Finite Group Databasebeta

← #14722726

Subgroups — #14722726

Order 2816.

924 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#13077748C211yesmaximal, characteristic, complemented
2#13077741C211yesmaximal, characteristic, complemented
3#13067351C211yesmaximal, characteristic, complemented
4#13067346C212yesmaximal, complemented
5#13067321C212yesmaximal, complemented
6#13067301C211yesmaximal, characteristic, complemented
7#13067293C212yesmaximal, complemented
8#13067288C211yesmaximal, characteristic, complemented
9#13067278C211yesmaximal, characteristic, complemented
10#13067273C212yesmaximal, complemented
11C11×#3511C211yesmaximal, characteristic
12C11×#556—21no—
13C11×#555—21no—
14C11×#554—21no—
15C11×#553—22no—
16C11×#548—22no—
17C11×#547—21no—
18C11×#542C414yes—
19C11×#537C412yes—
20C11×#533C2212yes—
21C11×#532C2211yescharacteristic
22C11×#532C2212yes—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520C412yes—
25C4×C11×#41C2211yescharacteristic
26#10622637—21no—
27Q8×C11⋊C8—21no—
28#10622625—21no—
29#10622625—22no—
30#10622624—22no—
31D4×C11⋊C8—21no—
32#10622539C2212yes—
33#10622538C2212yes—
34#10622538C2211yescharacteristic
35#10622538C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622537C2212yes—
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2212yes—
40#10622185C2212yes—
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622184C2211yescharacteristic
45#10622184C2212yes—
46#10622184C2211yescharacteristic
47#10622182C2211yescharacteristic
48#10622182C2211yescharacteristic
49#10622182C2212yes—
50C2×C11×#41—22no—
51C2×C11×#41C2×C412yes—
52C2×C11×#41C2×C411yescharacteristic
53C22×Q8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2×C412yes—
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×#127C2311yescharacteristic
60C11×#126—24no—
61C11×#125—22no—
62C11×#124—24no—
63C11×#124—22no—
64C11×#124C2×C412yes—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8C2×C414yes—
70C11×#121—22no—
71C11×#121—24no—
72C11×#121—21no—
73C11×#121—21no—
74C11×#121—22no—
75C11×#121C2×C414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2×C414yes—
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11D411yescharacteristic
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11—22no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C414yes—
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D412yes—
87C4×D4×C11D411yescharacteristic
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117C2×C411yescharacteristic
92C11×#117C2×C412yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4C2×C412yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—22no—
101C22×C11⋊C8—22no—
102C22⋊(C11⋊C8)—21no—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—22no—
105C22⋊(C11⋊C8)—22no—
106C4⋊(C11⋊C8)—22no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)—22no—
110C4⋊(C11⋊C8)C2311yescharacteristic
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2311yescharacteristic
114C4⋊(C11⋊C8)C2311yescharacteristic
115C4⋊(C11⋊C8)C2311yescharacteristic
116#66867—22no—
117C4×C11⋊C8—21no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—22no—
120#17781—111nomaximal, Sylow
121C11×#41—42no—
122C11×#41—44no—
123C11×#41—82no—
124C11×#41—82no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—81no—
128C2×Q8×C11—81no—
129C2×Q8×C11C22⋊C411yescharacteristic
130C2×Q8×C11C22×C412yes—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C22⋊C411yescharacteristic
