Finite Group Databasebeta

← #14722395

Subgroups — #14722395

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077244C211yesmaximal, characteristic
4#13067343C214yesmaximal, complemented
5#13067325C214yesmaximal, complemented
6#13067302C211yesmaximal, characteristic, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067297C211yesmaximal, characteristic, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C412yes—
12C2×Q8×Dic11C412yes—
13#10623259—21no—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259C412yes—
18#10623259C412yes—
19#10623259C2212yes—
20#10623259C2212yes—
21C2×#66950—21no—
22C2×#66945—21no—
23C2×#66943—21no—
24C2×#66940—21no—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450C2212yes—
34#10622448—21no—
35#10622448C2212yes—
36#10622448C2212yes—
37#10622446—21no—
38#10622446C2212yes—
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—21no—
43C11×#333C2214yescomplemented
44#10622184C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×Q8×C11C2×C412yes—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×Dic22—21no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2×C412yes—
56C11×C4⋊Q8C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60#66999—22no—
61#66999—22no—
62#66999C2×C414yes—
63#66999C2×C414yes—
64Q8×Dic11—22no—
65Q8×Dic11—22no—
66Q8×Dic11C2×C414yes—
67Q8×Dic11C2×C414yes—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2×C412yes—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×#4318—21no—
78C2×#4313—22no—
79#66950—22no—
80#66950—22no—
81#66950—22no—
82#66950—22no—
83#66945—22no—
84#66945—22no—
85#66945—22no—
86#66945—22no—
87#66943—22no—
88#66943—22no—
89#66943—22no—
90#66943—22no—
91#66940—22no—
92#66940—22no—
93#66940—22no—
94#66940—22no—
95C42×D11C2×C411yescharacteristic
96C42×D11C2×C411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11C2311yescharacteristic
102C42×D11C2311yescharacteristic
103#66922—21no—
104#66922—21no—
105#66922C2×C412yes—
106#66922C2312yes—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2312yes—
109C11×C4⋊C8C2312yes—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C22⋊(C11⋊C8)—21no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116#66879—22no—
117#66879—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123C4×C11⋊C8—21no—
124#17747—111nomaximal, Sylow
125C23×D11C22⋊C411yescharacteristic
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11C22×C414yes—
129C22×C4×C11—22no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11C22⋊C411yescharacteristic
142C2×C4×D11C22⋊C411yescharacteristic
143C2×C4×D11C22⋊C411yescharacteristic
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11C22⋊C411yescharacteristic
147C2×C4×D11C22×C411yescharacteristic
148C2×C4×D11C22×C411yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—44no—
156C11×M16—42no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C42×C11C22×C411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2411yescharacteristic
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11C22×C414yes—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177C4×Dic11—24no—
178C4×Dic11—24no—
179C4×Dic11C22⋊C411yescharacteristic
180C4×Dic11C22⋊C411yescharacteristic
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22⋊C411yescharacteristic
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22×C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C2×D411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191#4318—42no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194#4313—44no—
195C2×#533—111no—
196#2920—111no—
197#2920—111no—
198#1559—114no—
199#1554—114no—
200#1549—111no—
201#1549—111no—
202#1548—111no—
203#1548D1111yescharacteristic, complemented
204C23×C11C2×C22⋊C411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11C2×C22⋊C411yescharacteristic
209C22×D11C2×C22⋊C411yescharacteristic
210Q8×C11—44no—
211Q8×C11—44no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—44no—
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11#13712yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—44no—
229C2×Dic11C2×C22⋊C411yescharacteristic
230C2×Dic11C2×C22⋊C411yescharacteristic
231C2×Dic11C2×C22⋊C411yescharacteristic
232C2×Dic11C2×C22⋊C411yescharacteristic
233C2×Dic11C2×C22⋊C411yescharacteristic
234C2×Dic11C2×C22⋊C411yescharacteristic
235C4×D11—21no—
236C4×D11—21no—
237C4×D11—21no—
238C4×D11—21no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—41no—
246C4×D11—41no—
247C4×D11—41no—
248C4×D11—41no—
249Dic22—44no—
250Dic22—44no—
251C8×C11—42no—
252C8×C11—42no—
253C11⋊C8—42no—
254C11⋊C8—42no—
255#533—112no—
256#533—112no—
257#533—112no—
258#533—112no—
259#533—221no—
260#533—221no—
261#533—221no—
262#533—221no—
263C2×C4⋊Q8—111no—
264C2×C4⋊Q8C2×D1111yescharacteristic
265C2×#125—221no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—221no—
268C2×C4×Q8—112no—
269C2×C4×Q8—221no—
