Finite Group Databasebeta

← #14803662

Subgroups — #14803662

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic
2#13073821C211yesmaximal, characteristic, complemented
3#13071681C211yesmaximal, characteristic
4#13070022C212yesmaximal, complemented
5#13069929C212yesmaximal, complemented
6#13069563C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068952C212yesmaximal, complemented
9#13068614C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#460C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2212yes—
17C2×#66922C2211yescharacteristic
18C11×#460—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622843C2212yes—
22C2×#66899C2211yescharacteristic
23C2×#66899C2211yescharacteristic
24#10622834—21no—
25#10622834C2212yes—
26#10622833—22no—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×Dic11⋊C8C2212yes—
30#10622683—24no—
31#10622592—22no—
32#10622589C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622541—21no—
36#10622541—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×Dic11—22no—
48C22×Dic22—21no—
49C2×C11×SD16—24no—
50C2×C11×SD16—24no—
51C2×C11×SD16—42no—
52C22×C8×C11C2312yes—
53C11×#127—22no—
54C11×#127D414yes—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64D4×Dic11—24no—
65D4×Dic11—42no—
66D4×Dic11—44no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79#66922—22no—
80#66922—22no—
81C11×C4⋊C8—22no—
82C11×#102—24no—
83#66899—22no—
84#66899—22no—
85#66896—24no—
86#66896—24no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95D412yes—
91Dic11⋊C8—42no—
92C4×C11⋊C8—22no—
93#25322—111nomaximal, Sylow
94C24×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11#4112yes—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—81no—
111C2×D4×C11—81no—
112C2×D4×C11C2×D414yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11—21no—
121C22×Dic11—44no—
122C22×Dic11—44no—
123C22×Dic11—82no—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D412yes—
126C2×Dic22—42no—
127C2×Dic22—81no—
128C2×Dic22—81no—
129C11×SD16—48no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—42no—
136C42×C11—42no—
137C42×C11C2×D412yes—
138C42×C11#4112yes—
139C22⋊Dic11—44no—
140C22⋊Dic11—44no—
141C22⋊Dic11—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—42no—
149C4⋊Dic11SD1614yescomplemented
150C4⋊Dic11#4112yes—
151Dic11⋊C4—82no—
152Dic11⋊C4—82no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—42no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×#486—111no—
163C2×#460D1111yescharacteristic
164#2567—111no—
165#2366—111no—
166#2071—112no—
167#2055—112no—
168#1987—111no—
169#1939—111no—
170#1877—112no—
171#1802—112no—
172C4×#103—111no—
173C23×C11—24no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185D4×C11—24no—
186D4×C11—24no—
187D4×C11—42no—
188D4×C11—42no—
189D4×C11—48no—
190D4×C11—84no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—88no—
224C2×Dic11C2×SD1614yes—
225Dic22—84no—
226C8×C11—42no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C22×SD16C2×D1112yes—
230C2×C4⋊Q8—111no—
231C2×#127C2×D1111yescharacteristic
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4—112no—
234C2×C4×D4—221no—
235#486—224no—
236#460—24no—
237C2×C4⋊C8—112no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×#103—111no—
240C2×#103—111no—
241C2×#102—112no—
242C2×#102—112no—
243C2×#102C2×D1112yes—
244C2×C4×C8—111no—
245#395—222no—
246#391—112no—
247#390—112no—
248#390—221no—
249#389—221no—
250#389—221no—
251#386—222no—
252#384—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4—111no—
255#340—112no—
256#340—112no—
257#340—111no—
258#340—111no—
259#336—112no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11C2×#12111yescharacteristic
268C22×C11#54611yescharacteristic
269C22×C11#54811yescharacteristic
270C22×C11C22×SD1611yescharacteristic
271C22×C11C2×#13711yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57611yescharacteristic
274C4×C11—22no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11#46114yes—
278C4×C11#52911yescharacteristic
279C4×C11#54211yescharacteristic
280C4×C11#54611yescharacteristic
281C4×C11#54711yescharacteristic
