Finite Group Databasebeta

← #14804235

Subgroups — #14804235

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622312C211yesmaximal, characteristic, complemented
2C2×#10622458C212yesmaximal
3C2×#10622454C211yesmaximal, characteristic
4#13073611C211yesmaximal, characteristic
5#13071672C211yesmaximal, characteristic, complemented
6#13069939C212yesmaximal, complemented
7#13069713C212yesmaximal
8#13069538C211yesmaximal, characteristic, complemented
9#13068956C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×Dic44C2212yes—
13C22×Dic44C2212yes—
14C22×#4314C2212yes—
15C2×#66928C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66880C2212yes—
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29#10622600—21no—
30#10622600—21no—
31C4⋊C4×Dic11—21no—
32#10622586—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622542C2212yes—
35#10622542C2212yes—
36#10622458—28no—
37#10622454—24no—
38#10622312—24no—
39#10622287—22no—
40#10622267—22no—
41C11×#336C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2312yes—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11C2312yes—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C2×Dic44—24no—
69C2×Dic44—24no—
70C2×Dic44—24no—
71C2×Dic44—24no—
72C2×Dic44—42no—
73C2×Dic44—42no—
74C2×#4314—24no—
75C2×#4314—24no—
76C2×#4314—42no—
77#66928—24no—
78#66928—42no—
79C4×D44—22no—
80C4×D44—22no—
81#66922—22no—
82#66922—22no—
83#66922—22no—
84#66922D414yes—
85C4×Dic22—24no—
86C4×Dic22—42no—
87C11×C4⋊C8—24no—
88C11×C4⋊C8—22no—
89C4×C8×C11—22no—
90C11×#95D412yes—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96#66885—22no—
97#66885D414yes—
98#66880—24no—
99#66880—24no—
100#66880—42no—
101#25365—111nomaximal, Sylow
102C23×D11—21no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44C2×D412yes—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D414yes—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11#4112yes—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C42×C11—22no—
146C42×C11—22no—
147C42×C11C2×D412yes—
148C42×C11#4112yes—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—42no—
152C4⋊Dic11—24no—
153C4⋊Dic11—24no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161C4⋊Dic11C2×D412yes—
162Dic11⋊C4—44no—
163C4×Dic11—44no—
164C4×Dic11—42no—
165Dic44—48no—
166Dic44—48no—
167#4314—48no—
168C2×#494—111no—
169C2×#464—112no—
170C2×#461—111no—
171#2547—111no—
172#2365—111no—
173#2056—112no—
174#2015—112no—
175#1981—111no—
176#1939D1111yescharacteristic, complemented
177#1878—112no—
178C4×#102—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11#12112yes—
196C2×C4×C11#12112yes—
197C2×C4×C11#13512yes—
198C2×C4×C11#13712yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×Dic11—24no—
206C2×Dic11—22no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220D44—22no—
221D44—22no—
222D44—41no—
223D44—41no—
224C4×D11—84no—
225Dic22—24no—
226Dic22—24no—
227Dic22—42no—
228Dic22—42no—
229Dic22—42no—
230Dic22—42no—
231Dic22—42no—
232Dic22—42no—
233C8×C11—22no—
234C8×C11—22no—
235C8×C11—42no—
236C22×Q16—112no—
237C22×Q16—112no—
238C22×SD16—112no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8—111no—
241C2×#124—112no—
242C2×C4×Q8—112no—
243C2×C4×D4—111no—
244#494—224no—
245#464—228no—
246#461—224no—
247C2×C4⋊C8C2×D1112yes—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×#102—111no—
253C2×#102—111no—
254C2×C4×C8C2×D1111yescharacteristic
255#397—222no—
256#391—112no—
257#391—112no—
258#389—221no—
259#387—222no—
260#380—221no—
261#380—221no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—221no—
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—111no—
266#340—111no—
267#336C2×D1112yes—
268C22×C11C2×#12111yescharacteristic
269C22×C11D4211yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57811yescharacteristic
274C22×C11#57811yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11#46414yescomplemented
286C4×C11#53211yescharacteristic
287C4×C11#54011yescharacteristic
288C4×C11D4211yescharacteristic
289C4×C11#54611yescharacteristic
290Dic11—44no—
291Dic11—42no—
292Dic11—81no—
293Dic11—82no—
294Dic11—81no—
295C22×Q8—112no—
296C22×Q8—112no—
297C22×D4—111no—
298C23×C4—221no—
299C2×Q16—224no—
