Finite Group Databasebeta

← #14908840

Subgroups — #14908840

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#13079188C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic, complemented
3#13070815C211yesmaximal, characteristic, complemented
4#13070798C211yesmaximal, characteristic, complemented
5#13070770C211yesmaximal, characteristic, complemented
6#13070672C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070546C211yesmaximal, characteristic, complemented
9#13070529C211yesmaximal, characteristic
10#13070491C211yesmaximal, characteristic, complemented
11#13070489C211yesmaximal, characteristic, complemented
12#13070479C211yesmaximal, characteristic, complemented
13#13070477C211yesmaximal, characteristic, complemented
14#13070418C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623222—21no—
18C4×D4×D11—21no—
19C11×#499C2211yescharacteristic, complemented
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23C2×#66890C2211yescharacteristic
24#10622681—21no—
25C4×#4323—21no—
26C2×#66864C2211yescharacteristic
27C2×D176C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622496C2211yescharacteristic
30D11×#107C2211yescharacteristic
31#10622486C2211yescharacteristic, complemented
32#10622485C2211yescharacteristic
33#10622485C2211yescharacteristic, complemented
34#10622477—21no—
35#10622465—21no—
36D11×#102—21no—
37#10622369—21no—
38#10622309C2211yescharacteristic, complemented
39C4×D88C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#367C2211yescharacteristic, complemented
42C11×#366C2211yescharacteristic, complemented
43C11×C4⋊C16C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622147C2211yescharacteristic, complemented
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic, complemented
50#10622140C2211yescharacteristic, complemented
51#10622140C2211yescharacteristic, complemented
52#10622130C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C22×C4×D11—41no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C4×D4×C11—21no—
64D4×Dic11—21no—
65C2×#4323—21no—
66C4×C22⋊D11—41no—
67D8×D11—22no—
68D8×D11—22no—
69C2×Dic44C2311yescharacteristic
70C2×D88C2311yescharacteristic
71C2×D88C2311yescharacteristic
72C2×#4314—21no—
73C2×C8×D11D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66951—41no—
76#66950—21no—
77#66948—21no—
78#66947—41no—
79#66946—21no—
80#66946—21no—
81#66946—41no—
82#66945—41no—
83C4⋊C4×D11—21no—
84#66940—21no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87#66928—21no—
88C4×D44—21no—
89C42×D11D411yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66891—22no—
100#66890—22no—
101#66885—21no—
102#66882C2311yescharacteristic
103C8×Dic11D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66873—21no—
110#66873—21no—
111#66873—21no—
112#66871—21no—
113C4×C11⋊C8D411yescharacteristic
114#66864—22no—
115D176—22no—
116#33674—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122D4×D11—24no—
123D4×D11—42no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11—84no—
132C2×C4×D11D811yescharacteristic
133C2×C4×D11D811yescharacteristic
134C2×C4×D11C2×D411yescharacteristic
135C2×Dic22—21no—
136C11×D8—21no—
137C11×D8#4112yes—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148#4323—24no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160C4×Dic11—41no—
161C4×Dic11D811yescharacteristic
162C4×Dic11D811yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166Dic44—21no—
167Dic44—21no—
168D88—21no—
169D88—21no—
170D88—21no—
171D88#4112yes—
172#4314—42no—
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#2228D1111yescharacteristic, complemented
186#2210—111no—
187#2210—111no—
188#2187—111no—
189#2184—111no—
190#2177—111no—
191#2177—111no—
192#2175—111no—
193#2175—111no—
194#2163—111no—
195C23×C11—41no—
196C22×D11—44no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—82no—
200C22×D11—82no—
201C22×D11C2×D811yescharacteristic
202D4×C11—22no—
203D4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—82no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C22⋊D11—44no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—82no—
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—22no—
219D44—41no—
220D44—41no—
221D44—41no—
222D44—82no—
223C4×D11—22no—
224C4×D11—21no—
225C4×D11—21no—
226C4×D11—41no—
227C4×D11—82no—
228C4×D11—82no—
229C4×D11—82no—
230C4×D11—82no—
231Dic22—41no—
232Dic22—41no—
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×SD32—111no—
243C2×D16—111no—
244C2×D16—111no—
