Finite Group Databasebeta

← #14753837

Subgroups — #14753837

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic
3#13071009C211yesmaximal, characteristic
4#13068705C212yesmaximal
5#13068632C211yesmaximal, characteristic, complemented
6#13068631C211yesmaximal, characteristic, complemented
7#13068628C211yesmaximal, characteristic, complemented
8#13068549C212yesmaximal
9#13068448C212yesmaximal, complemented
10#13068445C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C4×Q8×D11—24no—
16C4×Q8×D11C418yescomplemented
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66940—21no—
20C2×#66940C2211yescharacteristic
21C2×C42×D11—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#382C2211yescharacteristic
28C2×#66899C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×#66879C2212yes—
32#10622600C2212yes—
33C4⋊C4×Dic11C2212yes—
34C2×#66874C2212yes—
35#10622549C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622448—24no—
38#10622279—21no—
39#10622277—21no—
40#10622264—21no—
41#10622261—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C2×Q8×D11—22no—
48C2×Q8×D11—22no—
49C2×Q8×D11—22no—
50C2×Q8×D11—22no—
51C2×Q8×D11—22no—
52C2×Q8×D11C2×C414yes—
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22—21no—
59C22×Dic22C2311yescharacteristic
60C22×C8×C11C2312yes—
61C4×Q8×C11—22no—
62C4×Q8×C11C2×C414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68Q8×Dic11—22no—
69Q8×Dic11C2×C414yes—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C4⋊C4×D11—28no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11C2×C414yes—
88#66940—28no—
89#66940—22no—
90#66940C2×C414yes—
91C42×D11—28no—
92C42×D11C2×C414yes—
93C42×D11D414yes—
94C4×Dic22—22no—
95C4×Dic22—28no—
96C4×Dic22C2×C414yes—
97C11×C4⋊C8—22no—
98C11×#103—24no—
99C11×#95—21no—
100C11×#95—21no—
101#66899—24no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106(C2×D11)⋊C8—24no—
107#66880—24no—
108#66879—24no—
109#66874—24no—
110C4⋊(C11⋊C8)—22no—
111#20741—111nomaximal, Sylow
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C22×C412yes—
117C2×Q8×C11#4112yes—
118C2×Q8×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131Q8×D11—28no—
132Q8×D11—28no—
133Q8×D11—28no—
134Q8×D11—28no—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—24no—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—42no—
145C2×C4×D11—44no—
146C2×C4×D11C22⋊C414yes—
147C2×C4×D11C22⋊C414yes—
148C2×C4×D11C22×C412yes—
149C2×C4×D11C2×D412yes—
150C2×Dic22—24no—
151C2×Dic22—24no—
152C2×Dic22—24no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C2×Dic22#4112yes—
158C2×Dic22#4112yes—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C22×C412yes—
167C42×C11—24no—
168C42×C11C22×C412yes—
169C42×C11C2×D412yes—
170(C2×D11)⋊C4—44no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22×C412yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179C4×Dic11—24no—
180C4×Dic11—24no—
181C4×Dic11—24no—
182C4×Dic11—44no—
183C4×Dic11C22⋊C414yes—
184C4×Dic11C22⋊C414yes—
185C4×Dic11C22×C412yes—
186C4×Dic11C2×D412yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C22×C4×Q8—111no—
191C2×#432—111no—
192#2283—111no—
193#1824—112no—
194#1805—111no—
195#1805—111no—
196#1805—111no—
197#1805D1111yescharacteristic, complemented
198#1787—112no—
199#1763—112no—
200#1763—112no—
201C23×C11C22×D411yescharacteristic
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—22no—
205C22×D11C2×C22⋊C412yes—
206C22×D11#13714yes—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11#11714yes—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11C2×C22⋊C412yes—
242C2×Dic11C2×C22⋊C412yes—
243C2×Dic11C2×C22⋊C412yes—
244C4×D11—216no—
245C4×D11—28no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—22no—
250C4×D11—44no—
251C4×D11—48no—
252Dic22—216no—
253Dic22—22no—
254Dic22—22no—
255Dic22—22no—
256Dic22#11714yes—
257C8×C11—42no—
258C11⋊C8—42no—
259C23×Q8—111no—
260C2×C4×Q8—111no—
261C2×C4×Q8—118no—
262C2×C4×Q8—111no—
263C2×C4×Q8—111no—
264C2×C4×Q8—221no—
265C2×C4×Q8—221no—
266C2×C4×Q8—224no—
267C2×C4×Q8C2×D1111yescharacteristic
268C22×C4⋊C4—111no—
269C22×C4⋊C4—221no—
270C22×C42—111no—
271C22×C42—221no—
272#432—224no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8C2×D1111yescharacteristic
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103C2×D1112yes—
279C2×C22⋊C8—112no—
280C2×#97—112no—
281#383—221no—
282#382—111no—
283#382C2×D1111yescharacteristic
284#381—221no—
285#380—112no—
286C4×C4⋊C4—112no—
287C4×C22⋊C4—221no—
288#376—221no—
289#340—112no—
290#340—112no—
