Finite Group Databasebeta

← #14910252

Subgroups — #14910252

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
4D8×D44C211yesmaximal, characteristic, complemented
5#13070883C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070657C211yesmaximal, characteristic, complemented
9#13070543C211yesmaximal, characteristic, complemented
10#13070540C211yesmaximal, characteristic, complemented
11#13070534C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070480C211yesmaximal, characteristic, complemented
14#13070440C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic, complemented
17C2×#66965C2211yescharacteristic, complemented
18C2×D8×D11C2211yescharacteristic
19C2×D8×D11C2211yescharacteristic
20#10623208—21no—
21D4×D44—21no—
22C2×C11×SD32C2211yescharacteristic
23C2×C11×D16C2211yescharacteristic
24C11×#495C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic
26#10622801C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic, complemented
29#10622786—21no—
30#10622783—21no—
31#10622770C2211yescharacteristic, complemented
32C2×#66891C2211yescharacteristic
33C2×#66890C2211yescharacteristic, complemented
34C2×#66890C2211yescharacteristic, complemented
35#10622667—21no—
36#10622628—21no—
37D11×SD32—24no—
38#10622524—24no—
39C2×#66864C2211yescharacteristic, complemented
40C2×#66864C2211yescharacteristic, complemented
41C2×#66862C2211yescharacteristic, complemented
42C2×C16×D11C2211yescharacteristic, complemented
43#10622496C2211yescharacteristic
44#10622496C2211yescharacteristic
45#10622386—21no—
46#10622386—21no—
47C4×Dic44C2211yescharacteristic, complemented
48#10622308C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57(C2×D11)⋊C16C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622127C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×#4341—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C22×D44—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×SD16—21no—
68C2×C11×D8C2311yescharacteristic
69C2×C11×D8C2311yescharacteristic
70C11×#124—21no—
71C4×D4×C11—21no—
72#66999—21no—
73C2×#4326—21no—
74#66991—21no—
75C2×#4324—21no—
76C2×#4323—21no—
77C2×#4323—21no—
78#66983—41no—
79Q16×D11—22no—
80Q16×D11—41no—
81#66965—22no—
82#66965—41no—
83D8×D11—22no—
84D8×D11—22no—
85D8×D11—41no—
86D8×D11—41no—
87C2×Dic44C2311yescharacteristic
88C2×D88—21no—
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×C8×D11C2311yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66948—21no—
94#66948—21no—
95#66938—41no—
96#66937—41no—
97#66935—41no—
98#66935—41no—
99(C22⋊D11)⋊C4—41no—
100#66931—41no—
101#66927—21no—
102C4×D44D411yescharacteristic
103C4×Dic22—21no—
104C11×SD32—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66892—22no—
114#66892—41no—
115#66891D414yescomplemented
116#66890—22no—
117#66890—41no—
118(C2×D11)⋊C8D411yescharacteristic
119(C2×D11)⋊C8D411yescharacteristic
120#66882C2311yescharacteristic
121#66880—21no—
122C2×C11⋊C16C2311yescharacteristic
123C2×C11⋊C16C2311yescharacteristic
124#66873—21no—
125#66873—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127#66864—22no—
128#66864—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—
137C22×C4×C11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C22×Dic11—41no—
143Q8×D11—42no—
144Q8×D11—81no—
145#4341—42no—
146#4341—81no—
147D4×D11—42no—
148D4×D11—42no—
149D4×D11—81no—
150D4×D11—81no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44—84no—
158C2×D44D811yescharacteristic
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×D8C2×D412yes—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C42×C11C2×D411yescharacteristic
178C22⋊Dic11—41no—
179#4326—42no—
180#4324—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)⋊C4D811yescharacteristic
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189C4⋊Dic11D811yescharacteristic
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192C4×Dic11—41no—
193C2×C11⋊C8C2×D411yescharacteristic
194C2×C11⋊C8C2×D411yescharacteristic
195Dic44—21no—
196Dic44C2×D412yescomplemented
197D88—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—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#2210D1111yescharacteristic, complemented
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—
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—41no—
238Q8×C11—41no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C22⋊D11—82no—
250C22⋊D11—82no—
251C22⋊D11—82no—
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—82no—
256C2×Dic11C2×D811yescharacteristic
257C2×Dic11C2×D811yescharacteristic
258D44—22no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—82no—
264D44—82no—
265D44—82no—
266D44—161no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
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—111no—
