Finite Group Databasebeta

← #14810724

Subgroups — #14810724

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic, complemented
2C2×#10622629C211yesmaximal, characteristic
3#13074104C211yesmaximal, characteristic, complemented
4#13069764C212yesmaximal, complemented
5#13069759C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal
9#13068950C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C22×#4324C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25#10622844—21no—
26C2×#66896C2212yes—
27#10622702—24no—
28#10622629—24no—
29#10622606—21no—
30#10622603—22no—
31C2×#66874C2211yescharacteristic
32C2×#66874C2212yes—
33C2×#66873C2211yescharacteristic
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622542C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11—22no—
50C22×D44C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C11×#125—24no—
55C11×#125—24no—
56C11×C22⋊Q8—28no—
57C11×C22⋊Q8—216no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—22no—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4324—22no—
77C2×#4324—24no—
78C2×#4323—22no—
79C2×#4323—24no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11C2312yes—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66928—22no—
90#66928—22no—
91#66896—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—21no—
95#66874—22no—
96#66874—24no—
97#66873—22no—
98#66873—24no—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#25940—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—42no—
107C2×Q8×C11—81no—
108C2×Q8×C11—81no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11C2×D412yes—
112C2×D4×C11#4114yes—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—28no—
116C22×C4×C11—24no—
117C22×C4×C11—44no—
118C22×C4×C11—82no—
119C22×C4×C11—82no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—22no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—28no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D414yes—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—24no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11C2×D412yes—
149C42×C11C2×D412yes—
150#4324—44no—
151#4323—44no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—42no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—82no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4×Dic11—81no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×#554D1111yescharacteristic, complemented
167C2×#489—111no—
168C2×#463—111no—
169#2592—111no—
170#2026—112no—
171#2025—112no—
172#1988—111no—
173#1985—111no—
174#1879—112no—
175#1877—112no—
176#1762—111no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11C22×D411yescharacteristic
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—41no—
187C22×D11—41no—
188Q8×C11—44no—
189Q8×C11—84no—
190D4×C11—22no—
191D4×C11—24no—
192D4×C11#12414yes—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—88no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4112yes—
214C2×C4×C112−1+412yes—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220D44—41no—
221D44—41no—
222D44—42no—
223Dic22—41no—
224Dic22—41no—
225Dic22—42no—
226C11⋊C8—41no—
227C11⋊C8—41no—
228C11⋊C8—42no—
229C22×SD16—111no—
230C22×D8—111no—
231#554—24no—
232#554—24no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#125C2×D1112yes—
235C2×#124—111no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—22no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4C2×D1112yes—
240C2×C4×D4C2×D1111yescharacteristic
241C22×C4⋊C4—21no—
242#489—224no—
243#463—224no—
244C2×C4⋊C8—111no—
245C2×#103—112no—
246C2×#103—111no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—111no—
250C2×#97—111no—
251#397—221no—
252#393—221no—
253#391—112no—
254#390—112no—
255#388—222no—
256C4×C4⋊C4—111no—
257#340—112no—
258#340—112no—
259#340—112no—
260#336—112no—
261#336—112no—
262C22×C11—24no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11C2×#12011yescharacteristic
268C22×C11#54812yes—
269C22×C11#57512yes—
270C22×C11#57611yescharacteristic
271C22×C11#57711yescharacteristic
