Finite Group Databasebeta

← #14762863

Subgroups — #14762863

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×#10622820C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic, complemented
3#13069055C212yesmaximal, complemented
4#13069050C212yesmaximal, complemented
5#13068934C212yesmaximal, complemented
6#13068924C212yesmaximal, complemented
7#13068711C212yesmaximal, complemented
8#13068556C212yesmaximal, complemented
9C2×C11×#525C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C11×#525—24no—
13C11×#525C418yescomplemented
14C2×C11×#123—21no—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C2×C11×#117C2211yescharacteristic
23C22×C22⋊Dic11—21no—
24C22×C4⋊Dic11C2212yes—
25C22×#4318C2212yes—
26C2×#66899C2214yescomplemented
27C2×#66896C2214yescomplemented
28#10622825—21no—
29#10622825—21no—
30#10622825C2212yes—
31#10622825C2212yes—
32C2×C11⋊#95—21no—
33#10622820—24no—
34C2×C22⋊(C11⋊C8)C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622167C2214yescomplemented
37#10622167C2214yescomplemented
38C25×C11D411yescharacteristic
39C2×C11×#41—22no—
40C2×C11×#41—44no—
41C2×C11×#41C2×C414yescomplemented
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—44no—
49C23×C4×C11C2×C414yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—22no—
58C11×#123—28no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8C2×C414yes—
62C11×C22⋊Q8C2×C414yescomplemented
63C11×#121—22no—
64C11×#121—22no—
65C11×#121C2×C414yes—
66C11×#121C2×C414yescomplemented
67C11×#120—28no—
68C4×D4×C11—28no—
69C4×D4×C11—28no—
70C11×#117—22no—
71C11×#117C2×C414yescomplemented
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—44no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—44no—
87C2×C4⋊Dic11C2314yes—
88C2×#4318—24no—
89C2×#4318—44no—
90C22×C11⋊C8C2314yes—
91#66899—44no—
92#66896—44no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C22⋊(C11⋊C8)—24no—
96C22⋊(C11⋊C8)—24no—
97#21769—111nomaximal, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—21no—
101C24×C11—42no—
102C24×C11—42no—
103C24×C11C22⋊C414yes—
104C24×C11C2×D411yescharacteristic
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C11×#41—48no—
108C11×#41—48no—
109C2×Q8×C11—21no—
110C2×Q8×C11—24no—
111C2×Q8×C11C22×C412yes—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—21no—
116C2×D4×C11—24no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C22×C412yes—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—48no—
130C22×C4×C11—48no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—44no—
135C22×C4×C11C22⋊C414yes—
136C22×C4×C11C22⋊C414yes—
137C22×C4×C11C22⋊C414yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—44no—
150C22×Dic11—44no—
151C22×Dic11—44no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C42×C11—24no—
164C22⋊Dic11—44no—
165C22⋊Dic11—44no—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—44no—
169#4318—48no—
170C2×C11⋊C8—24no—
171C2×C11⋊C8—24no—
172C2×C11⋊C8—24no—
173C2×#525D1111yescharacteristic
174C2×#407—111no—
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—22no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—42no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11C2×C22⋊C412yes—
203C23×C11C2×C22⋊C412yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11AGL(1,ℤ/8)12yes—
206C23×C11#13712yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—24no—
209Q8×C11—42no—
210D4×C11—24no—
211D4×C11—48no—
212D4×C11—48no—
213D4×C11—48no—
214D4×C11—42no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C2×C22⋊C412yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11H(5,𝔽2)14yes—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11—88no—
245C11⋊C8—44no—
246C22×#41C2×D1111yescharacteristic
247C24×C4C2×D1111yescharacteristic
248C22×M16—112no—
249#525—24no—
250#525Dic1118yescomplemented
251C2×#123—21no—
252C2×C22⋊Q8C2×D1111yescharacteristic
253C2×C22⋊Q8C2×D1111yescharacteristic
254C2×#121C2×D1111yescharacteristic
255C2×#121C2×D1111yescharacteristic
256C2×#120—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×#117C2×D1111yescharacteristic
260C22×C4⋊C4—112no—
261C22×C22⋊C4—221no—
262C2×#103—114no—
263C2×#102—114no—
264#407—224no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—112no—
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—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11#41714yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11#53412yes—
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11#57512yes—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11#51812yes—
307C4×C11#53412yes—
308Dic11—84no—
309C25C22⋊D1111yescharacteristic
310C2×#41—22no—
311C2×#41—44no—
312C2×#41C2×Dic1114yescomplemented
