Finite Group Databasebeta

← #14788521

Subgroups — #14788521

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic, complemented
4#13069855C212yesmaximal, complemented
5#13069691C212yesmaximal
6#13069552C211yesmaximal, characteristic, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13068968C212yesmaximal, complemented
9#13068867C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66989C2212yes—
16C22×#4324C2212yes—
17C2×#66979—21no—
18C2×#66977—21no—
19C2×#66977—21no—
20#10623073—24no—
21#10623073—24no—
22C2×#66940C2212yes—
23C2×#66932—22no—
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31#10622834C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34C2×#66880C2212yes—
35C2×#66880C2212yes—
36#10622632—24no—
37#10622586C2212yes—
38C2×#66874C2212yes—
39#10622561—22no—
40#10622548C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C22×Dic22D411yescharacteristic
50C22×Dic22C2312yes—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11D414yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69#66989—24no—
70#66989—24no—
71C2×#4324—24no—
72C2×#4324—24no—
73C2×#4324—42no—
74#66979—28no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2312yes—
81#66977—28no—
82#66977—44no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4D412yes—
86C2×C4×Dic11—22no—
87C2×C4×Dic11C2312yes—
88C22×C11⋊C8C2312yes—
89#66940—24no—
90#66940—24no—
91#66932—216no—
92#66922—22no—
93#66922D414yes—
94C4×Dic22—22no—
95C4×Dic22—22no—
96C11×#107—22no—
97C11×#102—22no—
98C11×#102—22no—
99C4×C8×C11—22no—
100#66896—42no—
101C11⋊#95—22no—
102#66880—24no—
103#66880—42no—
104#66874—24no—
105C4⋊(C11⋊C8)—22no—
106#24185—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C2×D4×C11#4112yes—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C2×D412yes—
135C22×Dic11C2×D412yes—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22C2×D414yes—
145C11×D8—28no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11#4112yes—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—42no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160C22⋊Dic11—28no—
161C22⋊Dic11—28no—
162C22⋊Dic11—44no—
163C22⋊Dic11—82no—
164#4324—48no—
165C4⋊Dic11—22no—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—81no—
172Dic11⋊C4—28no—
173Dic11⋊C4—24no—
174Dic11⋊C4—44no—
175C4×Dic11—28no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×#556—111no—
182C2×#461—111no—
183C2×C4×D8D1111yescharacteristic
184#2538—111no—
185#2042—112no—
186#2012—112no—
187#1984—111no—
188#1956—111no—
189#1880—112no—
190#1863—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11C22×D411yescharacteristic
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—48no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11#13512yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247Dic22—24no—
248Dic22—24no—
249Dic22—42no—
250Dic22—42no—
251Dic22—44no—
252C8×C11—22no—
253C8×C11—41no—
254C11⋊C8—42no—
255C22×SD16—112no—
256C22×D8C2×D1111yescharacteristic
257#556—224no—
258#556—224no—
259C2×C4⋊Q8—111no—
260C2×#126—222no—
261C2×#124—112no—
262C2×C22⋊Q8—221no—
263C2×C22⋊Q8—221no—
264C2×C4×Q8—111no—
265C2×C4×Q8—112no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—221no—
269#461—224no—
270C4×D8—24no—
271C2×#107C2×D1111yescharacteristic
272C2×C4⋊C8—111no—
273C2×#103—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—112no—
277C2×#102C2×D1111yescharacteristic
278C2×#102C2×D1111yescharacteristic
279C2×C4×C8C2×D1111yescharacteristic
280#396—222no—
281#390—112no—
282#389—112no—
283#384—111no—
284#380—221no—
285#340—112no—
286#336—112no—
287#336—112no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54811yescharacteristic
304C22×C11#55011yescharacteristic
305C22×C11C2×#13511yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57811yescharacteristic
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—81no—
312C4×C11#44914yes—
313C4×C11#52511yescharacteristic
314C4×C11#53711yescharacteristic
