Finite Group Databasebeta

← #14731494

Subgroups — #14731494

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13079171C211yesmaximal, characteristic, complemented
3#13078421C211yesmaximal, characteristic, complemented
4#13067879C212yesmaximal, complemented
5#13067816C212yesmaximal, complemented
6#13067781C212yesmaximal, complemented
7#13067743C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic, complemented
9#13067067C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3497C211yesmaximal, characteristic
12C2×C11×2−1+4—21no—
13C11×#550—21no—
14C11×#550C2212yes—
15D4×Q8×C11—21no—
16D4×Q8×C11C2212yes—
17C11×#548—22no—
18C11×#548—22no—
19C11×#537—22no—
20C11×#537—21no—
21C11×#532—22no—
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622838—21no—
27#10622707—21no—
28#10622706C2211yescharacteristic
29#10622692C2211yescharacteristic
30#10622689C2211yescharacteristic
31#10622688—21no—
32#10622683C2211yescharacteristic
33#10622654—22no—
34#10622654—22no—
35#10622635—22no—
36#10622634C2212yes—
37#10622633C2212yes—
38#10622632C2212yes—
39C4×#4324—22no—
40#10622621C2212yes—
41#10622577—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yes—
46#10622182C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C11×2−1+4—44no—
52C11×2−1+4—44no—
53C2×C11×#41—24no—
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11D411yescharacteristic
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127—22no—
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#124—24no—
68C11×#124—21no—
69C11×#124—21no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121D412yes—
82C11×#121D412yes—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11D412yes—
93C4×D4×C11C2312yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×#4324—22no—
99C2×#4324—22no—
100#66979—21no—
101#66977—21no—
102#66977—21no—
103C2×#4318—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106#66923—21no—
107#66922C2311yescharacteristic
108#66922C2311yescharacteristic
109C4×Dic22—21no—
110C4×Dic22—21no—
111#66899—22no—
112#66899—22no—
113#66896—22no—
114#66896—22no—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66872—22no—
119#66872—22no—
120#66871—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)C2312yes—
124C4⋊(C11⋊C8)C2312yes—
125C4×C11⋊C8—21no—
126C4×C11⋊C8C2311yescharacteristic
127C4×C11⋊C8C2311yescharacteristic
128#18675—111nomaximal, Sylow
129C11×#41—416no—
130C11×#41—44no—
131C11×#41—48no—
132C11×#41—44no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—42no—
136C11×#41—42no—
137C2×Q8×C11—24no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—21no—
142C2×Q8×C11—44no—
143C2×Q8×C11—48no—
144C2×Q8×C11—44no—
145C2×Q8×C11SD1614yescomplemented
146C2×Q8×C11C2×D412yes—
147C2×D4×C11—24no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—24no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C2×D412yes—
156C2×D4×C11C2×D412yes—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C2×Dic22—21no—
167C2×Dic22—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—41no—
190#4324—44no—
191#4324—82no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198C4×Dic11—41no—
199#4318—42no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—81no—
206#3497D1111yescharacteristic
207#3246—111no—
208#3167—111no—
209#3078—111no—
210#1651—112no—
211#1642—112no—
212#1637—112no—
213#1631—112no—
214#1547—111no—
215#1492—111no—
216C2×Q8⋊C8—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11#12011yescharacteristic
220Q8×C11—22no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—42no—
226Q8×C11C2×SD1614yes—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—48no—
231D4×C11—44no—
232D4×C11—44no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—42no—
238D4×C11—81no—
239D4×C11—84no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—48no—
249C2×C4×C11—48no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11—81no—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11C2×SD1612yes—
258C2×C4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×Dic11—41no—
263C2×Dic11—41no—
264Dic22—42no—
265Dic22—41no—
266Dic22—41no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C11⋊C8—42no—
270C11⋊C8—42no—
271C2×2−1+4—21no—
272#550—21no—
273#550C2×D1112yes—
274D4×Q8—21no—
275D4×Q8C2×D1112yes—
276#548—22no—
277#548—22no—
278#537—22no—
279#537—21no—
280#533—111no—
281#532—22no—
282#532C2×D1111yescharacteristic
283#532C2×D1111yescharacteristic
284C2×C4×Q8C2×D1111yescharacteristic
285#498—111no—
286#492—111no—
287#487—111no—
288#486—111no—
289#479—222no—
290#477—112no—
291#476—112no—
292#475—112no—
293#475—221no—
294#465—222no—
295#465—222no—
296#461—112no—
297#460—221no—
298C4×SD16—222no—
299#428—221no—
300#423—111no—
301C2×C4⋊C8—111no—
302#419—221no—
303C2×C4×C8—111no—
304#332—112no—
305#331—112no—
306Q8⋊C8—112no—
