Finite Group Databasebeta

← #14758159

Subgroups — #14758159

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077384C211yesmaximal, characteristic
2#13077259C211yesmaximal, characteristic, complemented
3#13077256C211yesmaximal, characteristic, complemented
4#13069503C211yesmaximal, characteristic
5#13069501C211yesmaximal, characteristic
6#13069363C211yesmaximal, characteristic, complemented
7#13069361C211yesmaximal, characteristic, complemented
8#13069322C211yesmaximal, characteristic, complemented
9#13069320C211yesmaximal, characteristic, complemented
10#13069318C211yesmaximal, characteristic, complemented
11#13068517C211yesmaximal, characteristic, complemented
12#104×Dic11C211yesmaximal, characteristic, complemented
13#13068420C211yesmaximal, characteristic, complemented
14C4×C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1937C211yesmaximal, characteristic, complemented
16#41×Dic11C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18#10623053C2211yescharacteristic
19C11×#424C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C11×#416C2211yescharacteristic
22C11×#408C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25#10622847C2211yescharacteristic
26C2×#66889C2211yescharacteristic
27#10622742C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30#10622732C2211yescharacteristic
31M16×Dic11C2211yescharacteristic
32M16×Dic11C2211yescharacteristic
33#10622726C2211yescharacteristic
34#10622723C2211yescharacteristic
35#10622715C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622612C2211yescharacteristic
41#10622611C2211yescharacteristic
42C42×Dic11C2211yescharacteristic
43C2×#66869C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622453—22no—
46#10622446—22no—
47#10622403C412yescomplemented
48#10622401C412yescomplemented
49#10622371C412yescomplemented
50#10622369C412yescomplemented
51#10622333—22no—
52#10622331—22no—
53C11×#341C2211yescharacteristic
54C11×#339C2211yescharacteristic
55#10622193C2211yescharacteristic
56#10622190C2211yescharacteristic
57#10622170C2211yescharacteristic
58#10622161C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C2×#4339C2311yescharacteristic
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67003—22no—
68#67003—22no—
69Q8×Dic11C2×C412yes—
70C2×#4326C2×C411yescharacteristic
71C2×#4325C2×C411yescharacteristic
72D4×Dic11—22no—
73D4×Dic11C2×C412yes—
74C2×#4324C2×C411yescharacteristic
75C2×#4323C2×C411yescharacteristic
76#66979—21no—
77#66979C2311yescharacteristic
78C2×C4×Dic11—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C2×#4318C2311yescharacteristic
83C2×#4318C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86#66946C2×C412yes—
87#66940C2×C412yes—
88(C22⋊D11)⋊C4—22no—
89#66925—21no—
90C42×D11—21no—
91C11×C4⋊C8—22no—
92C11×#104—22no—
93C11×#103C2×C412yes—
94C11×#102C2×C412yes—
95C11×C22⋊C8—22no—
96C4×C8×C11—22no—
97#66901—22no—
98C22⋊(C11⋊C8)—22no—
99#66889—22no—
100#66886—22no—
101#66886—22no—
102#66885C2×C412yes—
103(C2×D11)⋊C8—22no—
104(C2×D11)⋊C8—22no—
105#66880C2×C412yes—
106#66879—21no—
107#66879—21no—
108Dic11⋊C8—22no—
109Dic11⋊C8—22no—
110C8×Dic11—21no—
111C8×Dic11—21no—
112C8×Dic11—22no—
113C8×Dic11—22no—
114C8×Dic11C2×C412yes—
115C8×Dic11C2×C412yes—
116C8×Dic11D412yes—
117C8×Dic11D412yes—
118#66872C2×C412yes—
119#66871C2×C412yes—
120#66869—22no—
121C4⋊(C11⋊C8)—22no—
122C4×C11⋊C8—22no—
123#21292—111nomaximal, Sylow
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C11×#41—21no—
128C2×Q8×C11C22×C411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11C22×C411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—21no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11#4112yes—
138#4339—21no—
139#4339—21no—
140#4339—21no—
141#4339—21no—
142C2×D44C22×C411yescharacteristic
