Finite Group Databasebeta

← #14675387

Subgroups — #14675387

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622587C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3#13066851C212yesmaximal
4#13066848C211yesmaximal, characteristic
5#13066847C212yesmaximal
6C4×C11⋊#95C212yesmaximal
7#95×Dic11C212yesmaximal
8#95×Dic11C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×C4×Dic11C2211yescharacteristic
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622587C418yescomplemented
32#10622259C4116yescomplemented
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×Dic22—41no—
43C22×Dic22—42no—
44C22×Dic22—41no—
45C22×Dic22C2×C418yes—
46C22×Dic22C2×C414yes—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C42×C11—24no—
51C2×C42×C11—41no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4C2×C418yes—
55C2×C4×Dic11—24no—
56C2×C4×Dic11—24no—
57C2×C4×Dic11—24no—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11—42no—
62C2×C4×Dic11—42no—
63C2×C4×Dic11—42no—
64C2×C4×Dic11—42no—
65C2×C4×Dic11—41no—
66C2×C4×Dic11C2×C418yes—
67C2×C4×Dic11C2×C414yes—
68C11×#95—24no—
69C11×#95—41no—
70C11×#95C2×C418yes—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—41no—
74C11⋊#95C2×C418yes—
75C11⋊#95C2×C418yes—
76C11⋊#95C2×C418yes—
77C11⋊#95C2×C418yes—
78C11⋊#95C2×C418yes—
79C11⋊#95Q818yescomplemented
80#13826—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C414yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C414yes—
109C22×C4×C11C2×Q814yes—
110C22×C4×C11#4114yes—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C22×C414yes—
130C22×Dic11C22×C414yes—
131C22×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C22×C414yes—
134C22×Dic11C22×C414yes—
135C22×Dic11C2×Q814yes—
136C22×Dic11C2×Q814yes—
137C22×Dic11#4114yes—
138C22×Dic11#4114yes—
139C2×Dic22—44no—
140C2×Dic22—44no—
141C2×Dic22—48no—
142C2×Dic22—48no—
143C2×Dic22C42116yescomplemented
144C11×C4⋊C4—44no—
145C42×C11—44no—
146Dic11⋊C4—48no—
147C4×Dic11—44no—
148C4×Dic11—48no—
149C4×Dic11—48no—
150C4×Dic11—48no—
151C4×Dic11—44no—
152C2×#391—112no—
153C2×#391—111no—
154#1436—112no—
155#1436—112no—
156#1436—111no—
157#1436D1111yescharacteristic
158C4×#95—112no—
159C4×#95—112no—
160C4×#95—112no—
161C23×C11C23×C411yescharacteristic
162C23×C11C23×C412yes—
163C23×C11C22×Q812yes—
164C23×C11C2×#4112yes—
165C23×C11C2×#4112yes—
166C23×C11C2×#4112yes—
167C23×C11H(5,𝔽2)11yescharacteristic
168C23×C11H(5,𝔽2)11yescharacteristic
169C23×C11H(5,𝔽2)12yes—
170C2×C4×C11—24no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C2×C4214yes—
198C2×C4×C11C4×Q818yes—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C2×C4218yes—
225C2×Dic11C4×Q818yes—
226C2×Dic11C4×Q818yes—
227Dic22—416no—
228C23×Q8—111no—
229C22×C4⋊C4—112no—
230C22×C4⋊C4C2×D1111yescharacteristic
231C22×C42—112no—
232C22×C42—111no—
233C22×C42—112no—
234C22×C42—111no—
235C22×C42—112no—
236C22×C42C2×D1111yescharacteristic
237#391—118no—
238#391—1116no—
239C2×#95—112no—
240C2×#95—112no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95—112no—
246C2×#95—112no—
247C2×#95—111no—
248C2×#95C2×D1112yes—
249C2×#95C2×D1111yescharacteristic
250C2×#95C2×D1112yes—
251C22×C11C22×C4211yescharacteristic
252C22×C11C2×C4×Q812yes—
253C22×C11C2×C4×Q812yes—
254C22×C11C2×C4×Q812yes—
255C22×C11C4×#4112yes—
256C22×C11C4×#4112yes—
257C22×C11C4×#4112yes—
258C22×C11#51811yescharacteristic
259C22×C11#51811yescharacteristic
260C22×C11#51812yes—
261C22×C11#51812yes—
262C22×C11#55112yes—
263C22×C11#55111yescharacteristic
264C22×C11#55112yes—
265C22×C11#55111yescharacteristic
266C22×C11#55412yes—
267C22×C11#55412yes—
268C22×C11#55412yes—
269C22×C11#55512yes—
270C22×C11#55511yescharacteristic
271C22×C11Q8211yescharacteristic
272C4×C11—28no—
