Finite Group Databasebeta

← #14736669

Subgroups — #14736669

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078990C211yesmaximal, characteristic
2#13078655C211yesmaximal, characteristic, complemented
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068182C212yesmaximal, complemented
5#13068154C212yesmaximal, complemented
6#13068058C212yesmaximal, complemented
7#13068030C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic
11C2×C11×#460C211yesmaximal, characteristic
12C22×C11×SD16—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#460—21no—
17C11×#460—21no—
18C11×#460C2212yes—
19C11×#460C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102—21no—
22#10622841—21no—
23#10622828—21no—
24#10622828—21no—
25#10622684—22no—
26#10622683C2212yes—
27#10622683C2212yes—
28#10622644C2211yescharacteristic, complemented
29#10622644C2211yescharacteristic, complemented
30C4×#4326—21no—
31C4×#4326—21no—
32#10622637—22no—
33#10622637C2212yescomplemented
34Q8×C11⋊C8C2212yescomplemented
35#10622634C2211yescharacteristic, complemented
36#10622634C2211yescharacteristic, complemented
37#10622583—21no—
38#10622538C2211yescharacteristic
39#10622537—21no—
40#10622537C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622182C2212yes—
44#10622182C2212yes—
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—44no—
56C22×C8×C11—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11D411yescharacteristic
65C4×Q8×C11C2311yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4326—21no—
72C2×#4326—21no—
73#66979—21no—
74#66977—21no—
75#66977—21no—
76C2×#4318—21no—
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×#102—22no—
87C11×#102—22no—
88#66899—21no—
89#66899—21no—
90#66896—22no—
91#66896—22no—
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95#66874—21no—
96#66874—21no—
97#66871—21no—
98#66871—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105#66867—22no—
106#66867D412yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19174—111nomaximal, Sylow
111C24×C11—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11C2×D411yescharacteristic
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—82no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C2×Dic22—21no—
134C2×Dic22—21no—
135C11×SD16—44no—
136C11×SD16—44no—
137C2×C8×C11—22no—
138C2×C8×C11—42no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4C2×D411yescharacteristic
145C11×C4⋊C4C2×D411yescharacteristic
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—41no—
155#4326—42no—
156#4326—42no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164#4318—22no—
165#4318—22no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3138—111no—
173#3104—111no—
174C2×#460D1111yescharacteristic
175Q8×M16—111no—
176#1702—112no—
177#1698—112no—
178#1682—112no—
179#1678—112no—
180#1565—111no—
181#1550—111no—
182#1545—111no—
183C23×C11—42no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11#12111yescharacteristic
188Q8×C11—21no—
189Q8×C11—21no—
190Q8×C11—21no—
191Q8×C11—42no—
192Q8×C11AGL(1,ℤ/8)12yes—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—82no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—81no—
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#13512yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×Dic11—41no—
219C2×Dic11—41no—
220Dic22—41no—
221Dic22—41no—
222Dic22—81no—
223C8×C11—42no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—42no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C22×SD16—21no—
230#533—111no—
231C2×#127C2×D1111yescharacteristic
232C2×C4×Q8C2×D1111yescharacteristic
233#490—222no—
234#486—112no—
235#486—112no—
236#484—221no—
237#477—111no—
238#477—111no—
239#462—111no—
240#462—111no—
241#460—21no—
242#460—21no—
243#460C2×D1112yes—
244#460C2×D1112yes—
245#451—221no—
246#446—112no—
247#446—222no—
248C8×Q8—112no—
249C4×Q16—221no—
250C4×Q16—221no—
251#431—111no—
252#423—111no—
253#423—221no—
254C2×C4⋊C8C2×D1111yescharacteristic
255#418—221no—
256#418—221no—
257C2×#102—21no—
258C4×M16—111no—
259C4×M16—221no—
260#335—112no—
261#334—112no—
262#333—112no—
263#332—112no—
264#331—112no—
265#331—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—164no—
