Finite Group Databasebeta

← #14722127

Subgroups — #14722127

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067303C214yesmaximal, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13067300C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067270C214yesmaximal, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C412yes—
12C2×Q8×Dic11C412yes—
13C2×M16×D11—21no—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259—21no—
18#10623259C412yes—
19#10623259C412yes—
20#10623259C2212yes—
21#10623259C2212yes—
22C2×#66950—21no—
23C2×#66945—21no—
24C2×#66943—21no—
25C2×#66940—21no—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#431C2211yescharacteristic
29C11×#423C2211yescharacteristic
30#10622731—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450—21no—
34#10622450C2212yes—
35#10622446C2212yes—
36D11×C4⋊C8—21no—
37D11×C4⋊C8C2212yes—
38D11×C4⋊C8C2212yes—
39D11×C22⋊C8—21no—
40#10622331—21no—
41#10622298—21no—
42C4×C8×D11—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—
78M16×D11—44no—
79C2×#4313—22no—
80C2×C8×D11—22no—
81C2×C8×D11—22no—
82#66950—22no—
83#66950—22no—
84#66950—22no—
85#66950—22no—
86#66945—22no—
87#66945—22no—
88#66945—22no—
89#66945—22no—
90#66943—22no—
91#66943—22no—
92#66943—22no—
93#66943—22no—
94#66940—22no—
95#66940—22no—
96#66940—22no—
97#66940—22no—
98C42×D11C2×C411yescharacteristic
99C42×D11C2×C411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11C2311yescharacteristic
105C42×D11C2311yescharacteristic
106#66922—21no—
107#66922—21no—
108#66922C2×C412yes—
109#66922C2312yes—
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2312yes—
112C11×C4⋊C8C2312yes—
113C11×C22⋊C8—21no—
114C4×C8×C11—21no—
115C22⋊(C11⋊C8)—21no—
116(C2×D11)⋊C8—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125#17708—111nomaximal, Sylow
126C23×D11C22⋊C411yescharacteristic
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11C22×C414yes—
130C22×C4×C11—22no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11C22⋊C411yescharacteristic
141C2×C4×D11C22⋊C411yescharacteristic
142C2×C4×D11C22⋊C411yescharacteristic
143C2×C4×D11C22⋊C411yescharacteristic
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11SD1614yes—
147C2×C4×D11Q1614yes—
148C2×C4×D11C22×C411yescharacteristic
149C2×C4×D11C22×C411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—44no—
157C11×M16—42no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C42×C11C22×C411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2411yescharacteristic
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22×C414yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178C4×Dic11—24no—
179C4×Dic11—24no—
180C4×Dic11C22⋊C411yescharacteristic
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22⋊C411yescharacteristic
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C22×C411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191C4×Dic11C2×D411yescharacteristic
192#4318—42no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195#4313—44no—
196C8×D11—44no—
197C8×D11—44no—
198C2×#533—111no—
199C2×#431—111no—
200C2×#423—111no—
201#1550—114no—
202#1549—111no—
203#1549—111no—
204#1548—111no—
205#1548D1111yescharacteristic, complemented
206#1542—114no—
207C23×C11C2×C22⋊C411yescharacteristic
208C22×D11—41no—
209C22×D11—41no—
210C22×D11#10314yes—
211C22×D11C2×C22⋊C411yescharacteristic
212C22×D11C2×C22⋊C411yescharacteristic
213Q8×C11—44no—
214Q8×C11—44no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×SD1612yes—
223C2×C4×C11C2×Q1612yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×Dic11—24no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—44no—
231C2×Dic11#10314yes—
232C2×Dic11C2×C22⋊C411yescharacteristic
233C2×Dic11C2×C22⋊C411yescharacteristic
234C2×Dic11C2×C22⋊C411yescharacteristic
235C2×Dic11C2×C22⋊C411yescharacteristic
236C2×Dic11C2×C22⋊C411yescharacteristic
237C2×Dic11C2×C22⋊C411yescharacteristic
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—41no—
245C4×D11—41no—
246C4×D11#10314yes—
247C4×D11#10314yes—
248C4×D11C2×SD1612yes—
249C4×D11C2×SD1612yes—
250C4×D11C2×Q1612yes—
251C4×D11C2×Q1612yes—
252Dic22—44no—
253Dic22—44no—
254C8×C11—42no—
255C8×C11—42no—
256C11⋊C8—42no—
257C11⋊C8—42no—
258C22×M16—221no—
259#533—112no—
260#533—112no—
261#533—112no—
262#533—112no—
263#533—221no—
264#533—221no—
265#533—221no—
266#533—221no—
267C2×C4⋊Q8—111no—
268C2×C4⋊Q8C2×D1111yescharacteristic
269C2×#125—221no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8—221no—
272C2×C4×Q8—112no—
273C2×C4×Q8—221no—
274C2×#117—221no—
275C22×C42—111no—
276#431—111no—
277#431—112no—
278#431—221no—
279#431—221no—
280#431C2×D1111yescharacteristic
281#423—111no—
282#423—112no—
283#423—221no—
284#423—221no—
285#423C2×D1111yescharacteristic
