Finite Group Databasebeta

← #14910248

Subgroups — #14910248

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×#10622527C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13080358C211yesmaximal, characteristic, complemented
4D8×D44C211yesmaximal, characteristic, complemented
5#13070882C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070703C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070656C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070542C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070529C211yesmaximal, characteristic, complemented
14#13070443C211yesmaximal, characteristic, complemented
15C11×#2175C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic, complemented
17C2×Q16×D11C2211yescharacteristic, complemented
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623107—21no—
21D4×D44—21no—
22C2×C11×SD32C2211yescharacteristic
23C4×C11×Q16C2211yescharacteristic, complemented
24C4×C11×D8C2211yescharacteristic
25C2×#66892C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic, complemented
27C2×#66891C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29#10622641—21no—
30#10622628—21no—
31#10622527—24no—
32D11×SD32—24no—
33C2×#66864C2211yescharacteristic, complemented
34C2×#66864C2211yescharacteristic, complemented
35C2×D176C2211yescharacteristic, complemented
36C2×D176C2211yescharacteristic, complemented
37C2×#66862C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic, complemented
39#10622500C2211yescharacteristic, complemented
40#10622496C2211yescharacteristic
41#10622496C2211yescharacteristic
42#10622496C2211yescharacteristic, complemented
43#10622423—21no—
44#10622419—21no—
45#10622386—21no—
46#10622386—21no—
47#10622309C2211yescharacteristic, complemented
48#10622308C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×#366C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic
53C11×#346C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×Q8×D11—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C22×D44—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C4×Q8×C11—21no—
69C4×D4×C11—21no—
70C2×#4326—21no—
71C2×#4325—21no—
72C2×#4323—21no—
73C2×#4323—21no—
74#66983—41no—
75#66972—22no—
76#66972—41no—
77Q16×D11—22no—
78Q16×D11—41no—
79D8×D11—22no—
80D8×D11—22no—
81D8×D11—41no—
82D8×D11—41no—
83C2×Dic44C2311yescharacteristic
84C2×D88—21no—
85C2×D88C2311yescharacteristic
86C2×D88C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×#4314—21no—
89C2×C8×D11C2311yescharacteristic
90C2×C8×D11C2311yescharacteristic
91#66950—21no—
92#66950—41no—
93#66948—21no—
94#66948—21no—
95#66948—21no—
96#66948—41no—
97#66935—41no—
98#66935—41no—
99#66928—21no—
100#66928—41no—
101#66927—21no—
102C4×D44—41no—
103C4×D44D411yescharacteristic
104C11×SD32D414yescomplemented
105C2×C11×C16C2311yescharacteristic
106C2×C11×C16C2311yescharacteristic
107C11×#107C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C11×#102—21no—
111C4×C8×C11C2311yescharacteristic
112#66892—22no—
113#66892—22no—
114#66891—22no—
115#66890—22no—
116(C2×D11)⋊C8D411yescharacteristic
117(C2×D11)⋊C8D411yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120#66874—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124C4⋊(C11⋊C8)D411yescharacteristic
125#66864—22no—
126#66864—41no—
127D176—22no—
128D176—41no—
129#66862—22no—
130C16×D11—22no—
131#33831—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C22×C4×C11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139#4343—42no—
140#4343—81no—
141Q8×D11—42no—
142Q8×D11—81no—
143D4×D11—42no—
144D4×D11—42no—
145D4×D11—81no—
146D4×D11—81no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—84no—
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×Q16C2×D412yescomplemented
166C11×D8—21no—
167C11×D8C2×D412yes—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C22⋊C4—41no—
174C42×C11—41no—
175C42×C11C2×D411yescharacteristic
176#4326—42no—
177#4325—42no—
178#4323—42no—
179#4323—42no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4D811yescharacteristic
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—41no—
189C4⋊Dic11D811yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191C2×C11⋊C8C2×D411yescharacteristic
192Dic44—21no—
193Dic44—21no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88—81no—
201#4314—81no—
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#2250—111no—
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#2175D1111yescharacteristic, complemented
224#2168—111no—
225C23×C11—41no—
226C22×D11—41no—
227C22×D11—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—22no—
238Q8×C11—41no—
239D4×C11—22no—
240D4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11C2×D811yescharacteristic
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—82no—
249C22⋊D11—82no—
250C2×Dic11—41no—
251C2×Dic11C2×D811yescharacteristic
252C2×Dic11C2×D811yescharacteristic
253D44—22no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—82no—
261D44—82no—
262D44—82no—
263D44—82no—
264D44—82no—
265D44—161no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—82no—
271C4×D11—82no—
272Dic22—41no—
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—111no—
292C2×SD32—224no—
293C2×SD32C2×D1111yescharacteristic
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×M32—111no—
298C22×C16—111no—
299#495—111no—
300#493—111no—
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×Q16C2×D1111yescharacteristic, complemented
312C4×D8C2×D1111yescharacteristic
313C8×D4—111no—
314#366C2×D1111yescharacteristic, complemented
