Finite Group Databasebeta

← #14810722

Subgroups — #14810722

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3C2×#10622670C211yesmaximal, characteristic
4#13069757C212yesmaximal, complemented
5#13069752C212yesmaximal, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal
9#13068953C212yesmaximal, complemented
10#13068444C211yesmaximal, characteristic, complemented
11C11×#2592C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×#4325C2211yescharacteristic
16C22×#4323C2211yescharacteristic
17Q8×D44—24no—
18Q8×D44—24no—
19C2×#66950—22no—
20C2×#66950—21no—
21C2×C4×D44C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2212yes—
24C2×#66922C2211yescharacteristic
25C11×#397—21no—
26C11×#393—21no—
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#388—22no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2212yes—
33C2×#66896C2211yescharacteristic
34C2×#66896C2212yes—
35#10622670—24no—
36#10622668—24no—
37C2×#66873C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C2×Q8×D11—28no—
49C2×Q8×D11—48no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—21no—
53C22×Dic22—22no—
54C22×Dic22—21no—
55C11×#124—22no—
56C11×#124—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11—21no—
67C2×C42×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—22no—
70C2×#4325—24no—
71C2×#4323—22no—
72C2×#4323—24no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66950—28no—
83#66950—216no—
84C4×D44—24no—
85C4×D44—22no—
86C4×D44—24no—
87C4×D44D414yes—
88#66922—22no—
89#66922—24no—
90#66922—24no—
91#66922D414yes—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95#66899—24no—
96#66899—22no—
97#66896—24no—
98#66896—22no—
99#66873—24no—
100C4⋊(C11⋊C8)—22no—
101#66867—22no—
102#25939—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—22no—
124Q8×D11—432no—
125C2×D44—21no—
126C2×D44—22no—
127C2×D44C2×D412yes—
128C2×D44#4114yes—
129C2×C4×D11—28no—
130C2×C4×D11—24no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×Dic22—28no—
135C2×Dic22—24no—
136C2×Dic22—44no—
137C2×Dic22—44no—
138C2×Dic22—44no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—82no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—81no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152#4325—44no—
153#4323—44no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—24no—
156C4⋊Dic11—28no—
157C4⋊Dic11—24no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11C2×D414yes—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×D4×Q8—111no—
170C2×#489—111no—
171C2×#463—111no—
172#2592D1111yescharacteristic, complemented
173#2024—112no—
174#2023—112no—
175#1987—111no—
176#1985—111no—
177#1879—112no—
178#1877—112no—
179#1762—111no—
180C23×C11—41no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11C22×D411yescharacteristic
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—42no—
189C22×D11—41no—
190C22×D11—41no—
191Q8×C11—28no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—42no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—42no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11AGL(1,ℤ/8)14yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4112yes—
217C2×C4×C112−1+412yes—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223D44—22no—
224D44—24no—
225D44#12414yes—
226C4×D11—48no—
227C4×D11—416no—
228Dic22—48no—
229Dic22—416no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C11⋊C8—42no—
233C23×Q8—221no—
234C22×SD16—111no—
235C22×D8—111no—
236D4×Q8—224no—
237D4×Q8—224no—
238C2×C4⋊Q8—111no—
239C2×C4⋊Q8—112no—
240C2×#124C2×D1111yescharacteristic
241C2×C22⋊Q8—222no—
242C2×C22⋊Q8—221no—
243C2×C4×Q8C2×D1111yescharacteristic
244C2×C4×D4—111no—
245C2×C4×D4—112no—
246#489—224no—
247#463—224no—
248C2×C4⋊C8—111no—
249C2×#103—112no—
250C2×#103—111no—
251C2×#102—112no—
252C2×#102—111no—
253C2×#102—112no—
254C2×#97—111no—
255#397—21no—
256#393—21no—
257#391C2×D1112yes—
258#390C2×D1112yes—
259#388—22no—
260C4×C4⋊C4C2×D1111yescharacteristic
261#340—112no—
262#340—112no—
263#340—112no—
264#336—112no—
265#336—112no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11C2×#12011yescharacteristic
272C22×C11#54812yes—
273C22×C11C2×AGL(1,ℤ/8)12yes—
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C2×D11—24no—
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—42no—
280C2×D11—42no—
