Finite Group Databasebeta

← #14763500

Subgroups — #14763500

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic
3D11×#382C211yesmaximal, characteristic
4#13069587C212yesmaximal, complemented
5#13069434C212yesmaximal, complemented
6#13068922C212yesmaximal
7#13068920C212yesmaximal
8#13068632C211yesmaximal, characteristic, complemented
9#13068631C211yesmaximal, characteristic, complemented
10#13068628C211yesmaximal, characteristic, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15#10623109—24no—
16#10623109C418yescomplemented
17C2×#66950C2211yescharacteristic
18C2×#66949—21no—
19C2×C4⋊C4×D11C2212yes—
20C2×#66942—21no—
21C2×#66941C2211yescharacteristic
22C2×#66925—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#382C2211yescharacteristic
29C2×#66899C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×#66879C2212yes—
33#10622590C2212yes—
34C2×#66874C2212yes—
35#10622549C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622448—24no—
38D11×#95—21no—
39D11×#95—21no—
40#10622263—21no—
41#10622263—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C4×Q8×C11—22no—
55C4×Q8×C11C2×C414yescomplemented
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#66999—22no—
62#66999C2×C414yes—
63#66997—22no—
64#66997C2×C414yescomplemented
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81#66950—22no—
82#66950C2×C414yes—
83#66949—28no—
84C4⋊C4×D11—42no—
85C4⋊C4×D11—42no—
86#66942—28no—
87#66941—22no—
88#66941C2×C414yescomplemented
89#66925—28no—
90C42×D11C2×C414yes—
91C42×D11D414yes—
92C4×Dic22—22no—
93C4×Dic22—28no—
94C4×Dic22C2×C414yescomplemented
95C11×C4⋊C8—22no—
96C11×#103—42no—
97C11×#95—21no—
98C11×#95—21no—
99#66899—42no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66880—42no—
106#66879—24no—
107#66874—42no—
108C4⋊(C11⋊C8)—22no—
109#21866—111nomaximal, Sylow
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C22×C412yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C2×C4×D11—24no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—42no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×C4×D11C22⋊C414yes—
139C2×C4×D11C22⋊C414yes—
140C2×C4×D11C22×C412yes—
141C2×C4×D11C2×D412yes—
142C2×Dic22—24no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—44no—
149C2×Dic22C22×C412yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C22×C412yes—
158C42×C11—24no—
159C42×C11C22×C412yes—
160C42×C11C2×D412yes—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—44no—
174C4×Dic11—24no—
175C4×Dic11C22⋊C414yes—
176C4×Dic11C22⋊C414yes—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×#533—111no—
183C2×#432—111no—
184C2×#382—111no—
185#1993—112no—
186#1960—112no—
187#1872—112no—
188#1872—112no—
189#1805—111no—
190#1805—111no—
191#1805—111no—
192#1805D1111yescharacteristic, complemented
193C23×C11C22×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—22no—
197C22×D11C2×C22⋊C412yes—
198C22×D11#13714yes—
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—41no—
202Q8×C11—41no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236C4×D11—28no—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—44no—
242C4×D11—88no—
243Dic22—22no—
244Dic22—22no—
245Dic22—48no—
246Dic22—41no—
247Dic22—41no—
248C8×C11—42no—
249C11⋊C8—42no—
250#533—118no—
251#533—224no—
252C2×C4⋊Q8—111no—
253C2×C4⋊Q8—111no—
254C2×#125—221no—
255C2×C22⋊Q8—111no—
256C2×C22⋊Q8—111no—
257C2×C22⋊Q8—221no—
258C2×C4×Q8—111no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×#117—221no—
262C22×C4⋊C4—112no—
263C22×C42—111no—
264#432—224no—
265C2×C4⋊C8—111no—
266C2×C4⋊C8C2×D1111yescharacteristic
267C2×#103—112no—
268C2×#103—112no—
269C2×#103—112no—
270C2×#103C2×D1112yes—
271C2×C22⋊C8—112no—
272C2×#97—112no—
273#382—112no—
274#382—111no—
275#382—221no—
276#382—221no—
277#382C2×D1111yescharacteristic
278C2×#95—221no—
279C2×#95—221no—
280#340—112no—
281#340—112no—
282#340—112no—
283#340C2×D1112yes—
284C22×C11C22×C22⋊C411yescharacteristic
285C22×C11#53511yescharacteristic
286C22×C11#53611yescharacteristic
287C22×C11C2×#13712yes—
288C22×C11#57512yes—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—24no—
292C2×D11—24no—
293C2×D11#41914yes—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—82no—
