Finite Group Databasebeta

← #14722284

Subgroups — #14722284

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082529C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic, complemented
3#13077281C211yesmaximal, characteristic, complemented
4#13067320C212yesmaximal, complemented
5#13067315C212yesmaximal, complemented
6#13067301C211yesmaximal, characteristic, complemented
7#13067291C211yesmaximal, characteristic, complemented
8#13067279C212yesmaximal, complemented
9#13067266C211yesmaximal, characteristic, complemented
10#13067264C212yesmaximal, complemented
11C2×C11×#332C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13#10623348—22no—
14#10623265C412yes—
15#10623264—22no—
16#10623263—21no—
17#10623261C412yes—
18#10623259C2212yes—
19#10623257—21no—
20#10623256C2212yes—
21#10623045C414yes—
22#10623041—21no—
23#10623035—21no—
24#10623008C2211yescharacteristic
25C4×#4339C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622723—21no—
29C8×C22⋊D11—22no—
30#10622714—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622453—22no—
34#10622448C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37#10622446C2212yes—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622124C2212yes—
45#10622123C2211yescharacteristic
46#10622123C2212yes—
47#10622123C2211yescharacteristic
48#10622120C2211yescharacteristic
49#10622120C2211yescharacteristic
50C22×Q8×C11—21no—
51C2×#4343—22no—
52C2×#4339—21no—
53C2×#4339D411yescharacteristic
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8C2×C412yes—
59C11×C4⋊Q8C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2×C412yes—
62C2×C42×C11C2311yescharacteristic
63#67000—24no—
64#67000—22no—
65#66999—22no—
66#66999—24no—
67Q8×Dic11—22no—
68#66983—21no—
69#66983—24no—
70#66983C2×C412yes—
71C4×C22⋊D11—24no—
72C4×C22⋊D11C2×C412yes—
73C4×C22⋊D11D412yes—
74#66979D411yescharacteristic
75C2×#4318—21no—
76C2×C8×D11—22no—
77#66951—24no—
78#66950—22no—
79#66950—22no—
80#66948—22no—
81#66948—22no—
82#66948C2×C414yes—
83#66947—24no—
84#66946—22no—
85#66946C2×C414yes—
86#66945—22no—
87#66945C2×C414yes—
88C4⋊C4×D11—22no—
89#66943C2×C414yes—
90#66940—22no—
91#66928—21no—
92#66927C2311yescharacteristic
93C4×D44—21no—
94C4×D44C2×C411yescharacteristic
95C4×D44C2×C412yes—
96C4×D44D411yescharacteristic
97#66925D412yes—
98C42×D11C2312yes—
99#66922C2311yescharacteristic
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2312yes—
107C22⋊(C11⋊C8)—21no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111#66879—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114C8×Dic11—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)C2312yes—
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17727—111nomaximal, Sylow
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—81no—
124C2×Q8×C11—81no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—22no—
130C2×C22⋊D11C22⋊C412yes—
131#4343—82no—
132#4343—82no—
133#4339—22no—
134#4339—22no—
135#4339—42no—
136#4339—42no—
137C2×D44—24no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C22⋊C411yescharacteristic
141C2×D44C22×C412yes—
142C2×C4×D11—24no—
143C2×C4×D11—22no—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C2×D412yes—
146C2×C4×D11C2×D412yes—
147C2×Dic22—21no—
148C2×Dic22C22⋊C411yescharacteristic
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—42no—
153C2×C8×C11—81no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C22×C414yes—
158C42×C11C22×C411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2411yescharacteristic
