Finite Group Databasebeta

← #14739235

Subgroups — #14739235

Order 2816.

662 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#13078425C211yesmaximal, characteristic, complemented
2#13078065C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic, complemented
4#13068029C212yesmaximal, complemented
5#13068022C212yesmaximal, complemented
6#13067995C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622184C211yesmaximal, characteristic, complemented
11C11×#3227C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#67003—21no—
15C4×#4339C2211yescharacteristic
16C11×#498C2212yes—
17C11×#486C2212yes—
18C11×#481—22no—
19C11×#476—21no—
20C11×#476—21no—
21C11×#431C2211yescharacteristic
22#10622846—21no—
23#10622707—21no—
24#10622704C2212yes—
25#10622703C2211yescharacteristic
26#10622700—21no—
27#10622697C2212yes—
28#10622696C2211yescharacteristic
29#10622688C2211yescharacteristic
30#10622685C2211yescharacteristic
31#10622670—21no—
32#10622667—21no—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622184C2212yes—
45#10622184C2212yes—
46#10622182C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C2×#4339D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66#67003—44no—
67C2×#4326—21no—
68C2×#4325—21no—
69C2×#4324—21no—
70C2×#4323—21no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73#66979D411yescharacteristic
74C2×#4318—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C2×C8×D11—22no—
78C4×D44D411yescharacteristic
79C4×D44C2311yescharacteristic
80#66925—21no—
81C42×D11—21no—
82C4×Dic22D411yescharacteristic
83C4×Dic22C2311yescharacteristic
84C11×#106—22no—
85C11×#106—22no—
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×#102—22no—
89C11×#102—22no—
90C11×C22⋊C8D412yes—
91C4×C8×C11C2312yes—
92#66899—21no—
93#66899—21no—
94#66896—21no—
95#66896—21no—
96(C2×D11)⋊C8—22no—
97Dic11⋊C8—22no—
98C8×Dic11—22no—
99#66874—22no—
100#66873—22no—
101#66872—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19414—111nomaximal, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339SD1614yes—
129C2×D44C2×D411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C2×D411yescharacteristic
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—21no—
149#4326—42no—
150#4325—42no—
151#4324—42no—
152#4323—42no—
153(C2×D11)⋊C4—21no—
154(C2×D11)⋊C4—21no—
155C4⋊Dic11C2×D411yescharacteristic
156C4⋊Dic11C2×D411yescharacteristic
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159C4×Dic11—21no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162#4318—42no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—81no—
169C8×D11—82no—
170#3227D1111yescharacteristic, complemented
171#3079—111no—
172#3035—111no—
173#2988—111no—
174#1678—112no—
175#1677—112no—
176#1672—112no—
177#1671—112no—
178#1570—111no—
179#1547—111no—
180C2×#333—111no—
181C23×C11—41no—
182C23×C11#12111yescharacteristic
183C22×D11—21no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—82no—
187Q8×C11—82no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—81no—
193D4×C11—82no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11#13512yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C22⋊D11—24no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213D44—21no—
214D44C2×SD1612yes—
215C4×D11—24no—
216C4×D11—41no—
217C4×D11—41no—
218C4×D11—81no—
219Dic22—21no—
220Dic22C2×SD1612yes—
221C8×C11—22no—
222C8×C11—22no—
223C11⋊C8—41no—
224C11⋊C8—41no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×#135—221no—
228#532C2×D1111yescharacteristic
229C2×C4⋊Q8C2×D1111yescharacteristic
230C4×#41—111no—
231#498C2×D1112yes—
232#486C2×D1112yes—
233#481—22no—
234#477—112no—
235#476—21no—
236#476—21no—
237#476—112no—
238#475—221no—
239#474—221no—
240#464—221no—
241#463—221no—
242#462—111no—
243#461—111no—
244#460—111no—
245#459—111no—
246C8×Q8—112no—
247C8×D4—112no—
248C8×D4—222no—
249#431—221no—
250#431C2×D1111yescharacteristic
251#428—221no—
252#423—111no—
253C2×C4⋊C8—111no—
254C2×C4⋊C8—111no—
255C2×C4⋊C8—221no—
256#417—221no—
257#416—221no—
258#334—112no—
259#334—112no—
260#333—112no—
261#333—112no—
262#332—112no—
263#331—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#46512yes—
270C22×C11C2×#12111yescharacteristic
271C2×D11—22no—
272C2×D11—41no—
