Finite Group Databasebeta

← #14910629

Subgroups — #14910629

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#13081014C211yesmaximal, characteristic, complemented
2#13080301C211yesmaximal, characteristic, complemented
3#13070846C211yesmaximal, characteristic, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070806C211yesmaximal, characteristic, complemented
6#13070775C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070701C211yesmaximal, characteristic, complemented
9#13070670C211yesmaximal, characteristic, complemented
10#13070540C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070460C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14#13070320C211yesmaximal, characteristic, complemented
15C2×C11×#357C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623337—21no—
18C2×#66965C2211yescharacteristic
19#10623045—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622831—21no—
23#10622771—21no—
24#10622770C2211yescharacteristic
25#10622768C2211yescharacteristic
26#10622766—21no—
27D8×Dic11C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622581—21no—
34C2×#66864C2211yescharacteristic, complemented
35C2×C16×D11C2211yescharacteristic, complemented
36#10622504—21no—
37#10622498—21no—
38#10622496C2211yescharacteristic, complemented
39#10622493C2211yescharacteristic, complemented
40#10622491C2211yescharacteristic, complemented
41#10622485C2211yescharacteristic, complemented
42C11×#357C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic, complemented
50(C2×D11)⋊C16C2211yescharacteristic, complemented
51#10622143C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53Dic11⋊C16C2211yescharacteristic, complemented
54C16×Dic11C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×#4341—21no—
61C2×C11×D8—22no—
62C2×C11×D8—21no—
63C2×C11×D8—41no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68#67006—41no—
69C2×C22⋊Dic11—41no—
70#66992—41no—
71#66991—21no—
72#66989—21no—
73#66988—41no—
74D4×Dic11—21no—
75C2×#4324—21no—
76C2×#4324—21no—
77#66983—21no—
78#66983—41no—
79C4×C22⋊D11—41no—
80C4×C22⋊D11D411yescharacteristic
81#66977—21no—
82#66965—22no—
83#66965—41no—
84C2×Dic44C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66948—21no—
89#66947—41no—
90#66946—21no—
91#66945—21no—
92#66943—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66896—21no—
100#66896—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66890—22no—
103#66890—41no—
104#66885—21no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66873—21no—
115#66872—21no—
116#66872—21no—
117#66864—41no—
118C16×D11—41no—
119#33864—111nomaximal, Sylow
120C24×C11—41no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—81no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C22×Dic11—41no—
133C22×Dic11—41no—
134#4341—42no—
135#4341—81no—
136C2×D44—21no—
137C2×D44—41no—
138C2×C4×D11—41no—
139C2×C4×D11C2×D411yescharacteristic
140C2×Dic22—21no—
141C11×D8—21no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8—42no—
145C11×D8#4112yes—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11D811yescharacteristic
159#4324—42no—
160#4324—81no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4D811yescharacteristic
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178D88—21no—
179D88—21no—
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#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2184—111no—
197C4×D16—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#357D1111yescharacteristic, complemented
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—161no—
206C23×C11C2×D811yescharacteristic
207C22×D11—41no—
208C22×D11C2×D811yescharacteristic
209D4×C11—22no—
210D4×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—161no—
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—22no—
222C22⋊D11—82no—
223C22⋊D11—82no—
224C22⋊D11—161no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—82no—
229C2×Dic11—161no—
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C2×Dic11C2×D811yescharacteristic
233D44—41no—
234D44—41no—
235D44—161no—
236C4×D11—21no—
237C4×D11—21no—
238C4×D11—161no—
239Dic22—41no—
240Dic22—41no—
241C8×C11—21no—
242C8×C11C2×#4111yescharacteristic
243C8×C11H(5,𝔽2)11yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—21no—
246C2×#135—111no—
247C22×D8C2×D1111yescharacteristic
248#553—221no—
249#546—221no—
250C2×SD32—111no—
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#467—111no—
261#466—111no—
262#466—111no—
263#466—111no—
264#463—221no—
265#450—221no—
266#449—221no—
267C4×D8—111no—
268C4×D8—111no—
269C8×D4—111no—
270#427—111no—
271C2×#107C2×D1111yescharacteristic
272#367—111no—
273#366—111no—
274#366—111no—