313C22×Q8C22×D1111yescharacteristic
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C22×D1111yescharacteristic
318C23×C4—21no—
319C23×C4—44no—
320C23×C4—222no—
321C23×C4C2×Dic1114yes—
322C23×C4C22⋊D1111yescharacteristic
323C23×C4C22⋊D1111yescharacteristic
324C23×C4C22⋊D1111yescharacteristic
325C23×C4C22⋊D1114yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C2×M16—224no—
330C2×M16—444no—
331C22×C8—114no—
332#123—28no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8C2×Dic1114yes—
336C22⋊Q8C2×Dic1114yescomplemented
337#121—22no—
338#121—22no—
339#121C2×Dic1114yes—
340#121C2×Dic1114yescomplemented
341#120—28no—
342C4×D4—28no—
343C4×D4—28no—
344#117—22no—
345#117C2×Dic1114yescomplemented
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—114no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—444no—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—444no—
361C2×C42—21no—
362#103—444no—
363#102—444no—
364C22⋊C8—224no—
365C22⋊C8—224no—
366#95—222no—
367#95—222no—
368C2×C11—24no—
369C2×C11—42no—
370C2×C11—42no—
371C2×C11—82no—
372C2×C11#230811yescharacteristic
373C2×C11C2×#41711yescharacteristic
374C2×C11#289611yescharacteristic
375C2×C11#319412yes—
376C2×C11#319612yes—
377C24—22no—
378C24—22no—
379C24—21no—
380C24—42no—
381C24—42no—
382C24C22⋊Dic1114yes—
383C24C2×C22⋊D1111yescharacteristic
384C24C2×C22⋊D1111yescharacteristic
385C24C2×C22⋊D1111yescharacteristic
386#41—48no—
387#41—48no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8C22×Dic1112yes—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4C22×Dic1112yes—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—48no—
409C22×C4—48no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—44no—
414C22×C4—224no—
415C22×C4—444no—
416C22×C4—444no—
417C22×C4—444no—
418C22×C4C22⋊Dic1114yes—
419C22×C4C22⋊Dic1114yes—
420C22×C4C22⋊Dic1114yes—
421C22×C4C22×Dic1112yes—
422C22×C4C22×Dic1112yes—
423C22×C4C22×Dic1112yes—
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1112yes—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C23×D1111yescharacteristic
431M16—448no—
432C2×C8—224no—
433C2×C8—224no—
434C2×C8—224no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—224no—
440C4⋊C4—224no—
441C4⋊C4—444no—
442C4⋊C4C22×Dic1112yes—
443C4⋊C4C22×Dic1112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C42—24no—
452C11#2176911yescharacteristic, complemented, Sylow
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—21no—
458C23—21no—
459C23—22no—
460C23—22no—
461C23—21no—
462C23—21no—
463C23—28no—
464C23—22no—
465C23—44no—
466C23—44no—
467C23—48no—
468C23—48no—
469C23—42no—
470C23—41no—
471C23—42no—
472C23—41no—
473C23#6700212yes—
474C23#6700412yes—
475C23C2×C22⋊Dic1112yes—
476C23C2×C22⋊Dic1112yes—
477C23C2×C22⋊Dic1112yes—
478C23C22×C22⋊D1111yescharacteristic
479Q8—24no—
480Q8—42no—
481D4—24no—
482D4—48no—
483D4—48no—
484D4—48no—
485D4—42no—
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—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—888no—
510C2×C4C2×C22⋊Dic1112yes—
511C2×C4C2×C22⋊Dic1112yes—
512C2×C4C2×C22⋊Dic1112yes—
513C2×C4#6703714yes—
514C2×C4C23×Dic1111yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—444no—
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—42no—
533C22—42no—
534C22—42no—
535C22—82no—
536C22—82no—
537C22#1062284514yes—
538C22#1062333512yes—
539C22C2×#6700211yescharacteristic
540C22#1062335312yes—
541C22C2×#6700411yescharacteristic
542C22C22×C22⋊Dic1111yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—884no—
550C4#1062332912yes—
551C4#1062333512yes—
552C2—24no—
553C2—42no—
554C2—42no—
555C2—82no—
556C2#1307119411yescharacteristic
557C2C2×#1062284511yescharacteristic
558C2#1307713511yescharacteristic
559C2#1307942612yes—
560C2#1307944212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#525D11
hypocenterC11#21769
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. C2×#10622825C2semidirect
3. #13069055C2semidirect
4. #13069050C2semidirect
5. #13068934C2semidirect
6. #13068924C2semidirect
7. #13068711C2semidirect
8. #13068556C2semidirect
13. C11×#525C4semidirect
26. C2×#66899C22semidirect
27. C2×#66896C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
41. C2×C11×#41C2×C4semidirect
62. C11×C22⋊Q8C2×C4semidirect
66. C11×#121C2×C4semidirect
71. C11×#117C2×C4semidirect
250. #525Dic11semidirect
312. C2×#41C2×Dic11semidirect
336. C22⋊Q8C2×Dic11semidirect
340. #121C2×Dic11semidirect
345. #117C2×Dic11semidirect
452. C11#21769semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
C2×#106228252
#130690552
#130690502
#130689342
#130689242
#130687112
#130685562
C2×C11×#5252
#2176911