Finite Group Databasebeta

← #14770227

Subgroups — #14770227

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3#13069576C211yesmaximal, characteristic, complemented
4#13069564C211yesmaximal, characteristic, complemented
5#13069052C212yesmaximal, complemented
6#13068933C212yesmaximal, complemented
7#13068708C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic, complemented
9C4×#66873C211yesmaximal, characteristic, complemented
10#13068335C212yesmaximal, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66991—21no—
16C2×#66983C2212yes—
17C2×#66979C2212yes—
18C22×#4318C2212yes—
19#10623094—24no—
20#10623094C418yescomplemented
21C2×#66945—21no—
22C2×#66938—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#389—21no—
26C11×#385—22no—
27C11×#384C2211yescharacteristic
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622625—24no—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2212yes—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22—21no—
51C4×D4×C11—44no—
52C4×D4×C11C2×C414yes—
53C4×D4×C11D414yes—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68#66991—28no—
69#66983—24no—
70#66983C2×C418yescomplemented
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73#66979—24no—
74#66979C2×C418yescomplemented
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—22no—
79C2×#4318—24no—
80C2×#4318—24no—
81C2×#4318—42no—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85#66945—28no—
86#66938—216no—
87C4×D44—22no—
88C4×D44C2×C414yescomplemented
89#66922—22no—
90#66922C2×C414yescomplemented
91C11×#95—21no—
92C11×#95—22no—
93C22⋊(C11⋊C8)—24no—
94#66873—22no—
95#66873—22no—
96#66873—42no—
97C4⋊(C11⋊C8)—22no—
98C4×C11⋊C8—22no—
99#22503—111nomaximal, Sylow
100C24×C11C2×D412yes—
101C23×D11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11C22⋊C414yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—82no—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—82no—
123C2×C22⋊D11—82no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44C22×C412yes—
132C2×C4×D11—24no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×Dic22—24no—
136C2×Dic22—81no—
137C2×Dic22—81no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C11×C4⋊C4C22⋊C414yes—
147C11×C4⋊C4#4112yes—
148C11×C22⋊C4—44no—
149C11×C22⋊C4C22⋊C418yes—
150C42×C11—42no—
151C42×C11C22×C412yes—
152C42×C11C2×D412yes—
153C22⋊Dic11—28no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—28no—
156C4⋊Dic11—24no—
157C4⋊Dic11—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11C22×C414yes—
160C4⋊Dic11C22×C412yes—
161C4×Dic11—28no—
162#4318—48no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8#4112yes—
172C2×#555—111no—
173C2×#436—111no—
174D4×C4⋊C4D1111yescharacteristic, complemented
175#1990—111no—
176#1987—111no—
177#1895—112no—
178#1874—112no—
179#1825—112no—
180#1802—111no—
181C4×#102—111no—
182#1736—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11C2×C22⋊C414yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198D4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—88no—
217C2×C4×C11C2×C22⋊C414yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11AGL(1,ℤ/8)12yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C22⋊D11—88no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235D44—22no—
236D44—22no—
237D44—41no—
238D44—41no—
239C4×D11—48no—
240Dic22—84no—
241C11⋊C8—22no—
242C11⋊C8—42no—
243C11⋊C8—41no—
244C22×M16—112no—
245#555—118no—
246#555—224no—
247C2×C4⋊Q8—111no—
248C2×#124—222no—
249C2×#121—112no—
250C2×#121—221no—
251C2×C4×D4—21no—
252C2×C4×D4—111no—
253C2×C4×D4C2×D1111yescharacteristic
254C2×#117—112no—
255C2×#117—221no—
256C22×C4⋊C4C2×D1112yes—
257#436—224no—
258C2×C4⋊C8—111no—
259C2×#102—111no—
260C2×#102—111no—
261C2×#102—112no—
262C2×C22⋊C8—112no—
263C2×C4×C8—111no—
264#389—21no—
265#385—22no—
266#384C2×D1111yescharacteristic
267#380C2×D1112yes—
268C4×C4⋊C4C2×D1111yescharacteristic
269#340—112no—
270#340—111no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340—111no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11#54711yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57611yescharacteristic
289C22×C11#57711yescharacteristic
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—82no—
302C4×C11#41714yes—
303C4×C11C4×#4111yescharacteristic
304C4×C11#52011yescharacteristic
305C4×C11#54611yescharacteristic
306C4×C11#54711yescharacteristic
307Dic11—42no—
308Dic11—44no—
309C22×Q8—221no—
310C22×D4—111no—
311C22×D4—222no—
312C22×D4C22⋊D1111yescharacteristic
313C23×C4—22no—