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—44no—
283C4×C11C2×#12411yescharacteristic
284C4×C11#53611yescharacteristic
285C4×C11#54812yes—
286Dic11—82no—
287Dic11—81no—
288C22×Q8—21no—
289C22×Q8—111no—
290C22×Q8C22⋊D1111yescharacteristic
291C22×D4—111no—
292C22×D4C22×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—22no—
295C2×SD16—224no—
296C2×SD16—222no—
297C2×D8—224no—
298C2×D8—222no—
299C22×C8—111no—
300C22×C8—111no—
301C22×C8—112no—
302C4⋊Q8—22no—
303C4⋊Q8C22⋊D1114yes—
304#125—24no—
305#125—24no—
306#124—222no—
307#124—222no—
308C22⋊Q8—28no—
309C22⋊Q8—216no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×D4—24no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4C22⋊D1114yes—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C4⋊C4C22⋊D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C42—221no—
332C2×C42C22×D1112yes—
333C2×C42C22×D1111yescharacteristic
334C4⋊C8—222no—
335#103—222no—
336#103—224no—
337#102—224no—
338#102—222no—
339#102—224no—
340#97—222no—
341#95—221no—
342#95—222no—
343#95—222no—
344C2×C11—44no—
345C2×C11#243611yescharacteristic
346C2×C11#300511yescharacteristic
347C2×C11#301211yescharacteristic
348C2×C11#337012yes—
349C2×C11#337612yes—
350D11—161no—
351C24—21no—
352C24—221no—
353C2×Q8—22no—
354C2×Q8—24no—
355C2×Q8—42no—
356C2×Q8—81no—
357C2×Q8—81no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—222no—
365C2×D4—222no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4#434314yes—
369C2×D4C2×C22⋊D1112yes—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—28no—
373C22×C4—24no—
374C22×C4—44no—
375C22×C4—82no—
376C22×C4—82no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384SD16—444no—
385D8—444no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—221no—
392C2×C8—221no—
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4C2×C22⋊D1114yes—
403C4⋊C4C2×C22⋊D1112yes—
404C22⋊C4—28no—
405C22⋊C4—24no—
406C22⋊C4—444no—
407C22⋊C4—442no—
408C22⋊C4—442no—
409C22⋊C4—882no—
410C42—22no—
411C42—22no—
412C42—881no—
413C42C2×C22⋊D1112yes—
414C42C2×C22⋊D1112yes—
415C11#2594011yescharacteristic, complemented, Sylow
416C23—24no—
417C23—22no—
418C23—42no—
419C23—41no—
420C23—41no—
421C23—442no—
422C23—442no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23C22×C22⋊D1111yescharacteristic
427Q8—44no—
428Q8—84no—
429Q8—441no—
430Q8—441no—
431Q8—442no—
432D4—22no—
433D4—24no—
434D4—441no—
435D4—441no—
436D4—442no—
437D4#6700014yes—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—48no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—88no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—441no—
459C2×C4#6700612yes—
460C2×C4#6700612yes—
461C2×C4C2×#434312yes—
462C2×C4#6704012yes—
463C2×C4C22×C22⋊D1111yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—441no—
466C8—441no—
467C8—442no—
468C22—24no—
469C22—44no—
470C22—42no—
471C22—44no—
472C22—42no—
473C22—882no—
474C22—881no—
475C22—882no—
476C22—881no—
477C22—881no—
478C22#1062334812yes—
479C22#1062335312yes—
480C22#1062336611yescharacteristic
481C22#1062336711yescharacteristic
482C22C2×#6700611yescharacteristic
483C4—22no—
484C4—22no—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—44no—
489C4—882no—
490C4—881no—
491C4C2×#6700011yescharacteristic
492C4#1062334711yescharacteristic
493C4#1062334812yes—
494C2—44no—
495C2—1761no—
496C2#1307227011yescharacteristic
497C2#1307785811yescharacteristic
498C2#1307792011yescharacteristic
499C2#1308136912yes—
500C2#1308144312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#554D11
hypocenterC11#25940
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622702C2semidirect
3. #13074104C2semidirect
4. #13069764C2semidirect
5. #13069759C2semidirect
6. #13069569C2semidirect
7. #13069557C2semidirect
9. #13068950C2semidirect
10. #13068441C2semidirect
11. C2×C11×#554C2semidirect
166. C2×#554D11semidirect
415. C11#25940semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226292
#130741042
#130697642
#130697592
#130695692
#130695572
#130689642
#130689502
#130684412
C2×C11×#5542
#2594011