291#340—112no—
292#340C2×D1112yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11#52511yescharacteristic
295C22×C11#52511yescharacteristic
296C22×C11C2×#13712yes—
297C22×C11#57512yes—
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—22no—
301C2×D11—22no—
302C2×D11#41914yes—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11C2×#11711yescharacteristic
309C4×C11C2×#11711yescharacteristic
310C4×C11#52511yescharacteristic
311C4×C11#52511yescharacteristic
312Dic11—22no—
313Dic11—22no—
314Dic11—22no—
315Dic11—24no—
316Dic11—42no—
317Dic11—82no—
318C22×Q8—114no—
319C22×Q8—111no—
320C22×Q8—221no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×Q8—222no—
326C22×Q8C22×D1111yescharacteristic
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—221no—
331C23×C4—221no—
332C22×C8—112no—
333C22×C8C22×D1112yes—
334C4×Q8—22no—
335C4×Q8—114no—
336C4×Q8—114no—
337C4×Q8—114no—
338C4×Q8—228no—
339C4×Q8—228no—
340C4×Q8—222no—
341C4×Q8—222no—
342C4×Q8—222no—
343C4×Q8C4×D1114yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4C22×D1112yes—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4—222no—
357C2×C42—21no—
358C2×C42—111no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—114no—
362C2×C42—114no—
363C2×C42—228no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42—221no—
367C2×C42—222no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—22no—
370C4⋊C8—222no—
371#103—24no—
372#103—224no—
373#103—224no—
374#103—224no—
375C22⋊C8—224no—
376#97—224no—
377#95—21no—
378#95—21no—
379#95—222no—
380#95—222no—
381#95—221no—
382#95—221no—
383C2×C11#228011yescharacteristic
384C2×C11C2×#41911yescharacteristic
385C2×C11#289611yescharacteristic
386C2×C11#311712yes—
387C2×C11#311712yes—
388D11—24no—
389C24—111no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—112no—
394C2×Q8—112no—
395C2×Q8—112no—
396C2×Q8—224no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—228no—
400C2×Q8—228no—
401C2×Q8—228no—
402C2×Q8—228no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8C2×C4×D1112yes—
407C2×Q8#434112yes—
408C2×Q8#434312yes—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4—444no—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—112no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—221no—
452C4⋊C4—222no—
453C4⋊C4—222no—
454C4⋊C4C2×C4×D1112yes—
455C22⋊C4—444no—
456C42—24no—
457C42—114no—
458C42—114no—
459C42—112no—
460C42—112no—
461C42—224no—
462C42—224no—
463C42—224no—
464C42—444no—
465C42C2×C4×D1112yes—
466C42D4×D1112yes—
467C11#2074111yescharacteristic, complemented, Sylow
468C23—112no—
469C23—114no—
470C23—222no—
471C23—221no—
472C23—221no—
473C23C2×D4×D1111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—22no—
477Q8—114no—
478Q8—2216no—
479Q8—222no—
480Q8—222no—
481Q8—222no—
482Q8#6694514yes—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—228no—
497C2×C4—2216no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—221no—
502C2×C4—222no—
503C2×C4—221no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—444no—
511C2×C4—448no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4C22⋊C4×D1112yes—
517C2×C4C22⋊C4×D1112yes—
518C2×C4C22×C4×D1111yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C2×#434311yescharacteristic
522C2×C4#41×D1111yescharacteristic
523C2×C4#41×D1111yescharacteristic
524C8—42no—
525C8—442no—
526C22—114no—
527C22—224no—
528C22—224no—
529C22—222no—
530C22—222no—
531C22C2×C22⋊C4×D1111yescharacteristic
532C22#1062313711yescharacteristic
533C22#1062315811yescharacteristic
534C22#1062329912yes—
535C22D11×#13712yes—
536C4—22no—
537C4—22no—
538C4—24no—
539C4—42no—
540C4—82no—
541C4—222no—
542C4—222no—
543C4—222no—
544C4—224no—
545C4—442no—
546C4—882no—
547C4C2×#6694511yescharacteristic
548C4D11×#11711yescharacteristic
549C4#1062313711yescharacteristic
550C4#1062315811yescharacteristic
551C2—224no—
552C2#1307099811yescharacteristic
553C2D11×#41911yescharacteristic
554C2#1307713111yescharacteristic
555C2#1307878612yes—
556C2#1307879212yes—
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#20741
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
5. #13068632C2semidirect
6. #13068631C2semidirect
7. #13068628C2semidirect
9. #13068448C2semidirect
10. #13068445C2semidirect
11. C11×#1805C2semidirect
16. C4×Q8×D11C4semidirect
197. #1805D11semidirect
467. C11#20741semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106224482
#130710092
#130687052
#130686322
#130686312
#130686282
#130685492
#130684482
#130684452
C11×#18052
#2074111