Finite Group Databasebeta

← #14910639

Subgroups — #14910639

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081021C211yesmaximal, characteristic, complemented
2#13080298C211yesmaximal, characteristic, complemented
3#13070849C211yesmaximal, characteristic, complemented
4#13070816C211yesmaximal, characteristic, complemented
5#13070809C211yesmaximal, characteristic, complemented
6#13070772C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070673C211yesmaximal, characteristic, complemented
9#13070538C211yesmaximal, characteristic, complemented
10#13070527C211yesmaximal, characteristic, complemented
11#13070460C211yesmaximal, characteristic, complemented
12C16×C22⋊D11C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623161—21no—
19#10623149—21no—
20C2×C11×SD32C2211yescharacteristic, complemented
21C22×C11×C16C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622804C2211yescharacteristic
25#10622770C2211yescharacteristic, complemented
26D8×Dic11C2211yescharacteristic, complemented
27C2×#66890C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622659—21no—
32#10622647—21no—
33C2×C16×D11C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35#10622493C2211yescharacteristic, complemented
36#10622491C2211yescharacteristic, complemented
37#10622485C2211yescharacteristic
38#10622432—21no—
39#10622424—21no—
40#10622397—21no—
41#10622379—21no—
42C11×#367C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×#4343—21no—
60C22×D44—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×#121—21no—
66#67000—21no—
67C2×#4325—21no—
68C2×#4325—21no—
69#66992—41no—
70#66991—21no—
71D4×Dic11—21no—
72D4×Dic11—41no—
73C4×C22⋊D11D411yescharacteristic
74C2×C4⋊Dic11—21no—
75#66972—22no—
76#66972—41no—
77C2×D88—22no—
78C2×D88—21no—
79C2×D88—41no—
80C2×D88C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66948—21no—
84#66948—41no—
85#66947—41no—
86#66946—21no—
87#66945—21no—
88#66943—21no—
89#66939—41no—
90#66935—41no—
91C22⋊C4×D11—41no—
92#66932—41no—
93C11×SD32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100C11×#102—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66890—22no—
105#66890—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#66872—21no—
117#66872—21no—
118C16×D11—41no—
119#33864—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11D811yescharacteristic
127C22×Dic11—41no—
128C22×Dic11—41no—
129#4343—42no—
130#4343—81no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—42no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—81no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11C2×D411yescharacteristic
141C11×Q16—21no—
142C11×Q16—21no—
143C11×D8—21no—
144C11×D8—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11D811yescharacteristic
157#4325—42no—
158#4325—81no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4D811yescharacteristic
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—41no—
168C4⋊Dic11—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#3339—111no—
187#3280—111no—
188#2242—111no—
189#2236—111no—
190#2234—111no—
191#2228—111no—
192#2217D1111yescharacteristic, complemented
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2184—111no—
197C4×D16—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#357—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—161no—
208C22×D11C2×D811yescharacteristic
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—82no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—22no—
222C22⋊D11—161no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—161no—
226C2×Dic11—161no—
227C2×Dic11C2×D811yescharacteristic
228C2×Dic11C2×D811yescharacteristic
229C2×Dic11C2×D811yescharacteristic
230D44—22no—
231D44—41no—
232D44—41no—
233D44—41no—
234D44—82no—
235D44—82no—
236D44—161no—
237C4×D11—21no—
238C4×D11—21no—
239C4×D11—82no—
240C4×D11—161no—
241C8×C11—21no—
242C8×C11C2×#4111yescharacteristic
243C8×C11H(5,𝔽2)11yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—21no—
246C2×#135—111no—
247C22×D8—111no—
248#553—221no—
249#546—221no—
250C2×SD32C2×D1111yescharacteristic, complemented
251C2×D16—111no—
252C2×D16—111no—
253C22×C16—111no—
254C22×C16C2×D1111yescharacteristic
255#499—111no—
256#495—111no—
257#482—221no—
258#481—221no—
259#478—221no—
260#467C2×D1111yescharacteristic
261#466—111no—
262#466—111no—
263#466C2×D1111yescharacteristic
264#463—221no—
265#450—221no—
266#449—221no—
267C4×D8—111no—
268C4×D8—111no—
269C8×D4—111no—
270#427—111no—
271C2×#107—111no—
272#367C2×D1111yescharacteristic, complemented
273#366—111no—
274#366—111no—
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358C2×D1111yescharacteristic, complemented
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357C2×D1111yescharacteristic, complemented
286C22⋊C16—111no—
287C22⋊C16—111no—
288C4×C16—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11#50812yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—42no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—164no—
306C4×C11—21no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#54611yescharacteristic