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×Dic22C22×C411yescharacteristic
146C11×M16—21no—
147C11×M16—21no—
148C11×M16—21no—
149C11×M16—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C2×D412yes—
158C11×C4⋊C4C22×C412yes—
159C11×C22⋊C4—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11#4112yes—
163C22⋊Dic11—22no—
164C22⋊Dic11—21no—
165#4326—22no—
166#4325—22no—
167#4324—22no—
168#4323—22no—
169(C2×D11)⋊C4—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11C22×C412yes—
172Dic11⋊C4—22no—
173C4×Dic11—28no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11C22×C412yes—
179C4×Dic11C2×D411yescharacteristic
180C4×Dic11C2×D411yescharacteristic
181C4×Dic11#4112yes—
182#4318—21no—
183#4318—21no—
184#4318—21no—
185#4318—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C411yescharacteristic
191C2×C11⋊C8C22×C411yescharacteristic
192C2×C11⋊C8C2×D412yes—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195C4×#135—111no—
196#2922—111no—
197#2922—111no—
198#1974—111no—
199#1974—111no—
200#1945—111no—
201#1945—111no—
202#1937—111no—
203#1937—111no—
204#1937—111no—
205#1937D1111yescharacteristic, complemented
206C4×#108—111no—
207C4×#104—111no—
208C4×#104—111no—
209C42×C8—111no—
210C23×C11—21no—
211C23×C11C2×#4111yescharacteristic
212C22×D11—21no—
213Q8×C11—21no—
214Q8×C11—21no—
215D4×C11—21no—
216D4×C11—21no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C22⋊D11—41no—
232C22⋊D11—41no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—44no—
239C2×Dic11C4×D412yes—
240C2×Dic11C4×D412yes—
241D44—21no—
242D44—21no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—44no—
246Dic22—21no—
247Dic22—21no—
248C8×C11—22no—
249C8×C11—22no—
250C8×C11—41no—
251C8×C11—41no—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C11⋊C8#11712yes—
256C11⋊C8#11712yes—
257C2×#135—111no—
258C4×#41—111no—
259C4×#41—111no—
260C4×Q16—112no—
261C4×SD16—112no—
262C4×SD16—112no—
263C4×D8—112no—
264#433—222no—
265#433—222no—
266#431—222no—
267#431—222no—
268C2×#108—111no—
269C2×#108—111no—
270#427—111no—
271#424—111no—
272#424—111no—
273#424—111no—
274#424C2×D1111yescharacteristic
275C2×#104—111no—
276C2×#104—111no—
277C2×#104—111no—
278C2×#104C2×D1111yescharacteristic
279#416—111no—
280#416C2×D1111yescharacteristic
281#408—111no—
282#408—111no—
283#408—111no—
284#408C2×D1111yescharacteristic
285C4×M16—111no—
286C4×M16—111no—
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291C2×C4×C8—111no—
292C2×C4×C8C2×D1111yescharacteristic
293C43—111no—
294#341—111no—
295#341C2×D1111yescharacteristic
296#339—111no—
297#339—111no—
298#339—111no—
299#339C2×D1111yescharacteristic
300C22×C11—22no—
301C22×C11—42no—
302C22×C11—41no—
303C22×C11C2×C4×D411yescharacteristic
304C22×C11#52911yescharacteristic
305C22×C11#52911yescharacteristic
306C2×D11—42no—
307C2×D11—41no—
308C4×C11—24no—
309C4×C11—42no—
310C4×C11—41no—
311C4×C11C2×#11711yescharacteristic
312C4×C11C4×#4111yescharacteristic
313C4×C11#53211yescharacteristic
314C4×C11#53211yescharacteristic
315Dic11—24no—
316Dic11—22no—
317Dic11—42no—
318Dic11—41no—
319Dic11#44314yes—
320C2×#41—111no—
321C2×#41C22×D1111yescharacteristic
322#135—222no—
323#135—222no—
324C2×Q16—111no—
325C2×SD16—111no—
326C2×SD16—111no—
327C2×D8—111no—
328C2×M16—111no—
329C2×M16—111no—
330C2×M16C22×D1111yescharacteristic
331C2×M16C22×D1111yescharacteristic
332C22×C8—111no—
333C22×C8—111no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4×Q8—112no—
337C4×Q8—112no—
338C4×D4—112no—
339C4×D4—112no—
340C4×D4—222no—
341C4×D4—222no—
342#117—111no—
343#117—221no—
344#117—221no—
345#117C22×D1111yescharacteristic
346C2×C42—111no—
347C2×C42—111no—
348C2×C42—221no—
349C2×C42—221no—
350C2×C42—222no—
351C2×C42C22×D1111yescharacteristic
352#108—222no—
353#108—222no—
