Finite Group Databasebeta

← #14803891

Subgroups — #14803891

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×#10622447C211yesmaximal, characteristic, complemented
2#13073790C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13070050C212yesmaximal, complemented
5#13069804C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069041C212yesmaximal, complemented
9#13068638C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991C2212yes—
15C2×#66983—21no—
16C22×C8×D11C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#476—24no—
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2212yes—
22#10622844—22no—
23C2×#66896C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25#10622825—21no—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66881C2212yes—
28#10622601—21no—
29#10622600C2212yes—
30#10622600C2212yes—
31#10622600C2212yes—
32#10622590—21no—
33#10622574—22no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622447—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11C2312yes—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60#66991—24no—
61#66991—42no—
62#66983—44no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—21no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×C8×D11—24no—
77C2×C8×D11—24no—
78C2×C8×D11—42no—
79C4×D44—22no—
80C4×D44—22no—
81C11×#106—24no—
82C11×C4⋊C8D414yescomplemented
83C11×#102—24no—
84#66896—22no—
85#66896—22no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90(C2×D11)⋊C8—24no—
91#66881—42no—
92C4×C11⋊C8—22no—
93#25339—111nomaximal, Sylow
94C24×C11—21no—
95C23×D11C2×D412yes—
96C2×Q8×C11—42no—
97C2×Q8×C11—81no—
98C2×Q8×C11—81no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11#4112yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—44no—
114C2×C22⋊D11—44no—
115C2×C22⋊D11—82no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—22no—
119C22×Dic11C2×D412yes—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44SD1614yes—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11C2×D414yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C22⋊C4—42no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140C22⋊Dic11—44no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—82no—
144(C2×D11)⋊C4—82no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—42no—
153C4⋊Dic11—81no—
154C4×Dic11—42no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8#4112yes—
161C8×D11—48no—
162C2×#476D1111yescharacteristic, complemented
163C2×C8×D4—111no—
164#2563—111no—
165#2537—111no—
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—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11C2×SD1614yes—
188Q8×C11—84no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—84no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11#13512yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C22⋊D11—88no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225D44—28no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—42no—
229C4×D11—42no—
230C8×C11—24no—
231C11⋊C8—22no—
232C11⋊C8—41no—
233C23×C8—112no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#121—112no—
236C2×#121—221no—
237C2×C4×D4—111no—
238C2×C4×D4C2×D1111yescharacteristic
239#476—24no—
240C8×D4—224no—
241C2×#106—112no—
242C2×#106C2×D1112yes—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#102—111no—
245C2×#102—111no—
246C2×#102C2×D1112yes—
247C2×C22⋊C8—112no—
248C2×C4×C8—111no—
249#394—222no—
250#393—222no—
251#390—221no—
252#384—111no—
253#382—221no—
254#380—112no—
255#380—112no—
256#380—112no—
257#380—221no—
258C4×C4⋊C4—111no—
259#340—112no—
260#340—111no—
261#340—112no—
262#340—111no—
263#340—112no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11C2×#12111yescharacteristic
272C22×C11#54611yescharacteristic
273C22×C11#54711yescharacteristic
274C22×C11C22×SD1611yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11#57611yescharacteristic
277C22×C11#57711yescharacteristic
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C4×C11—22no—
286C4×C11—81no—
287C4×C11—82no—
288C4×C11#46514yes—
289C4×C11#52911yescharacteristic
290C4×C11#54211yescharacteristic
291C4×C11#54611yescharacteristic
292C4×C11#54811yescharacteristic
293Dic11—42no—
294Dic11—81no—
295Dic11—82no—