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357C2×D1111yescharacteristic
283#357C2×D1111yescharacteristic
284#357C2×D1111yescharacteristic
285#357C2×D1111yescharacteristic
286C22⋊C16—111no—
287C22⋊C16—111no—
288C4×C16—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—42no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—164no—
298C22×C11#50812yes—
299C22×C11C22×D811yescharacteristic
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—21no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11#54611yescharacteristic
310C4×C11#57711yescharacteristic
311Dic11—21no—
312Dic11—21no—
313Dic11—21no—
314Dic11—81no—
315Dic11—81no—
316Dic11—81no—
317C2×#41—221no—
318C22×D4—21no—
319#135—222no—
320#135—441no—
321C2×Q16—111no—
322C2×SD16—221no—
323C2×SD16—221no—
324C2×D8—22no—
325C2×D8—21no—
326C2×D8—41no—
327C2×D8—111no—
328C2×D8C22×D1111yescharacteristic
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—221no—
338#121—221no—
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—21no—
350C2×C22⋊C4—441no—
351SD32—441no—
352D16—222no—
353D16—441no—
354C2×C16—41no—
355C2×C16—111no—
356C2×C16—111no—
357C2×C16—441no—
358C2×C16C22×D1111yescharacteristic
359C2×C16C22×D1111yescharacteristic
360#107—21no—
361#107—111no—
362#107—111no—
363#107C22×D1111yescharacteristic
364#107C22×D1111yescharacteristic
365#106—221no—
366#106—221no—
367C4⋊C8—111no—
368#103—221no—
369#102—221no—
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—82no—
379C2×C11—161no—
380C2×C11#329411yescharacteristic
381C2×C11C2×#50811yescharacteristic
382C2×C11#341511yescharacteristic
383D11—41no—
384D11—161no—
385C24—41no—
386#41—442no—
387#41—881no—
388C2×Q8—221no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—41no—
393C2×D4—81no—
394C2×D4—111no—
395C2×D4—221no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—441no—
400C22×C4—41no—
401C22×C4—111no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4D4×D1111yescharacteristic
406Q16—221no—
407Q16—221no—
408SD16—442no—
409SD16—881no—
410D8—21no—
411D8—21no—
412D8—21no—
413D8—42no—
414D8—221no—
415D8—221no—
416D8#433912yes—
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—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
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—41no—
454C23—82no—
455C23—82no—
456C23—111no—
457C23—161no—
458C23—441no—
459C23D8×D1111yescharacteristic
460Q8—441no—
461Q8—441no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—82no—
467D4—222no—
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—111no—
479C2×C4—111no—
480C2×C4—111no—
481C2×C4—161no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—882no—
488C2×C4—1761no—
489C2×C4—1761no—
490C2×C4D8×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C8—21no—
493C8—221no—
494C8—221no—
495C8C2×#433911yescharacteristic
496C8#6703711yescharacteristic
497C22—21no—
498C22—21no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—164no—
506C22—221no—
507C22—221no—
508C22—221no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22#1062252912yes—
513C22C2×D8×D1111yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—221no—
518C4—221no—
519C4—221no—
520C4—881no—
521C4—881no—
522C4—881no—
523C4#1062302111yescharacteristic
524C4#1062329311yescharacteristic
525C2—22no—
526C2—82no—
527C2—161no—
528C2—441no—
529C2—1761no—
530C2#1308042511yescharacteristic
531C2C2×#1062252911yescharacteristic
532C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#357C2
socleC22×C11C22×D8
hypercenterC2×#357D11
hypocenterC11#33864
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. #13081014C2semidirect
2. #13080301C2semidirect
3. #13070846C2semidirect
4. #13070818C2semidirect
5. #13070806C2semidirect
6. #13070775C2semidirect
7. #13070712C2semidirect
8. #13070701C2semidirect
9. #13070670C2semidirect
10. #13070540C2semidirect
11. #13070528C2semidirect
12. #13070460C2semidirect
13. C16×C22⋊D11C2semidirect
14. #13070320C2semidirect
15. C2×C11×#357C2semidirect
34. C2×#66864C22semidirect
35. C2×C16×D11C22semidirect
38. #10622496C22semidirect
39. #10622493C22semidirect
40. #10622491C22semidirect
41. #10622485C22semidirect
49. #10622147C22semidirect
50. (C2×D11)⋊C16C22semidirect
51. #10622143C22semidirect
52. #10622141C22semidirect
53. Dic11⋊C16C22semidirect
54. C16×Dic11C22semidirect
55. #10622130C22semidirect
56. #10622130C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
200. C2×#357D11semidirect
451. C11#33864semidirect

Maximal subgroups

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

subgroupindex
#130810142
#130803012
#130708462
#130708182
#130708062
#130707752
#130707122
#130707012
#130706702
#130705402
#130705282
#130704602
C16×C22⋊D112
#130703202
C2×C11×#3572
#3386411