Finite Group Databasebeta

← #14910870

Subgroups — #14910870

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081005C211yesmaximal, characteristic, complemented
2#13080298C211yesmaximal, characteristic
3#13070854C211yesmaximal, characteristic, complemented
4#13070816C211yesmaximal, characteristic, complemented
5#13070798C211yesmaximal, characteristic, complemented
6#13070752C211yesmaximal, characteristic, complemented
7#13070732C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070555C211yesmaximal, characteristic, complemented
10#13070544C211yesmaximal, characteristic, complemented
11#13070483C211yesmaximal, characteristic, complemented
12#13070441C211yesmaximal, characteristic, complemented
13#13070327C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15C11×#2216C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623166—21no—
19#10623161—21no—
20C2×C11×Q32C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24#10622804C2211yescharacteristic
25#10622801C2211yescharacteristic, complemented
26Q16×Dic11C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622659—21no—
32#10622657—21no—
33C2×#66862C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35D11×#107C2211yescharacteristic, complemented
36#10622487C2211yescharacteristic, complemented
37#10622485C2211yescharacteristic
38#10622432—21no—
39#10622424—21no—
40#10622422—21no—
41#10622407—21no—
42C11×#366C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4343—21no—
60C22×D44—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66#67000—21no—
67#66999—21no—
68Q8×Dic11—21no—
69C2×#4325—21no—
70C2×#4325—21no—
71C4×C22⋊D11D411yescharacteristic
72C2×C4⋊Dic11—21no—
73#66972—22no—
74#66972—41no—
75C2×D88—22no—
76C2×D88—21no—
77C2×D88—41no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66950—41no—
82#66948—21no—
83#66948—41no—
84#66947—41no—
85#66946—21no—
86C4⋊C4×D11—21no—
87#66942—41no—
88#66941—21no—
89#66935—41no—
90(C22⋊D11)⋊C4—41no—
91C22⋊C4×D11—41no—
92#66931—41no—
93C11×Q32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C11×#103—21no—
101#66899—21no—
102#66899—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66892—22no—
105#66892—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66873—21no—
116#66871—21no—
117#66871—21no—
118#66862—41no—
119#33881—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11D811yescharacteristic
125C22×Dic11—41no—
126#4343—42no—
127#4343—81no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—42no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44—41no—
134C2×D44—81no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11C2×D411yescharacteristic
139C2×Dic22—41no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×Q16—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C22⋊Dic11D811yescharacteristic
155#4325—42no—
156#4325—81no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4D811yescharacteristic
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11—41no—
172C4×Dic11C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175D88—21no—
176D88—21no—
177D88—21no—
178D88—42no—
179D88#4112yes—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3338—111no—
187#3280—111no—
188#2243—111no—
189#2236—111no—
190#2232—111no—
191#2224—111no—
192#2220—111no—
193#2216D1111yescharacteristic, complemented
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168—111no—
199#2139—111no—
200C2×#357—111no—
201C23×C11C2×D811yescharacteristic
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—161no—
207C22×D11C2×D811yescharacteristic
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—41no—
211Q8×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—161no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227D44—22no—
228D44—41no—
229D44—41no—
230D44—41no—
231D44—82no—
232D44—82no—
233D44—161no—
234C4×D11—21no—
235C4×D11—21no—
236C4×D11—82no—
237C4×D11—161no—
238C4×D11—161no—
239Dic22—161no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C11⋊C8—21no—
244C11⋊C8—21no—
245C2×#135—111no—
246C22×D8—111no—
247#554—221no—
248#546—221no—
249C2×Q32C2×D1111yescharacteristic, complemented
250C2×SD32—111no—
251C2×SD32—111no—
252C2×M32—111no—
253C22×C16C2×D1111yescharacteristic
254#500—111no—
255#495—111no—
256#484—221no—
257#484—221no—
258#477—221no—
259#467—111no—
260#467C2×D1111yescharacteristic
261#467C2×D1111yescharacteristic
262#466—111no—
263#463—221no—
264#450—221no—
265#449—221no—
266C4×Q16—111no—
267C4×D8—111no—
268C8×D4—111no—
269C2×#107—111no—
270C2×#107—111no—
271#366—111no—
272#366—111no—
273#366C2×D1111yescharacteristic, complemented
274C4⋊C16—111no—
275#358—111no—
276#358—111no—
277#358C2×D1111yescharacteristic, complemented
278#358C2×D1111yescharacteristic, complemented
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285C22⋊C16—111no—
