Finite Group Databasebeta

← #14753851

Subgroups — #14753851

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13071018C211yesmaximal, characteristic, complemented
4#13068711C211yesmaximal, characteristic, complemented
5#13068620C212yesmaximal, complemented
6#13068615C212yesmaximal, complemented
7#13068557C211yesmaximal, characteristic
8#13068554C211yesmaximal, characteristic
9#13068445C212yesmaximal, complemented
10#13068440C212yesmaximal, complemented
11C11×#1825C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15#10623053—24no—
16#10623053C418yescomplemented
17C2×#66946C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×(C22⋊D11)⋊C4—21no—
23C2×#66930—21no—
24C2×#66925—21no—
25C2×C42×D11—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66880C2212yes—
32C2×#66879C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622589C2212yes—
35C4⋊C4×Dic11C2212yes—
36C2×#66874C2212yes—
37C2×#66873C2212yes—
38#10622555—21no—
39#10622332—24no—
40#10622263—21no—
41#10622262—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C2×#4339—22no—
51C2×#4339—24no—
52C2×#4339—24no—
53C2×#4339C2×C414yes—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11—21no—
57C22×C4×D11—21no—
58C22×Dic22C2311yescharacteristic
59C22×C8×C11C2312yes—
60C11×#117—22no—
61C11×#117C2×C414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11—21no—
68C2×C22⋊Dic11—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11C2×C414yes—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D414yes—
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66946—22no—
87#66946—22no—
88#66946C2×C414yes—
89#66946C2×C414yes—
90#66940—22no—
91#66940—22no—
92#66940C2×C414yes—
93#66940C2×C414yes—
94(C22⋊D11)⋊C4—28no—
95(C22⋊D11)⋊C4—28no—
96#66930—44no—
97#66925—28no—
98C42×D11—28no—
99C11×C22⋊C8—22no—
100C11×#95—21no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C22⋊(C11⋊C8)—22no—
104#66885—24no—
105#66880—24no—
106#66879—24no—
107Dic11⋊C8—24no—
108#66874—24no—
109#66873—24no—
110#20743—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C23×D11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—28no—
123C2×C22⋊D11—24no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11C22⋊C414yes—
130C22×Dic11C22⋊C414yes—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135#4339—216no—
136#4339—28no—
137#4339—28no—
138C2×D44—21no—
139C2×D44—22no—
140C2×D44C22×C412yes—
141C2×D44#4114yes—
142C2×C4×D11—28no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—44no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×Dic22—21no—
150C2×Dic22—22no—
151C2×Dic22C22×C412yes—
152C2×Dic22#4114yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C22×C412yes—
161C11×C4⋊C4C22×C412yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—42no—
164C42×C11—24no—
165C22⋊Dic11—42no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—44no—
173Dic11⋊C4—44no—
174C4×Dic11—24no—
175C4×Dic11—24no—
176C4×Dic11—44no—
177C4×Dic11C22⋊C414yes—
178C4×Dic11C22⋊C414yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C4×Dic11C2×D412yes—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C4×#41—111no—
187C2×#432—111no—
188#2285—111no—
189#1825—111no—
190#1825D1111yescharacteristic, complemented
191#1803—112no—
192#1802—112no—
193#1788—111no—
194#1788—111no—
195#1763—112no—
196#1762—112no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—22no—
201C23×C11C2×C22⋊C412yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—24no—
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—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4112yes—
224C2×C4×C11C2×#4112yes—
225C22⋊D11—216no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—28no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C412yes—
239C2×Dic11C2×C22⋊C412yes—
240C2×Dic11C2×C22⋊C412yes—
241C2×Dic11AGL(1,ℤ/8)12yes—
242C2×Dic11#13712yes—
243D44—22no—
244D44—24no—
245D44#11714yescomplemented
246C4×D11—216no—
247C4×D11—48no—
248C4×D11—48no—
249Dic22—22no—
250Dic22—24no—
251Dic22#11714yescomplemented
252C8×C11—42no—
253C11⋊C8—42no—
254C22×#41—111no—
255C4×#41—118no—
256C4×#41—224no—
257C2×C4×Q8—111no—
258C2×C4×Q8—111no—
259C2×C4×D4—111no—
260C2×C4×D4—111no—
261C2×C4×D4—221no—
262C2×C4×D4—221no—
263C2×#117—221no—
264C2×#117—221no—
265C2×#117C2×D1111yescharacteristic
266C22×C42—111no—
267C22×C42—221no—
268#432—224no—
269C2×C4⋊C8—112no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8—111no—
275C2×C22⋊C8C2×D1111yescharacteristic
276C2×#97—112no—
277#384—112no—
278#382—221no—
279#380—111no—
280#380—221no—
281#380C2×D1111yescharacteristic
282C4×C4⋊C4—112no—
283C4×C4⋊C4—221no—
284#340—112no—
285#340—112no—
286#340C2×D1112yes—