281C4×C11—22no—
282C4×C11—24no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11C2×#12411yescharacteristic
288C4×C11#53611yescharacteristic
289C4×C11#54812yes—
290Dic11—44no—
291Dic11—42no—
292C22×Q8—228no—
293C22×Q8—221no—
294C22×Q8—222no—
295C22×Q8—448no—
296C22×Q8C22⋊D1111yescharacteristic
297C22×Q8C22×D1111yescharacteristic
298C22×D4—111no—
299C22×D4C22×D1111yescharacteristic
300C23×C4—222no—
301C23×C4—221no—
302C2×SD16—224no—
303C2×SD16—222no—
304C2×D8—224no—
305C2×D8—222no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—112no—
309C4⋊Q8—114no—
310C4⋊Q8—224no—
311C4⋊Q8—224no—
312C4⋊Q8—222no—
313#124—22no—
314#124—22no—
315C22⋊Q8—228no—
316C22⋊Q8—2216no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×D4—114no—
320C4×D4—224no—
321C4×D4—224no—
322C4×D4—222no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4C22⋊D1112yes—
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—221no—
336C2×C42—21no—
337C2×C42C22×D1112yes—
338C2×C42C22×D1111yescharacteristic
339C4⋊C8—222no—
340#103—222no—
341#103—224no—
342#102—224no—
343#102—222no—
344#102—224no—
345#97—222no—
346#95—21no—
347#95—22no—
348#95—22no—
349C2×C11—161no—
350C2×C11#243611yescharacteristic
351C2×C11#300311yescharacteristic
352C2×C11#301311yescharacteristic
353C2×C11#336712yes—
354C2×C11#337312yes—
355D11—44no—
356C24—21no—
357C24—221no—
358C2×Q8—22no—
359C2×Q8—24no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—228no—
365C2×Q8—224no—
366C2×Q8—444no—
367C2×Q8—444no—
368C2×Q8—4432no—
369C2×Q8—444no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—112no—
375C2×D4—114no—
376C2×D4—221no—
377C2×D4—222no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—228no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4—224no—
384C22×C4—444no—
385C22×C4—444no—
386C22×C4—444no—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1112yes—
391C22×C4C23×D1111yescharacteristic
392SD16—444no—
393D8—444no—
394C2×C8—222no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—112no—
406C4⋊C4—114no—
407C4⋊C4—228no—
408C4⋊C4—224no—
409C4⋊C4—222no—
410C4⋊C4—221no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—44no—
414C22⋊C4—82no—
415C22⋊C4—228no—
416C22⋊C4—224no—
417C42—22no—
418C42—22no—
419C42—81no—
420C42D4×D1112yes—
421C42D4×D1112yes—
422C11#2593911yescharacteristic, complemented, Sylow
423C23—41no—
424C23—42no—
425C23—42no—
426C23—41no—
427C23—41no—
428C23—222no—
429C23—224no—
430C23—442no—
431C23—441no—
432C23—441no—
433C23C22×C22⋊D1111yescharacteristic
434Q8—28no—
435Q8—41no—
436Q8—41no—
437Q8—42no—
438Q8—448no—
439Q8—4416no—
440D4—41no—
441D4—41no—
442D4—42no—
443D4—114no—
444D4—222no—
445D4—224no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—224no—
460C2×C4—222no—
461C2×C4—448no—
462C2×C4—4416no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4#6699012yes—
467C2×C4#6699012yes—
468C2×C4#6700214yes—
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4#41×D1112yes—
472C2×C4#6704312yes—
473C8—441no—
474C8—441no—
475C8—442no—
476C22—82no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—82no—
481C22—224no—
482C22—444no—
483C22—442no—
484C22—442no—
485C22—444no—
486C22C2×#6699011yescharacteristic
487C22C2×#6700212yes—
488C22#1062336212yes—
489C22#1062336711yescharacteristic
490C22#1062336911yescharacteristic
491C4—22no—
492C4—24no—
493C4—22no—
494C4—42no—
495C4—82no—
496C4—81no—
497C4—444no—
498C4—442no—
499C4D11×#12411yescharacteristic
500C4#1062320611yescharacteristic
501C4#1062320812yes—
502C2—161no—
503C2—444no—
504C2#1307227111yescharacteristic
505C2#1307784211yescharacteristic
506C2#1307792811yescharacteristic
507C2#1308133012yes—
508C2#1308140412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2592C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2592D11
hypocenterC11#25939
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D44C2semidirect
2. C2×#10622668C2semidirect
4. #13069757C2semidirect
5. #13069752C2semidirect
6. #13069564C2semidirect
7. #13069557C2semidirect
9. #13068953C2semidirect
10. #13068444C2semidirect
11. C11×#2592C2semidirect
172. #2592D11semidirect
422. C11#25939semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106226682
C2×#106226702
#130697572
#130697522
#130695642
#130695572
#130689672
#130689532
#130684442
C11×#25922
#2593911