296Dic11—81no—
297C22×Q8—21no—
298C22×D4—111no—
299C22×D4—222no—
300C22×D4C22×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—112no—
303C22×C8—111no—
304C22×C8—111no—
305C22×C8—224no—
306C22×C8—224no—
307C22×C8—442no—
308C22×C8C22×D1112yes—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311#121—224no—
312#121—442no—
313#121—444no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—222no—
317C4×D4—222no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—112no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—221no—
334C2×C42C22×D1111yescharacteristic
335#106—24no—
336#106—442no—
337C4⋊C8C22⋊D1114yescomplemented
338#102—24no—
339#102—222no—
340#102—222no—
341C22⋊C8—224no—
342C4×C8—222no—
343#95—222no—
344#95—222no—
345#95—222no—
346#95—221no—
347C2×C11—82no—
348C2×C11#242711yescharacteristic
349C2×C11C2×#46511yescharacteristic
350C2×C11#306211yescharacteristic
351C2×C11#329511yescharacteristic
352C2×C11#330311yescharacteristic
353C2×C11#333511yescharacteristic
354C2×C11#334111yescharacteristic
355D11—44no—
356C24—21no—
357C24—112no—
358C2×Q8—42no—
359C2×Q8—81no—
360C2×Q8—81no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—114no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—444no—
370C2×D4—444no—
371C2×D4—882no—
372C2×D4#434312yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—112no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—222no—
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—112no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—448no—
400C2×C8C2×C22⋊D1114yes—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—42no—
406C4⋊C4—222no—
407C4⋊C4—221no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—442no—
414C4⋊C4—881no—
415C22⋊C4—42no—
416C22⋊C4—224no—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C22⋊C4—882no—
420C22⋊C4—882no—
421C42—442no—
422C42#434112yes—
423C42C2×C22⋊D1112yes—
424C11#2533911yescharacteristic, complemented, Sylow
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—114no—
433C23—222no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23C2×D4×D1111yescharacteristic
440Q8—84no—
441D4—22no—
442D4—22no—
443D4—41no—
444D4—41no—
445D4—228no—
446D4—888no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—84no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4SD16×D1112yes—
473C2×C4#6696912yes—
474C2×C4#6699112yes—
475C2×C4#6699112yes—
476C2×C4C2×#434111yescharacteristic
477C2×C4C2×#434311yescharacteristic
478C2×C4#6704011yescharacteristic
479C2×C4#41×D1111yescharacteristic
480C2×C4#6704211yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—24no—
483C8—222no—
484C8—441no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—224no—
493C22—224no—
494C22—224no—
495C22—442no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22#1062316111yescharacteristic
500C22#1062316211yescharacteristic
501C22C2×SD16×D1111yescharacteristic
502C22C2×#6696911yescharacteristic
503C22#1062330511yescharacteristic
504C22#1062330611yescharacteristic
505C22C2×#6699111yescharacteristic
506C4—22no—
507C4—82no—
508C4—81no—
509C4—442no—
510C4—882no—
511C4—881no—
512C4—881no—
513C4#1062278414yes—
514C4#1062315511yescharacteristic
515C4#1062317411yescharacteristic
516C4#1062334811yescharacteristic
517C4#1062336011yescharacteristic
518C2—82no—
519C2—444no—
520C2#1307218911yescharacteristic
521C2C2×#1062278411yescharacteristic
522C2#1307829011yescharacteristic
523C2#1308043711yescharacteristic
524C2#1308054111yescharacteristic
525C2#1308097011yescharacteristic
526C2#1308103711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#476D11
hypocenterC11#25339
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622447C2semidirect
2. #13073790C2semidirect
4. #13070050C2semidirect
5. #13069804C2semidirect
6. #13069578C2semidirect
7. #13069380C2semidirect
8. #13069041C2semidirect
9. #13068638C2semidirect
10. C4×#66896C2semidirect
11. C2×C11×#476C2semidirect
82. C11×C4⋊C8D4semidirect
162. C2×#476D11semidirect
337. C4⋊C8C22⋊D11semidirect
424. C11#25339semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
#130737902
#130735292
#130700502
#130698042
#130695782
#130693802
#130690412
#130686382
C4×#668962
C2×C11×#4762
#2533911