Finite Group Databasebeta

← #14808036

Subgroups — #14808036

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622692C211yesmaximal, characteristic, complemented
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13076969C211yesmaximal, characteristic, complemented
5#13069808C214yesmaximal, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13068878C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
9C11×#1990C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13#10623256—24no—
14#10623256—24no—
15C2×#66950—21no—
16C2×#66948—21no—
17C2×#66948C2212yes—
18C2×#66946—21no—
19C2×#66946C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66885C2214yes—
26C2×(C2×D11)⋊C8C2212yes—
27#10622692—24no—
28#10622600—21no—
29#10622600C2212yes—
30#10622598—21no—
31#10622598C2212yes—
32#10622587—21no—
33C2×#66873C2214yes—
34C2×#66872C2214yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622307—24no—
37C11×#340C2214yes—
38#10622188C2212yes—
39C22×Q8×C11—21no—
40C2×#4343—28no—
41C2×#4343—44no—
42C2×#4343—44no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—21no—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61#67000—28no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2312yes—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72#66950—44no—
73#66948—28no—
74#66948—24no—
75#66948—24no—
76#66946—28no—
77#66946—24no—
78#66946—24no—
79#66927—22no—
80#66927D414yes—
81C42×D11—22no—
82C42×D11—22no—
83#66922—22no—
84#66922—22no—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—28no—
89(C2×D11)⋊C8—24no—
90#66873—28no—
91#66872—28no—
92C4×C11⋊C8—22no—
93#25671—111nomaximal, Sylow
94C23×D11—22no—
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—24no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108#4343—432no—
109C2×D44—28no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—22no—
113C2×D44—24no—
114C2×D44—24no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44C2×D414yes—
122C2×C4×D11—28no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11SD1614yes—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4C2×D414yes—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—44no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—44no—
155C4⋊Dic11—42no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—21no—
159C4×Dic11—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8#4114yescomplemented
163C2×#532—111no—
164C2×#498—111no—
165C2×#486—111no—
166#2857—111no—
167#2034—114no—
168#1990D1111yescharacteristic, complemented
169#1957—111no—
170#1864—114no—
171C4×C22⋊C8—111no—
172C23×C11C22×D411yescharacteristic
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—24no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11C2×SD1612yes—
187Q8×C11—48no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11#12012yes—
195C2×C4×C11#12012yes—
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11#13512yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4112yes—
203C2×C4×C112−1+412yes—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11C2×SD1612yes—
216D44—28no—
217D44—416no—
218D44—44no—
219D44—48no—
220D44—48no—
221C4×D11—28no—
222C4×D11—416no—
223C4×D11—42no—
224C4×D11—42no—
225C4×D11—44no—
226Dic22—84no—
227C8×C11—42no—
228C11⋊C8—24no—
229C22×#41—221no—
230#532—224no—
231#532—224no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#127—111no—
235C2×#124—221no—
236C2×C22⋊Q8—221no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—112no—
240C2×C4×D4—221no—
241C22×C42—111no—
242#498—224no—
243#486—224no—
244C2×#106—114no—
245C2×#102—114no—
246C2×#102—114no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249C2×C4×C8C2×D1111yescharacteristic
250#391—221no—
251#389—112no—
252#389—221no—
253#384C2×D1111yescharacteristic
254#380—112no—
255#380—221no—
256#340C2×D1114yes—
257#336—112no—
258C22×C11C2×#12011yescharacteristic
259C22×C11#53211yescharacteristic
260C22×C11#53611yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11—41no—
271C2×D11—41no—
272C2×D11—44no—
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—44no—
280C4×C11—82no—
281C4×C11#44914yes—
282C4×C11#45014yes—
283C4×C11#54712yes—
284C4×C11#54812yes—
285Dic11—22no—
286Dic11—41no—
287Dic11—41no—
288Dic11—82no—
289C2×#41—228no—
290C2×#41—444no—
291C2×#41—444no—