273C4×C11—24no—
274C4×C11—44no—
275C4×C11—42no—
276C4×C11—42no—
277Dic11—28no—
278Dic11—28no—
279Dic11—28no—
280Dic11—44no—
281C22×Q8—114no—
282C22×Q8—118no—
283C22×Q8—441no—
284C22×Q8—441no—
285C22×Q8—442no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4—112no—
289C23×C4—112no—
290C23×C4C22×D1112yes—
291C23×C4C22×D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C23×C4C22×D1111yescharacteristic
294C23×C4C22×D1112yes—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—118no—
298C2×C4⋊C4—442no—
299C2×C4⋊C4—442no—
300C2×C4⋊C4C4×D1114yes—
301C2×C42—24no—
302C2×C42—41no—
303C2×C42—114no—
304C2×C42—118no—
305C2×C42—224no—
306C2×C42—224no—
307C2×C42—224no—
308C2×C42—224no—
309C2×C42—224no—
310C2×C42—442no—
311C2×C42—442no—
312C2×C42—442no—
313C2×C42—442no—
314C2×C42—441no—
315C2×C42—442no—
316#95—24no—
317#95—41no—
318#95—118no—
319#95—118no—
320#95—118no—
321#95—118no—
322#95—118no—
323#95—118no—
324#95—224no—
325#95—224no—
326#95—441no—
327#95C4×D1118yes—
328C2×C11C42×Q812yes—
329C2×C11#227311yescharacteristic
330C2×C11#236812yes—
331C2×C11#236812yes—
332C2×C11#236812yes—
333C2×C11#236912yes—
334C2×C11#236911yescharacteristic
335C2×C11#237212yes—
336C2×C11#237211yescharacteristic
337C24C23×D1111yescharacteristic
338C2×Q8—1116no—
339C2×Q8—444no—
340C2×Q8—444no—
341C2×Q8—448no—
342C2×Q8—448no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—114no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—114no—
368C22×C4—114no—
369C22×C4—114no—
370C22×C4—114no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—114no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4C2×C4×D1112yes—
393C22×C4C2×C4×D1112yes—
394C22×C4C2×C4×D1114yes—
395C22×C4C2×C4×D1114yes—
396C22×C4C2×C4×D1112yes—
397C22×C4C2×C4×D1114yes—
398C22×C4#434114yes—
399C22×C4Q8×D1114yes—
400C4⋊C4—44no—
401C4⋊C4—448no—
402C42—44no—
403C42—444no—
404C42—448no—
405C42—448no—
406C42—448no—
407C42—444no—
408C11#1382611yescharacteristic, complemented, Sylow
409C23C22×C4×D1111yescharacteristic
410C23C22×C4×D1112yes—
411C23C2×#434112yes—
412C23#6703711yescharacteristic
413C23#6703711yescharacteristic
414C23C2×Q8×D1112yes—
415C23#41×D1112yes—
416C23#41×D1112yes—
417C23#6704212yes—
418Q8—4416no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—118no—
447C2×C4—118no—
448C2×C4—118no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4C42×D1114yes—
475C2×C4#6694018yes—
476C22C2×C42×D1111yescharacteristic
477C22#1062301711yescharacteristic
478C22C2×#6694012yes—
479C22#1062305211yescharacteristic
480C22#1062305312yes—
481C22C4×#434112yes—
482C22C4×#434112yes—
483C22#1062307612yes—
484C22#1062307612yes—
485C22C4×Q8×D1112yes—
486C22C4×Q8×D1112yes—
487C22#1062311811yescharacteristic
488C22#1062314712yes—
489C22#1062316612yes—
490C22#1062316712yes—
491C22#1062318912yes—
492C22#1062319011yescharacteristic
493C22#1062320111yescharacteristic
494C22#1062322112yes—
495C22#1062323612yes—
496C22#1062325311yescharacteristic
497C4—28no—
498C4—24no—
499C4—44no—
500C4—42no—
501C4—42no—
502C4—228no—
503C4—228no—
504C4—228no—
505C4—444no—
506C2C4×#6694012yes—
507C2#1307096811yescharacteristic
508C2#1307169312yes—
509C2#1307169712yes—
510C2#1307169812yes—
511C2#1307170212yes—
512C2#1307170411yescharacteristic
513C2#1307172312yes—
514C2#1307172511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#13826
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622587C4semidirect
32. #10622259C4semidirect
79. C11⋊#95Q8semidirect
143. C2×Dic22C42semidirect
408. C11#13826semidirect

Maximal subgroups

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

subgroupindex
C2×#106225872
C2×#106222592
#130668512
#130668482
#130668472
C4×C11⋊#952
#95×Dic112
C11×#14362
#1382611