282Dic11—24no—
283Dic11—42no—
284Dic11—42no—
285Dic11—81no—
286Dic11—82no—
287C22×Q8—221no—
288C22×Q8C22×D1111yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C22×D1112yes—
292C23×C4—222no—
293C2×SD16—24no—
294C2×SD16—24no—
295C2×SD16—42no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8C22×D1112yes—
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#127—22no—
302#127C22⋊D1114yes—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×D4—224no—
306C4×D4—442no—
307C4×D4—444no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—21no—
322C2×C42—112no—
323C2×C42—221no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—442no—
327#103—222no—
328#103—222no—
329#102—24no—
330#102—224no—
331#102—224no—
332C4×C8—222no—
333#95—112no—
334#95—222no—
335#95—222no—
336#95—221no—
337C2×C11—84no—
338C2×C11#242711yescharacteristic
339C2×C11C2×#46111yescharacteristic
340C2×C11#304111yescharacteristic
341C2×C11#329511yescharacteristic
342C2×C11#333311yescharacteristic
343C2×C11#336211yescharacteristic
344C2×C11#337511yescharacteristic
345C24—22no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—442no—
352C2×Q8—881no—
353C2×Q8—881no—
354C2×Q8#434112yes—
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—81no—
365C2×D4—81no—
366C2×D4C2×C22⋊D1114yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—221no—
372C22×C4—222no—
373C22×C4—221no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4—882no—
377C22×C4D4×D1111yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380SD16—48no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—221no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—42no—
393C4⋊C4—114no—
394C4⋊C4—112no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—221no—
400C4⋊C4—222no—
401C4⋊C4—442no—
402C4⋊C4—882no—
403C4⋊C4—882no—
404C22⋊C4—444no—
405C22⋊C4—444no—
406C22⋊C4—882no—
407C42—42no—
408C42—222no—
409C42—222no—
410C42—442no—
411C42#434112yes—
412C42C2×C22⋊D1112yes—
413C11#2532211yescharacteristic, complemented, Sylow
414C23—24no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23C2×D4×D1111yescharacteristic
422Q8—22no—
423Q8—22no—
424Q8—41no—
425Q8—41no—
426Q8—884no—
427D4—24no—
428D4—24no—
429D4—48no—
430D4—42no—
431D4—42no—
432D4—84no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—114no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—441no—
456C2×C4—888no—
457C2×C4SD16×D1112yes—
458C2×C4#6696812yes—
459C2×C4#6699212yes—
460C2×C4#6699212yes—
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4#6703711yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#6704311yescharacteristic
466C2×C4C22×C22⋊D1111yescharacteristic
467C8—42no—
468C8—441no—
469C8—441no—
470C22—44no—
471C22—44no—
472C22—44no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22#1062312911yescharacteristic
478C22#1062314311yescharacteristic
479C22C2×SD16×D1111yescharacteristic
480C22C2×#6696811yescharacteristic
481C22#1062330511yescharacteristic
482C22#1062330511yescharacteristic
483C22C2×#6699211yescharacteristic
484C4—22no—
485C4—42no—
486C4—81no—
487C4—224no—
488C4—442no—
489C4—442no—
490C4—882no—
491C4—881no—
492C4#1062277514yes—
493C4#1062313111yescharacteristic
494C4#1062313411yescharacteristic
495C4#1062333711yescharacteristic
496C4#1062335511yescharacteristic
497C2—84no—
498C2#1307219511yescharacteristic
499C2C2×#1062277511yescharacteristic
500C2#1307812111yescharacteristic
501C2#1308044311yescharacteristic
502C2#1308095711yescharacteristic
503C2#1308128211yescharacteristic
504C2#1308143411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#460D11
hypocenterC11#25322
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13073821C2semidirect
4. #13070022C2semidirect
5. #13069929C2semidirect
6. #13069563C2semidirect
7. #13069332C2semidirect
8. #13068952C2semidirect
9. #13068614C2semidirect
10. C4×#66899C2semidirect
149. C4⋊Dic11SD16semidirect
413. C11#25322semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130738212
#130716812
#130700222
#130699292
#130695632
#130693322
#130689522
#130686142
C4×#668992
C2×C11×#4602
#2532211