272C22×C11#46412yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11#46412yes—
282C4×C11C2×#13511yescharacteristic
283C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C11C2×#13711yescharacteristic
285C4×C11#57511yescharacteristic
286Dic11—81no—
287Dic11—81no—
288C22×Q8C22⋊D1111yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—221no—
293C2×Q16—221no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—44no—
297C2×M16—111no—
298C2×M16—111no—
299C2×M16—221no—
300C22×C8—21no—
301C4⋊Q8—111no—
302C4⋊Q8—111no—
303#127—21no—
304#127—21no—
305#127—21no—
306#127C22×D1112yes—
307#125—221no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8C22⋊D1111yescharacteristic
315C4×Q8C22⋊D1111yescharacteristic
316C4×Q8C22×D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318#117—221no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C42—21no—
322C2×C42C22×D1111yescharacteristic
323#107—221no—
324#107—221no—
325C4⋊C8—21no—
326C4⋊C8—112no—
327C4⋊C8—111no—
328C4⋊C8—111no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331C4⋊C8—221no—
332C4⋊C8C22×D1112yes—
333#103—221no—
334#103—221no—
335#103—221no—
336#103—221no—
337#102—22no—
338#102—22no—
339#102—222no—
340#102—222no—
341#102—222no—
342#102—222no—
343C22⋊C8—221no—
344#97—112no—
345#97—222no—
346C4×C8—112no—
347C4×C8—222no—
348C4×C8—221no—
349C2×C11—22no—
350C2×C11—162no—
351C2×C11C2×#46411yescharacteristic
352C2×C11#305511yescharacteristic
353C2×C11#306811yescharacteristic
354C24—41no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×Q8C2×C22⋊D1111yescharacteristic
361C2×Q8C2×C22⋊D1111yescharacteristic
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—82no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4D4×D1111yescharacteristic
376C22×C4#434111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—442no—
379Q16—442no—
380SD16—44no—
381SD16—44no—
382M16—222no—
383M16—222no—
384M16—442no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8—112no—
388C2×C8—112no—
389C2×C8—222no—
390C2×C8—221no—
391C2×C8—221no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4C2×C22⋊D1111yescharacteristic
404C4⋊C4C2×C22⋊D1111yescharacteristic
405C22⋊C4—441no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—441no—
411C42D4×D1111yescharacteristic
412C42#434111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C23×D1111yescharacteristic
415C11#1917411yescharacteristic, complemented, Sylow
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23#6699211yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—21no—
424Q8—42no—
425Q8—441no—
426Q8—441no—
427Q8—881no—
428Q8#6698512yes—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4#6696812yes—
449C2×C4#6696912yes—
450C2×C4#6699211yescharacteristic
451C2×C4#6699211yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4C2×#434111yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—42no—
457C8—222no—
458C8—222no—
459C8—442no—
460C8—441no—
461C8—441no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22#1062277912yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—881no—
478C4—881no—
479C4#1062277912yes—
480C4C2×#6696811yescharacteristic
481C4C2×#6696911yescharacteristic
482C4C2×#6698511yescharacteristic
483C4#1062335311yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×#1062277911yescharacteristic
487C2#1307823111yescharacteristic
488C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC22×C11C2×#121
prime radicalC2×C11×#127C22
hypercenterC2×#460D11
hypocenterC11#19174
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13078655C2semidirect
3. Q8×#4318C2semidirect
4. #13068182C2semidirect
5. #13068154C2semidirect
6. #13068058C2semidirect
7. #13068030C2semidirect
8. #13067366C2semidirect
9. #13067304C2semidirect
28. #10622644C22semidirect
29. #10622644C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
35. #10622634C22semidirect
36. #10622634C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
415. C11#19174semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130786552
Q8×#43182
#130681822
#130681542
#130680582
#130680302
#130673662
#130673042
#130672842
C2×C11×#4602
#1917411