Dic11#509semidirect
407. D16C22⋊D11semidirect
484. D8C2×C22⋊D11semidirect
512. C16C2×C22⋊D11semidirect
513. C11#33838semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
#130803322
D8×C22⋊D112
#130708702
#130707292
#130707262
#130706592
#130706492
#130705452
#130705432
#130705392
#130705362
D16×Dic112
#130704462
C2×C11×#5092
#3383811