Finite Group Databasebeta

← #14682751

Subgroups — #14682751

Order 2816.

1166 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622587C211yesmaximal, characteristic
2#13066886C212yesmaximal
3#13066877C212yesmaximal
4#13066876C212yesmaximal
5#13066848C211yesmaximal, characteristic
6#13066843C212yesmaximal
7#13066842C212yesmaximal
8#13066841C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×C11×#95C2212yes—
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622587C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×Dic22—24no—
42C22×Dic22—42no—
43C22×Dic22—41no—
44C22×Dic22—41no—
45C22×Dic22C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C42×C11—24no—
50C2×C42×C11—41no—
51C2×C4×Dic11—24no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11—41no—
54C2×C4×Dic11C2×C414yes—
55C11×#95—24no—
56C11×#95—24no—
57C11×#95—41no—
58C11⋊#95—24no—
59C11⋊#95—24no—
60C11⋊#95—24no—
61C11⋊#95—24no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—41no—
69C11⋊#95C2×C418yes—
70C11⋊#95C2×C418yes—
71#14489—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
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×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11#4114yes—
101C22×C4×C11#4114yes—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
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×Dic11C22×C414yes—
128C22×Dic11C22×C414yes—
129C22×Dic11#4114yes—
130C2×Dic22—28no—
131C2×Dic22—44no—
132C2×Dic22—44no—
133C2×Dic22—48no—
134C2×Dic22—48no—
135C11×C4⋊C4—44no—
136C42×C11—44no—
137C4×Dic11—44no—
138C4×Dic11—44no—
139C2×#391—111no—
140#1446—112no—
141#1443—112no—
142#1443—112no—
143#1436—111no—
144#1436D1111yescharacteristic
145#1434—112no—
146#1434—112no—
147#1434—112no—
148C23×C11C23×C411yescharacteristic
149C23×C11C2×#4112yes—
150C23×C11C2×#4112yes—
151C23×C11C2×#4112yes—
152C23×C11H(5,𝔽2)11yescharacteristic
153C23×C11H(5,𝔽2)11yescharacteristic
154C23×C11H(5,𝔽2)12yes—
155C23×C112−1+412yes—
156C23×C112−1+412yes—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11#11714yes—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214Dic22—416no—
215C23×Q8—111no—
216C22×C4⋊C4C2×D1111yescharacteristic
217C22×C42—111no—
218C22×C42—111no—
219C22×C42C2×D1111yescharacteristic
220#391—118no—
221C2×#95—112no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—112no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—111no—
233C2×#95—112no—
234C2×#95C2×D1112yes—
235C2×#95C2×D1112yes—
236C2×#95C2×D1111yescharacteristic
237C22×C11C2×#11711yescharacteristic
238C22×C11C4×#4112yes—
239C22×C11#51811yescharacteristic
240C22×C11#51811yescharacteristic
241C22×C11#51912yes—
242C22×C11#53812yes—
243C22×C11#53812yes—
244C22×C11#53912yes—
245C22×C11#53912yes—
246C22×C11#54212yes—
247C22×C11#54212yes—
248C22×C11#55111yescharacteristic
249C22×C11#55111yescharacteristic
250C22×C11#55212yes—
251C22×C11#55212yes—
252C22×C11#55512yes—
253C22×C11#55612yes—
254C22×C11#55612yes—
255C22×C11#56311yescharacteristic
256C22×C11#56312yes—
257C22×C11#56311yescharacteristic
258C4×C11—24no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—82no—
263Dic11—44no—
264Dic11—44no—
265Dic11—44no—
266Dic11—82no—
267C22×Q8—114no—
268C22×Q8—224no—
269C22×Q8—441no—
270C22×Q8—441no—
271C22×Q8—442no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4—112no—
276C23×C4C22×D1112yes—
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C23×C4C22×D1112yes—
280C23×C4C22×D1111yescharacteristic
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4C4×D1114yes—
284C2×C42—24no—
285C2×C42—41no—
286C2×C42—114no—
287C2×C42—224no—
288C2×C42—442no—
289C2×C42—441no—
290#95—24no—
291#95—24no—
292#95—41no—
293#95—118no—
294#95—118no—
295#95—224no—
296#95—224no—
297#95—224no—
298#95—224no—
299#95—442no—
300#95—441no—
301#95—442no—
302#95—442no—
303#95—442no—
304#95—442no—
305#95—442no—
306C2×C11#231211yescharacteristic
307C2×C11#233212yes—
308C2×C11#235612yes—
309C2×C11#237211yescharacteristic
310C2×C11#238111yescharacteristic
311C2×C11#274512yes—
312C2×C11#274512yes—
313C2×C11#277512yes—
314C2×C11#277512yes—
315C24C23×D1111yescharacteristic
316C2×Q8—228no—
317C2×Q8—444no—
318C2×Q8—444no—
319C2×Q8—448no—
320C2×Q8—448no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—114no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4C2×C4×D1112yes—
374C22×C4C2×C4×D1112yes—
375C22×C4C2×C4×D1112yes—
376C22×C4#433914yes—
377C22×C4#434114yes—
378C4⋊C4—44no—
379C42—44no—
380C42—444no—
381C42—444no—
382C11#1448911yescharacteristic, complemented, Sylow
383C23C22×C4×D1111yescharacteristic
384C23C2×#433912yes—
385C23C2×#434112yes—
386C23#6703711yescharacteristic
387C23#6703711yescharacteristic
388C23#6704012yes—
389C23#41×D1112yes—
390C23#6704212yes—
391C23#6704312yes—
392Q8—4416no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—224no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4#6692514yes—
450C22C2×#6692511yescharacteristic
451C22#1062301711yescharacteristic
452C22#1062304412yes—
453C22#1062305211yescharacteristic
454C22#1062306012yes—
455C22C4×#434112yes—
456C22#1062307312yes—
457C22#1062309112yes—
458C22#1062309112yes—
459C22#1062309912yes—
460C22#1062310312yes—
461C22#1062311811yescharacteristic
462C22#1062314712yes—
463C22#1062317412yes—
464C22#1062317712yes—
465C22#1062319011yescharacteristic
466C22#1062319612yes—
467C22#1062320311yescharacteristic
468C22#1062322312yes—
469C22#1062324112yes—
470C22#1062326611yescharacteristic
471C4—24no—
472C4—44no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—444no—
477C4—444no—
478C4—444no—
479C4—882no—
480C2#1307121111yescharacteristic
481C2#1307136812yes—
482C2#1307157712yes—
483C2#1307172511yescharacteristic
484C2#1307179511yescharacteristic
485C2#1307578212yes—
486C2#1307578912yes—
487C2#1307618912yes—
488C2#1307619212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14489
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622587C4semidirect
382. C11#14489semidirect

Maximal subgroups

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

subgroupindex
C2×#106225872
#130668862
#130668772
#130668762
#130668482
#130668432
#130668422
#130668412
C11×#14362
#1448911