314C23×C4—221no—
315C23×C4C22×D1112yes—
316C2×M16—224no—
317C2×M16—224no—
318C2×M16—442no—
319C22×C8—111no—
320C22×C8—112no—
321C22×C8—111no—
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324#124—2216no—
325#121—118no—
326#121—228no—
327#121—224no—
328C4×D4—44no—
329C4×D4—114no—
330C4×D4—222no—
331C4×D4C4×D1114yes—
332C4×D4D4414yes—
333#117—118no—
334#117—224no—
335#117—228no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C4⋊C4C22×D1112yes—
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—22no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4C22⋊D1112yes—
353C2×C42—21no—
354C2×C42—222no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—222no—
357#102—222no—
358#102—222no—
359#102—442no—
360C22⋊C8—224no—
361C4×C8—222no—
362#95—21no—
363#95—22no—
364C2×C11—44no—
365C2×C11#233911yescharacteristic
366C2×C11C2×#41711yescharacteristic
367C2×C11#289711yescharacteristic
368C2×C11#332511yescharacteristic
369C2×C11#332911yescharacteristic
370C2×C11#335411yescharacteristic
371C2×C11#335711yescharacteristic
372D11—82no—
373C24—221no—
374C24C2×C22⋊D1112yes—
375C2×Q8—224no—
376C2×Q8—881no—
377C2×Q8—881no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—112no—
381C2×D4—228no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—882no—
388C2×D4—882no—
389C2×D4(C2×D11)⋊C414yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—82no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—224no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4C2×C4×D1114yes—
406C22×C4C2×D4414yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C23×D1111yescharacteristic
411M16—448no—
412C2×C8—112no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—222no—
417C2×C8—221no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—221no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—44no—
427C4⋊C4—42no—
428C4⋊C4—81no—
429C4⋊C4—112no—
430C4⋊C4—114no—
431C4⋊C4—224no—
432C4⋊C4—221no—
433C4⋊C4—222no—
434C4⋊C4(C2×D11)⋊C414yes—
435C4⋊C4#434112yes—
436C22⋊C4—44no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C22⋊C4—224no—
440C22⋊C4(C2×D11)⋊C418yes—
441C42—42no—
442C42—228no—
443C42C2×C4×D1112yes—
444C42C2×D4412yes—
445C11#2250311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—222no—
453C23—441no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23—441no—
458C23—441no—
459C23C2×(C2×D11)⋊C414yes—
460C23C22×C22⋊D1111yescharacteristic
461Q8—884no—
462D4—28no—
463D4—222no—
464D4—222no—
465D4—441no—
466D4—441no—
467D4—888no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—88no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—448no—
493C2×C4C2×(C2×D11)⋊C414yes—
494C2×C4C2×(C2×D11)⋊C412yes—
495C2×C4C2×(C2×D11)⋊C412yes—
496C2×C4#6698512yes—
497C2×C4#6699512yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C22×D4411yescharacteristic
500C2×C4C2×#434111yescharacteristic
501C2×C4#6703711yescharacteristic
502C2×C4#41×D1111yescharacteristic
503C2×C4#6704311yescharacteristic
504C8—222no—
505C8—442no—
506C8—441no—
507C22—24no—
508C22—24no—
509C22—24no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—881no—
518C22—881no—
519C22—881no—
520C22—881no—
521C22C22×(C2×D11)⋊C411yescharacteristic
522C22C2×#6698511yescharacteristic
523C22#1062333711yescharacteristic
524C22C2×#6699511yescharacteristic
525C22#1062335511yescharacteristic
526C22#1062336611yescharacteristic
527C22#1062336811yescharacteristic
528C4—24no—
529C4—22no—
530C4—42no—
531C4—82no—
532C4—81no—
533C4—442no—
534C4—444no—
535C4#1062257914yes—
536C4C4×#434111yescharacteristic
537C4#1062307711yescharacteristic
538C4#1062308511yescharacteristic
539C4#1062308611yescharacteristic
540C2—44no—
541C2—882no—
542C2#1307144111yescharacteristic
543C2C2×#1062257911yescharacteristic
544C2#1307713911yescharacteristic
545C2#1308085811yescharacteristic
546C2#1308091011yescharacteristic
547C2#1308121111yescharacteristic
548C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. #13069576C2semidirect
4. #13069564C2semidirect
5. #13069052C2semidirect
6. #13068933C2semidirect
7. #13068708C2semidirect
8. #13068613C2semidirect
9. C4×#66873C2semidirect
10. #13068335C2semidirect
11. D4×C11×C4⋊C4C2semidirect
20. #10623094C4semidirect
70. #66983C2×C4semidirect
74. #66979C2×C4semidirect
88. C4×D44C2×C4semidirect
90. #66922C2×C4semidirect
174. D4×C4⋊C4D11semidirect
445. C11#22503semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106226252
#130695762
#130695642
#130690522
#130689332
#130687082
#130686132
C4×#668732
#130683352
D4×C11×C4⋊C42
#2250311