Finite Group Databasebeta

← #14722412

Subgroups — #14722412

Order 2816.

996 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067345C214yesmaximal, complemented
5#13067305C214yesmaximal, complemented
6#13067298C211yesmaximal, characteristic, complemented
7#13067296C211yesmaximal, characteristic, complemented
8#13067288C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
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×#66950C412yes—
23C2×#66945—21no—
24C2×#66943—21no—
25C2×#66940C412yes—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#431C2211yescharacteristic
29C11×#423C2211yescharacteristic
30#10622731—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450—21no—
34#10622450C2212yes—
35#10622450C2212yes—
36#10622448C2212yes—
37D11×C4⋊C8—21no—
38D11×C4⋊C8C2212yes—
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622119C2214yescomplemented
46#10622119C2214yescomplemented
47C22×Q8×C11—21no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×Dic22C2×C412yes—
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⋊C4C2×C412yes—
59C2×C42×C11C2311yescharacteristic
60#66999—22no—
61#66999—22no—
62#66999—22no—
63#66999—22no—
64Q8×Dic11—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67Q8×Dic11—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
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×#4313—22no—
81C2×C8×D11—22no—
82#66950—22no—
83#66950—22no—
84#66950C2×C414yes—
85#66950C2×C414yes—
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#66940C2×C414yes—
97#66940C2×C414yes—
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—
117#66879—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125#17749—111nomaximal, Sylow
126C23×D11C22⋊C411yescharacteristic
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C22×C4×C11—22no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×Dic11—22no—
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C2×C4×D11—24no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×Dic22—22no—
156C2×Dic22—44no—
157C2×Dic22C22×C414yes—
158C11×M16—42no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C22×C414yes—
165C42×C11C22×C411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2411yescharacteristic
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179C4×Dic11—24no—
180C4×Dic11—24no—
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22⋊C411yescharacteristic
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22×C411yescharacteristic
188C4×Dic11C22×C411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191C4×Dic11C2×D411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193#4318—42no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196#4313—44no—
197#4313—44no—
198C8×D11—44no—
199C2×#533—111no—
200#2920—111no—
201C2×#423—111no—
202#1559—114no—
203#1550—114no—
204#1548—111no—
205#1548—111no—
206#1546—111no—
207#1546D1111yescharacteristic, complemented
208C23×C11C2×C22⋊C411yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—41no—
212C22×D11C2×C22⋊C411yescharacteristic
213C22×D11C2×C22⋊C411yescharacteristic
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—44no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—44no—
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11#13712yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—41no—
233C2×Dic11—44no—
234C2×Dic11C2×C22⋊C411yescharacteristic
235C2×Dic11C2×C22⋊C411yescharacteristic
236C2×Dic11C2×C22⋊C411yescharacteristic
237C2×Dic11C2×C22⋊C411yescharacteristic
238C2×Dic11C2×C22⋊C411yescharacteristic
239C2×Dic11C2×C22⋊C411yescharacteristic
240C4×D11—22no—
241C4×D11—21no—
242C4×D11—21no—
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11#13714yes—
254Dic22—44no—
255Dic22—44no—
256C8×C11—42no—
257C8×C11—42no—
258C11⋊C8—42no—
259C11⋊C8—42no—
260C22×M16—221no—
261#533—112no—
262#533—112no—
263#533—112no—
264#533—112no—
265#533—221no—
266#533—221no—
267#533—221no—
268#533—221no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×#125—221no—
272C2×C22⋊Q8—112no—
273C2×C22⋊Q8—221no—
274C2×C4×Q8—112no—
275C2×C4×Q8—221no—
276C2×#117—221no—
277C22×C42—111no—
278#432—112no—
279#432—221no—
280#431—111no—
281#431—221no—
282#431C2×D1111yescharacteristic
283#423—111no—
284#423—112no—
285#423—112no—
286#423—221no—
287#423—221no—
288#423C2×D1111yescharacteristic
289C2×C4⋊C8—112no—
290C2×C4⋊C8—221no—
291#407—221no—
292C4×M16—221no—
293#333—114no—
294#333—114no—
295#332—114no—
296#332C2×D1114yescomplemented
297C22×C11—21no—
298C22×C11—21no—
