Finite Group Databasebeta

← #14803897

Subgroups — #14803897

Order 2816.

958 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
1C2×#10622621C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073789C211yesmaximal, characteristic, complemented
4#13070052C212yesmaximal, complemented
5#13069802C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069377C211yesmaximal, characteristic, complemented
8#13069045C212yesmaximal, complemented
9#13068639C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C23×C11⋊C8C2212yes—
17C2×#66922C2211yescharacteristic
18C11×#394—22no—
19C11×#384C2211yescharacteristic
20C11×#380—21no—
21C11×#380C2212yes—
22#10622834—21no—
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825C2212yes—
27#10622825C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29D4×C11⋊C8—24no—
30#10622621—24no—
31#10622590—21no—
32C2×#66872C2212yes—
33C2×#66872C2212yes—
34#10622560—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D4×C11—22no—
44C22×D4×C11D411yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2312yes—
48C22×Dic22—21no—
49C11×#121—24no—
50C11×#121—42no—
51C11×#121—44no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4×Dic11—21no—
73C22×C11⋊C8—24no—
74C22×C11⋊C8—24no—
75C22×C11⋊C8—42no—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79#66922—22no—
80#66922—22no—
81C11×#95—22no—
82#66896—22no—
83#66896—24no—
84#66896—22no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—24no—
89#66872—24no—
90#66872—42no—
91C4⋊(C11⋊C8)D414yescomplemented
92C4×C11⋊C8—22no—
93#25339—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11C2×D412yes—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—82no—
106C2×D4×C11SD1614yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C2×Dic22—42no—
127C2×Dic22—81no—
128C2×Dic22—81no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—81no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—44no—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—42no—
140C42×C11C2×D412yes—
141C42×C11#4112yes—
142C22⋊Dic11—82no—
143C22⋊Dic11—82no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—42no—
151C4×Dic11—42no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—48no—
160C2×C11⋊C8C2×D414yes—
161C2×C11⋊C8#4112yes—
162C2×#476—111no—
163C2×C8×D4—111no—
164#2563—111no—
165#2537D1111yescharacteristic
166#2077—112no—
167#2034—112no—
168#1990—111no—
169#1948—111no—
170#1893—112no—
171#1807—112no—
172C4×#102—111no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C2×SD1614yes—
187C23×C11C22×D411yescharacteristic
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—28no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—88no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11#13512yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229Dic22—84no—
230C11⋊C8—22no—
231C11⋊C8—24no—
232C11⋊C8—41no—
233C23×C8—112no—
234C2×C4⋊Q8—111no—
235C2×#121—21no—
236C2×#121C2×D1112yes—
237C2×C4×D4C2×D1111yescharacteristic
238C2×C4×D4C2×D1111yescharacteristic
239#476—224no—
240C8×D4—224no—
241C2×#106—112no—
242C2×#106—112no—
243C2×C4⋊C8—111no—
244C2×#102—111no—
245C2×#102—112no—
246C2×#102—111no—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249#394—22no—
250#393—222no—
251#390—221no—
252#384C2×D1111yescharacteristic
253#382—221no—
254#380—21no—
255#380—112no—
256#380—112no—
257#380C2×D1112yes—
258C4×C4⋊C4—111no—
259#340—111no—
260#340—112no—
261#340—111no—
262#340—112no—
263#340—112no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
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#54711yescharacteristic
281C22×C11C22×SD1611yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11#57611yescharacteristic
284C22×C11#57711yescharacteristic
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11#46514yes—
290C4×C11#52911yescharacteristic
291C4×C11#54211yescharacteristic
292C4×C11#54611yescharacteristic
