Finite Group Databasebeta

← #14807420

Subgroups — #14807420

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic, complemented
2C2×#10622671C211yesmaximal, characteristic, complemented
3C2×#10622669C211yesmaximal, characteristic, complemented
4#13069617C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069584C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068953C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C11×#2620C211yesmaximal, characteristic, complemented
12C2×C11×#124C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×#4325C2212yes—
17C22×#4323C2212yes—
18C2×#66983C2212yes—
19#10623066—24no—
20#10623066—24no—
21C2×#66947—22no—
22C2×#66937—22no—
23C2×#66927C2211yescharacteristic
24C2×C4×D44C2212yes—
25C2×#66923C2211yescharacteristic
26C11×#396—22no—
27C11×#394—22no—
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622671—24no—
35#10622669—24no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66867C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—22no—
48C22×D44—22no—
49C22×D44C2312yes—
50C22×C4×D11—22no—
51C11×#124—22no—
52C11×#124—22no—
53C11×C22⋊Q8—42no—
54C11×#121—42no—
55C11×#117—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—42no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—42no—
75#66983—24no—
76#66983—24no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83#66947—216no—
84#66937—216no—
85#66927—22no—
86#66927D414yescomplemented
87C4×D44—24no—
88C4×D44—24no—
89#66923—22no—
90#66923D414yescomplemented
91C11×#95—22no—
92#66899—24no—
93#66896—24no—
94C22⋊(C11⋊C8)—24no—
95#66873—42no—
96#66873—42no—
97#66867—22no—
98C4×C11⋊C8—22no—
99#25611—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C23×D11—22no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—82no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—28no—
125C2×C22⋊D11—82no—
126C2×C22⋊D11—82no—
127C22×Dic11—22no—
128C2×D44—28no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—82no—
135C2×D44—82no—
136C2×D44C2×D414yes—
137C2×C4×D11—28no—
138C2×C4×D11—82no—
139C2×C4×D11—82no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—82no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—82no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154#4325—48no—
155#4323—48no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158C4⋊Dic11—22no—
159C4⋊Dic11C2×D414yes—
160Dic11⋊C4—28no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8#4114yes—
167C2×#540—111no—
168C2×#496—111no—
169C2×#488—111no—
170#2620D1111yescharacteristic, complemented
171#2000—112no—
172#1999—112no—
173#1992—111no—
174#1957—111no—
175#1879—112no—
176#1877—112no—
177#1750—111no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11C22×D411yescharacteristic
189C22×D11—24no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—84no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11#12014yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4112yes—
222C2×C4×C11H(5,𝔽2)12yes—
223C22⋊D11—88no—
224C2×Dic11—24no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—24no—
228D44—24no—
229D44—42no—
230D44—42no—
231D44—88no—
232C4×D11—88no—
233C11⋊C8—24no—
234C11⋊C8—42no—
235C22×SD16—112no—
236C22×D8—112no—
237#540—224no—
238#540—224no—
239C2×#127—111no—
240C2×#125—111no—
241C2×#124C2×D1111yescharacteristic
242C2×#123—222no—
243C2×C22⋊Q8C2×D1111yescharacteristic
244C2×#121—112no—
245C2×#121—222no—
246C2×#121C2×D1111yescharacteristic
247C2×C4×D4—112no—
248C2×#117C2×D1111yescharacteristic
249#496—224no—
250#488—224no—
251C2×#103—112no—
252C2×#102—112no—
253C2×#102—112no—
254C2×#102—112no—
255C2×C22⋊C8—112no—
256C2×#97—111no—
257C2×C4×C8—111no—
258#396—22no—
259#394—22no—
260#391C2×D1111yescharacteristic
261#390C2×D1111yescharacteristic
262#384C2×D1111yescharacteristic
263#340—112no—
264#340—112no—
265#336—112no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—42no—
271C22×C11—82no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—82no—
276C22×C11C2×#12011yescharacteristic
277C22×C11#53211yescharacteristic
278C22×C11#53511yescharacteristic
279C22×C11#57612yes—
280C22×C11#57712yes—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—24no—
289C4×C11—41no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11#54612yes—