311C4×C11#57711yescharacteristic
312Dic11—21no—
313Dic11—21no—
314Dic11—21no—
315Dic11—81no—
316Dic11—81no—
317C2×#41—221no—
318C22×D4—221no—
319#135—222no—
320#135—441no—
321C2×Q16C22×D1111yescharacteristic
322C2×SD16—221no—
323C2×SD16—221no—
324C2×D8—111no—
325C2×D8—111no—
326C2×D8—222no—
327C2×D8—221no—
328C2×D8—441no—
329C2×D8C22×D1111yescharacteristic
330C22×C8—111no—
331C22×C8C22×D1111yescharacteristic
332#126—441no—
333#125—221no—
334#124—221no—
335#123—441no—
336#123—441no—
337C22⋊Q8—21no—
338#121—21no—
339#121—221no—
340#121—221no—
341#121—441no—
342#121—441no—
343#120—441no—
344C4×D4—111no—
345C4×D4—221no—
346C4×D4—221no—
347C4×D4—441no—
348#117—221no—
349C2×C4⋊C4—221no—
350C2×C22⋊C4—441no—
351SD32—41no—
352D16—222no—
353D16—441no—
354C2×C16—41no—
355C2×C16—111no—
356C2×C16—111no—
357C2×C16—441no—
358C2×C16C22×D1111yescharacteristic
359C2×C16C22×D1111yescharacteristic
360#107—111no—
361#107—111no—
362#107—221no—
363#107C22×D1111yescharacteristic
364#107C22×D1111yescharacteristic
365#106—221no—
366#106—221no—
367C4⋊C8—111no—
368#103—21no—
369#102—21no—
370#102—221no—
371#102—221no—
372#102—221no—
373#102—221no—
374C22⋊C8—111no—
375C22⋊C8—111no—
376C4×C8—111no—
377C2×C11—22no—
378C2×C11—161no—
379C2×C11#329411yescharacteristic
380C2×C11C2×#50811yescharacteristic
381C2×C11#341511yescharacteristic
382D11—41no—
383D11—82no—
384D11—161no—
385C24—441no—
386#41—442no—
387#41—881no—
388C2×Q8—21no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—442no—
395C2×D4—441no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—881no—
400C22×C4—111no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4D4×D1111yescharacteristic
406Q16—21no—
407Q16—21no—
408SD16—442no—
409SD16—881no—
410D8—21no—
411D8—21no—
412D8—112no—
413D8—221no—
414D8—221no—
415D8—221no—
416D8—442no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—111no—
420C2×C8—111no—
421C2×C8—221no—
422C2×C8—221no—
423C2×C8D4×D1111yescharacteristic
424C2×C8C23×D1111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—111no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—111no—
437C22⋊C4—111no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C22⋊C4—441no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C42—111no—
446C42—441no—
447C16—21no—
448C16—21no—
449C16—221no—
450C16—221no—
451C11#3386411yescharacteristic, complemented, Sylow
452C23—41no—
453C23—111no—
454C23—441no—
455C23—441no—
456C23—882no—
457C23—882no—
458C23—1761no—
459C23D8×D1111yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—41no—
463D4—41no—
464D4—82no—
465D4—222no—
466D4—222no—
467D4—441no—
468D4—441no—
469D4—441no—
470D4—882no—
471D4—882no—
472D4—1761no—
473D4—1761no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—111no—
480C2×C4—111no—
481C2×C4—111no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—882no—
487C2×C4—1761no—
488C2×C4—1761no—
489C2×C4—1761no—
490C2×C4D8×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C8—21no—
493C8—221no—
494C8—221no—
495C8#6703711yescharacteristic
496C8#41×D1111yescharacteristic
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—221no—
503C22—221no—
504C22—221no—
505C22—442no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22—1764no—
512C22#1062252912yes—
513C22C2×D8×D1111yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—221no—
519C4—221no—
520C4—221no—
521C4—881no—
522C4—881no—
523C4#1062314111yescharacteristic
524C4#1062330111yescharacteristic
525C2—22no—
526C2—161no—
527C2—441no—
528C2—882no—
529C2—1761no—
530C2#1308042411yescharacteristic
531C2C2×#1062252911yescharacteristic
532C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
hypercenter#2217D11
hypocenterC11#33864
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13081021C2semidirect
2. #13080298C2semidirect
3. #13070849C2semidirect
4. #13070816C2semidirect
5. #13070809C2semidirect
6. #13070772C2semidirect
7. #13070701C2semidirect
8. #13070673C2semidirect
9. #13070538C2semidirect
10. #13070527C2semidirect
11. #13070460C2semidirect
12. C16×C22⋊D11C2semidirect
13. #13070322C2semidirect
14. C2×#10622147C2semidirect
15. C11×#2217C2semidirect
20. C2×C11×SD32C22semidirect
25. #10622770C22semidirect
26. D8×Dic11C22semidirect
33. C2×C16×D11C22semidirect
35. #10622493C22semidirect
36. #10622491C22semidirect
42. C11×#367C22semidirect
43. C11×#358C22semidirect
44. C11×#357C22semidirect
45. #10622202C22semidirect
46. #10622202C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. Dic11⋊C16C22semidirect
54. C16×Dic11C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
192. #2217D11semidirect
250. C2×SD32C2×D11semidirect
272. #367C2×D11semidirect
278. #358C2×D11semidirect
285. #357C2×D11semidirect
451. C11#33864semidirect

Maximal subgroups

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

subgroupindex
#130810212
#130802982
#130708492
#130708162
#130708092
#130707722
#130707012
#130706732
#130705382
#130705272
#130704602
C16×C22⋊D112
#130703222
C2×#106221472
C11×#22172
#3386411