Finite Group Databasebeta

← #14683857

Subgroups — #14683857

Order 2816.

1358 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622592C211yesmaximal, characteristic
2C2×#10622259C212yesmaximal
3C2×#10622546C212yesmaximal
4#13066884C211yesmaximal, characteristic
5#13066876C212yesmaximal
6#13066871C212yesmaximal
7#13066847C212yesmaximal
8#13066842C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C2×C11×#95C2212yes—
17C2×C11×#95C2212yes—
18C2×C11×#95C2211yescharacteristic
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622592C418yescomplemented
32#10622546—28no—
33#10622259—28no—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×Dic22—24no—
44C22×Dic22—24no—
45C22×Dic22—41no—
46C22×Dic22—41no—
47C22×Dic22C2×C414yes—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C42×C11—24no—
52C2×C42×C11—41no—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—24no—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4—42no—
58C2×Dic11⋊C4C2×C418yes—
59C2×C4×Dic11—24no—
60C2×C4×Dic11—24no—
61C2×C4×Dic11—42no—
62C11×#95—24no—
63C11×#95—24no—
64C11×#95—41no—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—41no—
73C11⋊#95—41no—
74C11⋊#95C2×C414yes—
75C11⋊#95C2×C418yes—
76C11⋊#95D418yes—
77#14574—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D414yes—
107C22×C4×C11#4114yes—
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×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C2×D414yes—
134C22×Dic11C2×D414yes—
135C22×Dic11#4114yes—
136C2×Dic22—216no—
137C2×Dic22—44no—
138C2×Dic22—44no—
139C2×Dic22—48no—
140C2×Dic22—44no—
141C11×C4⋊C4—44no—
142C42×C11—44no—
143Dic11⋊C4—216no—
144Dic11⋊C4—48no—
145C4×Dic11—48no—
146C2×#395—111no—
147C2×#391—112no—
148C2×#387—112no—
149#1445—111no—
150#1443—112no—
151#1442—112no—
152#1436—112no—
153#1436D1111yescharacteristic
154#1434—112no—
155C23×C11C23×C411yescharacteristic
156C23×C11C22×D412yes—
157C23×C11C2×#4112yes—
158C23×C11C2×#4112yes—
159C23×C11H(5,𝔽2)11yescharacteristic
160C23×C11H(5,𝔽2)11yescharacteristic
161C23×C112−1+412yes—
162C23×C112−1+412yes—
163C23×C112−1+412yes—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
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—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
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—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11C4×D418yes—
221Dic22—416no—
222C23×Q8—111no—
223C22×C4⋊C4—112no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4C2×D1111yescharacteristic
226C22×C42—112no—
227C22×C42C2×D1111yescharacteristic
228#395—118no—
229#391—228no—
230#387—228no—
231C2×#95—112no—
232C2×#95—111no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95—112no—
241C2×#95—111no—
242C2×#95—111no—
243C2×#95C2×D1112yes—
244C2×#95C2×D1112yes—
245C2×#95C2×D1111yescharacteristic
246C22×C11C2×C4×D412yes—
247C22×C11C4×#4111yescharacteristic
248C22×C11#51811yescharacteristic
249C22×C11#51911yescharacteristic
250C22×C11#51912yes—
251C22×C11#53612yes—
252C22×C11#53612yes—
253C22×C11#53912yes—
254C22×C11#54112yes—
255C22×C11#54112yes—
256C22×C11#54212yes—
257C22×C11D4211yescharacteristic
258C22×C11#54612yes—
259C22×C11#54712yes—
260C22×C11#54812yes—
261C22×C11#55111yescharacteristic
262C22×C11#55212yes—
263C22×C11#55612yes—
264C22×C11#56311yescharacteristic
265C22×C11#56312yes—
266C22×C11#56311yescharacteristic