273C2×D11—41no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—82no—
279C4×C11#46512yes—
280C4×C11C22×SD1611yescharacteristic
281C4×C11C2×#13511yescharacteristic
282C4×C11#57711yescharacteristic
283C4×C11#57811yescharacteristic
284Dic11—22no—
285Dic11—41no—
286Dic11—41no—
287C2×#41—21no—
288C2×#41—111no—
289C22×Q8—21no—
290#135—444no—
291C2×Q16—221no—
292C2×SD16—221no—
293C2×SD16—221no—
294C2×D8—221no—
295C2×M16—221no—
296C22×C8—221no—
297C22×C8—221no—
298C22×C8—222no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8C22×D1112yes—
303C4⋊Q8C22×D1111yescharacteristic
304#127C22×D1111yescharacteristic
305#124—21no—
306#121—21no—
307#121—21no—
308C4×Q8—111no—
309C4×Q8—111no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—111no—
313C4×D4—111no—
314C4×D4—221no—
315C4×D4—221no—
316#117—111no—
317#117—221no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322#107—222no—
323#106—22no—
324#106—22no—
325#106—222no—
326C4⋊C8—112no—
327C4⋊C8—112no—
328C4⋊C8—111no—
329C4⋊C8—111no—
330C4⋊C8—222no—
331C4⋊C8—221no—
332C4⋊C8—221no—
333C4⋊C8—221no—
334C4⋊C8C22⋊D1111yescharacteristic
335C4⋊C8C22⋊D1111yescharacteristic
336#103—222no—
337#103—221no—
338#103—221no—
339#102—22no—
340#102—22no—
341#102—222no—
342#102—221no—
343#102—221no—
344C22⋊C8—222no—
345C22⋊C8C22⋊D1112yes—
346C4×C8—222no—
347C4×C8C22×D1112yes—
348C2×C11—22no—
349C2×C11—161no—
350C2×C11#304611yescharacteristic
351C2×C11C2×#46511yescharacteristic
352C2×C11#306811yescharacteristic
353D11—42no—
354#41—42no—
355#41—42no—
356#41—114no—
357#41—222no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×Q8—111no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—41no—
367C2×D4—111no—
368C2×D4—221no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—442no—
378SD16—442no—
379SD16—442no—
380D8—442no—
381M16—442no—
382C2×C8—222no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—222no—
386C2×C8—442no—
387C2×C8—882no—
388C2×C8—881no—
389C2×C8C2×C22⋊D1112yes—
390C2×C8C2×C22⋊D1112yes—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—111no—
398C4⋊C4—111no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—221no—
404C22⋊C4—221no—
405C22⋊C4—221no—
406C42—221no—
407C42—221no—
408C42—221no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1941411yescharacteristic, complemented, Sylow
414C23—41no—
415C23—221no—
416C23#6699111yescharacteristic
417Q8—41no—
418Q8—41no—
419Q8—82no—
420Q8—82no—
421Q8—112no—
422Q8—221no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4—112no—
430D4—224no—
431D4—221no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—221no—
440C2×C4—224no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—881no—
446C2×C4SD16×D1112yes—
447C2×C4#6696912yes—
448C2×C4#6699111yescharacteristic
449C2×C4#6699111yescharacteristic
450C2×C4#6699111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C2×C4C2×#434111yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—22no—
455C8—22no—
456C8—441no—
457C8—441no—
458C8—442no—
459C8—442no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—222no—
466C22—441no—
467C22—441no—
468C22#1062278412yes—
469C22C2×#6699111yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—82no—
474C4—81no—
475C4—222no—
476C4—441no—
477C4—441no—
478C4#1062278412yes—
479C4C2×SD16×D1111yescharacteristic
480C4C2×#6696911yescharacteristic
481C4#1062336811yescharacteristic
482C4#1062336911yescharacteristic
483C2—22no—
484C2—161no—
485C2—442no—
486C2#1307816211yescharacteristic
487C2C2×#1062278411yescharacteristic
488C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3227C2
socleC22×C11C2×#121
prime radical#13078065C2
hypercenter#3227D11
hypocenterC11#19414
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
1. #13078425C2semidirect
3. #13077724C2semidirect
4. #13068029C2semidirect
5. #13068022C2semidirect
6. #13067995C2semidirect
7. #13067988C2semidirect
8. #13067387C2semidirect
9. #13067293C2semidirect
10. C2×#10622184C2semidirect
11. C11×#3227C2semidirect
170. #3227D11semidirect
413. C11#19414semidirect

Maximal subgroups

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

subgroupindex
#130784252
#130780652
#130777242
#130680292
#130680222
#130679952
#130679882
#130673872
#130672932
C2×#106221842
C11×#32272
#1941411