Finite Group Databasebeta

← #14732455

Subgroups — #14732455

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079557C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3#13078421C211yesmaximal, characteristic, complemented
4#13067816C214yesmaximal, complemented
5#13067743C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#550C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#550—22no—
12C11×#550—22no—
13C11×#550—22no—
14C11×#550C2214yes—
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22#10623001C2211yescharacteristic
23#10622838—21no—
24#10622831—22no—
25#10622831—21no—
26#10622689C2212yescomplemented
27#10622688—22no—
28#10622683C2212yescomplemented
29#10622635—22no—
30#10622634C2212yescomplemented
31#10622633C2212yescomplemented
32#10622632C2212yescomplemented
33C4×#4324—22no—
34#10622621C2212yescomplemented
35#10622584—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622182C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C22×D4×C11D412yes—
54C23×C4×C11—22no—
55C23×C4×C11—21no—
56C11×#127—24no—
57C11×#127—24no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127D412yes—
61C11×#127C2312yes—
62C11×#121—24no—
63C11×#121—28no—
64C11×#121—28no—
65C11×#121—24no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11D412yes—
69C4×Q8×C11C2312yes—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11D412yes—
75C4×D4×C11C2312yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4324—22no—
84C2×#4324—24no—
85#66979—21no—
86#66977—21no—
87#66977—21no—
88C2×#4318—21no—
89#66923—21no—
90#66922C2311yescharacteristic
91#66922C2311yescharacteristic
92C4×Dic22—21no—
93C4×Dic22—21no—
94#66899—22no—
95#66899—22no—
96#66896—22no—
97#66896—24no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100#66874—22no—
101#66872—22no—
102#66872—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110#18767—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—21no—
113C11×#41—48no—
114C11×#41—416no—
115C11×#41—48no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11SD1614yescomplemented
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—44no—
130C2×D4×C11—48no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—82no—
134C2×D4×C11—84no—
135C2×D4×C11C2×D412yes—
136C2×D4×C11C2×D414yes—
137C22×C4×C11—21no—
138C22×C4×C11—28no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—48no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2411yescharacteristic
166C22⋊Dic11—41no—
167#4324—44no—
168#4324—84no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173Dic11⋊C4—41no—
174Dic11⋊C4—41no—
175C4×Dic11—41no—
176#4318—42no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×#550D1111yescharacteristic
181#3208—111no—
182#3101—111no—
183#3078—111no—
184#1642—114no—
185#1631—114no—
186#1545—111no—
187#1486—111no—
188#1479—111no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—42no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—42no—
195C23×C11—44no—
196C23×C11—42no—
197C23×C11#12011yescharacteristic
198Q8×C11—22no—
199Q8×C11—24no—
200Q8×C11C2×SD1614yes—
201D4×C11—22no—
202D4×C11—22no—
203D4×C11—44no—
204D4×C11—42no—
205D4×C11—44no—
206D4×C11—416no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—44no—
211D4×C11—82no—
212D4×C11—88no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—416no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11C2×SD1612yes—
229C2×C4×C11AGL(1,ℤ/8)12yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×Dic11—41no—
234C2×Dic11—41no—
235Dic22—42no—
236Dic22—42no—
237C11⋊C8—42no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C22×#41—21no—
241#550—22no—
242#550—22no—
243#550—22no—
244#550C2×D1114yes—
245#533—111no—
246C2×#127—21no—
247C2×#127C2×D1111yescharacteristic
248C2×#121—22no—
249C2×#121—21no—
250C2×C4×Q8C2×D1111yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C2×D1111yescharacteristic
253#492—112no—
254#486—112no—
255#483—221no—
256#479—222no—
257#477—112no—
258#476—112no—
259#475—112no—
260#461—112no—
261#460—222no—
262#450—221no—
263#450—222no—
264C4×SD16—222no—
265#431—111no—
266#431—111no—
267#428—221no—
268#423—111no—
269#419—221no—
270#331—114no—
271Q8⋊C8—114no—
272D4⋊C8—114no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—84no—
282C22×C11—88no—
283C22×C11#45012yes—
284C22×C11C2×#12011yescharacteristic
285C4×C11—24no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11#45012yes—
292C4×C11C22×SD1611yescharacteristic