245#499C2×D1111yescharacteristic, complemented
246#495—111no—
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#367C2×D1111yescharacteristic, complemented
265#366—111no—
266#366C2×D1111yescharacteristic, complemented
267C4⋊C16—111no—
268C4⋊C16C2×D1111yescharacteristic, complemented
269#358—111no—
270#358—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276#357C2×D1111yescharacteristic
277C22⋊C16—111no—
278C22⋊C16—111no—
279#346—111no—
280#346—111no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—42no—
288C2×D11—88no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11#50912yes—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11#52511yescharacteristic
301C4×C11#57511yescharacteristic
302Dic11—21no—
303Dic11—21no—
304Dic11—21no—
305Dic11—81no—
306Dic11—81no—
307C22×D4—221no—
308C23×C4—441no—
309C2×Q16—111no—
310C2×SD16—221no—
311C2×D8—111no—
312C2×D8—111no—
313C2×D8—221no—
314C2×D8—222no—
315C2×D8—222no—
316C2×D8C22×D1111yescharacteristic
317C22×C8—111no—
318C22×C8—111no—
319#126—441no—
320#125—21no—
321#124—221no—
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—222no—
339SD32—222no—
340D16—222no—
341D16—222no—
342C2×C16—111no—
343C2×C16—111no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—221no—
348#107C22×D1111yescharacteristic
349#107C22×D1111yescharacteristic
350#107C22×D1111yescharacteristic
351#106—21no—
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#310011yescharacteristic
366C2×C11C2×#50911yescharacteristic
367C2×C11#341411yescharacteristic
368D11—22no—
369D11—82no—
370D11—161no—
371C24—441no—
372C2×Q8—221no—
373C2×D4—21no—
374C2×D4—224no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—441no—
378C2×D4—441no—
379C2×D4—442no—
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—221no—
391Q16—221no—
392SD16—442no—
393D8—21no—
394D8—112no—
395D8—224no—
396D8—221no—
397D8—221no—
398D8—221no—
399D8#434312yes—
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—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—221no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C22⋊C4—41no—
417C22⋊C4—441no—
418C22⋊C4—441no—
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—111no—
437C23—444no—
438C23—441no—
439C23—441no—
440C23—882no—
441C23—882no—
442Q8—441no—
443Q8—441no—
444D4—22no—
445D4—41no—
446D4—222no—
447D4—444no—
448D4—441no—
449D4—441no—
450D4—441no—
451D4—882no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4—111no—
457C2×C4—111no—
458C2×C4—111no—
459C2×C4—222no—
460C2×C4—221no—
461C2×C4—221no—
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×#434311yescharacteristic
477C8#41×D1111yescharacteristic
478C22—42no—
479C22—81no—
480C22—81no—
481C22—112no—
482C22—221no—
483C22—221no—
484C22—442no—
485C22—888no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×D8×D1111yescharacteristic
492C4—21no—
493C4—21no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—221no—
498C4—221no—
499C4—221no—
500C4—881no—
501C4—881no—
502C4#1062315811yescharacteristic
503C4#1062330811yescharacteristic
504C2—82no—
505C2—222no—
506C2—882no—
507C2—1761no—
508C2#1307861811yescharacteristic
509C2D11×#50911yescharacteristic
510C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radical#13070529C2
hypercenter#2228D11
hypocenterC11#33674
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079188C2semidirect
2. C4×D8×D11C2semidirect
3. #13070815C2semidirect
4. #13070798C2semidirect
5. #13070770C2semidirect
6. #13070672C2semidirect
7. #13070671C2semidirect
8. #13070546C2semidirect
10. #13070491C2semidirect
11. #13070489C2semidirect
12. #13070479C2semidirect
13. #13070477C2semidirect
14. #13070418C2semidirect
15. C11×#2228C2semidirect
19. C11×#499C22semidirect
31. #10622486C22semidirect
33. #10622485C22semidirect
38. #10622309C22semidirect
41. C11×#367C22semidirect
42. C11×#366C22semidirect
43. C11×C4⋊C16C22semidirect
46. #10622147C22semidirect
49. #10622141C22semidirect
50. #10622140C22semidirect
51. #10622140C22semidirect
52. #10622130C22semidirect
55. #10622129C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
185. #2228D11semidirect
245. #499C2×D11semidirect
264. #367C2×D11semidirect
266. #366C2×D11semidirect
268. C4⋊C16C2×D11semidirect
434. C11#33674semidirect

Maximal subgroups

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

subgroupindex
#130791882
C4×D8×D112
#130708152
#130707982
#130707702
#130706722
#130706712
#130705462
#130705292
#130704912
#130704892
#130704792
#130704772
#130704182
C11×#22282
#3367411