Finite Group Databasebeta

← #14758205

Subgroups — #14758205

Order 2816.

738 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#13077414C211yesmaximal, characteristic
2#13077268C211yesmaximal, characteristic, complemented
3#13077267C211yesmaximal, characteristic, complemented
4#13069506C211yesmaximal, characteristic
5#13069501C211yesmaximal, characteristic
6#13069368C211yesmaximal, characteristic, complemented
7#13069363C211yesmaximal, characteristic, complemented
8#13069328C211yesmaximal, characteristic, complemented
9#13069324C211yesmaximal, characteristic, complemented
10#13069321C211yesmaximal, characteristic, complemented
11#13069317C211yesmaximal, characteristic, complemented
12#13068523C211yesmaximal, characteristic, complemented
13C4×#66869C211yesmaximal, characteristic, complemented
14C4×#66867C211yesmaximal, characteristic, complemented
15C4×C11×#104C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C2×C11×#104C2211yescharacteristic
20C2×C11×#104C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22C43×C11C2211yescharacteristic
23#10622847C2211yescharacteristic
24#10622847C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622742C2211yescharacteristic
27#10622742C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30#10622732C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622643C412yescomplemented
33#10622639C412yescomplemented
34#10622631C412yescomplemented
35#10622627C412yescomplemented
36#10622615C2211yescharacteristic
37#10622613—22no—
38#10622612C2211yescharacteristic
39#10622612C2211yescharacteristic
40#10622611C2211yescharacteristic
41C2×#66869C2211yescharacteristic
42C2×#66869C2211yescharacteristic
43#10622539—22no—
44C4×#4318C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622318—22no—
52#10622303—22no—
53C11×#339C2211yescharacteristic
54C11×#339C2211yescharacteristic
55#10622196C2211yescharacteristic
56#10622196C2211yescharacteristic
57#10622161C2211yescharacteristic
58#10622161C2211yescharacteristic
59C2×C11×#41C2311yescharacteristic
60C2×#4339C2311yescharacteristic
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2311yescharacteristic
63C4×Q8×C11C2×C412yes—
64C4×D4×C11—22no—
65C4×D4×C11C2×C412yes—
66C11×#117—21no—
67C11×#117C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11—22no—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67003—22no—
74#67003—22no—
75C2×#4326C2×C411yescharacteristic
76C2×#4325C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—22no—
80#66979C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82C2×#4318C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C4×D44C2×C412yes—
88#66925—21no—
89C42×D11—21no—
90C4×Dic22C2×C412yes—
91C11×#104—22no—
92C11×#104—22no—
93C11×#97—21no—
94C4×C8×C11—21no—
95#66899C2×C412yes—
96#66896C2×C412yes—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—22no—
99#66886—22no—
100#66886—22no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—22no—
103Dic11⋊C8—22no—
104Dic11⋊C8—22no—
105#66874C2×C412yes—
106#66873C2×C412yes—
107#66872C2×C412yes—
108#66871C2×C412yes—
109#66869—22no—
110#66869—22no—
111C4⋊(C11⋊C8)—22no—
112C4⋊(C11⋊C8)—22no—
113#66867—21no—
114#66867—22no—
115#66867—22no—
116#66867C2×C412yes—
117#66867C2×C412yes—
118#66867D412yes—
119#66867D412yes—
120C4×C11⋊C8—21no—
121C4×C11⋊C8—22no—
122C4×C11⋊C8—22no—
123#21297—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×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—21no—
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—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—22no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—44no—
161C42×C11C22×C412yes—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11#4112yes—
165C42×C11#4112yes—
166C22⋊Dic11—21no—
167#4326—22no—
168#4325—22no—
169#4324—22no—
170#4323—22no—
171(C2×D11)⋊C4—22no—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—22no—
174C4×Dic11—22no—
175C4×Dic11—21no—
176#4318—21no—
177#4318—21no—
178#4318—21no—
179#4318—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8C22×C412yes—
189C2×C11⋊C8C22×C411yescharacteristic
190C2×C11⋊C8C22×C411yescharacteristic
191C2×C11⋊C8C2×D412yes—
192C2×C11⋊C8C2×D412yes—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195#2943—111no—
196#2923—111no—
197#2923—111no—
198#1975—111no—
199#1974—111no—
200#1946—111no—
201#1945—111no—
202#1938—111no—
203#1938—111no—
204#1937—111no—
205#1937—111no—
206#1778—111no—
207C4×#104—111no—
208C4×#104D1111yescharacteristic, complemented
209C4×#97—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—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—82no—
229C2×C4×C11C4×D412yes—
230C2×C4×C11C4×D412yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C22⋊D11—41no—
238C22⋊D11—41no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241D44—21no—
242D44—21no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—82no—
246Dic22—21no—
247Dic22—21no—
248C8×C11—41no—
249C8×C11—41no—
250C11⋊C8—22no—