136C2×D4×C11C22⋊C412yes—
137C2×D4×C11C22×C412yes—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C22⋊C411yescharacteristic
155C11×C4⋊C4C22⋊C411yescharacteristic
156C11×C4⋊C4C22⋊C412yes—
157C11×C4⋊C4C22⋊C412yes—
158C11×C4⋊C4C22×C414yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4C22⋊C412yes—
165C11×C22⋊C4C22⋊C412yes—
166C11×C22⋊C4C22⋊C412yes—
167C42×C11—24no—
168C42×C11C22×C412yes—
169C42×C11C22×C411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C42×C11C2411yescharacteristic
175#4318—81no—
176#4318—82no—
177#4318—81no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—82no—
185#3511D1111yescharacteristic
186#2991—111no—
187#2990—111no—
188#1560—111no—
189#1559—112no—
190#1553—112no—
191#1549—111no—
192#1547—112no—
193#1546—111no—
194#1543—111no—
195#1542—112no—
196C23×C11—22no—
197C23×C11C2×C22⋊C412yes—
198C23×C11C2×C22⋊C411yescharacteristic
199Q8×C11—22no—
200Q8×C11—42no—
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—82no—
204D4×C11—22no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—84no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—84no—
227C2×C4×C11—82no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C11⋊C8—42no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—41no—
241C11⋊C8—42no—
242C11⋊C8—41no—
243#556—21no—
244#555—21no—
245#554—21no—
246#553—22no—
247#548—22no—
248#547—21no—
249#542Dic1114yes—
250#537Dic1112yes—
251#533C2×D1112yes—
252#532C2×D1111yescharacteristic
253#532C2×D1112yes—
254C2×C4⋊Q8C2×D1111yescharacteristic
255#520Dic1112yes—
256C4×#41C2×D1111yescharacteristic
257#446—221no—
258C8×Q8—221no—
259#436—221no—
260#436—222no—
261#435—222no—
262C8×D4—221no—
263#432—112no—
264#431—112no—
265#431—111no—
266#431—111no—
267#423—111no—
268#423—112no—
269#423—111no—
270C2×C4⋊C8—112no—
271#333—111no—
272#333—112no—
273#333—111no—
274#332—112no—
275#332—112no—
276#332—112no—
277#332—112no—
278#331—111no—
279#331—111no—
280#331—112no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—21no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11C22×C22⋊C411yescharacteristic
291C4×C11—21no—
292C4×C11—22no—
293C4×C11—22no—
294C4×C11—21no—
295C4×C11—22no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11#41312yes—
300C4×C11#57611yescharacteristic
301C4×C11#57711yescharacteristic
302C4×C11#57711yescharacteristic
303C4×C11#57811yescharacteristic
304C2×#41—22no—
305C2×#41C2×Dic1112yes—
306C2×#41C2×Dic1111yescharacteristic
307C22×Q8—21no—
308C2×M16—221no—
309C2×M16—221no—
310C2×M16—222no—
311C22×C8—222no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C2×Dic1112yes—
315C4⋊Q8C22×D1111yescharacteristic
316C4⋊Q8C22×D1112yes—
317#127C22×D1111yescharacteristic
318#126—24no—
319#125—22no—
320#124—24no—
321#124—22no—
322#124C2×Dic1112yes—
323#123—24no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8C2×Dic1114yes—
328#121—22no—
329#121—24no—
330#121—21no—
331#121—21no—
332#121—22no—
333#121C2×Dic1114yes—
334C4×Q8—22no—
335C4×Q8C2×Dic1114yes—
336C4×Q8C22⋊D1111yescharacteristic
337C4×Q8C22⋊D1111yescharacteristic
338C4×D4—24no—
339C4×D4—21no—
340C4×D4—22no—
341C4×D4—21no—
342C4×D4C2×Dic1114yes—
343C4×D4C22⋊D1111yescharacteristic
344C4×D4C22⋊D1112yes—
345C4×D4C22⋊D1112yes—
346C4×D4C22⋊D1111yescharacteristic
347#117—22no—
348#117—22no—
349#117C2×Dic1111yescharacteristic
350#117C2×Dic1112yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4C2×Dic1112yes—
