Finite Group Databasebeta

← #14736667

Subgroups — #14736667

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#13078651C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic
3M16×Dic22C211yesmaximal, characteristic, complemented
4#13068181C212yesmaximal, complemented
5#13068153C212yesmaximal, complemented
6#13068057C212yesmaximal, complemented
7#13068029C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic
11C11×#3138C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C22×#4324—21no—
15C2×C4×Dic22C2211yescharacteristic
16C11×#490—22no—
17C11×#486C2212yes—
18C11×#486C2212yes—
19C11×#418—21no—
20C11×#418—21no—
21C4×C11×M16C2211yescharacteristic
22C2×#66896—21no—
23#10622731—21no—
24M16×Dic11—21no—
25#10622704C2211yescharacteristic, complemented
26#10622704C2211yescharacteristic, complemented
27#10622703C2211yescharacteristic, complemented
28#10622703C2211yescharacteristic, complemented
29#10622688—21no—
30#10622688—21no—
31#10622688C2212yes—
32#10622688C2212yes—
33#10622663—21no—
34#10622657—21no—
35C4×#4326—21no—
36C4×#4326—21no—
37#10622538C2211yescharacteristic
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622314—22no—
41#10622292C2212yescomplemented
42C8×Dic22C2212yescomplemented
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622182C2212yes—
46#10622182C2212yes—
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×Dic22D411yescharacteristic
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C11×#125—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C11×#117—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4326—21no—
69C2×#4326—21no—
70C2×#4324—22no—
71C2×#4324—22no—
72C2×#4324—44no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×#4318—21no—
77C22×C11⋊C8—21no—
78C4×Dic22—21no—
79C4×Dic22—21no—
80C4×Dic22D411yescharacteristic
81C4×Dic22D411yescharacteristic
82C4×Dic22C2311yescharacteristic
83C4×Dic22C2311yescharacteristic
84C11×#102—22no—
85C11×#102—22no—
86C11×#102—22no—
87C11×#102—22no—
88C11×#97D412yes—
89C4×C8×C11C2312yes—
90#66899—21no—
91#66899—21no—
92#66896—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95#66879—22no—
96Dic11⋊C8—22no—
97Dic11⋊C8—22no—
98C8×Dic11—22no—
99#66874—21no—
100#66874—21no—
101#66871—21no—
102#66871—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—21no—
110#19174—111nomaximal, Sylow
111C24×C11—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—82no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C2×Dic22—22no—
131C2×Dic22—21no—
132C2×Dic22—41no—
133C2×Dic22C2×D411yescharacteristic
134C2×Dic22C2×D411yescharacteristic
135C11×M16—22no—
136C11×M16—22no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151#4326—42no—
152#4326—42no—
153#4324—44no—
154#4324—44no—
155C4⋊Dic11—21no—
156C4⋊Dic11C2×D411yescharacteristic
157C4⋊Dic11C2×D411yescharacteristic
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166#4318—42no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172#3138D1111yescharacteristic
173#3104—111no—
174C2×#460—111no—
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—41no—
189Q8×C11—41no—
190Q8×C11—81no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—82no—
196D4×C11—82no—
197D4×C11—82no—
198D4×C11—82no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#13512yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—42no—
217C2×Dic11—81no—
218Dic22—21no—
219Dic22—21no—
220Dic22—21no—
221Dic22—42no—
222Dic22AGL(1,ℤ/8)12yes—
223C8×C11—22no—
224C8×C11—22no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C22×SD16—221no—
230#533C2×D1111yescharacteristic
231C2×#127C2×D1111yescharacteristic
232C2×C4×Q8—111no—
233#490—22no—
234#486C2×D1112yes—
235#486C2×D1112yes—
236#484—221no—
237#477—111no—
238#477—111no—
239#462—111no—
240#462—111no—
241#460—112no—
242#460—112no—
243#460—221no—
244#460—221no—
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⋊C8—111no—
255#418—21no—
256#418—21no—
257C2×#102—221no—
258C4×M16—221no—
259C4×M16C2×D1111yescharacteristic
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—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#46412yes—
280C4×C11C2×#13511yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C11C2×#13711yescharacteristic
283C4×C11#57511yescharacteristic
284Dic11—22no—
