Finite Group Databasebeta

← #14725254

Subgroups — #14725254

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4318C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic
3#13077351C211yesmaximal, characteristic
4#13067521C212yesmaximal, complemented
5#13067491C212yesmaximal, complemented
6#13067476C212yesmaximal, complemented
7#13067431C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067042C211yesmaximal, characteristic
10#13066906C211yesmaximal, characteristic, complemented
11C11×#1487C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C411yescharacteristic
14C2×M16×D11—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C11×#423C2211yescharacteristic
18C2×#66899C411yescharacteristic
19#10622739—21no—
20C4×#4325C411yescharacteristic
21C4×#4325C411yescharacteristic
22C4×#4325C411yescharacteristic
23C4×#4325C411yescharacteristic
24C4×#4325C2211yescharacteristic
25C4×#4325C2211yescharacteristic
26C4×#4325C2211yescharacteristic
27C4×#4325C2211yescharacteristic
28#10622637—22no—
29#10622637C2212yescomplemented
30Q8×C11⋊C8C2212yescomplemented
31C2×#66873C411yescharacteristic
32C2×#66872C411yescharacteristic
33#10622537—21no—
34#10622537C2211yescharacteristic
35C4×#4318—21no—
36C4×#4318C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622451C2212yes—
39#10622449—22no—
40#10622447C2212yes—
41C11×Q8⋊C8C2212yescomplemented
42C11×Q8⋊C8C2212yescomplemented
43#10622117C2212yescomplemented
44#10622117C2212yescomplemented
45#10622097C2212yes—
46#10622097C2212yes—
47#10622093C2212yescomplemented
48#10622092C2212yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×D44C2×C411yescharacteristic
51C22×C4×D11—21no—
52C2×C11×M16—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11C2×C411yescharacteristic
56C4×Q8×C11C2×C411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—24no—
64C2×#4325C2×C411yescharacteristic
65C2×#4325C2×C411yescharacteristic
66C2×#4325C2×C411yescharacteristic
67C2×#4325C2×C411yescharacteristic
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×#4318—21no—
71C2×#4318D411yescharacteristic
72C2×#4318D411yescharacteristic
73C22×C11⋊C8C2×C411yescharacteristic
74C22×C11⋊C8C2×C411yescharacteristic
75M16×D11—44no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44C2×C411yescharacteristic
81C4×D44C2×C411yescharacteristic
82C4×D44C2311yescharacteristic
83C4×D44C2311yescharacteristic
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×C22⋊C8—21no—
88C4×C8×C11C2312yes—
89#66899C2×C411yescharacteristic
90#66899C2×C411yescharacteristic
91#66899C2×C411yescharacteristic
92#66899C2×C411yescharacteristic
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—22no—
95#66873C2×C411yescharacteristic
96#66873C2×C411yescharacteristic
97#66873C2×C411yescharacteristic
98#66873C2×C411yescharacteristic
99#66872C2×C411yescharacteristic
100#66872C2×C411yescharacteristic
101#66872C2×C411yescharacteristic
102#66872C2×C411yescharacteristic
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)—22no—
106C4⋊(C11⋊C8)C2312yes—
107#66867—22no—
108#66867D412yes—
109C4×C11⋊C8—22no—
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2×C411yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114C4×C11⋊C8C2312yes—
115#18040—111nomaximal, Sylow
116C23×D11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11C22×C411yescharacteristic
121C2×Q8×C11C22×C411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×Dic11—21no—
128C2×D44—22no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44C22×C411yescharacteristic
132C2×D44C22×C411yescharacteristic
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C22×C411yescharacteristic
148C11×C4⋊C4C22×C411yescharacteristic
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C22×C411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11#4111yescharacteristic