315C4×C11#54611yescharacteristic
316C4×C11#54711yescharacteristic
317Dic11—44no—
318Dic11—42no—
319Dic11—42no—
320Dic11—82no—
321C22×Q8—111no—
322C22×Q8—112no—
323C22×D4C22×D1111yescharacteristic
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C2×SD16—224no—
328C2×SD16—224no—
329C2×SD16—442no—
330C2×D8—22no—
331C2×D8—22no—
332C2×D8—22no—
333C22×C8—112no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—114no—
337C4⋊Q8—222no—
338#126—2216no—
339#124—224no—
340#124—224no—
341C22⋊Q8—228no—
342C22⋊Q8—444no—
343C4×Q8—224no—
344C4×Q8—224no—
345C4×Q8—222no—
346C4×Q8—222no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4C22⋊D1114yes—
351#117—228no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—112no—
370C2×C42—222no—
371C2×C42C22×D1111yescharacteristic
372#107—22no—
373C4⋊C8—222no—
374#103—224no—
375#103—224no—
376#103—442no—
377#102—22no—
378#102—22no—
379#102—442no—
380C4×C8—22no—
381#95—222no—
382C2×C11—82no—
383C2×C11—82no—
384C2×C11#240711yescharacteristic
385C2×C11C2×#44911yescharacteristic
386C2×C11#301311yescharacteristic
387C2×C11#336011yescharacteristic
388C2×C11#336711yescharacteristic
389C2×C11#339311yescharacteristic
390C2×C11#339711yescharacteristic
391C24—21no—
392C24—21no—
393C2×Q8—114no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#433912yes—
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429SD16—448no—
430D8—28no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8#433912yes—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—228no—
444C4⋊C4—222no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4—224no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—444no—
451C4⋊C4—442no—
452C4⋊C4—881no—
453C4⋊C4C2×C22⋊D1112yes—
454C22⋊C4—24no—
455C22⋊C4—42no—
456C22⋊C4—228no—
457C22⋊C4—228no—
458C22⋊C4—444no—
459C22⋊C4—882no—
460C42—228no—
461C42—222no—
462C42—222no—
463C42D4×D1112yes—
464C42C2×C22⋊D1112yes—
465C11#2418511yescharacteristic, complemented, Sylow
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C2×D4×D1111yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—444no—
484Q8—442no—
485Q8—442no—
486D4—22no—
487D4—22no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—48no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—84no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4#6696412yes—
517C2×C4#6696512yes—
518C2×C4#6699012yes—
519C2×C4#6699012yes—
520C2×C4C2×#433911yescharacteristic
521C2×C4C2×#433911yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#6704211yescharacteristic
524C2×C4#6704311yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—22no—
527C8—41no—
528C8—442no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22#1062308311yescharacteristic
544C22#1062308411yescharacteristic
545C22C2×#6696411yescharacteristic
546C22C2×#6696511yescharacteristic
547C22#1062330111yescharacteristic
548C22#1062330211yescharacteristic
549C22C2×#6699011yescharacteristic
550C4—22no—
551C4—42no—
552C4—81no—
553C4—442no—
554C4—444no—
555C4—442no—
556C4—882no—
557C4#1062277114yes—
558C4#1062308111yescharacteristic
559C4#1062308211yescharacteristic
560C4#1062332211yescharacteristic
561C4#1062336411yescharacteristic
562C2—82no—
563C2—82no—
564C2#1307196111yescharacteristic
565C2C2×#1062277111yescharacteristic
566C2#1307792711yescharacteristic
567C2#1308126311yescharacteristic
568C2#1308133211yescharacteristic
569C2#1308160211yescharacteristic
570C2#1308163411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11#24185
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. C2×#10622632C2semidirect
3. #13073538C2semidirect
4. #13069855C2semidirect
6. #13069552C2semidirect
7. #13069418C2semidirect
8. #13068968C2semidirect
9. #13068867C2semidirect
10. #13068616C2semidirect
465. C11#24185semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106226322
#130735382
#130698552
#130696912
#130695522
#130694182
#130689682
#130688672
#130686162
C2×C4×C11×D82
#2418511