Finite Group Databasebeta

← #14910241

Subgroups — #14910241

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
4#13080291C211yesmaximal, characteristic, complemented
5#13070880C211yesmaximal, characteristic, complemented
6#13070728C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070546C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070531C211yesmaximal, characteristic, complemented
12#13070529C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14#13070440C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic, complemented
17C2×Q16×D11C2211yescharacteristic, complemented
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623248—21no—
21#10623107—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×SD32C2211yescharacteristic, complemented
24C11×#493C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic, complemented
26C2×#66892C2211yescharacteristic
27#10622770C2211yescharacteristic
28#10622770C2211yescharacteristic
29#10622769—21no—
30#10622769—21no—
31C2×#66891C2211yescharacteristic, complemented
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic, complemented
34C2×#66890C2211yescharacteristic, complemented
35#10622685—21no—
36#10622641—21no—
37#10622527—24no—
38D11×SD32—24no—
39C2×#66864C2211yescharacteristic
40C2×D176C2211yescharacteristic
41C2×#66862C2211yescharacteristic, complemented
42C2×C16×D11C2211yescharacteristic, complemented
43#10622500C2211yescharacteristic, complemented
44#10622496C2211yescharacteristic, complemented
45#10622423—21no—
46#10622419—21no—
47#10622309C2211yescharacteristic, complemented
48C4×D88C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53#10622202C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic
59#10622127C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×Q8×D11—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C2×D4×D11—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8—21no—
68C2×C11×D8C2311yescharacteristic
69C2×C11×D8C2311yescharacteristic
70C11×#127—21no—
71C4×Q8×C11—21no—
72C2×#4326—21no—
73C2×#4325—21no—
74#66991—21no—
75#66991—21no—
76#66991—41no—
77#66990—41no—
78#66990—41no—
79C2×#4323—21no—
80C2×#4323—21no—
81#66972—22no—
82#66972—41no—
83Q16×D11—22no—
84Q16×D11—41no—
85D8×D11—22no—
86D8×D11—22no—
87D8×D11—41no—
88D8×D11—41no—
89C2×Dic44C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×D88C2311yescharacteristic
92C2×#4314—21no—
93C2×C8×D11C2311yescharacteristic
94C2×C8×D11C2311yescharacteristic
95#66950—21no—
96#66950—41no—
97#66948—21no—
98#66948—41no—
99#66928—21no—
100#66928—41no—
101C4×D44—21no—
102C4×D44—41no—
103C4×D44D411yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66896—21no—
113#66892D414yescomplemented
114#66891—22no—
115#66891—41no—
116#66890—22no—
117#66890—41no—
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121#66882C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123C2×C11⋊C16C2311yescharacteristic
124#66874—21no—
125#66873—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127#66864—22no—
128D176—22no—
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—41no—
138C2×D4×C11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143#4343—42no—
144#4343—81no—
145Q8×D11—42no—
146Q8×D11—81no—
147D4×D11—42no—
148D4×D11—42no—
149D4×D11—81no—
150D4×D11—81no—
151D4×D11—84no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44D811yescharacteristic
157C2×C4×D11—41no—
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×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—81no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C42×C11—41no—
176C42×C11C2×D411yescharacteristic
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179#4326—42no—
180#4325—42no—
181#4323—42no—
182#4323—42no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4D811yescharacteristic
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11D811yescharacteristic
193C2×C11⋊C8C2×D411yescharacteristic
194C2×C11⋊C8C2×D411yescharacteristic
195Dic44—21no—
196Dic44—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88C2×D412yes—
201#4314—81no—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
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#2207D1111yescharacteristic, complemented
219#2187—111no—
220#2186—111no—
221#2185—111no—
222#2184—111no—
223#2175—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—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—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—82no—
244D4×C11—161no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C2×D811yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—82no—
251C22⋊D11—82no—
252C22⋊D11—82no—
253C22⋊D11—82no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11C2×D811yescharacteristic
257C2×Dic11C2×D811yescharacteristic
258D44—22no—
259D44—22no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—82no—
264D44—82no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—82no—
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—224no—