156C42×C11C2411yescharacteristic
157#4325—22no—
158#4325—22no—
159#4325—22no—
160#4325M1614yescomplemented
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—21no—
164(C2×D11)⋊C4—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11C22×C411yescharacteristic
167C4⋊Dic11C22×C411yescharacteristic
168#4318—22no—
169#4318—22no—
170#4318—42no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8C22×C411yescharacteristic
175C2×C11⋊C8C22×C411yescharacteristic
176C2×C11⋊C8C22×C411yescharacteristic
177C2×C11⋊C8C22×C411yescharacteristic
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8C2×D412yes—
180#4313—44no—
181C8×D11—44no—
182Q8×M16—111no—
183C2×C4×SD16—111no—
184D4×M16—111no—
185#1592—112no—
186#1588—112no—
187#1585—112no—
188SD16⋊C8—112no—
189#1567—111no—
190#1487D1111yescharacteristic, complemented
191#1486—111no—
192#1451—111no—
193C23×C11C4×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—81no—
199Q8×C11—21no—
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—42no—
203Q8×C11C2×M1612yescomplemented
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—81no—
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×D411yescharacteristic
215C2×C4×C11C4×D411yescharacteristic
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11#13712yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—42no—
224D44—21no—
225D44—21no—
226D44—21no—
227D44—42no—
228D44C2×M1612yes—
229C4×D11—41no—
230C4×D11—41no—
231C4×D11—41no—
232C4×D11—41no—
233C4×D11—42no—
234C4×D11—42no—
235C8×C11—42no—
236C8×C11—42no—
237C11⋊C8—21no—
238C11⋊C8—21no—
239C11⋊C8—21no—
240C11⋊C8—22no—
241C11⋊C8—22no—
242C11⋊C8—42no—
243C11⋊C8C2×M1612yescomplemented
244C22×SD16—111no—
245C22×M16—221no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—111no—
248#446—112no—
249#446—222no—
250C8×Q8—112no—
251C4×SD16—111no—
252C4×SD16—111no—
253C4×SD16—111no—
254C4×SD16—111no—
255C4×SD16—111no—
256C4×SD16—111no—
257C4×SD16—111no—
258C4×SD16—111no—
259#436—112no—
260#435—222no—
261C8×D4—112no—
262#431C2×D1111yescharacteristic
263C2×#106—111no—
264#423—111no—
265#423—221no—
266#423C2×D1111yescharacteristic
267C2×#103—111no—
268C2×#102—111no—
269#407—221no—
270C4×M16—111no—
271C4×M16—221no—
272C2×C4×C8—111no—
273#335—112no—
274#335—112no—
275Q8⋊C8C2×D1112yescomplemented
276Q8⋊C8C2×D1112yescomplemented
277D4⋊C8—112no—
278D4⋊C8—112no—
279#322—112no—
280#322—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11#44012yes—
284C22×C11C2×C4×D411yescharacteristic
285C2×D11—22no—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C2×D11—41no—
290C2×D11—41no—
291C2×D11—84no—
292C4×C11—21no—
293C4×C11—22no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11#44012yes—
300C4×C11C22×M1611yescharacteristic
301C4×C11#56811yescharacteristic
302C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C11C2×#13711yescharacteristic
304Dic11—41no—
305Dic11—41no—
306C22×Q8C4×D1111yescharacteristic
307C22×D4—111no—
308C23×C4—221no—
309C2×SD16—111no—
310C2×SD16—111no—
311C2×SD16—111no—
312C2×SD16—111no—
313C2×SD16—224no—
314C2×M16—21no—
315C2×M16—111no—
316C2×M16—111no—
317C2×M16—222no—
318C2×M16—221no—
319C2×M16—444no—
320C22×C8—111no—
321C22×C8—111no—
322C22×C8—222no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8C4×D1111yescharacteristic
326C4×Q8C4×D1111yescharacteristic
327C4×Q8C22×D1111yescharacteristic
328C4×Q8C22×D1111yescharacteristic
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—111no—
333C4×D4—221no—
334C4×D4—221no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4C4×D1111yescharacteristic
338C2×C22⋊C4—221no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341#106—111no—
342#106—111no—
343#106—111no—
344#106—111no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—112no—
348C4⋊C8—222no—
349C4⋊C8—222no—
350C4⋊C8—221no—
351C4⋊C8C22×D1112yes—
352#103—111no—
