Finite Group Databasebeta

← #14803612

Subgroups — #14803612

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13071680C211yesmaximal, characteristic, complemented
4#13070020C212yesmaximal, complemented
5#13069926C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068613C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4323C2212yes—
17C2×#66946—21no—
18C2×#66927C2211yescharacteristic
19C2×C4×D44C2212yes—
20C11×#399—22no—
21C11×#390C2212yes—
22C11×#384C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622701—24no—
27#10622628—24no—
28#10622601—21no—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32#10622552C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622278—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C22⋊Q8—44no—
53C11×C22⋊Q8—44no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—24no—
69C2×#4323—24no—
70C2×#4323—42no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4×Dic11—21no—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80#66946—44no—
81#66927—22no—
82#66927D414yes—
83C4×D44—24no—
84C4×D44—42no—
85C11×#95D412yes—
86#66896—22no—
87#66896—22no—
88C11⋊#95—21no—
89#66873—24no—
90#66873—24no—
91#66873—24no—
92C4⋊(C11⋊C8)—22no—
93C4⋊(C11⋊C8)—42no—
94C4×C11⋊C8—22no—
95#25318—111nomaximal, Sylow
96C24×C11—21no—
97C23×D11—22no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11#4112yes—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C2×D44—24no—
120C2×D44—24no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—42no—
127C2×D44—42no—
128C2×D44—81no—
129C2×D44—81no—
130C2×D44C2×D414yes—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—82no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4D814yescomplemented
143C11×C22⋊C4—44no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—44no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11C2×D412yes—
149C42×C11#4112yes—
150#4323—48no—
151(C2×D11)⋊C4—44no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—82no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11#4112yes—
158C4×Dic11—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×#486—111no—
169C2×#459—111no—
170#2542D1111yescharacteristic, complemented
171#2366—111no—
172#2071—112no—
173#2054—112no—
174#1988—111no—
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102—111no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194Q8×C11—84no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—84no—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11C2×D814yes—
216C2×C4×C11C2×D812yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C2×Dic11—22no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230D44—24no—
231D44—24no—
232D44—42no—
233D44—42no—
234D44—48no—
235D44—84no—
236C4×D11—88no—
237C11⋊C8—41no—
238C11⋊C8—42no—
239C11⋊C8—41no—
240C22×D8—112no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×#127—111no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C4×D4—112no—
246C2×C4×D4—221no—
247C2×C4×D4C2×D1111yescharacteristic
248#486—224no—
249#459—224no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—111no—
253C2×#102—111no—
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—112no—
257C2×C4×C8—111no—
258#399—22no—
259#390—112no—
260#390—221no—
261#390C2×D1112yes—
262#386—222no—
263#384C2×D1112yes—
264C4×C4⋊C4—111no—
265C4×C4⋊C4C2×D1111yescharacteristic
266#340—112no—
267#340—111no—
268#340—112no—
269#340—111no—
270#336—112no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C2×#12111yescharacteristic
279C22×C11#54611yescharacteristic
280C22×C11#54811yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57711yescharacteristic
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C2×D11—82no—
292C4×C11—24no—
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—81no—
296C4×C11—82no—
297C4×C11#45914yes—
298C4×C11#52911yescharacteristic
299C4×C11#54211yescharacteristic
300C4×C11#54611yescharacteristic
301C4×C11#54711yescharacteristic
302Dic11—42no—
303Dic11—81no—
304C22×Q8—21no—
305C22×D4—112no—
306C22×D4—221no—
307C22×D4—221no—
308C22×D4C22×D1111yescharacteristic
309C23×C4—21no—