295C4×C11#55012yes—
296Dic11—44no—
297C22×Q8C22×D1111yescharacteristic
298C22×D4—21no—
299C22×D4—112no—
300C22×D4—222no—
301C22×D4—222no—
302C22×D4C22×D1111yescharacteristic
303C23×C4—222no—
304C23×C4C22×D1111yescharacteristic
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C2×D8—224no—
309C2×D8—224no—
310C2×D8—442no—
311C22×C8—112no—
312C22×C8—112no—
313#127—114no—
314#127—222no—
315#125—114no—
316#125—222no—
317#124—22no—
318#124—22no—
319#123—2216no—
320C22⋊Q8—42no—
321#121—42no—
322#121—2216no—
323#121—224no—
324#121—224no—
325C4×D4—224no—
326C4×D4—224no—
327#117—22no—
328#117—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4C22⋊D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4C22⋊D1112yes—
343C2×C42C22×D1111yescharacteristic
344C2×C42C22×D1111yescharacteristic
345#103—224no—
346#102—224no—
347#102—442no—
348#102—442no—
349C22⋊C8—224no—
350#97—222no—
351C4×C8—222no—
352#95—22no—
353C2×C11—81no—
354C2×C11—161no—
355C2×C11#243111yescharacteristic
356C2×C11#301212yes—
357C2×C11#317912yes—
358C2×C11#322011yescharacteristic
359C2×C11#322111yescharacteristic
360D11—84no—
361C24—21no—
362C24—222no—
363C24C2×C22⋊D1111yescharacteristic
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—82no—
374C2×D4—114no—
375C2×D4—228no—
376C2×D4—228no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—882no—
383C2×D4—882no—
384C2×D4—882no—
385C2×D4—882no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—228no—
394C22×C4—222no—
395C22×C4—882no—
396C22×C4—882no—
397C22×C4C2×C22⋊D1112yes—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1112yes—
400C22×C4C23×D1111yescharacteristic
401SD16—448no—
402D8—448no—
403C2×C8—114no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8—222no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—42no—
413C4⋊C4—82no—
414C4⋊C4—114no—
415C4⋊C4—228no—
416C4⋊C4—222no—
417C22⋊C4—24no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—44no—
421C22⋊C4—82no—
422C22⋊C4—228no—
423C22⋊C4—228no—
424C42—21no—
425C42—21no—
426C42D4×D1112yes—
427C42D4×D1112yes—
428C11#2561111yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—22no—
433C23—22no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23—224no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23C22×C22⋊D1111yescharacteristic
447Q8—42no—
448Q8—42no—
449D4—42no—
450D4—42no—
451D4—84no—
452D4—224no—
453D4—224no—
454D4—442no—
455D4—442no—
456D4—888no—
457D4—888no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—224no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—888no—
479C2×C4#6699014yes—
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4#6703712yes—
483C2×C4#41×D1112yes—
484C8—224no—
485C8—442no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—42no—
490C22—42no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—82no—
495C22—82no—
496C22—444no—
497C22—444no—
498C22—444no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22C2×#6699011yescharacteristic
504C22#1062333611yescharacteristic
505C22#1062336311yescharacteristic
506C22#1062336612yes—
507C22#1062336812yes—
508C4—24no—
509C4—41no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—444no—
515C4#1062313012yes—
516C4#1062314312yes—
517C2—81no—
518C2—161no—
519C2—884no—
520C2#1307223611yescharacteristic
521C2#1307791712yes—
522C2#1307929312yes—
523C2#1307966611yescharacteristic
524C2#1307967711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2620C2
socleC23×C11C22×D4
hypercenter#2620D11
hypocenterC11#25611
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2620

Complements

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

NH ≅ G/Ntype
1. C2×#10623066C2semidirect
2. C2×#10622671C2semidirect
3. C2×#10622669C2semidirect
4. #13069617C2semidirect
5. #13069612C2semidirect
6. #13069584C2semidirect
7. #13069421C2semidirect
8. #13068967C2semidirect
9. #13068953C2semidirect
10. #13068382C2semidirect
11. C11×#2620C2semidirect
86. #66927D4semidirect
90. #66923D4semidirect
170. #2620D11semidirect
428. C11#25611semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
C2×#106226712
C2×#106226692
#130696172
#130696122
#130695842
#130694212
#130689672
#130689532
#130683822
C11×#26202
#2561111