286C2×C4⋊C8—112no—
287C2×C4⋊C8—112no—
288C2×C4⋊C8—221no—
289C2×C22⋊C8—221no—
290C2×C4×C8—221no—
291#333—114no—
292#333C2×D1114yescomplemented
293#332—114no—
294#332—114no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11C2×#10312yes—
298C22×C11C22×C22⋊C411yescharacteristic
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—44no—
304C2×D11C2×#10312yes—
305C2×D11C2×#10312yes—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—44no—
309C4×C11#41312yes—
310C4×C11C2×#10312yes—
311C4×C11C22×SD1611yescharacteristic
312C4×C11C22×Q1611yescharacteristic
313C4×C11#57512yes—
314Dic11—21no—
315Dic11—21no—
316Dic11—21no—
317Dic11—21no—
318Dic11—44no—
319Dic11C2×#10312yes—
320Dic11C2×#10312yes—
321C22×Q8—221no—
322C22×Q8C4×D1112yes—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—111no—
326C2×M16—21no—
327C2×M16—222no—
328C2×M16—221no—
329C2×M16—444no—
330C22×C8—222no—
331C22×C8—222no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—112no—
335C4⋊Q8—112no—
336C4⋊Q8—221no—
337C4⋊Q8—221no—
338C4⋊Q8C4×D1112yes—
339C4⋊Q8C22×D1112yes—
340#125—222no—
341#125—222no—
342#125—222no—
343#125—222no—
344C22⋊Q8—114no—
345C22⋊Q8—114no—
346C22⋊Q8—222no—
347C22⋊Q8—222no—
348C22⋊Q8—222no—
349C22⋊Q8—222no—
350C22⋊Q8—222no—
351C22⋊Q8—222no—
352C4×Q8—114no—
353C4×Q8—114no—
354C4×Q8—222no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×Q8—222no—
358C4×Q8—222no—
359C4×Q8—222no—
360#117—222no—
361#117—222no—
362#117—222no—
363#117—222no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C22⋊C4—222no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—222no—
383C2×C42C22×D1111yescharacteristic
384C4⋊C8—21no—
385C4⋊C8—112no—
386C4⋊C8—112no—
387C4⋊C8—222no—
388C4⋊C8—222no—
389C4⋊C8—222no—
390C4⋊C8—221no—
391C4⋊C8C22×D1112yes—
392C4⋊C8C22×D1112yes—
393C22⋊C8—21no—
394C22⋊C8—222no—
395C22⋊C8—221no—
396C4×C8—21no—
397C4×C8—222no—
398C4×C8—221no—
399C2×C11—22no—
400C2×C11C2×#41311yescharacteristic
401C2×C11C22×#10311yescharacteristic
402C2×C11#289611yescharacteristic
403D11—22no—
404D11—22no—
405C24—111no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—444no—
411C2×Q8C2×C4×D1114yes—
412C22×C4—22no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4D4×D1111yescharacteristic
436M16—42no—
437M16—444no—
438M16—442no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—444no—
444C2×C8—444no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—114no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—222no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C22⋊C4—224no—
458C22⋊C4—224no—
459C42—111no—
460C42—111no—
461C42—111no—
462C42—111no—
463C42—111no—
464C42—111no—
465C42—111no—
466C42—111no—
467C42—111no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—224no—
472C42—224no—
473C42C2×C4×D1111yescharacteristic
474C42D4×D1111yescharacteristic
475C42D4×D1111yescharacteristic
476C42C23×D1111yescharacteristic
477C11#1770811yescharacteristic, complemented, Sylow
478C23—111no—
479C23—111no—
480C23—114no—
481C23—441no—
482C23—441no—
483C23C22⋊C4×D1111yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—444no—
487Q8—444no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—111no—
493C2×C4—111no—
494C2×C4—114no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—111no—
504C2×C4—111no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—444no—
517C2×C4C22⋊C4×D1111yescharacteristic
518C2×C4C22⋊C4×D1111yescharacteristic
519C2×C4C22⋊C4×D1111yescharacteristic
520C2×C4SD16×D1112yes—
521C2×C4Q16×D1112yes—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C8—42no—
526C8—42no—
527C8—442no—
528C8—442no—
529C22—21no—
530C22—21no—
531C22—112no—
532C22—112no—
533C22—221no—
534C22—221no—
535C22—221no—
536C22—221no—
537C22—444no—
538C22D11×#10312yes—
539C22C2×C22⋊C4×D1111yescharacteristic
540C4—21no—
541C4—21no—
542C4—44no—
543C4—112no—
544C4—112no—
545C4—221no—
546C4—221no—
547C4—221no—
548C4—221no—
549C4—444no—
550C4#1062235812yes—
551C4D11×#10312yes—
552C4C2×SD16×D1111yescharacteristic
553C4C2×Q16×D1111yescharacteristic
554C4#1062330812yes—
555C2—22no—
556C2—222no—
557C2—222no—
558C2C2×#1062235811yescharacteristic
559C2C2×D11×#10311yescharacteristic
560C2#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#17708
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. #13067303C2semidirect
5. #13067302C2semidirect
6. #13067300C2semidirect
7. #13067297C2semidirect
8. #13067270C2semidirect
9. C11×#1548C2semidirect
43. C11×#333C22semidirect
44. #10622184C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
205. #1548D11semidirect
292. #333C2×D11semidirect
477. C11#17708semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
D11×#4312
D11×#4232
#130673032
#130673022
#130673002
#130672972
#130672702
C11×#15482
#1770811