293C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11#57512yes—
295Dic11—81no—
296Dic11—81no—
297C2×#41—24no—
298C2×#41—24no—
299C2×#41—44no—
300C2×#41—44no—
301C22×Q8C22⋊D1111yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C22⋊D1111yescharacteristic
307C22×D4C22⋊D1112yes—
308C23×C4—22no—
309C23×C4—21no—
310C2×SD16—222no—
311C2×SD16—224no—
312C2×M16—221no—
313C4⋊Q8—111no—
314C4⋊Q8—111no—
315#127—24no—
316#127—24no—
317#127—21no—
318#127—21no—
319#127C22⋊D1112yes—
320#127C22×D1112yes—
321#125—221no—
322C22⋊Q8—221no—
323C22⋊Q8—221no—
324#121—24no—
325#121—28no—
326#121—28no—
327#121—24no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8—221no—
331C4×Q8—221no—
332C4×Q8C22⋊D1112yes—
333C4×Q8C22×D1112yes—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4C22⋊D1112yes—
339C4×D4C22×D1112yes—
340#117—221no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C42—21no—
347C2×C42C22×D1111yescharacteristic
348#107—222no—
349#106—222no—
350#106—222no—
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355#103—222no—
356#103—222no—
357#103—222no—
358#102—222no—
359#102—224no—
360C22⋊C8—221no—
361C22⋊C8—221no—
362C4×C8—112no—
363C4×C8—221no—
364C2×C11—22no—
365C2×C11—82no—
366C2×C11—84no—
367C2×C11C2×#45011yescharacteristic
368C2×C11#300511yescharacteristic
369C2×C11#301911yescharacteristic
370C24—22no—
371C24—21no—
372#41—48no—
373#41—416no—
374#41—48no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×Q8#432414yescomplemented
380C2×Q8C2×C22⋊D1112yes—
381C2×D4—28no—
382C2×D4—28no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—42no—
390C2×D4—48no—
391C2×D4—44no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—82no—
395C2×D4—84no—
396C2×D4C2×C22⋊D1112yes—
397C2×D4C2×C22⋊D1114yes—
398C22×C4—21no—
399C22×C4—28no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—48no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1111yescharacteristic
410SD16—444no—
411SD16—884no—
412M16—442no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4C2×C22⋊D1112yes—
427C4⋊C4C2×C22⋊D1112yes—
428C22⋊C4—28no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—441no—
432C42—22no—
433C42—22no—
434C42—441no—
435C42C2×C22⋊D1111yescharacteristic
436C42C2×C22⋊D1111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C23×D1111yescharacteristic
439C11#1876711yescharacteristic, complemented, Sylow
440C23—22no—
441C23—24no—
442C23—42no—
443C23—44no—
444C23—44no—
445C23—42no—
446C23—44no—
447C23—42no—
448C23#6700611yescharacteristic
449Q8—22no—
450Q8—24no—
451Q8—442no—
452Q8—442no—
453Q8C2×#432414yes—
454D4—22no—
455D4—22no—
456D4—44no—
457D4—42no—
458D4—44no—
459D4—416no—
460D4—42no—
461D4—42no—
462D4—44no—
463D4—44no—
464D4—82no—
465D4—88no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—416no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—44no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4#6698512yes—
481C2×C4C2×#432412yes—
482C2×C4#6700611yescharacteristic
483C2×C4#6700611yescharacteristic
484C2×C4#6700611yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—442no—
489C8—442no—
490C8—442no—
491C22—21no—
492C22—21no—
493C22—44no—
494C22—42no—
495C22—42no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—84no—
500C22—88no—
501C22#1062283112yes—
502C22C2×#6700611yescharacteristic
503C4—24no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—881no—
510C4—881no—
511C4#1062283112yes—
512C4C2×#6698511yescharacteristic
513C4C22×#432411yescharacteristic
514C4#1062335312yes—
515C2—22no—
516C2—82no—
517C2—84no—
518C2C2×#1062283111yescharacteristic
519C2#1307785811yescharacteristic
520C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC22×C11C2×#120
hypercenterC2×#550D11
hypocenterC11#18767
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078624C2semidirect
3. #13078421C2semidirect
4. #13067816C2semidirect
5. #13067743C2semidirect
6. #13067284C2semidirect
7. #13067041C2semidirect
8. #13067011C2semidirect
26. #10622689C22semidirect
28. #10622683C22semidirect
30. #10622634C22semidirect
31. #10622633C22semidirect
32. #10622632C22semidirect
34. #10622621C22semidirect
40. #10622182C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
118. C2×Q8×C11SD16semidirect
379. C2×Q8#4324semidirect
439. C11#18767semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130786242
#130784212
#130678162
#130677432
#130672842
#130670412
#130670112
C2×C11×#5502
#1876711