310C23×C4—222no—
311C2×D8—224no—
312C2×D8—224no—
313C2×D8—442no—
314C22×C8—112no—
315C22×C8—111no—
316C22×C8—111no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319#127—114no—
320#127—222no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—224no—
326C4×D4—442no—
327C4×D4—444no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4C22⋊D1111yescharacteristic
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—221no—
344C2×C42C22×D1112yes—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—224no—
349#102—224no—
350#102—224no—
351#102—222no—
352#102—222no—
353C4×C8—222no—
354#95—221no—
355#95C22⋊D1112yes—
356C2×C11—82no—
357C2×C11#242711yescharacteristic
358C2×C11C2×#45911yescharacteristic
359C2×C11#304211yescharacteristic
360C2×C11#329411yescharacteristic
361C2×C11#333211yescharacteristic
362C2×C11#335811yescharacteristic
363C2×C11#337311yescharacteristic
364D11—84no—
365C24—21no—
366C24—222no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—114no—
376C2×D4—224no—
377C2×D4—224no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—881no—
386C2×D4—881no—
387C2×D4#434312yes—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—444no—
396C22×C4—444no—
397C22×C4—882no—
398C22×C4C2×C22⋊D1112yes—
399C22×C4C2×C22⋊D1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—448no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—222no—
407C2×C8—221no—
408C2×C8—222no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—222no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—44no—
419C4⋊C4—44no—
420C4⋊C4—42no—
421C4⋊C4—112no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4#432314yescomplemented
426C22⋊C4—44no—
427C22⋊C4—44no—
428C22⋊C4—42no—
429C22⋊C4—444no—
430C22⋊C4—444no—
431C22⋊C4—882no—
432C42—22no—
433C42—22no—
434C42—442no—
435C42D4×D1112yes—
436C42#434112yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—224no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23—442no—
451C23—442no—
452C23C22×C22⋊D1111yescharacteristic
453Q8—84no—
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4—224no—
459D4—224no—
460D4—442no—
461D4—442no—
462D4—448no—
463D4—884no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—84no—
478C2×C4—222no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—888no—
485C2×C4C2×#432314yes—
486C2×C4C2×#432312yes—
487C2×C4#6698512yes—
488C2×C4#6699112yes—
489C2×C4#6699112yes—
490C2×C4C2×D4×D1111yescharacteristic
491C2×C4C2×#434111yescharacteristic
492C2×C4C2×#434311yescharacteristic
493C2×C4#6704011yescharacteristic
494C2×C4#41×D1111yescharacteristic
495C2×C4#6704211yescharacteristic
496C8—442no—
497C8—441no—
498C8—441no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—882no—
510C22—882no—
511C22—882no—
512C22—882no—
513C22C22×#432311yescharacteristic
514C22C2×#6698511yescharacteristic
515C22C2×#6699111yescharacteristic
516C22#1062334811yescharacteristic
517C22#1062336011yescharacteristic
518C22#1062336811yescharacteristic
519C22#1062336811yescharacteristic
520C4—24no—
521C4—22no—
522C4—42no—
523C4—81no—
524C4—82no—
525C4—442no—
526C4—881no—
527C4#1062268514yes—
528C4#1062315511yescharacteristic
529C4#1062316111yescharacteristic
530C4#1062316211yescharacteristic
531C4#1062317411yescharacteristic
532C2—82no—
533C2—884no—
534C2#1307218911yescharacteristic
535C2C2×#1062268511yescharacteristic
536C2#1307812411yescharacteristic
537C2#1308042311yescharacteristic
538C2#1308093711yescharacteristic
539C2#1308125111yescharacteristic
540C2#1308140811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenter#2542D11
hypocenterC11#25318
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #13071680C2semidirect
4. #13070020C2semidirect
5. #13069926C2semidirect
6. #13069569C2semidirect
7. #13069335C2semidirect
8. #13068967C2semidirect
9. #13068613C2semidirect
10. C4×#66896C2semidirect
11. C11×#2542C2semidirect
142. C11×C4⋊C4D8semidirect
170. #2542D11semidirect
425. C4⋊C4#4323semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226282
#130716802
#130700202
#130699262
#130695692
#130693352
#130689672
#130686132
C4×#668962
C11×#25422
#2531811