Finite Group Databasebeta

← #14810746

Subgroups — #14810746

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic
2C2×#10622641C211yesmaximal, characteristic
3#13074104C211yesmaximal, characteristic
4#13069754C212yesmaximal, complemented
5#13069749C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal
9#13068957C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×Q82×C11C211yesmaximal, characteristic, complemented
12Q82×C11—24no—
13Q82×C11—24no—
14C2×C11×C4⋊Q8—22no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25#10622844—21no—
26C2×#66899C2212yes—
27#10622702—24no—
28#10622641—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—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11D411yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C22×D44C2311yescharacteristic
50C22×Dic22C2311yescharacteristic
51C11×C4⋊Q8—216no—
52C11×C4⋊Q8—28no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D414yes—
57C4×Q8×C11—28no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11D414yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D412yes—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4326—22no—
77C2×#4326—24no—
78C2×#4325—22no—
79C2×#4325—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#66899—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#25942—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—28no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—81no—
110C2×Q8×C11—81no—
111C2×Q8×C11—82no—
112C2×Q8×C11—82no—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11#4114yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—22no—
128C2×D44—22no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C2×D414yes—
142C11×C4⋊C4C2×D412yes—
143C42×C11—28no—
144C42×C11—24no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149#4326—44no—
150#4325—44no—
151(C2×D11)⋊C4—42no—
152(C2×D11)⋊C4—42no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—82no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4×Dic11—81no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×Q82D1111yescharacteristic, complemented
166C2×#489—111no—
167C2×#464—111no—
168#2592—111no—
169#2024—112no—
170#2023—112no—
171#1988—111no—
172#1985—111no—
173#1880—112no—
174#1878—112no—
175#1763—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—41no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—41no—
182Q8×C11—28no—
183Q8×C11—22no—
184Q8×C11—24no—
185Q8×C11—84no—
186Q8×C11—88no—
187Q8×C11#12414yes—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11#12012yes—
205C2×C4×C11#12012yes—
206C2×C4×C11#13714yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C112−1+412yes—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216D44—41no—
217D44—41no—
218D44—42no—
219Dic22—41no—
220Dic22—41no—
221Dic22—42no—
222C11⋊C8—41no—
223C11⋊C8—41no—
224C11⋊C8—42no—
225C22×Q16—111no—
226C22×SD16—111no—
227Q82—24no—
228Q82—24no—
229C2×C4⋊Q8—22no—
230C2×C4⋊Q8—21no—
231C2×C4⋊Q8C2×D1112yes—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#124—111no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2×D1112yes—
236C2×C4×Q8C2×D1111yescharacteristic
237C2×C4×Q8C2×D1111yescharacteristic
238#489—224no—
239#464—224no—
240C2×C4⋊C8—111no—
241C2×#103—112no—
242C2×#103—112no—
243C2×#103—111no—
244C2×#102—112no—
245C2×#102—111no—
246C2×#97—111no—
247#397—221no—
248#393—221no—
249#391—112no—
250#390—112no—
251#388—222no—
252C4×C4⋊C4—111no—
253#340—112no—
254#340—112no—
255#340—112no—
256#336—112no—
257#336—112no—
258C22×C11C2×#12011yescharacteristic
259C22×C11#54812yes—
260C22×C11C2×#13712yes—
261C22×C11#57611yescharacteristic
262C22×C11#57711yescharacteristic
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—24no—
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—44no—
274C4×C11—42no—
275C4×C11C2×#12411yescharacteristic
276C4×C11#53611yescharacteristic
277C4×C11#54812yes—
278Dic11—82no—
279Dic11—81no—
280C22×Q8—22no—
281C22×Q8—21no—
282C22×Q8—111no—
283C22×Q8C22⋊D1111yescharacteristic
284C22×Q8C22×D1111yescharacteristic
285C22×D4—111no—
286C2×Q16—224no—
287C2×Q16—222no—
288C2×SD16—224no—
289C2×SD16—222no—
290C22×C8—111no—
291C22×C8—111no—
292C22×C8—112no—
293C4⋊Q8—216no—
294C4⋊Q8—28no—
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8C22⋊D1114yes—
299#124—222no—
300#124—222no—
301C4×Q8—28no—
302C4×Q8—24no—
303C4×Q8—24no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8C22⋊D1114yes—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4C22⋊D1112yes—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42—221no—
324C2×C42C22×D1112yes—
325C2×C42C22×D1111yescharacteristic
326C4⋊C8—222no—
327#103—224no—
328#103—222no—
329#103—224no—
330#102—222no—
331#102—224no—
332#97—222no—
333#95—221no—
334#95—222no—
335#95—222no—
336C2×C11#243611yescharacteristic
337C2×C11#300411yescharacteristic
338C2×C11#301211yescharacteristic
339C2×C11#336912yes—
340C2×C11#337512yes—
341D11—161no—
342C24—221no—
343C2×Q8—28no—
344C2×Q8—24no—
345C2×Q8—22no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—81no—
350C2×Q8—81no—
351C2×Q8—82no—
352C2×Q8—82no—
353C2×Q8—222no—
354C2×Q8—222no—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8#434314yes—
358C2×Q8C2×C22⋊D1112yes—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—221no—
362C2×D4—221no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—221no—
367C22×C4—222no—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373Q16—444no—
374SD16—444no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—221no—
381C2×C8—221no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4C2×C22⋊D1114yes—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—444no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—882no—
398C42—28no—
399C42—24no—
400C42—22no—
401C42—22no—
402C42—881no—
403C42C2×C22⋊D1112yes—
404C42C2×C22⋊D1112yes—
405C11#2594211yescharacteristic, complemented, Sylow
406C23—442no—
407C23—442no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23C22×C22⋊D1111yescharacteristic
412Q8—28no—
413Q8—22no—
414Q8—24no—
415Q8—84no—
416Q8—88no—
417Q8—441no—
418Q8—441no—
419Q8—442no—
420Q8#6700014yes—
421D4—441no—
422D4—441no—
423D4—442no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4#6699514yes—
446C2×C4#6700612yes—
447C2×C4#6700612yes—
448C2×C4C2×#434312yes—
449C2×C4#6704012yes—
450C2×C4C22×C22⋊D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—441no—
453C8—441no—
454C8—442no—
455C22—882no—
456C22—882no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22C2×#6699512yes—
461C22#1062334812yes—
462C22#1062336611yescharacteristic
463C22#1062336711yescharacteristic
464C22C2×#6700611yescharacteristic
465C4—24no—
466C4—22no—
467C4—24no—
468C4—22no—
469C4—42no—
470C4—44no—
471C4—42no—
472C4—882no—
473C4—881no—
474C4C2×#6700011yescharacteristic
475C4#1062334711yescharacteristic
476C4#1062334812yes—
477C2—1761no—
478C2#1307227011yescharacteristic
479C2#1307785011yescharacteristic
480C2#1307792011yescharacteristic
481C2#1308135612yes—
482C2#1308143012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×Q82×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×Q82D11
hypocenterC11#25942
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
4. #13069754C2semidirect
6. #13069569C2semidirect
7. #13069557C2semidirect
9. #13068957C2semidirect
10. #13068446C2semidirect
11. C2×Q82×C11C2semidirect
165. C2×Q82D11semidirect
405. C11#25942semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226412
#130741042
#130697542
#130697492
#130695692
#130695572
#130689712
#130689572
#130684462
C2×Q82×C112
#2594211