Finite Group Databasebeta

← #14910616

Subgroups — #14910616

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080980C211yesmaximal, characteristic, complemented
2#13080298C211yesmaximal, characteristic
3#13070849C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070772C211yesmaximal, characteristic, complemented
6#13070713C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070681C211yesmaximal, characteristic, complemented
9#13070559C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070467C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic, complemented
14C2×#10622129C211yesmaximal, characteristic, complemented
15C11×#2235C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623161—21no—
19#10623044—21no—
20C11×#467C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622804C2211yescharacteristic
23C2×#66893C2211yescharacteristic, complemented
24#10622729C2211yescharacteristic
25C8×C22⋊D11C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622659—21no—
28#10622584—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic, complemented
32#10622501—21no—
33#10622500C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35#10622493C2211yescharacteristic, complemented
36#10622491C2211yescharacteristic, complemented
37#10622490—21no—
38#10622486C2211yescharacteristic, complemented
39#10622485C2211yescharacteristic
40#10622432—21no—
41#10622424—21no—
42C11×#367C2211yescharacteristic, complemented
43C11×#367C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×C22⋊C16C2211yescharacteristic
47#10622202C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51Dic11⋊C16C2211yescharacteristic, complemented
52C16×Dic11C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic, complemented
59C2×#4343—21no—
60C22×D44—21no—
61C2×C11×Q16C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C2×C11×C4⋊C4—21no—
65#67000—21no—
66C2×#4325—21no—
67C2×#4325—21no—
68#66982—41no—
69C4×C22⋊D11D411yescharacteristic
70#66979—41no—
71#66977—21no—
72#66972—22no—
73#66972—41no—
74C2×Dic44C2311yescharacteristic
75C2×D88—22no—
76C2×D88—21no—
77C2×D88—41no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66951—41no—
82#66950—21no—
83#66948—21no—
84#66948—41no—
85#66947—41no—
86#66946—21no—
87#66945—21no—
88#66943—21no—
89#66942—41no—
90#66940—21no—
91#66935—41no—
92C22⋊C4×D11—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C22⋊(C11⋊C8)D411yescharacteristic
101#66893—41no—
102(C2×D11)⋊C8D411yescharacteristic
103#66882C2311yescharacteristic
104#66880—21no—
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—41no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66874—21no—
112#66873—21no—
113#66873—21no—
114#66872—21no—
115#66872—21no—
116#66864—22no—
117#66864—41no—
118C16×D11—41no—
119#33863—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11D811yescharacteristic
125#4343—42no—
126#4343—81no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—42no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44—81no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11D811yescharacteristic
152#4325—42no—
153#4325—81no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4D811yescharacteristic
161C4⋊Dic11—21no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4D811yescharacteristic
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—21no—
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#3336—111no—
187#3280—111no—
188#2242—111no—
189#2235D1111yescharacteristic, complemented
190#2234—111no—
191#2228—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—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—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225D44—22no—
226D44—41no—
227D44—41no—
228D44—41no—
229D44—82no—
230D44—82no—
231D44—161no—
232C4×D11—21no—
233C4×D11—21no—
234C4×D11—82no—
235C4×D11—161no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×D8—111no—
245#552—221no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499—111no—
253#495—111no—
254#485—221no—
255#483—221no—
256#479—221no—
257#467—111no—
258#467—111no—
259#467C2×D1111yescharacteristic
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268C2×#107C2×D1111yescharacteristic
269#367C2×D1111yescharacteristic, complemented
270#367C2×D1111yescharacteristic, complemented
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic, complemented
276#358C2×D1111yescharacteristic, complemented
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16C2×D1111yescharacteristic
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11#50812yes—
289C22×C11C22×D811yescharacteristic
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—42no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—164no—
300C4×C11—21no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11#54611yescharacteristic
