Finite Group Databasebeta

← #14755029

Subgroups — #14755029

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10622617C211yesmaximal, characteristic, complemented
3C22×#66874C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic
5#13068928C214yesmaximal, complemented
6#13068923C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#520C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C11×#520—24no—
13C11×#520—24no—
14C2×C4×Q8×C11—21no—
15C2×C4×D4×C11—22no—
16C2×C4×D4×C11—21no—
17C2×C11×#117C2212yes—
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623356—24no—
22#10623356C418yescomplemented
23C2×#66997—21no—
24C2×#66989—21no—
25C2×#66988—22no—
26C2×#66979C2211yescharacteristic
27C2×#66977C2214yes—
28C22×#4318C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10622847—24no—
31C2×C22⋊(C11⋊C8)C2214yes—
32#10622617—24no—
33C2×#66874—24no—
34C2×#66874C2214yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D412yes—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—22no—
50C23×C4×C11—21no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22C2×C414yescomplemented
61C22×Dic22C2312yes—
62C4×Q8×C11—28no—
63C4×D4×C11—216no—
64C4×D4×C11—28no—
65C11×#117—22no—
66C11×#117—24no—
67C11×#117—24no—
68C11×#117D414yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4D414yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—22no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—21no—
84#66997—28no—
85#66989—28no—
86#66988—216no—
87#66979—22no—
88#66979C2×C414yescomplemented
89C2×C4⋊Dic11C2312yes—
90#66977—28no—
91#66977C2×C4116yescomplemented
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102C22⋊(C11⋊C8)—28no—
103#66874—28no—
104#66874—24no—
105#66874—24no—
106#20913—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C11×#41—28no—
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22⋊C414yes—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C22⋊C418yes—
121C2×D4×C11C22⋊C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—28no—
130C22×C4×C11—24no—
131C22×C4×C11—82no—
132C22×C4×C11—84no—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C2×Dic22—24no—
150C2×Dic22—28no—
151C2×Dic22—28no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—42no—
158C2×Dic22—44no—
159C2×Dic22—44no—
160C2×Dic22—42no—
161C2×Dic22C22×C414yes—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D414yes—
169C11×C4⋊C4C2×D412yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—24no—
172C42×C11—28no—
173C42×C11—24no—
174C22⋊Dic11—216no—
175C22⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11C22×C414yes—
178Dic11⋊C4—216no—
179C4×Dic11—24no—
180#4318—44no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—44no—
188C2×#536—111no—
189C2×#520D1111yescharacteristic
190C2×#419—111no—
191C22×#103—111no—
192C2×#408—111no—
193#1873—114no—
194#1872—114no—
195#1736—111no—
196#1735—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11C2×C22⋊C414yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11#12012yes—
206C23×C11#12312yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—28no—
209D4×C11—216no—
210D4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—84no—
224C2×C4×C11—88no—
225C2×C4×C11C2×C22⋊C414yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C4×D414yes—
228C2×C4×C11C4×D414yes—
229C2×C4×C11#12012yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12312yes—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—48no—
246Dic22—24no—
247Dic22—24no—
248Dic22—42no—
249Dic22—42no—
250Dic22—48no—
251C11⋊C8—42no—
252C11⋊C8—42no—
253C22×#41C2×D1111yescharacteristic
254C23×Q8—111no—
255C22×M16—111no—
256C23×C8—111no—
257#536—118no—
258#536—224no—
259C2×C4⋊Q8—221no—
260C2×#124—221no—
261C2×#123—222no—
262C2×C22⋊Q8—114no—
263#520—24no—
264#520—24no—
265C2×C4×Q8—21no—
266C2×C4×D4—22no—
267C2×C4×D4—21no—
268C2×#117—111no—
269C2×#117C2×D1112yes—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1112yes—
272C22×C4⋊C4C2×D1111yescharacteristic
273#419—224no—
274C2×#103—114no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—224no—
278#408—224no—
279C2×C22⋊C8—114no—
280#340—112no—
281#340—114no—
282#340—112no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—28no—
288C22×C11—24no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11#38614yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12311yescharacteristic
296C22×C11#57712yes—
297C22×C11#57812yes—
298C4×C11—24no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11#38614yes—
303C4×C11C2×C4×D411yescharacteristic
304C4×C11C2×C4×D411yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12111yescharacteristic