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—44no—
271C4×C11—44no—
272Dic11—28no—
273Dic11—44no—
274Dic11—44no—
275Dic11—82no—
276C22×Q8—114no—
277C22×Q8—224no—
278C22×Q8—224no—
279C22×Q8—441no—
280C22×Q8—441no—
281C23×C4—112no—
282C23×C4—112no—
283C23×C4—112no—
284C23×C4—112no—
285C23×C4C22×D1111yescharacteristic
286C23×C4C22×D1111yescharacteristic
287C23×C4C22×D1111yescharacteristic
288C23×C4C22×D1112yes—
289C23×C4C22×D1112yes—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—118no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4—224no—
296C2×C4⋊C4—224no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4C4×D1114yes—
299C2×C42—24no—
300C2×C42—41no—
301C2×C42—224no—
302C2×C42—224no—
303C2×C42—442no—
304#95—24no—
305#95—24no—
306#95—41no—
307#95—118no—
308#95—114no—
309#95—118no—
310#95—224no—
311#95—224no—
312#95—224no—
313#95—224no—
314#95—224no—
315#95—224no—
316#95—224no—
317#95—441no—
318#95—441no—
319C2×C11#232712yes—
320C2×C11#233211yescharacteristic
321C2×C11#235811yescharacteristic
322C2×C11#236212yes—
323C2×C11#238111yescharacteristic
324C2×C11#267412yes—
325C2×C11#268912yes—
326C2×C11#269012yes—
327C2×C11#276212yes—
328C24C23×D1111yescharacteristic
329C2×Q8—2216no—
330C2×Q8—444no—
331C2×Q8—444no—
332C2×Q8—448no—
333C2×Q8—444no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—114no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—114no—
362C22×C4—114no—
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×C4—222no—
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×C4C2×C4×D1112yes—
387C22×C4C2×C4×D1112yes—
388C22×C4C2×C4×D1112yes—
389C22×C4#433914yes—
390C22×C4D4×D1114yes—
391C4⋊C4—44no—
392C4⋊C4—2216no—
393C4⋊C4—448no—
394C42—44no—
395C42—448no—
396C11#1457411yescharacteristic, complemented, Sylow
397C23C22×C4×D1111yescharacteristic
398C23C2×#433912yes—
399C23C2×D4×D1112yes—
400C23#6703711yescharacteristic
401C23#6703711yescharacteristic
402C23#6704012yes—
403C23#41×D1112yes—
404C23#6704312yes—
405C23#6704312yes—
406Q8—4416no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—118no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C22C4×#433911yescharacteristic
465C22#1062301711yescharacteristic
466C22#1062303812yes—
467C22#1062304711yescharacteristic
468C22#1062306212yes—
469C22C4×D4×D1112yes—
470C22#1062308312yes—
471C22#1062309212yes—
472C22#1062309512yes—
473C22#1062309912yes—
474C22#1062310312yes—
475C22#1062312111yescharacteristic
476C22#1062314312yes—
477C22#1062315912yes—
478C22#1062317712yes—
479C22#1062317912yes—
480C22#1062319011yescharacteristic
481C22#1062320311yescharacteristic
482C22#1062322712yes—
483C22#1062323212yes—
484C22#1062326611yescharacteristic
485C4—42no—
486C4—44no—
487C4—44no—
488C4—42no—
489C4—42no—
490C4—228no—
491C4—444no—
492C4—444no—
493C4—882no—
494C2#1307133112yes—
495C2#1307137211yescharacteristic
496C2#1307159911yescharacteristic
497C2#1307164412yes—
498C2#1307179511yescharacteristic
499C2#1307490112yes—
500C2#1307506812yes—
501C2#1307508312yes—
502C2#1307601512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14574
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622592C4semidirect
396. C11#14574semidirect

Maximal subgroups

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

subgroupindex
C2×#106225922
C2×#106222592
C2×#106225462
#130668842
#130668762
#130668712
#130668472
#130668422
C11×#14362
#1457411