299C22×C11#41712yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—21no—
306C2×D11—44no—
307C2×D11#41912yes—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—44no—
311C4×C11#41312yes—
312C4×C11#41712yes—
313C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C11C2×#13711yescharacteristic
315C4×C11C2×#13712yes—
316Dic11—21no—
317Dic11—21no—
318Dic11—21no—
319Dic11—21no—
320Dic11—21no—
321Dic11—44no—
322Dic11#41912yes—
323C22×Q8—21no—
324C22×Q8—112no—
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—111no—
328C2×M16—21no—
329C2×M16—222no—
330C2×M16—222no—
331C2×M16—221no—
332C2×M16—444no—
333C22×C8—222no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—112no—
337C4⋊Q8—112no—
338C4⋊Q8—221no—
339C4⋊Q8—221no—
340C4⋊Q8C4×D1112yes—
341C4⋊Q8C22×D1112yes—
342#125—222no—
343#125—222no—
344#125—222no—
345#125—222no—
346C22⋊Q8—114no—
347C22⋊Q8—114no—
348C22⋊Q8—222no—
349C22⋊Q8—222no—
350C22⋊Q8—222no—
351C22⋊Q8—222no—
352C22⋊Q8—222no—
353C22⋊Q8—222no—
354C4×Q8—114no—
355C4×Q8—114no—
356C4×Q8—222no—
357C4×Q8—222no—
358C4×Q8—222no—
359C4×Q8—222no—
360C4×Q8—222no—
361C4×Q8—222no—
362#117—222no—
363#117—222no—
364#117—222no—
365#117—222no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C4×D1112yes—
372C2×C22⋊C4—222no—
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—111no—
383C2×C42—111no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—112no—
388C4⋊C8—112no—
389C4⋊C8—222no—
390C4⋊C8—222no—
391C4⋊C8—222no—
392C4⋊C8—221no—
393C4⋊C8C22×D1112yes—
394C4⋊C8C22×D1112yes—
395C22⋊C8—21no—
396C22⋊C8—222no—
397C22⋊C8—221no—
398#97—222no—
399C4×C8—21no—
400C4×C8—221no—
401C2×C11—22no—
402C2×C11C2×#41311yescharacteristic
403C2×C11C2×#41911yescharacteristic
404C2×C11C2×#41711yescharacteristic
405D11—22no—
406D11—41no—
407C24—111no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—114no—
413C2×Q8—222no—
414C2×Q8—444no—
415C22×C4—22no—
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—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—442no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4D4×D1111yescharacteristic
439M16—42no—
440M16—444no—
441M16—444no—
442M16—442no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—444no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4C2×C4×D1114yes—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C42—111no—
463C42—111no—
464C42—111no—
465C42—111no—
466C42—111no—
467C42—111no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—111no—
472C42—111no—
473C42—111no—
474C42—224no—
475C42—224no—
476C42C2×C4×D1111yescharacteristic
477C42D4×D1111yescharacteristic
478C42D4×D1111yescharacteristic
479C42C23×D1111yescharacteristic
480C11#1774911yescharacteristic, complemented, Sylow
481C23—111no—
482C23—111no—
483C23—222no—
484C23—222no—
485C23—441no—
486C23C22⋊C4×D1111yescharacteristic
487Q8—42no—
488Q8—42no—
489Q8—44no—
490Q8—444no—
491Q8—444no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—44no—
496C2×C4—111no—
497C2×C4—114no—
498C2×C4—111no—
499C2×C4—111no—
500C2×C4—111no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—224no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—444no—
521C2×C4C22⋊C4×D1111yescharacteristic
522C2×C4C22⋊C4×D1111yescharacteristic
523C2×C4C22⋊C4×D1111yescharacteristic
524C2×C4#6696412yes—
525C2×C4#6696812yes—
526C2×C4C22×C4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C8—42no—
530C8—42no—
531C8—442no—
532C8—442no—
533C22—21no—
534C22—21no—
535C22—112no—
536C22—221no—
537C22—221no—
538C22—221no—
539C22—221no—
540C22—221no—
541C22—444no—
542C22#1062238412yes—
543C22C2×C22⋊C4×D1111yescharacteristic
544C4—21no—
545C4—21no—
546C4—44no—
547C4—112no—
548C4—221no—
549C4—221no—
550C4—221no—
551C4—221no—
552C4—221no—
553C4—444no—
554C4#1062236412yes—
555C4#1062238412yes—
556C4C2×#6696411yescharacteristic
557C4C2×#6696811yescharacteristic
558C4D11×#13712yes—
559C2—22no—
560C2—222no—
561C2—441no—
562C2C2×#1062236411yescharacteristic
563C2D11×#41911yescharacteristic
564C2C2×#1062238411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17749
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #13067345C2semidirect
5. #13067305C2semidirect
6. #13067298C2semidirect
7. #13067296C2semidirect
8. #13067288C2semidirect
9. C11×#1546C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622119C22semidirect
46. #10622119C22semidirect
207. #1546D11semidirect
296. #332C2×D11semidirect
480. C11#17749semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772442
D11×#4232
#130673452
#130673052
#130672982
#130672962
#130672882
C11×#15462
#1774911