285Dic11—41no—
286Dic11—41no—
287Dic11—41no—
288C22×Q8—111no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—221no—
293C2×Q16—221no—
294C2×SD16—222no—
295C2×SD16—222no—
296C2×SD16—444no—
297C2×M16—221no—
298C2×M16C22⋊D1111yescharacteristic
299C2×M16C22⋊D1111yescharacteristic
300C22×C8—221no—
301C4⋊Q8C22×D1111yescharacteristic
302C4⋊Q8C22×D1111yescharacteristic
303#127—21no—
304#127—21no—
305#127—21no—
306#127C22×D1112yes—
307#125—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—111no—
313C4×Q8—111no—
314C4×Q8—111no—
315C4×Q8—111no—
316C4×Q8—221no—
317C4×Q8—221no—
318#117—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C42—221no—
322C2×C42C22×D1111yescharacteristic
323#107—221no—
324#107—221no—
325C4⋊C8—112no—
326C4⋊C8—111no—
327C4⋊C8—111no—
328C4⋊C8—112no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331C4⋊C8—221no—
332C4⋊C8—221no—
333#103—221no—
334#103—221no—
335#103—221no—
336#103—221no—
337#102—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—222no—
342#102—222no—
343C22⋊C8—221no—
344#97—222no—
345#97C22⋊D1112yes—
346C4×C8—222no—
347C4×C8—221no—
348C4×C8C22×D1112yes—
349C2×C11—22no—
350C2×C11—162no—
351C2×C11C2×#46411yescharacteristic
352C2×C11#305511yescharacteristic
353C2×C11#306811yescharacteristic
354C24—41no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—111no—
358C2×Q8—111no—
359C2×Q8—222no—
360C2×Q8—221no—
361C2×Q8—441no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—82no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4D4×D1111yescharacteristic
376C22×C4#434111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—442no—
379Q16—442no—
380SD16—444no—
381SD16—444no—
382M16—22no—
383M16—22no—
384M16—442no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8—442no—
390C2×C8C2×C22⋊D1112yes—
391C2×C8C2×C22⋊D1112yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—111no—
399C4⋊C4—111no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C22⋊C4—41no—
406C42—41no—
407C42—221no—
408C42—221no—
409C42—221no—
410C42—221no—
411C42D4×D1111yescharacteristic
412C42#434111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C23×D1111yescharacteristic
415C11#1917411yescharacteristic, complemented, Sylow
416C23—42no—
417C23—82no—
418C23—82no—
419C23—82no—
420C23#6699111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—81no—
424Q8—112no—
425Q8—221no—
426Q8—221no—
427Q8—221no—
428Q8—442no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—82no—
434D4—82no—
435D4—82no—
436D4—82no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—442no—
447C2×C4—881no—
448C2×C4#6699111yescharacteristic
449C2×C4#6699111yescharacteristic
450C2×C4#6699111yescharacteristic
451C2×C4#6700312yes—
452C2×C4#6700412yes—
453C2×C4C2×D4×D1111yescharacteristic
454C2×C4C2×#434111yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—22no—
457C8—22no—
458C8—442no—
459C8—441no—
460C8—441no—
461C8—442no—
462C22—21no—
463C22—21no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22#1062266712yes—
469C22C2×#6699111yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—81no—
474C4—81no—
475C4—222no—
476C4—441no—
477C4—441no—
478C4—441no—
479C4#1062266712yes—
480C4D11×AGL(1,ℤ/8)11yescharacteristic
481C4#1062330411yescharacteristic
482C4C2×#6700311yescharacteristic
483C4C2×#6700411yescharacteristic
484C2—22no—
485C2—162no—
486C2C2×#1062266711yescharacteristic
487C2#1307822911yescharacteristic
488C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#121
prime radicalC2×C11×#127C22
hypercenter#3138D11
hypocenterC11#19174
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13078651C2semidirect
3. M16×Dic22C2semidirect
4. #13068181C2semidirect
5. #13068153C2semidirect
6. #13068057C2semidirect
7. #13068029C2semidirect
8. #13067368C2semidirect
9. #13067306C2semidirect
25. #10622704C22semidirect
26. #10622704C22semidirect
27. #10622703C22semidirect
28. #10622703C22semidirect
41. #10622292C22semidirect
42. C8×Dic22C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
415. C11#19174semidirect

Maximal subgroups

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

subgroupindex
#130786512
C2×#106226882
M16×Dic222
#130681812
#130681532
#130680572
#130680292
#130673682
#130673062
#130672842
C11×#31382
#1917411