354C2×C42C22×D1111yescharacteristic
355C2×C42C22×D1112yes—
356C4⋊C8—111no—
357C4⋊C8—112no—
358C4⋊C8—111no—
359C4⋊C8—112no—
360C4⋊C8—111no—
361C4⋊C8—111no—
362C4⋊C8—222no—
363C4⋊C8—221no—
364C4⋊C8—221no—
365C4⋊C8—222no—
366C22⋊C8—221no—
367C22⋊C8—221no—
368C22⋊C8—222no—
369C22⋊C8—222no—
370#97—222no—
371C4×C8—221no—
372C4×C8—221no—
373C4×C8—222no—
374C2×C11—41no—
375C2×C11—42no—
376C2×C11—82no—
377C2×C11C2×#41311yescharacteristic
378C2×C11#289711yescharacteristic
379C2×C11#289811yescharacteristic
380#41—42no—
381#41—44no—
382#41—82no—
383#41—82no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—81no—
387C2×Q8—81no—
388C2×Q8C22⋊Dic1111yescharacteristic
389C2×Q8C22×Dic1112yes—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C22⋊Dic1111yescharacteristic
395C2×D4C22⋊Dic1112yes—
396C2×D4C22×Dic1112yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4C22×Dic1111yescharacteristic
401C22×C4C22×Dic1112yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1112yes—
406M16—881no—
407M16—882no—
408M16—881no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—882no—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4C22⋊Dic1111yescharacteristic
424C4⋊C4C22⋊Dic1111yescharacteristic
425C4⋊C4C22⋊Dic1112yes—
426C4⋊C4C22⋊Dic1112yes—
427C4⋊C4C22×Dic1114yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4C22⋊Dic1112yes—
434C22⋊C4C22⋊Dic1112yes—
435C22⋊C4C22⋊Dic1112yes—
436C42—24no—
437C42C22×Dic1112yes—
438C42C22×Dic1111yescharacteristic
439C42C2×C22⋊D1111yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C2×C22⋊D1112yes—
442C42C2×C22⋊D1112yes—
443C42C23×D1111yescharacteristic
444C11#1778111yescharacteristic, complemented, Sylow
445C23—22no—
446C23C2×C22⋊Dic1112yes—
447C23C2×C22⋊Dic1111yescharacteristic
448Q8—22no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—82no—
453D4—22no—
454D4—42no—
455D4—42no—
456D4—44no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—84no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—84no—
476C2×C4—82no—
477C2×C4C2×C22⋊Dic1112yes—
478C2×C4C2×C22⋊Dic1111yescharacteristic
479C2×C4C2×C22⋊Dic1111yescharacteristic
480C2×C4C2×C22⋊Dic1112yes—
481C2×C4C2×C22⋊Dic1112yes—
482C2×C4C2×C22⋊Dic1111yescharacteristic
483C2×C4C23×Dic1111yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C8—442no—
487C8—441no—
488C8—441no—
489C8—441no—
490C8—442no—
491C8—441no—
492C22—21no—
493C22—22no—
494C22—21no—
495C22—22no—
496C22—22no—
497C22—21no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22C22×C22⋊Dic1111yescharacteristic
502C4—21no—
503C4—22no—
504C4—22no—
505C4—21no—
506C4—22no—
507C4—21no—
508C4—42no—
509C4—44no—
510C4#1062285012yes—
511C4#1062336611yescharacteristic
512C4#1062336711yescharacteristic
513C4#1062336811yescharacteristic
514C4#1062336911yescharacteristic
515C2—41no—
516C2—42no—
517C2—82no—
518C2C2×#1062285011yescharacteristic
519C2#1307714211yescharacteristic
520C2#1307714911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3511D11
hypocenterC11#17781
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13077741C2semidirect
3. #13067351C2semidirect
4. #13067346C2semidirect
5. #13067321C2semidirect
6. #13067301C2semidirect
7. #13067293C2semidirect
8. #13067288C2semidirect
9. #13067278C2semidirect
10. #13067273C2semidirect
444. C11#17781semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130777412
#130673512
#130673462
#130673212
#130673012
#130672932
#130672882
#130672782
#130672732
C11×#35112
#1778111