Finite Group Databasebeta

← #14908834

Subgroups — #14908834

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079183C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic, complemented
3#13070812C211yesmaximal, characteristic, complemented
4#13070795C211yesmaximal, characteristic, complemented
5#13070774C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070543C211yesmaximal, characteristic, complemented
9#13070526C211yesmaximal, characteristic
10#13070492C211yesmaximal, characteristic, complemented
11#13070489C211yesmaximal, characteristic, complemented
12#13070483C211yesmaximal, characteristic, complemented
13#13070481C211yesmaximal, characteristic, complemented
14#13070418C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623211—21no—
18C4×D4×D11—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×D16C2211yescharacteristic
21C11×#495C2211yescharacteristic, complemented
22C4×C11×D8C2211yescharacteristic
23#10622801C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic, complemented
25C2×#66892C2211yescharacteristic
26#10622784—21no—
27SD16×Dic11—21no—
28#10622770C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic, complemented
31C2×#66890C2211yescharacteristic
32#10622669—21no—
33C4×#4323—21no—
34D11×#107C2211yescharacteristic
35#10622485C2211yescharacteristic
36D11×#102—21no—
37#10622369—21no—
38C4×D88C2211yescharacteristic
39C4×C8×D11C2211yescharacteristic
40#10622296C2211yescharacteristic, complemented
41C11×C4⋊C16C2211yescharacteristic, complemented
42C11×#358C2211yescharacteristic, complemented
43C11×#357C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622143C2211yescharacteristic, complemented
53#10622142C2211yescharacteristic, complemented
54#10622140C2211yescharacteristic, complemented
55#10622140C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C22×C4×D11—41no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C11×#124—21no—
66C4×D4×C11—21no—
67#66999—21no—
68Q8×Dic11—21no—
69#66991—21no—
70D4×Dic11—21no—
71D4×Dic11—21no—
72C2×#4323—21no—
73C4×C22⋊D11—41no—
74D8×D11—22no—
75D8×D11—22no—
76C2×D88C2311yescharacteristic
77C2×C8×D11D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66946—21no—
80C4⋊C4×D11—21no—
81#66936—41no—
82(C22⋊D11)⋊C4—41no—
83(C22⋊D11)⋊C4—41no—
84C22⋊C4×D11—41no—
85#66932—41no—
86#66930—41no—
87C4×D44—21no—
88C42×D11D411yescharacteristic
89#66923—21no—
90C11×SD32—22no—
91C11×D16—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96C4×C8×C11C2311yescharacteristic
97#66899—21no—
98#66899—21no—
99#66896—21no—
100#66896—21no—
101#66896—21no—
102#66892—22no—
103#66890—22no—
104#66885—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66871—21no—
115C4×C11⋊C8D411yescharacteristic
116#33674—111nomaximal, Sylow
117C23×D11—41no—
118C2×Q8×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C22×C4×C11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126D4×D11—24no—
127D4×D11—42no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—84no—
133C2×C4×D11D811yescharacteristic
134C2×C4×D11D811yescharacteristic
135C2×C4×D11C2×D411yescharacteristic
136C11×Q16—21no—
137C11×Q16—21no—
138C11×SD16—42no—
139C11×D8—21no—
140C11×D8—21no—
141C11×D8—21no—
142C11×D8#4112yes—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11C2×D411yescharacteristic
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153#4323—24no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166C4×Dic11D811yescharacteristic
167C4×Dic11D811yescharacteristic
168C4×Dic11C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171D88—21no—
172D88#4112yes—
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—41no—
176C11×C16—21no—
177C11×C16—21no—
178C11⋊C16—21no—
179C11⋊C16—21no—
180#3168—111no—
181C2×C4×D8—111no—
182#2235—111no—
183#2232—111no—
184#2228—111no—
185#2228—111no—
186#2210—111no—
187#2210D1111yescharacteristic, complemented
188#2187—111no—
189#2184—111no—
190#2177—111no—
191#2177—111no—
192#2175—111no—
193#2175—111no—
194#2163—111no—
195C23×C11—41no—
196C23×C11—41no—
197C22×D11—44no—
198C22×D11—41no—
199C22×D11—82no—
200C22×D11—82no—
201C22×D11C2×D811yescharacteristic
202Q8×C11—41no—
203Q8×C11—41no—
204D4×C11—22no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—44no—
215C22⋊D11—82no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—82no—
220C2×Dic11—82no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224D44—22no—
225D44—41no—
226C4×D11—22no—
227C4×D11—21no—
228C4×D11—21no—
229C4×D11—41no—
230C4×D11—82no—
231C4×D11—82no—
232C4×D11—82no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8—21no—
238C22×D8—111no—
239#529—221no—
240C2×C4×D4—221no—
241C2×SD32—111no—
242C2×SD32C2×D1111yescharacteristic
243C2×D16—111no—
244C2×D16C2×D1111yescharacteristic
245#499—111no—
246#495C2×D1111yescharacteristic, complemented
247#488—221no—
248#467—111no—
249#466—111no—
250#465—221no—
251C4×Q16—111no—
252C4×SD16—221no—
253C4×D8—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257C4×D8—221no—
258C4×D8—221no—
259C4×D8C2×D1111yescharacteristic
260C2×#107—111no—
261C2×#102—221no—
262C2×C4×C8—111no—
263#367—111no—
264#367—111no—
265#366—111no—
266#366—111no—