293C4×C11#54811yescharacteristic
294Dic11—81no—
295Dic11—81no—
296Dic11—82no—
297C22×Q8—221no—
298C22×D4—22no—
299C22×D4C22⋊D1111yescharacteristic
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4C22×D1112yes—
303C22×C8—111no—
304C22×C8—112no—
305C22×C8—111no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—442no—
309C4⋊Q8—222no—
310C4⋊Q8—222no—
311#121—24no—
312#121—42no—
313#121—44no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4C22⋊D1111yescharacteristic
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4C22⋊D1112yes—
333C2×C42—221no—
334C2×C42C22×D1111yescharacteristic
335#106—224no—
336#106—442no—
337C4⋊C8—114no—
338#102—222no—
339#102—224no—
340#102—222no—
341C22⋊C8—224no—
342C4×C8—222no—
343#95—22no—
344#95—221no—
345#95—222no—
346#95—222no—
347C2×C11—44no—
348C2×C11—82no—
349C2×C11#242711yescharacteristic
350C2×C11C2×#46511yescharacteristic
351C2×C11#306211yescharacteristic
352C2×C11#329511yescharacteristic
353C2×C11#330311yescharacteristic
354C2×C11#333511yescharacteristic
355C2×C11#334111yescharacteristic
356C24—21no—
357C24C2×C22⋊D1112yes—
358C2×Q8—442no—
359C2×Q8—881no—
360C2×Q8—881no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—82no—
371C2×D4#432414yes—
372C2×D4#434112yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391C2×C8—114no—
392C2×C8—112no—
393C2×C8—221no—
394C2×C8—222no—
395C2×C8—221no—
396C2×C8—222no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—448no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—81no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—442no—
415C22⋊C4—24no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—42no—
419C22⋊C4—882no—
420C22⋊C4—882no—
421C42—442no—
422C42D4×D1112yes—
423C42#434112yes—
424C11#2533911yescharacteristic, complemented, Sylow
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23C2×#432414yes—
439C23C22×C22⋊D1111yescharacteristic
440Q8—884no—
441D4—22no—
442D4—22no—
443D4—28no—
444D4—41no—
445D4—41no—
446D4—88no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—84no—
463C2×C4—442no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4C2×#432412yes—
473C2×C4#6699212yes—
474C2×C4#6699212yes—
475C2×C4#6700312yes—
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×#434111yescharacteristic
478C2×C4C2×#434111yescharacteristic
479C2×C4#6703711yescharacteristic
480C2×C4#41×D1111yescharacteristic
481C2×C4#6704311yescharacteristic
482C8—222no—
483C8—224no—
484C8—441no—
485C22—24no—
486C22—24no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C22×#432411yescharacteristic
500C22C2×#6699211yescharacteristic
501C22#1062333711yescharacteristic
502C22C2×#6700311yescharacteristic
503C22#1062335511yescharacteristic
504C22#1062336611yescharacteristic
505C22#1062336811yescharacteristic
506C4—22no—
507C4—42no—
508C4—82no—
509C4—81no—
510C4—882no—
511C4—881no—
512C4—881no—
513C4#1062265414yes—
514C4#1062312911yescharacteristic
515C4#1062313111yescharacteristic
516C4#1062313411yescharacteristic
517C4#1062314311yescharacteristic
518C2—44no—
519C2—82no—
520C2#1307219511yescharacteristic
521C2C2×#1062265411yescharacteristic
522C2#1307829811yescharacteristic
523C2#1308044011yescharacteristic
524C2#1308054411yescharacteristic
525C2#1308097311yescharacteristic
526C2#1308103411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#25339
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10622621C2semidirect
2. C2×D4×C11⋊C8C2semidirect
3. #13073789C2semidirect
4. #13070052C2semidirect
5. #13069802C2semidirect
6. #13069576C2semidirect
7. #13069377C2semidirect
8. #13069045C2semidirect
9. #13068639C2semidirect
10. C4×#66896C2semidirect
91. C4⋊(C11⋊C8)D4semidirect
424. C11#25339semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
C2×D4×C11⋊C82
#130737892
#130700522
#130698022
#130695762
#130693772
#130690452
#130686392
C4×#668962
C11×#25372
#2533911