Finite Group Databasebeta

← #14684594

Subgroups — #14684594

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622599C211yesmaximal, characteristic
2#13066880C212yesmaximal
3#13066879C212yesmaximal
4#13066876C212yesmaximal
5#13066871C212yesmaximal
6#13066868C212yesmaximal
7#13066845C211yesmaximal, characteristic
8#13066841C212yesmaximal
9C11×#1441C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C2×C11×#95C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622599C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—41no—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4—42no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4C2×C414yes—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11—41no—
49C2×C4⋊Dic11—41no—
50C2×C4⋊Dic11—41no—
51C2×C4⋊Dic11C2×C414yes—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4—42no—
57C2×Dic11⋊C4—42no—
58C2×C4×Dic11—41no—
59C2×C4×Dic11—41no—
60C2×C4×Dic11Q814yes—
61C11×#95—24no—
62C11×#95—42no—
63C11×#95—41no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95C2×C414yes—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C418yes—
75#14639—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
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×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×Q812yes—
107C22×C4×C11#4112yes—
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×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11C22×C414yes—
134C22×Dic11C22×C414yes—
135C22×Dic11C2×Q814yes—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—44no—
138C4⋊Dic11—44no—
139C4⋊Dic11—44no—
140Dic11⋊C4—48no—
141Dic11⋊C4—48no—
142C4×Dic11—44no—
143C2×#400—111no—
144#1444—112no—
145#1444—112no—
146#1443—112no—
147#1442—112no—
148#1441—112no—
149#1441D1111yescharacteristic
150C4⋊#95—111no—
151#1434—112no—
152C23×C11C23×C411yescharacteristic
153C23×C11C22×Q811yescharacteristic
154C23×C11C2×#4111yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)12yes—
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)12yes—
160C23×C112−1+412yes—
161C23×C112−1+411yescharacteristic
162C23×C112−1+412yes—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
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—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
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—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C4×Q814yes—
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—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—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—111no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4—112no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C42—111no—
229#400—118no—
230C2×#95—112no—
231C2×#95—111no—
232C2×#95—112no—
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×#95C2×D1112yes—
242C2×#95C2×D1112yes—
243C2×#95C2×D1111yescharacteristic
244C22×C11C2×C4×Q811yescharacteristic
245C22×C11#51811yescharacteristic
246C22×C11#52011yescharacteristic
247C22×C11#52012yes—
248C22×C11#52012yes—
249C22×C11#53811yescharacteristic
250C22×C11#53911yescharacteristic
251C22×C11#54012yes—
252C22×C11#54112yes—
253C22×C11#54311yescharacteristic
254C22×C11#54412yes—
255C22×C11#54411yescharacteristic
256C22×C11#54412yes—
257C22×C11#56011yescharacteristic
258C22×C11#56012yes—
259C22×C11H(3,𝔽4)11yescharacteristic
260C22×C11#56212yes—
261C22×C11#56212yes—
262C22×C11#56312yes—
263C22×C11#56311yescharacteristic
264C22×C11#56312yes—
265C22×C11#56311yescharacteristic
266C22×C11#56312yes—
267C4×C11—24no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11—82no—
272Dic11—44no—
273Dic11—44no—
274Dic11—44no—
275Dic11—82no—
276C23×C4—112no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4C22×D1112yes—
281C23×C4C22×D1112yes—
282C23×C4C22×D1111yescharacteristic
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—114no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4—442no—
295C2×C4⋊C4—442no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4—441no—
298C2×C4⋊C4—441no—
299C2×C4⋊C4—441no—
300C2×C4⋊C4—441no—
301C2×C4⋊C4C4×D1114yes—
302C2×C42—114no—
303C2×C42—441no—
304C2×C42—441no—
305#95—24no—
306#95—42no—
307#95—41no—
308#95—114no—
309#95—118no—
310#95—118no—
311#95—442no—
312#95—442no—
313#95—442no—
314#95—442no—
315#95—442no—
316#95—442no—
317#95—442no—
318#95—442no—
319C2×C11#232911yescharacteristic
320C2×C11#233012yes—
321C2×C11#237611yescharacteristic
322C2×C11#237911yescharacteristic
323C2×C11#238312yes—
324C2×C11#282811yescharacteristic
325C2×C11#283311yescharacteristic
326C2×C11#283612yes—
327C2×C11#284112yes—
328C2×C11#284311yescharacteristic
329C2×C11#284411yescharacteristic
330C24C23×D1111yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
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—114no—
358C22×C4—114no—
359C22×C4—114no—
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×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×C4C2×C4×D1112yes—
386C22×C4C2×C4×D1112yes—
387C22×C4C2×C4×D1112yes—
388C22×C4#434112yes—
389C22×C4Q8×D1112yes—
390C4⋊C4—44no—
391C4⋊C4—44no—
392C4⋊C4—444no—
393C4⋊C4—444no—
394C4⋊C4—448no—
395C4⋊C4—448no—
396C42—444no—
397C11#1463911yescharacteristic, complemented, Sylow
398C23C22×C4×D1111yescharacteristic
399C23C2×#434111yescharacteristic
400C23#6703712yes—
401C23#6703711yescharacteristic
402C23#6703711yescharacteristic
403C23C2×Q8×D1111yescharacteristic
404C23#6704012yes—
405C23#6704212yes—
406C23#6704211yescharacteristic
407C23#6704311yescharacteristic
408C23#6704312yes—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
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—442no—
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—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4#6694014yes—
468C22#1062301711yescharacteristic
469C22C2×#6694011yescharacteristic
470C22#1062305411yescharacteristic
471C22#1062307712yes—
472C22#1062310512yes—
473C22#1062312611yescharacteristic
474C22#1062313311yescharacteristic
475C22#1062314811yescharacteristic
476C22#1062315012yes—
477C22#1062315212yes—
478C22#1062315411yescharacteristic
479C22#1062315612yes—
480C22#1062316511yescharacteristic
481C22#1062317712yes—
482C22#1062317812yes—
483C22#1062318211yescharacteristic
484C22#1062319712yes—
485C22#1062321411yescharacteristic
486C22#1062322012yes—
487C22#1062323012yes—
488C22#1062324312yes—
489C22#1062326012yes—
490C22#1062326611yescharacteristic
491C4—24no—
492C4—42no—
493C4—42no—
494C4—82no—
495C4—82no—
496C4—444no—
497C4—444no—
498C4—444no—
499C4—882no—
500C2#1307134611yescharacteristic
501C2#1307135612yes—
502C2#1307175911yescharacteristic
503C2#1307178811yescharacteristic
504C2#1307180612yes—
505C2#1307673911yescharacteristic
506C2#1307679611yescharacteristic
507C2#1307681712yes—
508C2#1307687412yes—
509C2#1307688211yescharacteristic
510C2#1307688911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
31. #10622599C4semidirect
397. C11#14639semidirect

Maximal subgroups

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

subgroupindex
C2×#106225992
#130668802
#130668792
#130668762
#130668712
#130668682
#130668452
#130668412
C11×#14412
#1463911