300C2×Q16—224no—
301C2×Q16—224no—
302C2×Q16—224no—
303C2×Q16—442no—
304C2×Q16—442no—
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C22×C8C22×D1112yes—
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1111yescharacteristic
311C4⋊Q8—114no—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315#124—224no—
316#124—442no—
317C4×Q8—224no—
318C4×Q8—442no—
319C4×D4—222no—
320C4×D4—222no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4D4411yescharacteristic
330C2×C4⋊C4D4411yescharacteristic
331C2×C22⋊C4—221no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—222no—
335C2×C42—221no—
336C2×C42C22×D1112yes—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—24no—
339C4⋊C8—22no—
340#103—224no—
341#103—224no—
342#103—442no—
343#102—114no—
344#102—222no—
345C4×C8—22no—
346#95—221no—
347#95—222no—
348#95—222no—
349#95—222no—
350#95—222no—
351#95D4412yes—
352C2×C11#242811yescharacteristic
353C2×C11C2×#46411yescharacteristic
354C2×C11#304411yescharacteristic
355C2×C11#327611yescharacteristic
356C2×C11#328311yescharacteristic
357C2×C11#339311yescharacteristic
358C2×C11#339811yescharacteristic
359D11—82no—
360C24—221no—
361C2×Q8—114no—
362C2×Q8—222no—
363C2×Q8—222no—
364C2×Q8—222no—
365C2×Q8—222no—
366C2×Q8—222no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×D4—112no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C22×C4—222no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—222no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4C2×D4412yes—
388C22×C4C2×D4412yes—
389C22×C4C2×D4411yescharacteristic
390C22×C4C2×D4411yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—448no—
393Q16—448no—
394SD16—448no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8D4×D1112yes—
403C2×C8#434312yes—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—112no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—444no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C22⋊C4—442no—
420C42—22no—
421C42—22no—
422C42—444no—
423C42—442no—
424C42D4×D1112yes—
425C42#434312yes—
426C11#2536511yescharacteristic, complemented, Sylow
427C23—222no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23C22×D4411yescharacteristic
435Q8—224no—
436Q8—224no—
437Q8—442no—
438Q8—442no—
439Q8—442no—
440Q8—442no—
441Q8—442no—
442Q8—442no—
443D4—222no—
444D4—222no—
445D4—441no—
446D4—441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—224no—
456C2×C4—222no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—884no—
471C2×C4#6694812yes—
472C2×C4#6694812yes—
473C2×C4#6695712yes—
474C2×C4#6696212yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×#434311yescharacteristic
478C2×C4C2×#434311yescharacteristic
479C2×C4#6704211yescharacteristic
480C2×C4#6704211yescharacteristic
481C8—22no—
482C8—22no—
483C8—42no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×#6694811yescharacteristic
492C22D4×D4411yescharacteristic
493C22#1062310811yescharacteristic
494C22C2×#6695711yescharacteristic
495C22C2×#6696211yescharacteristic
496C22#1062328411yescharacteristic
497C22#1062328411yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—442no—
502C4—444no—
503C4—881no—
504C4—881no—
505C4—882no—
506C4#1062245814yescomplemented
507C4#1062314011yescharacteristic
508C4#1062316111yescharacteristic
509C4#1062322911yescharacteristic
510C4#1062325611yescharacteristic
511C2—882no—
512C2#1307220211yescharacteristic
513C2C2×#1062245811yescharacteristic
514C2#1307814711yescharacteristic
515C2#1308026411yescharacteristic
516C2#1308033811yescharacteristic
517C2#1308160511yescharacteristic
518C2#1308164911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#25365
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622312C2semidirect
5. #13071672C2semidirect
6. #13069939C2semidirect
8. #13069538C2semidirect
9. #13068956C2semidirect
11. C11×#1939C2semidirect
176. #1939D11semidirect
285. C4×C11#464semidirect
426. C11#25365semidirect
506. C4#10622458semidirect

Maximal subgroups

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

subgroupindex
C2×#106223122
C2×#106224582
C2×#106224542
#130736112
#130716722
#130699392
#130697132
#130695382
#130689562
C4×#668852
C11×#19392
#2536511