Finite Group Databasebeta

← #14803913

Subgroups — #14803913

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622447C211yesmaximal, characteristic
2#13073612C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic
4#13070050C212yesmaximal, complemented
5#13069811C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069036C212yesmaximal, complemented
9#13068638C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#67000—21no—
15C2×#66999C2212yes—
16C22×C8×D11C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#475—24no—
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2212yes—
22#10622843—21no—
23C2×#66899C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66881C2212yes—
27#10622607—22no—
28#10622606—22no—
29#10622600C2212yes—
30#10622600C2212yes—
31#10622600C2212yes—
32#10622552—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622541—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622447—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44D411yescharacteristic
46C22×C4×D11C2312yes—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#67000—44no—
59#66999—24no—
60#66999—42no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4D412yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
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⋊C8D414yes—
83C11×#103—24no—
84#66899—22no—
85#66899—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#25341—111nomaximal, Sylow
94C23×D11C2×D412yes—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44SD1614yes—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11C2×D414yes—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—42no—
132C42×C11—42no—
133C42×C11C2×D412yes—
134C42×C11#4112yes—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—42no—
148C4⋊Dic11—81no—
149Dic11⋊C4—44no—
150C4×Dic11—42no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8#4112yes—
157C8×D11—48no—
158C2×#475D1111yescharacteristic, complemented
159C2×C8×D4—111no—
160#2547—111no—
161#2538—111no—
162#2077—112no—
163#2035—112no—
164#1990—111no—
165#1948—111no—
166#1892—112no—
167#1807—112no—
168C4×#103—111no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11C2×SD1614yes—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—84no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11#12112yes—
194C2×C4×C11#12112yes—
195C2×C4×C11C2×SD1612yes—
196C2×C4×C11#13512yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215D44—28no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—42no—
220C8×C11—24no—
221C11⋊C8—22no—
222C11⋊C8—41no—
223C23×C8—112no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×#124—221no—
226C2×C22⋊Q8—112no—
227C2×C4×Q8C2×D1111yescharacteristic
228C2×C4×D4—111no—
229#475—24no—
230C8×D4—224no—
231C2×#106—112no—
232C2×#106C2×D1112yes—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×#103—111no—
235C2×#103—111no—
236C2×#103C2×D1112yes—
237C2×C22⋊C8—112no—
238C2×C4×C8—111no—
239#397—222no—
240#396—222no—
241#391—221no—
242#390—221no—
243#389—221no—
244#384—111no—
245#380—112no—
246#380—112no—
247#380—112no—
248C4×C4⋊C4—111no—
249#340—112no—
250#340—111no—
251#340—112no—
252#340—111no—
253#340—112no—
254C22×C11C2×#12111yescharacteristic
255C22×C11#54611yescharacteristic
256C22×C11#54711yescharacteristic
257C22×C11C22×SD1611yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—24no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11—81no—
272C4×C11#46514yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54811yescharacteristic
277Dic11—42no—
278Dic11—81no—
279Dic11—81no—
280Dic11—82no—
281C22×Q8—21no—
282C22×Q8C22×D1111yescharacteristic
283C22×D4—111no—
284C23×C4—112no—
285C22×C8—111no—
286C22×C8—111no—
287C22×C8—224no—
288C22×C8—224no—
289C22×C8—442no—
290C22×C8C22×D1112yes—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293#124—444no—
294C22⋊Q8—224no—
295C22⋊Q8—442no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×D4—222no—
299C4×D4—222no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1112yes—
311C2×C22⋊C4—112no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#106—24no—
320#106—442no—
321C4⋊C8C22⋊D1114yes—
322#103—24no—
323#103—222no—
324#103—222no—
325C22⋊C8—224no—
326C4×C8—222no—
327#95—222no—
328#95—222no—
329#95—222no—
330#95—221no—
331C2×C11#242711yescharacteristic
332C2×C11C2×#46511yescharacteristic
333C2×C11#306311yescharacteristic
334C2×C11#329811yescharacteristic
335C2×C11#330411yescharacteristic
336C2×C11#333511yescharacteristic
337C2×C11#334211yescharacteristic
338D11—44no—
339C24—112no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8#434312yes—
349C2×D4—114no—
350C2×D4—222no—
351C2×D4—222no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—112no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—112no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8—448no—
377C2×C8C2×C22⋊D1114yes—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—222no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—444no—
392C4⋊C4—442no—
393C4⋊C4—881no—
394C22⋊C4—224no—
395C22⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C22⋊C4—882no—
399C42—42no—
400C42—442no—
401C42#434112yes—
402C42C2×C22⋊D1112yes—
403C11#2534111yescharacteristic, complemented, Sylow
404C23—114no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23C2×D4×D1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416Q8—84no—
417D4—228no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4SD16×D1112yes—
446C2×C4#6696912yes—
447C2×C4#6699112yes—
448C2×C4#6699112yes—
449C2×C4C2×#434111yescharacteristic
450C2×C4C2×#434311yescharacteristic
451C2×C4#6704011yescharacteristic
452C2×C4#41×D1111yescharacteristic
453C2×C4#6704211yescharacteristic
454C2×C4C22×C22⋊D1111yescharacteristic
455C8—24no—
456C8—222no—
457C8—441no—
458C22—224no—
459C22—224no—
460C22—224no—
461C22—442no—
462C22—442no—
463C22—442no—
464C22—442no—
465C22#1062316111yescharacteristic
466C22#1062316211yescharacteristic
467C22C2×SD16×D1111yescharacteristic
468C22C2×#6696911yescharacteristic
469C22#1062330911yescharacteristic
470C22#1062331011yescharacteristic
471C22C2×#6699111yescharacteristic
472C4—22no—
473C4—42no—
474C4—81no—
475C4—82no—
476C4—442no—
477C4—881no—
478C4—881no—
479C4—882no—
480C4#1062278414yes—
481C4#1062315511yescharacteristic
482C4#1062317411yescharacteristic
483C4#1062334811yescharacteristic
484C4#1062336011yescharacteristic
485C2—444no—
486C2#1307218911yescharacteristic
487C2C2×#1062278411yescharacteristic
488C2#1307830111yescharacteristic
489C2#1308047811yescharacteristic
490C2#1308055211yescharacteristic
491C2#1308097611yescharacteristic
492C2#1308104511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#475D11
hypocenterC11#25341
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
4. #13070050C2semidirect
5. #13069811C2semidirect
6. #13069578C2semidirect
7. #13069380C2semidirect
8. #13069036C2semidirect
9. #13068638C2semidirect
10. C4×#66899C2semidirect
11. C2×C11×#475C2semidirect
158. C2×#475D11semidirect
403. C11#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
#130736122
#130735342
#130700502
#130698112
#130695782
#130693802
#130690362
#130686382
C4×#668992
C2×C11×#4752
#2534111