Finite Group Databasebeta

← #14762864

Subgroups — #14762864

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13069054C212yesmaximal, complemented
4#13069049C212yesmaximal, complemented
5#13068931C212yesmaximal, complemented
6#13068921C212yesmaximal, complemented
7#13068712C212yesmaximal, complemented
8#13068557C212yesmaximal, complemented
9C2×C11×#407C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2212yes—
13C2×#67006—21no—
14C22×C22⋊Dic11—21no—
15#10623322—24no—
16#10623322C418yescomplemented
17C2×#66983C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66982—21no—
20C2×C4×C22⋊D11—21no—
21C2×C4×C22⋊D11—21no—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C11×#407—24no—
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29#10622825—21no—
30#10622825—21no—
31#10622825C2212yes—
32#10622825C2212yes—
33C2×C11⋊#95—21no—
34C2×#66885C2214yescomplemented
35C2×#66880C2214yescomplemented
36#10622189C2214yescomplemented
37#10622189C2214yescomplemented
38C25×C11D411yescharacteristic
39C23×C4×C11—44no—
40C23×C4×C11C2×C414yes—
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D414yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C23×Dic11—22no—
52C2×#4339—22no—
53C2×#4339—44no—
54C2×#4339C2×C414yescomplemented
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C22×Dic22C2311yescharacteristic
58C2×C11×M16—24no—
59C2×C11×M16—44no—
60C22×C8×C11C2314yes—
61#67006—28no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—44no—
68#66983—22no—
69#66983—22no—
70#66983C2×C414yes—
71#66983C2×C414yescomplemented
72#66982—28no—
73C4×C22⋊D11—28no—
74C4×C22⋊D11—28no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77#66979—22no—
78#66979C2×C414yescomplemented
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—44no—
81C2×C4⋊Dic11C2314yes—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84#66977—22no—
85#66977—22no—
86#66977C2×C414yes—
87#66977C2×C414yescomplemented
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C11×C22⋊C8—24no—
92C11×C22⋊C8—24no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95#66885—44no—
96#66880—44no—
97#21769—111nomaximal, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11C22⋊C414yes—
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C23×D11—21no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—24no—
110C22×C4×C11—48no—
111C22×C4×C11—48no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C22⋊C414yes—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—24no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—24no—
139C22×Dic11—44no—
140C22×Dic11—44no—
141C22×Dic11—44no—
142#4339—48no—
143#4339—48no—
144C2×D44—21no—
145C2×D44—24no—
146C2×D44C22×C412yes—
147C2×C4×D11—24no—
148C2×C4×D11—44no—
149C2×Dic22—21no—
150C2×Dic22—24no—
151C2×Dic22C22×C412yes—
152C11×M16—48no—
153C2×C8×C11—24no—
154C2×C8×C11—24no—
155C2×C8×C11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159C22⋊Dic11—44no—
160C22⋊Dic11—44no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—44no—
168C4⋊Dic11C22×C412yes—
169C4⋊Dic11C22×C412yes—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172C4×Dic11—24no—
173C2×#525—111no—
174C2×#407D1111yescharacteristic, complemented
175C2×#380—111no—
176#1895—112no—
177#1894—112no—
178#1874—112no—
179#1872—112no—
180#1825—112no—
181#1788—112no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—28no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11C2×C22⋊C412yes—
198C23×C11C2×C22⋊C412yes—
199C23×C11C2×C22⋊C412yes—
200C23×C11AGL(1,ℤ/8)12yes—
201C23×C11#13712yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—42no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—42no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11H(5,𝔽2)14yes—
226C22⋊D11—48no—
227C22⋊D11—48no—
228C22⋊D11—48no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11—88no—
240D44—24no—
241D44—42no—
242C4×D11—48no—
243Dic22—24no—
244Dic22—42no—
245C8×C11—44no—
246C22×#41—111no—
247C24×C4C2×D1111yescharacteristic
248C22×M16C2×D1112yes—
249#525—118no—
250#525—224no—
251C2×#123—221no—
252C2×C22⋊Q8—111no—
253C2×C22⋊Q8—111no—
254C2×#121—111no—
255C2×#121—111no—
256C2×#120—221no—
257C2×C4×D4—221no—
258C2×C4×D4—221no—
259C2×#117—111no—
260C22×C4⋊C4—112no—
261C22×C22⋊C4—221no—
262C2×#103—114no—
263C2×#102—114no—
264#407—24no—
265C2×C22⋊C8C2×D1112yes—
266C2×C22⋊C8C2×D1112yes—
267#380—112no—
268#380—112no—
269#380—221no—
270#380—221no—
271C2×#95—221no—
272#340—114no—
273#340—114no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—416no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11#41714yes—
290C22×C11C22×C22⋊C411yescharacteristic
291C22×C11#53412yes—
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11C2×#13711yescharacteristic
294C22×C11#57512yes—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—82no—