315C4⋊C16—111no—
316#358—111no—
317#358C2×D1111yescharacteristic, complemented
318#357—111no—
319#357—111no—
320#357—111no—
321#357C2×D1111yescharacteristic
322C22⋊C16—111no—
323C22⋊C16—111no—
324#346C2×D1111yescharacteristic, complemented
325C22×C11—42no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11C22×D811yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—164no—
344C2×D11—164no—
345C2×D11#50912yescomplemented
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11D4211yescharacteristic
352C4×C11#57611yescharacteristic
353Dic11—21no—
354Dic11—21no—
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—221no—
369C2×SD16—221no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—222no—
376C2×D8—222no—
377C2×D8—221no—
378C2×D8—441no—
379C2×D8—441no—
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#127—221no—
384#124—221no—
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—21no—
396C4×D4—21no—
397C4×D4—111no—
398C4×D4—441no—
399SD32—222no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—441no—
404SD32D4414yescomplemented
405D16—222no—
406D16—222no—
407D16—441no—
408M32—222no—
409C2×C16—111no—
410C2×C16—111no—
411C2×C16—222no—
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107C22×D1111yescharacteristic
415#107C22×D1111yescharacteristic
416C4⋊C8—111no—
417#103—21no—
418#103—221no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C4×C8C22×D1111yescharacteristic
426C2×C11—82no—
427C2×C11D4×D811yescharacteristic
428C2×C11C2×#50911yescharacteristic
429C2×C11#341611yescharacteristic
430D11—22no—
431D11—41no—
432D11—161no—
433D11—161no—
434D11—161no—
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—111no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—442no—
456C2×D4—442no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—884no—
460C2×D4—881no—
461C2×D4—881no—
462C22×C4—41no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—441no—
466C22×C4—441no—
467Q16—21no—
468Q16—221no—
469Q16—221no—
470Q16—442no—
471Q16C2×D4412yescomplemented
472SD16—442no—
473SD16—881no—
474D8—21no—
475D8—221no—
476D8—221no—
477D8—221no—
478D8—221no—
479D8—221no—
480D8—221no—
481D8—442no—
482D8—442no—
483D8—881no—
484D8C2×D4412yes—
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—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—111no—
497C4⋊C4—441no—
498C22⋊C4—41no—
499C22⋊C4—111no—
500C22⋊C4—111no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C42—41no—
508C42D4×D1111yescharacteristic
509C16—21no—
510C16—221no—
511C16—221no—
512C16C2×D4412yescomplemented
513C11#3383111yescharacteristic, complemented, Sylow
514C23—41no—
515C23—111no—
516C23—111no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23—882no—
524C23—1761no—
525C23—1761no—
526Q8—22no—
527Q8—41no—
528Q8—441no—
529Q8—441no—
530Q8—882no—
531D4—22no—
532D4—41no—
533D4—222no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—882no—
541D4—882no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—882no—
547D4—1761no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—111no—
553C2×C4—111no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—441no—
559C2×C4—882no—
560C2×C4—882no—
561C2×C4D8×D1111yescharacteristic
562C2×C4D8×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C8—21no—
565C8—221no—
566C8—221no—
567C8C22×D4411yescharacteristic
568C8#6704211yescharacteristic
569C22—42no—
570C22—81no—
571C22—81no—
572C22—112no—
573C22—221no—
574C22—221no—
575C22—221no—
576C22—221no—
577C22—221no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—1764no—
588C22—1764no—
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—21no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—221no—
596C4—221no—
597C4—881no—
598C4D4×D4411yescharacteristic
599C4#1062330011yescharacteristic
600C2—82no—
601C2—222no—
602C2—441no—
603C2—1761no—
604C2—1761no—
605C2—1761no—
606C2D8×D4411yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2175C2
socleC22×C11C22×D8
hypercenter#2175D11
hypocenterC11#33831
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080358C2semidirect
4. D8×D44C2semidirect
5. #13070882C2semidirect
6. #13070730C2semidirect
7. #13070703C2semidirect
8. #13070671C2semidirect
9. #13070656C2semidirect
10. #13070546C2semidirect
11. #13070542C2semidirect
12. #13070534C2semidirect
13. #13070529C2semidirect
14. #13070443C2semidirect
15. C11×#2175C2semidirect
16. C2×#66972C22semidirect
17. C2×Q16×D11C22semidirect
23. C4×C11×Q16C22semidirect
25. C2×#66892C22semidirect
26. C2×#66892C22semidirect
33. C2×#66864C22semidirect
34. C2×#66864C22semidirect
35. C2×D176C22semidirect
36. C2×D176C22semidirect
37. C2×#66862C22semidirect
38. C2×C16×D11C22semidirect
39. #10622500C22semidirect
42. #10622496C22semidirect
47. #10622309C22semidirect
50. C11×#366C22semidirect
51. C11×#358C22semidirect
53. C11×#346C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. #10622130C22semidirect
57. #10622129C22semidirect
58. #10622129C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
104. C11×SD32D4semidirect
165. C11×Q16C2×D4semidirect
207. C11×C16C2×D4semidirect
223. #2175D11semidirect
311. C4×Q16C2×D11semidirect
314. #366C2×D11semidirect
317. #358C2×D11semidirect
324. #346C2×D11semidirect
345. C2×D11#509semidirect
404. SD32D44semidirect
471. Q16C2×D44semidirect
512. C16C2×D44semidirect
513. C11#33831semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
C2×D11×SD322
#130803582
D8×D442
#130708822
#130707302
#130707032
#130706712
#130706562
#130705462
#130705422
#130705342
#130705292
#130704432
C11×#21752
#3383111