292C22×Q8—21no—
293C22×Q8—221no—
294C22×D4—112no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—221no—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—222no—
302C22×C8—112no—
303C22×C8C22×D1112yes—
304C4⋊Q8—22no—
305C4⋊Q8—222no—
306C4⋊Q8—222no—
307C4⋊Q8D4414yes—
308#127—114no—
309#127—222no—
310#124—228no—
311C22⋊Q8—444no—
312#121—224no—
313#121—228no—
314#121—224no—
315C4×D4—224no—
316C4×D4—228no—
317C4×D4—224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4C22×D1112yes—
325C2×C4⋊C4C22×D1112yes—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—222no—
333C2×C42—222no—
334C2×C42C22×D1111yescharacteristic
335#106—228no—
336#102—228no—
337#102—228no—
338C22⋊C8—224no—
339C4×C8—22no—
340C4×C8—222no—
341#95—222no—
342#95—222no—
343C2×C11#243211yescharacteristic
344C2×C11C2×#45011yescharacteristic
345C2×C11C2×#44911yescharacteristic
346C2×C11#316711yescharacteristic
347C2×C11#318411yescharacteristic
348C2×C11#322711yescharacteristic
349C2×C11#322811yescharacteristic
350D11—42no—
351D11—84no—
352C24—111no—
353C24—222no—
354#41—4432no—
355C2×Q8—24no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—442no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—114no—
362C2×D4—228no—
363C2×D4—224no—
364C2×D4—224no—
365C2×D4—222no—
366C2×D4—224no—
367C2×D4—224no—
368C2×D4—444no—
369C2×D4—444no—
370C2×D4—442no—
371C2×D4—442no—
372C2×D4—442no—
373C2×D4—442no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—111no—
377C22×C4—114no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—228no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—444no—
392C22×C4—444no—
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—114no—
400C2×C8—222no—
401C2×C8—222no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—444no—
410C4⋊C4—442no—
411C4⋊C4C2×D4414yes—
412C22⋊C4—228no—
413C22⋊C4—228no—
414C22⋊C4—444no—
415C42—222no—
416C42—222no—
417C42—221no—
418C42—221no—
419C42C2×D4412yes—
420C42D4×D1112yes—
421C11#2567111yescharacteristic, complemented, Sylow
422C23—112no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—224no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23—442no—
436C23C2×D4×D1111yescharacteristic
437Q8—48no—
438Q8—884no—
439D4—228no—
440D4—4416no—
441D4—444no—
442D4—448no—
443D4—448no—
444C2×C4—24no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—112no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—228no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—4416no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—444no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4#6693512yes—
468C2×C4#6693512yes—
469C2×C4#6696412yes—
470C2×C4SD16×D1112yes—
471C2×C4#6696712yes—
472C2×C4#6697212yes—
473C2×C4C22×D4411yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4#6704012yes—
476C2×C4#41×D1112yes—
477C8—42no—
478C8—224no—
479C22—222no—
480C22—222no—
481C22—222no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—444no—
487C22—444no—
488C22—444no—
489C22—882no—
490C22—882no—
491C22—882no—
492C22—882no—
493C22C2×#6693511yescharacteristic
494C22#1062319911yescharacteristic
495C22#1062325511yescharacteristic
496C22C2×#6696411yescharacteristic
497C22C2×SD16×D1111yescharacteristic
498C22C2×#6696711yescharacteristic
499C22C2×#6697211yescharacteristic
500C4—44no—
501C4—82no—
502C4—222no—
503C4—441no—
504C4—441no—
505C4—882no—
506C4#1062238914yes—
507C4#1062242414yes—
508C4#1062310712yes—
509C4#1062316212yes—
510C2—442no—
511C2—884no—
512C2#1307224311yescharacteristic
513C2C2×#1062238911yescharacteristic
514C2C2×#1062242411yescharacteristic
515C2#1307917811yescharacteristic
516C2#1307935311yescharacteristic
517C2#1307974511yescharacteristic
518C2#1307975511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenter#1990D11
hypocenterC11#25671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×#10622692C2semidirect
3. C2×#10622307C2semidirect
4. #13076969C2semidirect
5. #13069808C2semidirect
6. #13069421C2semidirect
7. #13068878C2semidirect
8. C4×(C2×D11)⋊C8C2semidirect
9. C11×#1990C2semidirect
162. C2×C11⋊C8#41semidirect
168. #1990D11semidirect
421. C11#25671semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106226922
C2×#106223072
#130769692
#130698082
#130694212
#130688782
C4×(C2×D11)⋊C82
C11×#19902
#2567111