251C11⋊C8—22no—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C11⋊C8—41no—
255C11⋊C8#11712yes—
256C11⋊C8#11712yes—
257C2×#135—111no—
258C4×#41—111no—
259C4×#41C2×D1111yescharacteristic
260#442—112no—
261#441—112no—
262#440—112no—
263#440—112no—
264#433—222no—
265#433—222no—
266#432—222no—
267#432—222no—
268C2×#108—111no—
269C2×#108—111no—
270#427—111no—
271#424—111no—
272#424—111no—
273#424—111no—
274#424—111no—
275C2×#104—111no—
276C2×#104—111no—
277C2×#104C2×D1111yescharacteristic
278C2×#104C2×D1111yescharacteristic
279#416—111no—
280#416—111no—
281#408—111no—
282#408—111no—
283#408—111no—
284#408—111no—
285C4×M16—111no—
286C4×M16C2×D1111yescharacteristic
287C2×#97—111no—
288C2×#97—111no—
289C2×#97—111no—
290C2×#97—111no—
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293C43C2×D1111yescharacteristic
294#341—111no—
295#341—111no—
296#339—111no—
297#339—111no—
298#339C2×D1111yescharacteristic
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—22no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11C2×#11711yescharacteristic
315C4×C11C4×#4111yescharacteristic
316C4×C11#53211yescharacteristic
317C4×C11#53211yescharacteristic
318Dic11—42no—
319Dic11—41no—
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×C8—111no—
335C22×C8—111no—
336C4×Q8—112no—
337C4×Q8C4×D1112yes—
338C4×D4—22no—
339C4×D4—112no—
340C4×D4—222no—
341C4×D4C4×D1112yes—
342#117—21no—
343#117—111no—
344#117—221no—
345#117C22×D1111yescharacteristic
346C2×C42—21no—
347C2×C42—22no—
348C2×C42—221no—
349C2×C42C22×D1111yescharacteristic
350C2×C42C22×D1111yescharacteristic
351C2×C42C22×D1111yescharacteristic
352#108—222no—
353#108—222no—
354#107—112no—
355#106—112no—
356C4⋊C8—222no—
357C4⋊C8—222no—
358C4⋊C8—222no—
359C4⋊C8—222no—
360#104—22no—
361#104—22no—
362#104—222no—
363#104—222no—
364#103—112no—
365#103—112no—
366#102—112no—
367#102—112no—
368C22⋊C8—222no—
369C22⋊C8—222no—
370C22⋊C8—222no—
371C22⋊C8—222no—
372#97—21no—
373#97—112no—
374#97—112no—
375#97—112no—
376#97—112no—
377#97—222no—
378#97—222no—
379#97—221no—
380C4×C8—21no—
381C4×C8—222no—
382C4×C8—222no—
383C4×C8—221no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—81no—
387C2×C11#229311yescharacteristic
388C2×C11#295612yes—
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—21no—
407C22×C4—22no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4#434112yes—
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—111no—
427C2×C8—111no—
428C2×C8—112no—
429C2×C8—112no—
430C2×C8—112no—
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C4⋊C4—22no—
442C4⋊C4—112no—
443C4⋊C4—222no—
444C4⋊C4C2×C4×D1112yes—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—221no—
448C22⋊C4—222no—
449C42—22no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—44no—
454C42—222no—
455C42—221no—
456C42C2×C4×D1112yes—
457C42#433912yes—
458C42#433912yes—
459C42D4×D1111yescharacteristic
460C42D4×D1111yescharacteristic
461C11#2129711yescharacteristic, complemented, Sylow
462C23—21no—
463C23—221no—
464C23C2×#434111yescharacteristic
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—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—222no—
488C2×C4—221no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—882no—
492C2×C4(C22⋊D11)⋊C412yes—
493C2×C4(C22⋊D11)⋊C412yes—
494C2×C4C22×C4×D1111yescharacteristic
495C2×C4C2×#433911yescharacteristic
496C2×C4C2×#433911yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4#41×D1111yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C8—41no—
501C8—41no—
502C8—112no—
503C8—112no—
504C8—222no—
505C8—222no—
506C8—222no—
507C8—441no—
508C8—441no—
509C22—22no—
510C22—42no—
511C22—41no—
512C22—442no—
513C22—441no—
514C22C2×(C22⋊D11)⋊C411yescharacteristic
515C22#1062306911yescharacteristic
516C22#1062306911yescharacteristic
517C4—24no—
518C4—22no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—442no—
524C4—441no—
525C4C4×#433911yescharacteristic
526C4D11×#11711yescharacteristic
527C4#1062307911yescharacteristic
528C4#1062307911yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—881no—
533C2#1307107911yescharacteristic
534C2#1307752212yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11#21297
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #13077268C2semidirect
3. #13077267C2semidirect
6. #13069368C2semidirect
7. #13069363C2semidirect
8. #13069328C2semidirect
9. #13069324C2semidirect
10. #13069321C2semidirect
11. #13069317C2semidirect
12. #13068523C2semidirect
13. C4×#66869C2semidirect
14. C4×#66867C2semidirect
15. C4×C11×#104C2semidirect
32. #10622643C4semidirect
33. #10622639C4semidirect
34. #10622631C4semidirect
35. #10622627C4semidirect
208. C4×#104D11semidirect
461. C11#21297semidirect

Maximal subgroups

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

subgroupindex
#130774142
#130772682
#130772672
#130695062
#130695012
#130693682
#130693632
#130693282
#130693242
#130693212
#130693172
#130685232
C4×#668692
C4×#668672
C4×C11×#1042
#2129711