287#340C2×D1112yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11#52512yes—
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11C2×#13711yescharacteristic
297C22×C11#57512yes—
298C2×D11—24no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11—42no—
302C2×D11—42no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—82no—
307C4×C11C2×#11711yescharacteristic
308C4×C11C2×#11711yescharacteristic
309C4×C11#52512yes—
310Dic11—22no—
311Dic11—22no—
312Dic11—22no—
313Dic11—24no—
314Dic11—82no—
315Dic11#41714yes—
316C2×#41—114no—
317C2×#41—224no—
318C2×#41—224no—
319C2×#41—222no—
320C22×Q8—111no—
321C22×D4—111no—
322C22×D4—221no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22×D1111yescharacteristic
329C22×C8—112no—
330C22×C8C22×D1112yes—
331C4×Q8—114no—
332C4×Q8—114no—
333C4×Q8—222no—
334C4×Q8—222no—
335C4×D4—114no—
336C4×D4—114no—
337C4×D4—222no—
338C4×D4—222no—
339C4×D4—228no—
340C4×D4—228no—
341#117—22no—
342#117—228no—
343#117—444no—
344#117C4×D1114yes—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4C22×D1112yes—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C42—21no—
359C2×C42—114no—
360C2×C42—111no—
361C2×C42—114no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—111no—
365C2×C42—228no—
366C2×C42—221no—
367C2×C42—221no—
368C2×C42—222no—
369C4⋊C8—224no—
370#103—224no—
371#103—224no—
372#102—224no—
373#102—224no—
374C22⋊C8—22no—
375C22⋊C8—222no—
376#97—224no—
377#95—21no—
378#95—222no—
379#95—221no—
380C2×C11—42no—
381C2×C11#228011yescharacteristic
382C2×C11C2×#41711yescharacteristic
383C2×C11#289611yescharacteristic
384C2×C11#311512yes—
385C2×C11#311612yes—
386D11—44no—
387C24—221no—
388C24D4×D1111yescharacteristic
389#41—228no—
390#41—228no—
391#41—2216no—
392C2×Q8—112no—
393C2×Q8—114no—
394C2×Q8—221no—
395C2×Q8—222no—
396C2×D4—112no—
397C2×D4—114no—
398C2×D4—228no—
399C2×D4—224no—
400C2×D4—221no—
401C2×D4—222no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—111no—
408C22×C4—114no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—114no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—228no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—442no—
425C22×C4C2×C4×D1112yes—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1112yes—
428C22×C4C23×D1111yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—224no—
440C4⋊C4—224no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4—444no—
444C4⋊C4—444no—
445C4⋊C4C2×C4×D1112yes—
446C4⋊C4C2×C4×D1112yes—
447C22⋊C4—24no—
448C22⋊C4—42no—
449C22⋊C4—224no—
450C22⋊C4—224no—
451C22⋊C4—442no—
452C42—24no—
453C42—114no—
454C42—114no—
455C42—112no—
456C42—112no—
457C42—112no—
458C42—112no—
459C42—224no—
460C42—224no—
461C42—444no—
462C11#2074311yescharacteristic, complemented, Sylow
463C23—22no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—222no—
468C23—224no—
469C23—442no—
470C23—441no—
471C23—441no—
472C23C22⋊C4×D1112yes—
473C23C2×D4×D1111yescharacteristic
474Q8—114no—
475Q8—222no—
476Q8—224no—
477D4—114no—
478D4—2216no—
479D4—222no—
480D4—224no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—2216no—
500C2×C4—228no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—224no—
507C2×C4—448no—
508C2×C4—448no—
509C2×C4—444no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4C22⋊C4×D1112yes—
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4#41×D1112yes—
517C2×C4#41×D1112yes—
518C8—42no—
519C8—442no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—42no—
524C22—42no—
525C22—224no—
526C22—442no—
527C22—442no—
528C22—444no—
529C22—444no—
530C22C2×C22⋊C4×D1111yescharacteristic
531C22#1062318712yes—
532C22#1062329912yes—
533C22D11×AGL(1,ℤ/8)11yescharacteristic
534C22D11×#13711yescharacteristic
535C4—22no—
536C4—42no—
537C4—42no—
538C4—82no—
539C4—114no—
540C4—222no—
541C4—222no—
542C4—222no—
543C4—224no—
544C4—882no—
545C4D11×#11711yescharacteristic
546C4D11×#11711yescharacteristic
547C4#1062318712yes—
548C2—42no—
549C2—444no—
550C2#1307099611yescharacteristic
551C2D11×#41711yescharacteristic
552C2#1307713111yescharacteristic
553C2#1307876212yes—
554C2#1307877312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#20743
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13071018C2semidirect
4. #13068711C2semidirect
5. #13068620C2semidirect
6. #13068615C2semidirect
9. #13068445C2semidirect
10. #13068440C2semidirect
11. C11×#1825C2semidirect
16. #10623053C4semidirect
190. #1825D11semidirect
245. D44#117semidirect
251. Dic22#117semidirect
462. C11#20743semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
C2×#106223322
#130710182
#130687112
#130686202
#130686152
#130685572
#130685542
#130684452
#130684402
C11×#18252
#2074311