307Dic11—44no—
308Dic11—44no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C4×D1114yes—
314C2×#41D4414yes—
315C22×Q8—114no—
316C22×Q8—112no—
317C22×Q8—222no—
318C22×Q8—221no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8C22⋊D1111yescharacteristic
324C22×D4C22⋊D1112yes—
325C22×D4C22⋊D1111yescharacteristic
326C23×C4—22no—
327C23×C4—21no—
328C23×C4—221no—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C2×M16—222no—
332C2×M16—222no—
333C2×M16—222no—
334C22×C8—112no—
335C22×C8—112no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8—222no—
339C4⋊Q8—228no—
340#124—228no—
341#123—2216no—
342C22⋊Q8—1116no—
343C22⋊Q8—228no—
344C4×Q8—28no—
345C4×D4—216no—
346C4×D4—28no—
347#117—22no—
348#117—24no—
349#117—24no—
350#117—114no—
351#117—222no—
352#117C22⋊D1114yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4C22⋊D1114yes—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—224no—
368C2×C42—22no—
369C2×C42—21no—
370C2×C42—221no—
371#103—228no—
372#103—224no—
373#103—224no—
374C22⋊C8—228no—
375C2×C11—24no—
376C2×C11—44no—
377C2×C11C2×#38611yescharacteristic
378C2×C11#289812yes—
379C2×C11#300911yescharacteristic
380C2×C11#301111yescharacteristic
381C2×C11#309712yes—
382C24C2×C22⋊D1112yes—
383C24C2×C22⋊D1111yescharacteristic
384#41—28no—
385#41—28no—
386#41—28no—
387#41—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—114no—
391C2×Q8—224no—
392C2×Q8—222no—
393C2×Q8—228no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—442no—
400C2×Q8—444no—
401C2×Q8—444no—
402C2×Q8—442no—
403C2×Q8(C2×D11)⋊C414yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4(C2×D11)⋊C418yes—
409C2×D4(C2×D11)⋊C414yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—82no—
420C22×C4—84no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4C2×C4×D1114yes—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×D4414yes—
429C22×C4C2×D4412yes—
430C22×C4#433912yes—
431C22×C4#433912yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—444no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C4⋊C4—28no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—114no—
451C4⋊C4—2216no—
452C4⋊C4—222no—
453C4⋊C4C2×C22⋊D1112yes—
454C4⋊C4C2×C22⋊D1114yes—
455C4⋊C4C2×C22⋊D1112yes—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—224no—
459C22⋊C4—2216no—
460C42—28no—
461C42—24no—
462C42—224no—
463C11#2091311yescharacteristic, complemented, Sylow
464C23—22no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—24no—
469C23—22no—
470C23C2×(C2×D11)⋊C414yes—
471C23C2×(C2×D11)⋊C412yes—
472C23#6698212yes—
473C23#6700612yes—
474C23C22×C22⋊D1111yescharacteristic
475Q8—28no—
476Q8—224no—
477Q8—224no—
478Q8—442no—
479Q8—442no—
480Q8—448no—
481D4—216no—
482D4—28no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—84no—
496C2×C4—88no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—448no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4C2×(C2×D11)⋊C414yes—
505C2×C4C2×(C2×D11)⋊C412yes—
506C2×C4C4×C22⋊D1114yes—
507C2×C4C4×C22⋊D1114yes—
508C2×C4#6698212yes—
509C2×C4#6698314yes—
510C2×C4#6698314yes—
511C2×C4#6700612yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C22×D4411yescharacteristic
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C22×C22⋊D1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—442no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—28no—
525C22—24no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22#1062282614yes—
530C22C22×(C2×D11)⋊C411yescharacteristic
531C22C2×#6698211yescharacteristic
532C22#1062336712yes—
533C22#1062336912yes—
534C22C2×#6700611yescharacteristic
535C4—24no—
536C4—44no—
537C4—42no—
538C4—42no—
539C4—444no—
540C4—444no—
541C4#1062282614yes—
542C4C2×C4×C22⋊D1111yescharacteristic
543C4C2×C4×C22⋊D1111yescharacteristic
544C4C2×#6698311yescharacteristic
545C4C2×#6698311yescharacteristic
546C2—24no—
547C2—44no—
548C2C2×#1062282611yescharacteristic
549C2#1307714612yes—
550C2#1307789311yescharacteristic
551C2#1307791111yescharacteristic
552C2#1307858512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#20913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#10622617C2semidirect
3. C22×#66874C2semidirect
5. #13068928C2semidirect
6. #13068923C2semidirect
7. #13068335C2semidirect
8. #13068332C2semidirect
22. #10623356C4semidirect
60. C22×Dic22C2×C4semidirect
88. #66979C2×C4semidirect
91. #66977C2×C4semidirect
463. C11#20913semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106226172
C22×#668742
C2×#106228472
#130689282
#130689232
#130683352
#130683322
C2×C11×#5202
#2091311