270C2×#117—221no—
271C22×C42—111no—
272#432—112no—
273#432—112no—
274#432—221no—
275#432—221no—
276#431—111no—
277#431—112no—
278#431—221no—
279#431—221no—
280#431C2×D1111yescharacteristic
281#423—111no—
282#423—112no—
283#423C2×D1111yescharacteristic
284#407—221no—
285#407—221no—
286C4×M16—221no—
287C4×M16—221no—
288#333—114no—
289#333C2×D1114yescomplemented
290#332—114no—
291#332—114no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11#41912yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—44no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—44no—
306C4×C11#41312yes—
307C4×C11#41912yes—
308C4×C11C2×#13711yescharacteristic
309C4×C11C2×#13711yescharacteristic
310C4×C11#57512yes—
311Dic11—21no—
312Dic11—21no—
313Dic11—21no—
314Dic11—21no—
315Dic11—21no—
316Dic11—21no—
317Dic11—44no—
318C22×Q8—221no—
319C22×Q8C4×D1112yes—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C2×M16—21no—
324C2×M16—222no—
325C2×M16—221no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—112no—
329C4⋊Q8—112no—
330C4⋊Q8—221no—
331C4⋊Q8—221no—
332C4⋊Q8C4×D1112yes—
333C4⋊Q8C22×D1112yes—
334#125—222no—
335#125—222no—
336#125—222no—
337#125—222no—
338C22⋊Q8—114no—
339C22⋊Q8—114no—
340C22⋊Q8—222no—
341C22⋊Q8—222no—
342C22⋊Q8—222no—
343C22⋊Q8—222no—
344C22⋊Q8—222no—
345C22⋊Q8—222no—
346C4×Q8—114no—
347C4×Q8—114no—
348C4×Q8—222no—
349C4×Q8—222no—
350C4×Q8—222no—
351C4×Q8—222no—
352C4×Q8—222no—
353C4×Q8—222no—
354#117—222no—
355#117—222no—
356#117—222no—
357#117—222no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C22⋊C4—222no—
365C2×C42—111no—
366C2×C42—111no—
367C2×C42—111no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—222no—
377C2×C42C22×D1111yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—112no—
380C4⋊C8—112no—
381C4⋊C8—222no—
382C4⋊C8—221no—
383C4⋊C8C22×D1112yes—
384C4⋊C8C22×D1112yes—
385C22⋊C8—21no—
386C22⋊C8—222no—
387C22⋊C8—222no—
388C22⋊C8—222no—
389C22⋊C8—221no—
390#97—222no—
391#97—222no—
392C4×C8—21no—
393C4×C8—222no—
394C4×C8—221no—
395C2×C11—22no—
396C2×C11C2×#41311yescharacteristic
397C2×C11C2×#41911yescharacteristic
398C2×C11#289611yescharacteristic
399D11—41no—
400D11—41no—
401C24—111no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×Q8—444no—
407C2×Q8C2×C4×D1114yes—
408C22×C4—22no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432M16—42no—
433M16—444no—
434M16—442no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—222no—
438C2×C8—222no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—114no—
444C4⋊C4—224no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4—224no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C22⋊C4—224no—
452C22⋊C4—224no—
453C42—111no—
454C42—111no—
455C42—111no—
456C42—111no—
457C42—111no—
458C42—111no—
459C42—111no—
460C42—111no—
461C42—111no—
462C42—111no—
463C42—111no—
464C42—111no—
465C42—224no—
466C42—224no—
467C42C2×C4×D1111yescharacteristic
468C42D4×D1111yescharacteristic
469C42D4×D1111yescharacteristic
470C42C23×D1111yescharacteristic
471C11#1774711yescharacteristic, complemented, Sylow
472C23—111no—
473C23—111no—
474C23—222no—
475C23—441no—
476C23—441no—
477C23C22⋊C4×D1111yescharacteristic
478Q8—44no—
479Q8—44no—
480Q8—444no—
481Q8—444no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—111no—
487C2×C4—111no—
488C2×C4—111no—
489C2×C4—111no—
490C2×C4—111no—
491C2×C4—111no—
492C2×C4—222no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—444no—
511C2×C4C22⋊C4×D1111yescharacteristic
512C2×C4C22⋊C4×D1111yescharacteristic
513C2×C4C22⋊C4×D1111yescharacteristic
514C2×C4#6696812yes—
515C2×C4#6697112yes—
516C2×C4C22×C4×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C8—42no—
520C8—42no—
521C8—442no—
522C8—442no—
523C22—21no—
524C22—21no—
525C22—221no—
526C22—221no—
527C22—221no—
528C22—221no—
529C22—221no—
530C22—221no—
531C22—444no—
532C22#1062241512yes—
533C22C2×C22⋊C4×D1111yescharacteristic
534C4—21no—
535C4—21no—
536C4—44no—
537C4—221no—
538C4—221no—
539C4—221no—
540C4—221no—
541C4—221no—
542C4—221no—
543C4—444no—
544C4#1062235812yes—
545C4#1062241512yes—
546C4C2×#6696811yescharacteristic
547C4C2×#6697111yescharacteristic
548C4#1062330812yes—
549C2—22no—
550C2—441no—
551C2—441no—
552C2C2×#1062235811yescharacteristic
553C2C2×#1062241511yescharacteristic
554C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1548D11
hypocenterC11#17747
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. #13067343C2semidirect
5. #13067325C2semidirect
6. #13067302C2semidirect
7. #13067300C2semidirect
8. #13067297C2semidirect
9. C11×#1548C2semidirect
43. C11×#333C22semidirect
44. #10622184C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
203. #1548D11semidirect
289. #333C2×D11semidirect
471. C11#17747semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772482
#130772442
#130673432
#130673252
#130673022
#130673002
#130672972
C11×#15482
#1774711