292C2×SD32—224no—
293C2×SD32C2×D1111yescharacteristic
294C2×D16—111no—
295C2×D16—111no—
296C2×D16C2×D1111yescharacteristic
297C2×M32—111no—
298C22×C16—111no—
299#495C2×D1111yescharacteristic, complemented
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×Q16—111no—
312C4×D8C2×D1111yescharacteristic
313C8×D4—111no—
314#366—111no—
315C4⋊C16C2×D1111yescharacteristic, complemented
316#358—111no—
317#358C2×D1111yescharacteristic, complemented
318#357—111no—
319#357—111no—
320#357—111no—
321#357C2×D1111yescharacteristic, complemented
322C22⋊C16—111no—
323C22⋊C16—111no—
324#346—111no—
325C22×C11—42no—
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—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—81no—
349C4×C11—81no—
350C4×C11D4211yescharacteristic
351C4×C11#57611yescharacteristic
352Dic11—21no—
353Dic11—21no—
354Dic11—42no—
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—111no—
371C2×D8—111no—
372C2×D8—221no—
373C2×D8—221no—
374C2×D8—222no—
375C2×D8—222no—
376C2×D8—221no—
377C2×D8—441no—
378C2×D8—441no—
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#127—221no—
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—21no—
397C4×D4—111no—
398C4×D4—441no—
399SD32—22no—
400SD32—114no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405D16—22no—
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—221no—
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×C11—161no—
428C2×C11D4×D811yescharacteristic
429C2×C11C2×#50911yescharacteristic
430C2×C11#341611yescharacteristic
431D11—22no—
432D11—41no—
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—21no—
446C2×D4—111no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—441no—
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—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—21no—
469Q16—112no—
470Q16—221no—
471Q16—442no—
472SD16—81no—
473SD16—442no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—221no—
478D8—221no—
479D8—221no—
480D8—221no—
481D8—442no—
482D8—442no—
483D8—881no—
484D8D4×D1112yes—
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—111no—
495C4⋊C4—221no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—111no—
502C22⋊C4—111no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C42—441no—
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—41no—
527Q8—41no—
528Q8—222no—
529Q8—441no—
530Q8—882no—
531D4—22no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—222no—
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—82no—
551C2×C4—111no—
552C2×C4—111no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—441no—
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—
567C8C2×D4×D1111yescharacteristic
568C8#6704211yescharacteristic
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—112no—
576C22—221no—
577C22—221no—
578C22—221no—
579C22—221no—
580C22—221no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—1764no—
588C22—1764no—
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—21no—
592C4—81no—
593C4—81no—
594C4—221no—
595C4—221no—
596C4—442no—
597C4—881no—
598C4#1062314011yescharacteristic
599C4#1062330511yescharacteristic
600C2—82no—
601C2—161no—
602C2—222no—
603C2—441no—
604C2—1761no—
605C2—1761no—
606C2#1308028811yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
hypercenter#2210D11
hypocenterC11#33831
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080356C2semidirect
4. D8×D44C2semidirect
5. #13070883C2semidirect
6. #13070732C2semidirect
7. #13070701C2semidirect
8. #13070657C2semidirect
9. #13070543C2semidirect
10. #13070540C2semidirect
11. #13070534C2semidirect
12. #13070526C2semidirect
13. #13070480C2semidirect
14. #13070440C2semidirect
15. C11×#2210C2semidirect
16. C2×Q16×D11C22semidirect
17. C2×#66965C22semidirect
24. C11×#495C22semidirect
26. #10622801C22semidirect
27. C2×#66892C22semidirect
28. C2×#66892C22semidirect
31. #10622770C22semidirect
33. C2×#66890C22semidirect
34. C2×#66890C22semidirect
39. C2×#66864C22semidirect
40. C2×#66864C22semidirect
41. C2×#66862C22semidirect
42. C2×C16×D11C22semidirect
47. C4×Dic44C22semidirect
50. C11×C4⋊C16C22semidirect
51. C11×#358C22semidirect
52. C11×#357C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. (C2×D11)⋊C16C22semidirect
58. #10622130C22semidirect
59. #10622127C22semidirect
60. #10622099C22semidirect
115. #66891D4semidirect
196. Dic44C2×D4semidirect
209. C11⋊C16C2×D4semidirect
217. #2210D11semidirect
299. #495C2×D11semidirect
315. C4⋊C16C2×D11semidirect
317. #358C2×D11semidirect
321. #357C2×D11semidirect
345. C2×D11#509semidirect
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
D8×D442
#130708832
#130707322
#130707012
#130706572
#130705432
#130705402
#130705342
#130705262
#130704802
#130704402
C11×#22102
#3383111