162C22⋊Dic11C22⋊C412yes—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4C22⋊C412yes—
169(C2×D11)⋊C4C22⋊C412yes—
170C4⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11C22⋊C411yescharacteristic
173C4⋊Dic11C22⋊C411yescharacteristic
174C4⋊Dic11C22×C412yes—
175Dic11⋊C4—24no—
176Dic11⋊C4C22⋊C412yes—
177Dic11⋊C4C22⋊C412yes—
178C4×Dic11—24no—
179C4×Dic11C22×C412yes—
180C4×Dic11C2×D412yes—
181C4×Dic11C2×D412yes—
182#4318—42no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C8×D11—82no—
187#3511—111no—
188#2988—111no—
189#2925—111no—
190#1553—112no—
191#1552—112no—
192#1549—111no—
193#1547—111no—
194#1544—112no—
195#1540—111no—
196#1540—112no—
197C2×#332D1111yescharacteristic, complemented
198C23×C11C2×C22⋊C411yescharacteristic
199C22×D11—22no—
200C22×D11C2×C22⋊C412yes—
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—82no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—41no—
208C2×C4×C11—82no—
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11#13512yes—
213C2×C4×C11#13512yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—24no—
218C22⋊D11—44no—
219C2×Dic11—22no—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C412yes—
222C2×Dic11C2×C22⋊C412yes—
223D44—22no—
224D44—42no—
225D44—41no—
226D44—41no—
227D44—41no—
228D44—41no—
229D44—84no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—42no—
235C4×D11—44no—
236C4×D11—84no—
237Dic22—22no—
238Dic22—41no—
239Dic22—41no—
240C8×C11—41no—
241C8×C11—41no—
242C8×C11—42no—
243C11⋊C8—42no—
244C11⋊C8—41no—
245C11⋊C8—41no—
246#556—221no—
247#555—112no—
248#554—112no—
249#553—114no—
250#548—222no—
251#547—221no—
252#542—222no—
253#537—221no—
254#533—112no—
255#532—112no—
256#532—111no—
257C2×C4⋊Q8C2×D1111yescharacteristic
258#520—221no—
259C4×#41—111no—
260C8×Q8—221no—
261C8×D4—221no—
262C8×D4—222no—
263#433—222no—
264#432—112no—
265#431—111no—
266#431—112no—
267#431—112no—
268#423—111no—
269C2×C4⋊C8—112no—
270C2×C4⋊C8C2×D1111yescharacteristic
271C2×C4⋊C8C2×D1111yescharacteristic
272#408—221no—
273#405—221no—
274#332—112no—
275#332—112no—
276#332—111no—
277#332—111no—
278#332—112no—
279#332C2×D1112yes—
280#332C2×D1112yes—
281#331—111no—
282#331—112no—
283#331—111no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11#41612yes—
287C22×C11C22×C22⋊C411yescharacteristic
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—44no—
298C4×C11#41612yes—
299C4×C11C2×#13511yescharacteristic
300C4×C11C2×#13511yescharacteristic
301C4×C11#57611yescharacteristic
302C4×C11#57711yescharacteristic
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—42no—
307C2×#41—111no—
308C2×#41—222no—
309C2×#41—221no—
310C22×Q8—21no—
311C2×M16—221no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—222no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—111no—
318C4⋊Q8C4×D1112yes—
319C4⋊Q8C22×D1112yes—
320#127—111no—
321#126—224no—
322#125—114no—
323#124—222no—
324#124—224no—
325#124—221no—
326#123—224no—
327C22⋊Q8—222no—
328C22⋊Q8—222no—
329C22⋊Q8—224no—
330C22⋊Q8—222no—
331#121—112no—
332#121—114no—
333#121—222no—
334#121—222no—
335#121—224no—
336#121—221no—
337C4×Q8—111no—
338C4×Q8—111no—
339C4×Q8—222no—
340C4×Q8—222no—
341C4×D4—112no—
342C4×D4—112no—
343C4×D4—114no—
344C4×D4—111no—
345C4×D4—112no—
346C4×D4—111no—
347C4×D4—222no—
348C4×D4—224no—
349C4×D4—221no—
350#117—111no—
351#117—112no—
352#117—114no—
353#117—222no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4C4×D1112yes—
357C2×C42—112no—
358C2×C42C22×D1111yescharacteristic
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—111no—
362C4⋊C8—112no—
363C4⋊C8—111no—