286C22⋊C16—111no—
287#346—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11#51012yes—
291C22×C11C22×D811yescharacteristic
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—42no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—164no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11#54611yescharacteristic
308C4×C11#57711yescharacteristic
309Dic11—21no—
310Dic11—21no—
311Dic11—21no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C22×D4—221no—
316#135—222no—
317#135—441no—
318C2×Q16C22×D1111yescharacteristic
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C2×D8—222no—
325C2×D8—221no—
326C2×D8—441no—
327C22×C8—111no—
328C22×C8C22×D1111yescharacteristic
329C4⋊Q8—221no—
330#125—441no—
331#124—221no—
332#123—441no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—221no—
339#121—441no—
340#120—441no—
341C4×Q8—221no—
342C4×D4—111no—
343C4×D4—221no—
344C4×D4—441no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C22⋊C4—441no—
348Q32—41no—
349SD32—222no—
350SD32—441no—
351M32—441no—
352C2×C16—41no—
353C2×C16—111no—
354C2×C16—111no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—221no—
360#107—221no—
361#107—221no—
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—21no—
366#103—21no—
367#103—221no—
368#103—221no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8—111no—
374C2×C11—22no—
375C2×C11#329411yescharacteristic
376C2×C11C2×#51011yescharacteristic
377C2×C11#341511yescharacteristic
378D11—41no—
379D11—82no—
380D11—161no—
381C24—441no—
382#41—442no—
383#41—881no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—441no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—442no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—881no—
395C22×C4—111no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4D4×D1111yescharacteristic
401Q16—21no—
402Q16—21no—
403Q16—21no—
404Q16—21no—
405SD16—442no—
406SD16—881no—
407D8—112no—
408D8—221no—
409D8—221no—
410D8—221no—
411D8—442no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—111no—
415C2×C8—111no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8D4×D1111yescharacteristic
419C2×C8C23×D1111yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—111no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C42—111no—
442C42—441no—
443C16—21no—
444C16—21no—
445C16—221no—
446C16—221no—
447C11#3388111yescharacteristic, complemented, Sylow
448C23—111no—
449C23—441no—
450C23—441no—
451C23—882no—
452C23—882no—
453C23—1761no—
454C23D8×D1111yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—1761no—
460D4—222no—
461D4—222no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—1761no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—111no—
475C2×C4—111no—
476C2×C4—111no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—882no—
482C2×C4—1761no—
483C2×C4—1761no—
484C2×C4—1761no—
485C2×C4D8×D1111yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C8—21no—
488C8—221no—
489C8—221no—
490C8#6703711yescharacteristic
491C8#41×D1111yescharacteristic
492C22—21no—
493C22—21no—
494C22—221no—
495C22—221no—
496C22—221no—
497C22—442no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—1764no—
504C22#1062253112yes—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—81no—
511C4—221no—
512C4—221no—
513C4—221no—
514C4—881no—
515C4—881no—
516C4#1062314111yescharacteristic
517C4#1062330111yescharacteristic
518C2—22no—
519C2—441no—
520C2—882no—
521C2—1761no—
522C2#1308042411yescharacteristic
523C2C2×#1062253111yescharacteristic
524C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radical#13080298C2
hypercenter#2216D11
hypocenterC11#33881
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. #13081005C2semidirect
3. #13070854C2semidirect
4. #13070816C2semidirect
5. #13070798C2semidirect
6. #13070752C2semidirect
7. #13070732C2semidirect
8. #13070680C2semidirect
9. #13070555C2semidirect
10. #13070544C2semidirect
11. #13070483C2semidirect
12. #13070441C2semidirect
13. #13070327C2semidirect
14. C2×#10622147C2semidirect
15. C11×#2216C2semidirect
20. C2×C11×Q32C22semidirect
25. #10622801C22semidirect
26. Q16×Dic11C22semidirect
33. C2×#66862C22semidirect
35. D11×#107C22semidirect
36. #10622487C22semidirect
42. C11×#366C22semidirect
43. C11×#358C22semidirect
44. C11×#358C22semidirect
45. #10622202C22semidirect
46. #10622202C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
193. #2216D11semidirect
249. C2×Q32C2×D11semidirect
273. #366C2×D11semidirect
277. #358C2×D11semidirect
278. #358C2×D11semidirect
447. C11#33881semidirect

Maximal subgroups

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

subgroupindex
#130810052
#130802982
#130708542
#130708162
#130707982
#130707522
#130707322
#130706802
#130705552
#130705442
#130704832
#130704412
#130703272
C2×#106221472
C11×#22162
#3388111