306C4×C11#57711yescharacteristic
307Dic11—21no—
308Dic11—21no—
309Dic11—21no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—221no—
313C22×D4—221no—
314#135—222no—
315#135—441no—
316C2×Q16—111no—
317C2×Q16C22×D1111yescharacteristic
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—111no—
321C2×D8—111no—
322C2×D8—222no—
323C2×D8—221no—
324C2×D8—441no—
325C22×C8—111no—
326C22×C8C22×D1111yescharacteristic
327#126—441no—
328#125—221no—
329#125—441no—
330#124—221no—
331#123—441no—
332#123—441no—
333C22⋊Q8—21no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—221no—
340C4×D4—111no—
341C4×D4—221no—
342#117—221no—
343#117—441no—
344C2×C4⋊C4—21no—
345C2×C22⋊C4—441no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16—441no—
353C2×C16C22×D1111yescharacteristic
354C2×C16C22×D1111yescharacteristic
355#107—21no—
356#107—111no—
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#106—221no—
361#106—221no—
362C4⋊C8—111no—
363#103—21no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—221no—
368#102—221no—
369C22⋊C8—111no—
370C22⋊C8—111no—
371C4×C8—111no—
372C2×C11—22no—
373C2×C11#329411yescharacteristic
374C2×C11C2×#50811yescharacteristic
375C2×C11#341611yescharacteristic
376D11—41no—
377D11—82no—
378D11—161no—
379C24—441no—
380#41—442no—
381#41—881no—
382C2×Q8—21no—
383C2×Q8—221no—
384C2×D4—111no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—442no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—881no—
392C22×C4—41no—
393C22×C4—111no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—221no—
400Q16—221no—
401SD16—442no—
402SD16—881no—
403D8—112no—
404D8—221no—
405D8—221no—
406D8—221no—
407D8—442no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—111no—
411C2×C8—111no—
412C2×C8—221no—
413C2×C8—221no—
414C2×C8D4×D1111yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—111no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C22⋊C4—41no—
429C22⋊C4—111no—
430C22⋊C4—111no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C42—111no—
439C42—441no—
440C42—441no—
441C16—21no—
442C16—21no—
443C16—221no—
444C16—221no—
445C11#3386311yescharacteristic, complemented, Sylow
446C23—111no—
447C23—441no—
448C23—441no—
449C23—882no—
450C23—882no—
451C23—1761no—
452C23D8×D1111yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—441no—
456Q8—441no—
457D4—222no—
458D4—222no—
459D4—441no—
460D4—441no—
461D4—441no—
462D4—882no—
463D4—882no—
464D4—1761no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—111no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—882no—
480C2×C4—1761no—
481C2×C4D8×D1111yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C8—21no—
484C8—221no—
485C8—221no—
486C8#41×D1111yescharacteristic
487C8#6704211yescharacteristic
488C22—21no—
489C22—21no—
490C22—221no—
491C22—221no—
492C22—221no—
493C22—442no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22—1764no—
500C22#1062252912yes—
501C22C2×D8×D1111yescharacteristic
502C4—21no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—221no—
508C4—221no—
509C4—221no—
510C4—881no—
511C4—881no—
512C4#1062318511yescharacteristic
513C4#1062330911yescharacteristic
514C2—22no—
515C2—441no—
516C2—882no—
517C2—1761no—
518C2#1308042711yescharacteristic
519C2C2×#1062252911yescharacteristic
520C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2235C2
socleC22×C11C22×D8
prime radical#13080298C2
hypercenter#2235D11
hypocenterC11#33863
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
1. #13080980C2semidirect
3. #13070849C2semidirect
4. #13070809C2semidirect
5. #13070772C2semidirect
6. #13070713C2semidirect
7. #13070705C2semidirect
8. #13070681C2semidirect
9. #13070559C2semidirect
10. #13070547C2semidirect
11. #13070467C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. #13070322C2semidirect
14. C2×#10622129C2semidirect
15. C11×#2235C2semidirect
23. C2×#66893C22semidirect
31. C2×C16×D11C22semidirect
33. #10622500C22semidirect
35. #10622493C22semidirect
36. #10622491C22semidirect
38. #10622486C22semidirect
42. C11×#367C22semidirect
43. C11×#367C22semidirect
44. C11×#358C22semidirect
45. C11×#358C22semidirect
47. #10622202C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. Dic11⋊C16C22semidirect
52. C16×Dic11C22semidirect
53. #10622130C22semidirect
58. #10622127C22semidirect
189. #2235D11semidirect
269. #367C2×D11semidirect
270. #367C2×D11semidirect
275. #358C2×D11semidirect
276. #358C2×D11semidirect
445. C11#33863semidirect

Maximal subgroups

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

subgroupindex
#130809802
#130802982
#130708492
#130708092
#130707722
#130707132
#130707052
#130706812
#130705592
#130705472
#130704672
(C22⋊D11)⋊C162
#130703222
C2×#106221292
C11×#22352
#3386311