364C4⋊C8—222no—
365C4⋊C8—221no—
366C4⋊C8C22×D1112yes—
367C4⋊C8C22×D1111yescharacteristic
368C4⋊C8C22×D1111yescharacteristic
369C22⋊C8—222no—
370C22⋊C8—222no—
371C22⋊C8—222no—
372C22⋊C8—221no—
373#97—222no—
374C4×C8—222no—
375C4×C8—222no—
376C4×C8—221no—
377C2×C11—22no—
378C2×C11#288911yescharacteristic
379C2×C11C2×#41611yescharacteristic
380C2×C11#289711yescharacteristic
381D11—42no—
382D11—82no—
383#41—222no—
384#41—222no—
385#41—442no—
386#41—442no—
387#41—882no—
388#41—882no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—81no—
392C2×Q8—81no—
393C2×Q8—111no—
394C2×Q8—221no—
395C2×D4—112no—
396C2×D4—111no—
397C2×D4—112no—
398C2×D4—224no—
399C2×D4—222no—
400C2×D4—221no—
401C2×D4—221no—
402C22×C4—22no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4C2×C4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411M16—442no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—21no—
415C2×C8—42no—
416C2×C8—81no—
417C2×C8—221no—
418C2×C8—222no—
419C2×C8—221no—
420C2×C8—882no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—111no—
425C4⋊C4—111no—
426C4⋊C4—112no—
427C4⋊C4—112no—
428C4⋊C4—112no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4—221no—
432C4⋊C4C2×C4×D1114yes—
433C22⋊C4—112no—
434C22⋊C4—112no—
435C22⋊C4—112no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C22⋊C4—224no—
439C22⋊C4—222no—
440C22⋊C4—222no—
441C42—112no—
442C42—112no—
443C42—112no—
444C42—224no—
445C42C2×C4×D1111yescharacteristic
446C42D4×D1111yescharacteristic
447C42D4×D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1772711yescharacteristic, complemented, Sylow
450C23—112no—
451C23—222no—
452C23C22⋊C4×D1111yescharacteristic
453Q8—42no—
454Q8—42no—
455Q8—82no—
456Q8—222no—
457Q8—441no—
458Q8—441no—
459D4—224no—
460D4—222no—
461D4—442no—
462D4—444no—
463D4—441no—
464D4—441no—
465D4—441no—
466D4—441no—
467D4—884no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—442no—
482C2×C4—444no—
483C2×C4—884no—
484C2×C4C22⋊C4×D1111yescharacteristic
485C2×C4C22⋊C4×D1111yescharacteristic
486C2×C4C22⋊C4×D1111yescharacteristic
487C2×C4#6696912yes—
488C2×C4#6697212yes—
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C8—42no—
493C8—41no—
494C8—41no—
495C8—441no—
496C8—441no—
497C8—442no—
498C22—21no—
499C22—21no—
500C22—222no—
501C22—222no—
502C22—222no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22#1062241712yes—
507C22C2×C22⋊C4×D1111yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—44no—
512C4—222no—
513C4—222no—
514C4—222no—
515C4—442no—
516C4#1062241712yes—
517C4#1062328811yescharacteristic
518C4C2×#6696911yescharacteristic
519C4#1062329311yescharacteristic
520C4C2×#6697211yescharacteristic
521C2—22no—
522C2—442no—
523C2—882no—
524C2#1307709611yescharacteristic
525C2C2×#1062241711yescharacteristic
526C2#1307713711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC22×C11C22×C22⋊C4
prime radical#13082529C2
cosocleC42×C11C24
hypercenterC2×#332D11
hypocenterC11#17727
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #13077725C2semidirect
3. #13077281C2semidirect
4. #13067320C2semidirect
5. #13067315C2semidirect
6. #13067301C2semidirect
7. #13067291C2semidirect
8. #13067279C2semidirect
9. #13067266C2semidirect
10. #13067264C2semidirect
11. C2×C11×#332C2semidirect
197. C2×#332D11semidirect
449. C11#17727semidirect

Maximal subgroups

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

subgroupindex
#130825292
#130777252
#130772812
#130673202
#130673152
#130673012
#130672912
#130672792
#130672662
#130672642
C2×C11×#3322
#1772711