354#107—112no—
355#106—112no—
356C4⋊C8—22no—
357C4⋊C8—222no—
358C4⋊C8—222no—
359C4⋊C8—222no—
360#104—22no—
361#104—222no—
362#104—222no—
363#104—222no—
364#103—112no—
365#103C4×D1112yes—
366#102—112no—
367#102C4×D1112yes—
368C22⋊C8—22no—
369C22⋊C8—222no—
370C22⋊C8—222no—
371C22⋊C8—222no—
372#97—221no—
373#97—221no—
374C4×C8—22no—
375C4×C8—112no—
376C4×C8—112no—
377C4×C8—112no—
378C4×C8—112no—
379C4×C8—222no—
380C4×C8—222no—
381C4×C8—221no—
382C4×C8—221no—
383C4×C8—222no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—81no—
387C2×C11#229311yescharacteristic
388C2×C11C2×#44312yes—
389D11—81no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—221no—
395#41—221no—
396#41—221no—
397#41—221no—
398C2×Q8—111no—
399C2×Q8C2×C4×D1111yescharacteristic
400C2×D4—21no—
401C2×D4—111no—
402C2×D4—221no—
403C2×D4C2×C4×D1111yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—112no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4C23×D1111yescharacteristic
412Q16—222no—
413SD16—222no—
414SD16—222no—
415D8—222no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—221no—
421M16—221no—
422M16—221no—
423M16—221no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—111no—
431C2×C8—111no—
432C2×C8—112no—
433C2×C8—112no—
434C2×C8—112no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8C2×C4×D1112yes—
440C2×C8D4×D1112yes—
441C4⋊C4—112no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4C2×C4×D1112yes—
445C22⋊C4—21no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C22⋊C4—221no—
449C42—21no—
450C42—21no—
451C42—112no—
452C42—111no—
453C42—111no—
454C42—112no—
455C42—222no—
456C42—222no—
457C42—228no—
458C42—221no—
459C42—221no—
460C42#434112yes—
461C11#2129211yescharacteristic, complemented, Sylow
462C23—21no—
463C23—221no—
464C23#41×D1111yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—221no—
468Q8—221no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—221no—
474D4—221no—
475D4—441no—
476D4—441no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—221no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4C22×C4×D1111yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×#434111yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#41×D1111yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—112no—
505C8—112no—
506C8—222no—
507C8—441no—
508C8—441no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—441no—
513C22—442no—
514C22C4×D4×D1111yescharacteristic
515C22#1062318011yescharacteristic
516C22#1062323711yescharacteristic
517C4—24no—
518C4—41no—
519C4—42no—
520C4—114no—
521C4—224no—
522C4—222no—
523C4—441no—
524C4—442no—
525C4D11×#11711yescharacteristic
526C4C4×#434111yescharacteristic
527C4#1062312711yescharacteristic
528C4#1062319911yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—881no—
533C2#1307107611yescharacteristic
534C2D11×#44312yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1937C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#1937D11
hypocenterC11#21292
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. #13077259C2semidirect
3. #13077256C2semidirect
6. #13069363C2semidirect
7. #13069361C2semidirect
8. #13069322C2semidirect
9. #13069320C2semidirect
10. #13069318C2semidirect
11. #13068517C2semidirect
12. #104×Dic11C2semidirect
13. #13068420C2semidirect
14. C4×C8×Dic11C2semidirect
15. C11×#1937C2semidirect
47. #10622403C4semidirect
48. #10622401C4semidirect
49. #10622371C4semidirect
50. #10622369C4semidirect
205. #1937D11semidirect
461. C11#21292semidirect

Maximal subgroups

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

subgroupindex
#130773842
#130772592
#130772562
#130695032
#130695012
#130693632
#130693612
#130693222
#130693202
#130693182
#130685172
#104×Dic112
#130684202
C4×C8×Dic112
C11×#19372
#2129211