299C2×D11—82no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11#51812yes—
304C4×C11#53412yes—
305Dic11—42no—
306Dic11—42no—
307Dic11—42no—
308Dic11—84no—
309C25D4411yescharacteristic
310C2×#41—114no—
311C2×#41—222no—
312C2×#41—444no—
313C22×Q8—111no—
314C22×D4—111no—
315C22×D4—221no—
316C22×D4—221no—
317C22×D4—221no—
318C23×C4—44no—
319C23×C4—221no—
320C23×C4—222no—
321C23×C4C4×D1114yes—
322C23×C4D4411yescharacteristic
323C23×C4D4411yescharacteristic
324C23×C4D4411yescharacteristic
325C23×C4C22⋊D1114yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C2×M16—24no—
330C2×M16—44no—
331C22×C8C22×D1114yes—
332#123—228no—
333C22⋊Q8—114no—
334C22⋊Q8—114no—
335C22⋊Q8—222no—
336C22⋊Q8—222no—
337#121—114no—
338#121—114no—
339#121—222no—
340#121—222no—
341#120—228no—
342C4×D4—228no—
343C4×D4—228no—
344#117—114no—
345#117—222no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—114no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—444no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—444no—
361C2×C42—221no—
362#103—444no—
363#102—444no—
364C22⋊C8—24no—
365C22⋊C8—24no—
366#95—222no—
367#95—222no—
368C2×C11—24no—
369C2×C11—42no—
370C2×C11—42no—
371C2×C11#230811yescharacteristic
372C2×C11C2×#41711yescharacteristic
373C2×C11#289611yescharacteristic
374C2×C11#319412yes—
375C2×C11#319612yes—
376D11—82no—
377C24—22no—
378C24—22no—
379C24—42no—
380C24—42no—
381C24—221no—
382C24(C2×D11)⋊C414yes—
383C24C2×D4411yescharacteristic
384C24C2×D4411yescharacteristic
385C24C2×D4411yescharacteristic
386#41—448no—
387#41—448no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—224no—
391C2×D4—112no—
392C2×D4—224no—
393C2×D4—224no—
394C2×D4—224no—
395C2×D4—224no—
396C2×D4—221no—
397C2×D4—444no—
398C2×D4—444no—
399C2×D4—442no—
400C2×D4—442no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—48no—
405C22×C4—48no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—444no—
415C22×C4—444no—
416C22×C4—444no—
417C22×C4—444no—
418C22×C4(C2×D11)⋊C414yes—
419C22×C4(C2×D11)⋊C414yes—
420C22×C4(C2×D11)⋊C414yes—
421C22×C4C2×C4×D1112yes—
422C22×C4C2×C4×D1112yes—
423C22×C4C2×C4×D1112yes—
424C22×C4C2×D4411yescharacteristic
425C22×C4C2×D4411yescharacteristic
426C22×C4C2×D4411yescharacteristic
427C22×C4C2×C22⋊D1112yes—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C23×D1111yescharacteristic
431M16—48no—
432C2×C8—24no—
433C2×C8—24no—
434C2×C8—24no—
435C4⋊C4—112no—
436C4⋊C4—112no—
437C4⋊C4—224no—
438C4⋊C4—224no—
439C4⋊C4—221no—
440C4⋊C4—221no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4—444no—
444C22⋊C4—224no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C42—224no—
452C11#2176911yescharacteristic, complemented, Sylow
453C23—22no—
454C23—22no—
455C23—28no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—44no—
465C23—44no—
466C23—48no—
467C23—48no—
468C23—222no—
469C23—441no—
470C23—441no—
471C23—442no—
472C23—442no—
473C23#6696112yes—
474C23#6696212yes—
475C23C2×(C2×D11)⋊C412yes—
476C23C2×(C2×D11)⋊C412yes—
477C23C2×(C2×D11)⋊C412yes—
478C23C22×D4411yescharacteristic
479Q8—224no—
480Q8—442no—
481D4—224no—
482D4—448no—
483D4—448no—
484D4—448no—
485D4—442no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—448no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—888no—
510C2×C4C2×(C2×D11)⋊C412yes—
511C2×C4C2×(C2×D11)⋊C412yes—
512C2×C4C2×(C2×D11)⋊C412yes—
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4#6703714yes—
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—44no—
517C22—22no—
518C22—24no—
519C22—22no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—442no—
533C22—442no—
534C22—442no—
535C22—882no—
536C22—882no—
537C22#1062274614yes—
538C22#1062302412yes—
539C22C2×#6696111yescharacteristic
540C22C2×#6696211yescharacteristic
541C22#1062327912yes—
542C22C22×(C2×D11)⋊C411yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—442no—
547C4—442no—
548C4—442no—
549C4—884no—
550C4#1062301712yes—
551C4#1062333512yes—
552C2—24no—
553C2—42no—
554C2—42no—
555C2—882no—
556C2#1307119111yescharacteristic
557C2C2×#1062274611yescharacteristic
558C2#1307713611yescharacteristic
559C2#1307943212yes—
560C2#1307944812yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21769
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. #13069054C2semidirect
4. #13069049C2semidirect
5. #13068931C2semidirect
6. #13068921C2semidirect
7. #13068712C2semidirect
8. #13068557C2semidirect
9. C2×C11×#407C2semidirect
16. #10623322C4semidirect
34. C2×#66885C22semidirect
35. C2×#66880C22semidirect
36. #10622189C22semidirect
37. #10622189C22semidirect
54. C2×#4339C2×C4semidirect
71. #66983C2×C4semidirect
78. #66979C2×C4semidirect
87. #66977C2×C4semidirect
174. C2×#407D11semidirect
452. C11#21769semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106228252
#130690542
#130690492
#130689312
#130689212
#130687122
#130685572
C2×C11×#4072
#2176911