307Q8⋊C8—112no—
308D4⋊C8—112no—
309D4⋊C8—112no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11#45012yes—
319C22×C11C2×#12011yescharacteristic
320C4×C11—24no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11#45012yes—
328C4×C11C22×SD1611yescharacteristic
329C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C4×C11#57711yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—81no—
333Dic11—81no—
3342−1+4—44no—
3352−1+4—44no—
336C2×#41—24no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—21no—
340C2×#41—21no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8C22⋊D1111yescharacteristic
344C2×SD16—222no—
345C2×SD16—222no—
346C2×M16—221no—
347C22×C8—221no—
348C22×C8—221no—
349C4⋊Q8—22no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8C22⋊D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354#127—22no—
355#127C22⋊D1111yescharacteristic
356#127C22×D1111yescharacteristic
357#125—221no—
358#124—24no—
359#124—21no—
360#124—21no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8—22no—
364C22⋊Q8—24no—
365C22⋊Q8—221no—
366C22⋊Q8—221no—
367#121—24no—
368#121—22no—
369#121—24no—
370#121—24no—
371#121—21no—
372#121—21no—
373#121—22no—
374#121C22⋊D1112yes—
375#121C22⋊D1112yes—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8C22⋊D1112yes—
381C4×Q8C22×D1112yes—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C22⋊D1112yes—
388C4×D4C22×D1112yes—
389#117—221no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C22⋊D1111yescharacteristic
392C2×C42—21no—
393C2×C42C22×D1111yescharacteristic
394#107—222no—
395#106—222no—
396#106—222no—
397#106—222no—
398C4⋊C8—112no—
399C4⋊C8—112no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402#103—222no—
403#103—222no—
404#103—222no—
405#103—222no—
406#102—222no—
407#102—222no—
408C4×C8—111no—
409C4×C8—111no—
410C4×C8—221no—
411C2×C11—22no—
412C2×C11—82no—
413C2×C11—82no—
414C2×C11C2×#45011yescharacteristic
415C2×C11#301311yescharacteristic
416C2×C11#301811yescharacteristic
417#41—416no—
418#41—44no—
419#41—48no—
420#41—44no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—42no—
425C2×Q8—24no—
426C2×Q8—22no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—44no—
431C2×Q8—48no—
432C2×Q8—44no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8#432414yescomplemented
436C2×Q8C2×C22⋊D1112yes—
437C2×D4—24no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C22⋊D1112yes—
446C2×D4C2×C22⋊D1112yes—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456SD16—444no—
457SD16—882no—
458M16—442no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—442no—
464C2×C8—881no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4C2×C22⋊D1112yes—
478C4⋊C4C2×C22⋊D1112yes—
479C4⋊C4C2×C22⋊D1112yes—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—441no—
487C42—22no—
488C42—22no—
489C42—441no—
490C42C2×C22⋊D1111yescharacteristic
491C42C2×C22⋊D1111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1867511yescharacteristic, complemented, Sylow
495C23—22no—
496C23—22no—
497C23#6700611yescharacteristic
498Q8—22no—
499Q8—24no—
500Q8—48no—
501Q8—41no—
502Q8—41no—
503Q8—42no—
504Q8—442no—
505Q8—441no—
506Q8—441no—
507Q8C2×#432414yes—
508D4—22no—
509D4—22no—
510D4—42no—
511D4—48no—
512D4—44no—
513D4—44no—
514D4—41no—
515D4—41no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—81no—
520D4—84no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—48no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—81no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4#6698512yes—
538C2×C4C2×#432412yes—
539C2×C4#6700611yescharacteristic
540C2×C4#6700611yescharacteristic
541C2×C4#6700611yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—222no—
546C8—441no—
547C8—442no—
548C8—442no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22#1062283112yes—
558C22C2×#6700611yescharacteristic
559C4—24no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—881no—
567C4—881no—
568C4#1062283112yes—
569C4C2×#6698511yescharacteristic
570C4C22×#432411yescharacteristic
571C4#1062336811yescharacteristic
572C4#1062336911yescharacteristic
573C2—22no—
574C2—82no—
575C2—82no—
576C2C2×#1062283111yescharacteristic
577C2#1307793111yescharacteristic
578C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#18675
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13079171C2semidirect
3. #13078421C2semidirect
4. #13067879C2semidirect
5. #13067816C2semidirect
6. #13067781C2semidirect
7. #13067743C2semidirect
8. #13067293C2semidirect
9. #13067067C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
145. C2×Q8×C11SD16semidirect
435. C2×Q8#4324semidirect
494. C11#18675semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130791712
#130784212
#130678792
#130678162
#130677812
#130677432
#130672932
#130670672
C2×Q8⋊(C11⋊C8)2
C11×#34972
#1867511