292C2×SD32C2×D1111yescharacteristic, complemented
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×M32—111no—
298C22×C16—111no—
299#495—111no—
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×Q16C2×D1111yescharacteristic, complemented
312C4×D8—111no—
313C8×D4—111no—
314#366—111no—
315C4⋊C16C2×D1111yescharacteristic, complemented
316#358—111no—
317#358—111no—
318#357—111no—
319#357—111no—
320#357C2×D1111yescharacteristic, complemented
321#357C2×D1111yescharacteristic, complemented
322C22⋊C16—111no—
323C22⋊C16—111no—
324#346—111no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11C22×D811yescharacteristic
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—42no—
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×C11D4211yescharacteristic
351C4×C11#57611yescharacteristic
352Dic11—21no—
353Dic11—21no—
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—221no—
369C2×SD16—221no—
370C2×D8—21no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—222no—
376C2×D8—222no—
377C2×D8—441no—
378C2×D8—441no—
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#127—21no—
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—111no—
397C4×D4—221no—
398C4×D4—441no—
399SD32—22no—
400SD32—22no—
401SD32—114no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405D16—222no—
406D16—222no—
407D16—441no—
408M32—222no—
409C2×C16—111no—
410C2×C16—111no—
411C2×C16—222no—
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107—111no—
415#107C22×D1111yescharacteristic
416C4⋊C8—111no—
417#103—21no—
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×C11D4×D811yescharacteristic
429C2×C11C2×#50911yescharacteristic
430C2×C11#341611yescharacteristic
431D11—22no—
432D11—41no—
433D11—82no—
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—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
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—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—221no—
469Q16—221no—
470Q16—442no—
471Q16D4×D1112yescomplemented
472SD16—442no—
473SD16—881no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—81no—
479D8—112no—
480D8—221no—
481D8—221no—
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—21no—
494C4⋊C4—41no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—441no—
498C22⋊C4—111no—
499C22⋊C4—111no—
500C22⋊C4—441no—
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—21no—
511C16—112no—
512C16—221no—
513C11#3383111yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—111no—
517C23—111no—
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—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—82no—
536D4—161no—
537D4—222no—
538D4—222no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—882no—
547D4—882no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—111no—
551C2×C4—111no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
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#6704211yescharacteristic
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—112no—
576C22—221no—
577C22—221no—
578C22—221no—
579C22—221no—
580C22—221no—
581C22—442no—
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—221no—
595C4—221no—
596C4—881no—
597C4—881no—
598C4#1062314011yescharacteristic
599C4#1062330511yescharacteristic
600C2—161no—
601C2—161no—
602C2—222no—
603C2—441no—
604C2—882no—
605C2—1761no—
606C2#1308028811yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
hypercenter#2207D11
hypocenterC11#33831
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080358C2semidirect
4. #13080291C2semidirect
5. #13070880C2semidirect
6. #13070728C2semidirect
7. #13070701C2semidirect
8. #13070672C2semidirect
9. #13070546C2semidirect
10. #13070538C2semidirect
11. #13070531C2semidirect
12. #13070529C2semidirect
13. #13070478C2semidirect
14. #13070440C2semidirect
15. C11×#2207C2semidirect
16. C2×#66972C22semidirect
17. C2×Q16×D11C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×SD32C22semidirect
25. C4×C11×Q16C22semidirect
31. C2×#66891C22semidirect
32. C2×#66891C22semidirect
33. C2×#66890C22semidirect
34. C2×#66890C22semidirect
41. C2×#66862C22semidirect
42. C2×C16×D11C22semidirect
43. #10622500C22semidirect
44. #10622496C22semidirect
47. #10622309C22semidirect
50. C11×C4⋊C16C22semidirect
51. C11×#357C22semidirect
52. C11×#357C22semidirect
53. #10622202C22semidirect
54. #10622147C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622141C22semidirect
59. #10622127C22semidirect
60. #10622099C22semidirect
113. #66892D4semidirect
165. C11×Q16C2×D4semidirect
209. C11⋊C16C2×D4semidirect
218. #2207D11semidirect
292. C2×SD32C2×D11semidirect
293. C2×SD32C2×D11semidirect
311. C4×Q16C2×D11semidirect
315. C4⋊C16C2×D11semidirect
320. #357C2×D11semidirect
321. #357C2×D11semidirect
345. C2×D11#509semidirect
471. Q16D4×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×#106225272
C2×D11×SD322
#130803582
#130802912
#130708802
#130707282
#130707012
#130706722
#130705462
#130705382
#130705312
#130705292
#130704782
#130704402
C11×#22072
#3383111