353#103—111no—
354#103—111no—
355#103—111no—
356#102—111no—
357#102—111no—
358#102—111no—
359#102—111no—
360C22⋊C8—21no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363#97—112no—
364#97—222no—
365C4×C8—111no—
366C4×C8—111no—
367C4×C8—111no—
368C4×C8—111no—
369C4×C8—112no—
370C4×C8—222no—
371C4×C8C22×D1112yes—
372C2×C11—22no—
373C2×C11D4×M1611yescharacteristic
374C2×C11C2×#44011yescharacteristic
375C2×C11#295711yescharacteristic
376D11—42no—
377D11—81no—
378C24—221no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—41no—
382C2×Q8C2×C4×D1111yescharacteristic
383C2×Q8C2×C4×D1111yescharacteristic
384C2×D4—111no—
385C2×D4—111no—
386C2×D4—222no—
387C2×D4—221no—
388C2×D4—441no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4C2×C4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4#434111yescharacteristic
401SD16—114no—
402SD16—222no—
403SD16—222no—
404SD16—222no—
405M16—42no—
406M16—222no—
407M16—222no—
408M16—444no—
409M16—442no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—111no—
413C2×C8—111no—
414C2×C8—111no—
415C2×C8—111no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—444no—
421C2×C8—441no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—111no—
428C4⋊C4—111no—
429C4⋊C4—221no—
430C4⋊C4C2×C4×D1111yescharacteristic
431C4⋊C4C2×C4×D1111yescharacteristic
432C22⋊C4—221no—
433C22⋊C4—221no—
434C22⋊C4—221no—
435C22⋊C4—221no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42C2×C4×D1111yescharacteristic
441C42D4×D1111yescharacteristic
442C42#434111yescharacteristic
443C42C23×D1111yescharacteristic
444C11#1804011yescharacteristic, complemented, Sylow
445C23—221no—
446C23—221no—
447C23—442no—
448C23—442no—
449C23—881no—
450C23(C22⋊D11)⋊C411yescharacteristic
451Q8—21no—
452Q8—21no—
453Q8—21no—
454Q8—42no—
455Q8M16×D1112yescomplemented
456D4—112no—
457D4—221no—
458D4—221no—
459D4—221no—
460D4—442no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—81no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4(C22⋊D11)⋊C411yescharacteristic
480C2×C4(C22⋊D11)⋊C411yescharacteristic
481C2×C4(C22⋊D11)⋊C411yescharacteristic
482C2×C4#6696712yes—
483C2×C4#6697112yes—
484C2×C4C22×C4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C8—42no—
488C8—42no—
489C8—112no—
490C8—221no—
491C8—221no—
492C8—221no—
493C8—222no—
494C8—222no—
495C8—442no—
496C22—21no—
497C22—21no—
498C22—222no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22—441no—
503C22—441no—
504C22—884no—
505C22#1062243012yes—
506C22C2×(C22⋊D11)⋊C411yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—441no—
515C4—441no—
516C4#1062243012yes—
517C4C2×M16×D1111yescharacteristic
518C4#1062327611yescharacteristic
519C4C2×#6696711yescharacteristic
520C4C2×#6697111yescharacteristic
521C2—22no—
522C2—442no—
523C2—881no—
524C2#1307734811yescharacteristic
525C2C2×#1062243011yescharacteristic
526C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#18040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
1. Q8×#4318C2semidirect
4. #13067521C2semidirect
5. #13067491C2semidirect
6. #13067476C2semidirect
7. #13067431C2semidirect
8. #13067374C2semidirect
10. #13066906C2semidirect
11. C11×#1487C2semidirect
29. #10622637C22semidirect
30. Q8×C11⋊C8C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×Q8⋊C8C22semidirect
43. #10622117C22semidirect
44. #10622117C22semidirect
47. #10622093C22semidirect
48. #10622092C22semidirect
160. #4325M16semidirect
190. #1487D11semidirect
203. Q8×C11C2×M16semidirect
243. C11⋊C8C2×M16semidirect
275. Q8⋊C8C2×D11semidirect
276. Q8⋊C8C2×D11semidirect
444. C11#18040semidirect
455. Q8M16×D11semidirect

Maximal subgroups

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

subgroupindex
Q8×#43182
C2×C4×#43252
#130773512
#130675212
#130674912
#130674762
#130674312
#130673742
#130670422
#130669062
C11×#14872
#1804011