299C4×C11#52011yescharacteristic
300C4×C11#52011yescharacteristic
301C4×C11#53711yescharacteristic
302C4×C11#53711yescharacteristic
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—42no—
307Dic11—42no—
308Dic11—82no—
309C22×Q8—111no—
310C22×Q8—221no—
311C22×Q8C22×D1111yescharacteristic
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—222no—
316C22×C8—112no—
317C22×C8C22×D1112yes—
318C4⋊Q8—114no—
319C4⋊Q8—114no—
320C4⋊Q8—222no—
321C4⋊Q8—222no—
322#125—228no—
323C22⋊Q8—114no—
324C22⋊Q8—114no—
325C22⋊Q8—222no—
326C22⋊Q8—228no—
327C22⋊Q8—222no—
328C4×Q8—22no—
329C4×Q8—114no—
330C4×Q8—228no—
331C4×Q8—222no—
332C4×Q8C4×D1114yescomplemented
333#117—228no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—442no—
345C2×C4⋊C4—442no—
346C2×C4⋊C4C22×D1112yes—
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C42—21no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—114no—
355C2×C42—114no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—22no—
359C4⋊C8—222no—
360#103—42no—
361#103—442no—
362#103—442no—
363#103—442no—
364C22⋊C8—224no—
365#97—224no—
366#95—21no—
367#95—21no—
368#95—222no—
369#95—222no—
370#95—221no—
371#95—221no—
372C2×C11#231111yescharacteristic
373C2×C11C2×#41911yescharacteristic
374C2×C11#289611yescharacteristic
375C2×C11#321512yes—
376C2×C11#323612yes—
377D11—24no—
378C24—111no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—112no—
385C2×Q8—224no—
386C2×Q8—221no—
387C2×Q8—221no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—444no—
392C2×Q8C2×C4×D1112yes—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—224no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—444no—
413C22×C4—444no—
414C22×C4—444no—
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—112no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—221no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—444no—
439C4⋊C4C2×C4×D1112yes—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C42—24no—
443C42—114no—
444C42—114no—
445C42—112no—
446C42—112no—
447C42—224no—
448C42C2×C4×D1112yes—
449C42D4×D1112yes—
450C11#2186611yescharacteristic, complemented, Sylow
451C23—112no—
452C23—114no—
453C23—222no—
454C23—221no—
455C23—221no—
456C23C2×D4×D1111yescharacteristic
457Q8—22no—
458Q8—22no—
459Q8—41no—
460Q8—41no—
461Q8—222no—
462Q8—222no—
463Q8—448no—
464Q8—441no—
465Q8—441no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—228no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—444no—
491C2×C4—442no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—888no—
498C2×C4C22⋊C4×D1112yes—
499C2×C4C22⋊C4×D1112yes—
500C2×C4C22×C4×D1111yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4#6703711yescharacteristic
503C2×C4#6704011yescharacteristic
504C2×C4#6704211yescharacteristic
505C2×C4#6704311yescharacteristic
506C8—42no—
507C8—442no—
508C22—114no—
509C22—224no—
510C22—224no—
511C22—222no—
512C22—222no—
513C22C2×C22⋊C4×D1111yescharacteristic
514C22#1062313811yescharacteristic
515C22#1062315911yescharacteristic
516C22#1062329912yes—
517C22D11×#13712yes—
518C4—22no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—82no—
523C4—222no—
524C4—222no—
525C4—222no—
526C4—442no—
527C4—442no—
528C4—882no—
529C4#1062303511yescharacteristic
530C4#1062305411yescharacteristic
531C4#1062313911yescharacteristic
532C4#1062316011yescharacteristic
533C2—224no—
534C2#1307120511yescharacteristic
535C2D11×#41911yescharacteristic
536C2#1307713111yescharacteristic
537C2#1307961712yes—
538C2#1307982012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1805D11
hypocenterC11#21866
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
4. #13069587C2semidirect
5. #13069434C2semidirect
8. #13068632C2semidirect
9. #13068631C2semidirect
10. #13068628C2semidirect
11. C11×#1805C2semidirect
16. #10623109C4semidirect
55. C4×Q8×C11C2×C4semidirect
64. #66997C2×C4semidirect
88. #66941C2×C4semidirect
94. C4×Dic22C2×C4semidirect
192. #1805D11semidirect
332. C4×Q8C4×D11semidirect
450. C11#21866semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106224482
D11×#3822
#130695872
#130694342
#130689222
#130689202
#130686322
#130686312
#130686282
C11×#18052
#2186611