267C4⋊C16—111no—
268C4⋊C16C2×D1111yescharacteristic, complemented
269#358—111no—
270#358C2×D1111yescharacteristic, complemented
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357—111no—
276#357C2×D1111yescharacteristic, complemented
277C22⋊C16—111no—
278C22⋊C16—111no—
279#346—111no—
280#346—111no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C22×D811yescharacteristic
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—42no—
291C2×D11—88no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11#50912yes—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11#52511yescharacteristic
300C4×C11#57511yescharacteristic
301Dic11—21no—
302Dic11—21no—
303Dic11—21no—
304Dic11—81no—
305Dic11—81no—
306Dic11—81no—
307C22×D4—221no—
308C23×C4—441no—
309C2×Q16C22×D1111yescharacteristic
310C2×SD16—21no—
311C2×D8—111no—
312C2×D8—221no—
313C2×D8—222no—
314C2×D8—222no—
315C2×D8C22×D1111yescharacteristic
316C2×D8C22×D1111yescharacteristic
317C22×C8—111no—
318C22×C8—111no—
319#126—441no—
320#125—221no—
321#124—21no—
322#123—441no—
323C22⋊Q8—221no—
324#121—221no—
325C4×Q8—221no—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—221no—
331C4×D4—441no—
332C4×D4—441no—
333C4×D4—441no—
334#117—441no—
335C2×C4⋊C4—221no—
336C2×C22⋊C4—441no—
337C2×C42—111no—
338SD32—22no—
339SD32—222no—
340D16—22no—
341D16—222no—
342C2×C16—111no—
343C2×C16—111no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—111no—
348#107—111no—
349#107—221no—
350#107C22×D1111yescharacteristic
351#106—221no—
352#103—221no—
353#103—221no—
354#102—21no—
355#102—221no—
356#102—221no—
357#102—221no—
358#102—221no—
359#102—221no—
360C4×C8—111no—
361C4×C8—111no—
362C4×C8—111no—
363C4×C8C22×D1111yescharacteristic
364C2×C11—82no—
365C2×C11—161no—
366C2×C11#310011yescharacteristic
367C2×C11C2×#50911yescharacteristic
368C2×C11#341411yescharacteristic
369D11—22no—
370D11—82no—
371C24—441no—
372C2×Q8—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—224no—
376C2×D4—221no—
377C2×D4—441no—
378C2×D4—442no—
379C2×D4—441no—
380C22×C4—41no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—884no—
390Q16—21no—
391Q16—21no—
392SD16—42no—
393D8—21no—
394D8—21no—
395D8—21no—
396D8—112no—
397D8—224no—
398D8—221no—
399D8#434112yes—
400C2×C8—111no—
401C2×C8—111no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—441no—
405C2×C8D4×D1111yescharacteristic
406C2×C8C23×D1111yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C42—111no—
426C42—111no—
427C42—111no—
428C42—441no—
429C42D4×D1111yescharacteristic
430C16—21no—
431C16—21no—
432C16—221no—
433C16—221no—
434C11#3367411yescharacteristic, complemented, Sylow
435C23—41no—
436C23—41no—
437C23—111no—
438C23—444no—
439C23—441no—
440C23—882no—
441C23—882no—
442Q8—41no—
443Q8—41no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—222no—
449D4—444no—
450D4—441no—
451D4—882no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—111no—
456C2×C4—111no—
457C2×C4—111no—
458C2×C4—222no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—882no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4—882no—
469C2×C4—882no—
470C2×C4D8×D1111yescharacteristic
471C2×C4D8×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—21no—
474C8—221no—
475C8—221no—
476C8C2×#434111yescharacteristic
477C8#41×D1111yescharacteristic
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—112no—
485C22—221no—
486C22—221no—
487C22—442no—
488C22—888no—
489C22—881no—
490C22—881no—
491C22C2×D8×D1111yescharacteristic
492C4—21no—
493C4—21no—
494C4—81no—
495C4—81no—
496C4—221no—
497C4—221no—
498C4—221no—
499C4—881no—
500C4—881no—
501C4—881no—
502C4#1062313711yescharacteristic
503C4#1062330411yescharacteristic
504C2—82no—
505C2—161no—
506C2—222no—
507C2—882no—
508C2#1307861511yescharacteristic
509C2D11×#50911yescharacteristic
510C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
prime radical#13070526C2
hypercenter#2210D11
hypocenterC11#33674
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. #13079183C2semidirect
2. C4×D8×D11C2semidirect
3. #13070812C2semidirect
4. #13070795C2semidirect
5. #13070774C2semidirect
6. #13070773C2semidirect
7. #13070668C2semidirect
8. #13070543C2semidirect
10. #13070492C2semidirect
11. #13070489C2semidirect
12. #13070483C2semidirect
13. #13070481C2semidirect
14. #13070418C2semidirect
15. C11×#2210C2semidirect
21. C11×#495C22semidirect
24. Q16×Dic11C22semidirect
30. D8×Dic11C22semidirect
40. #10622296C22semidirect
41. C11×C4⋊C16C22semidirect
42. C11×#358C22semidirect
43. C11×#357C22semidirect
44. #10622202C22semidirect
47. #10622200C22semidirect
52. #10622143C22semidirect
53. #10622142C22semidirect
54. #10622140C22semidirect
55. #10622140C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
187. #2210D11semidirect
246. #495C2×D11semidirect
268. C4⋊C16C2×D11semidirect
270. #358C2×D11semidirect
276. #357C2×D11semidirect
434. C11#33674semidirect

Maximal subgroups

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

subgroupindex
#130791832
C4×D8×D112
#130708122
#130707952
#130707742
#130707732
#130706682
#130705432
#130705262
#130704922
#130704892
#130704832
#130704812
#130704182
C11×#22102
#3367411