Finite Group Databasebeta

← #14680958

Subgroups — #14680958

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×#10622568C212yesmaximal
3#13066865C211yesmaximal, characteristic, complemented
4#13066864C214yesmaximal, complemented
5#13066863C212yesmaximal, complemented
6(C2×D11)⋊#95C214yesmaximal, complemented
7C11×#1440C211yesmaximal, characteristic, complemented
8C25×D11C2211yescharacteristic
9C23×C4×D11C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C22⋊Dic11C2211yescharacteristic
13C22×C22⋊Dic11C2212yes—
14C22×(C2×D11)⋊C4C2214yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C2×C22⋊C4×D11—28no—
18C2×C22⋊C4×D11C418yescomplemented
19C2×C11×#95C2214yescomplemented
20C2×C11⋊#95C2214yescomplemented
21C2×C11⋊#95C2214yescomplemented
22C2×C11⋊#95C2214yescomplemented
23#10622568—28no—
24C25×C11C2311yescharacteristic
25C24×D11—28no—
26C24×D11—44no—
27C24×D11—44no—
28C24×D11C2×C414yes—
29C24×D11D418yes—
30C24×D11C2311yescharacteristic
31C24×D11C2311yescharacteristic
32C23×C4×C11C2314yes—
33C23×C4×C11C2312yes—
34C23×Dic11C2314yes—
35C23×Dic11C2312yes—
36C22×C4×D11—24no—
37C22×C4×D11—24no—
38C22×C4×D11—44no—
39C22×C4×D11—44no—
40C22×C4×D11C2×C418yes—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—44no—
44C2×C11×C22⋊C4C2×C414yes—
45C2×C22⋊Dic11—24no—
46C2×C22⋊Dic11—24no—
47C2×C22⋊Dic11—44no—
48C2×C22⋊Dic11C2×C414yes—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—28no—
52C2×(C2×D11)⋊C4—28no—
53C2×(C2×D11)⋊C4—28no—
54C2×(C2×D11)⋊C4—28no—
55C2×(C2×D11)⋊C4—44no—
56C2×(C2×D11)⋊C4—44no—
57C2×(C2×D11)⋊C4C2×C418yes—
58C22⋊C4×D11—232no—
59C11×#95—44no—
60C11⋊#95—44no—
61C11⋊#95—44no—
62C11⋊#95—44no—
63#14341—111nomaximal, Sylow
64C24×C11—24no—
65C24×C11—24no—
66C24×C11—24no—
67C24×C11C22×C412yes—
68C24×C11C2×D414yes—
69C24×C11C2411yescharacteristic
70C23×D11—24no—
71C23×D11—24no—
72C23×D11—24no—
73C23×D11—24no—
74C23×D11—24no—
75C23×D11—216no—
76C23×D11—232no—
77C23×D11—416no—
78C23×D11—416no—
79C23×D11—48no—
80C23×D11—48no—
81C23×D11—416no—
82C23×D11—416no—
83C23×D11—416no—
84C23×D11—416no—
85C23×D11C22⋊C4116yes—
86C23×D11C22×C412yes—
87C23×D11C22×C412yes—
88C23×D11C2×D414yes—
89C23×D11C2×D414yes—
90C23×D11#4118yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11C22×C414yes—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11—24no—
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11C22×C414yes—
115C2×C4×D11—216no—
116C2×C4×D11—416no—
117C2×C4×D11—48no—
118C2×C4×D11—416no—
119C2×C4×D11—48no—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—48no—
122C22⋊Dic11—28no—
123C22⋊Dic11—48no—
124(C2×D11)⋊C4—216no—
125(C2×D11)⋊C4—416no—
126(C2×D11)⋊C4—416no—
127C23×C22⋊C4—111no—
128C2×#379—112no—
129#1440—114no—
130#1440—112no—
131#1440—111no—
132#1440D1111yescharacteristic, complemented
133C22⋊#95—114no—
134C23×C11—24no—
135C23×C11—28no—
136C23×C11—28no—
137C23×C11—24no—
138C23×C11—24no—
139C23×C11—28no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—44no—
144C23×C11C2×C22⋊C414yes—
145C23×C11C23×C411yescharacteristic
146C23×C11C22×D412yes—
147C23×C11C2×#4114yes—
148C23×C11H(5,𝔽2)14yes—
149C23×C11H(5,𝔽2)14yes—
150C22×D11—28no—
151C22×D11—24no—
152C22×D11—28no—
153C22×D11—24no—
154C22×D11—28no—
155C22×D11—28no—
156C22×D11—28no—
157C22×D11—28no—
158C22×D11—24no—
159C22×D11—28no—
160C22×D11—28no—
161C22×D11—28no—
162C22×D11—24no—
163C22×D11—24no—
164C22×D11—232no—
165C22×D11—432no—
166C22×D11—464no—
167C22×D11—464no—
168C22×D11—464no—
169C22×D11—44no—
170C22×D11—44no—
171C22×D11—44no—
172C22×D11—44no—
173C22×D11C2×C22⋊C414yes—
174C22×D11C2×C22⋊C414yes—
175C22×D11#11718yes—
176C22×D11#123116yes—
177C2×C4×C11—24no—
178C2×C4×C11—28no—
179C2×C4×C11—42no—
180C2×C4×C11—44no—
181C2×C4×C11—42no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—44no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×Dic11—24no—
190C2×Dic11—28no—
191C2×Dic11—42no—
192C2×Dic11—44no—
193C2×Dic11—42no—
194C2×Dic11—44no—
195C2×Dic11—44no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—44no—
199C2×Dic11—44no—
200C2×Dic11—44no—
201C4×D11—432no—
202C26—111no—
203C24×C4—112no—
204C22×C22⋊C4—111no—
205C22×C22⋊C4—112no—
206C22×C22⋊C4—118no—
207C22×C22⋊C4—114no—
208C22×C22⋊C4—112no—
209C22×C22⋊C4—114no—
210C22×C22⋊C4—228no—
211C22×C22⋊C4C2×D1111yescharacteristic
212C22×C22⋊C4C2×D1112yes—
213#379—228no—
214C2×#95—114no—
215C2×#95—114no—
216C2×#95—114no—
217C2×#95C2×D1114yescomplemented
218C22×C11—28no—
219C22×C11—24no—
220C22×C11—48no—
221C22×C11—48no—
222C22×C11—48no—
223C22×C11C22×C22⋊C411yescharacteristic
224C22×C11C2×#11712yes—
225C22×C11#51814yes—
226C22×C11C2×#12314yes—
227C22×C11#53412yes—
228C22×C11#53414yes—
229C22×C11#53412yes—
230C22×C11#53814yes—
231C22×C11#53814yes—
232C22×C11#53814yes—
233C22×C11#53814yes—
234C2×D11—28no—
235C2×D11—216no—
236C2×D11—216no—
237C2×D11—216no—
238C2×D11—28no—
239C2×D11—24no—
240C2×D11—464no—
241C2×D11—48no—
242C2×D11—48no—
243C2×D11—48no—
244C2×D11#38118yes—
245C4×C11—44no—
246C4×C11—84no—
247Dic11—44no—
248Dic11—84no—
249C25—111no—
250C25—111no—
251C25—114no—
252C25—118no—
253C25—228no—
254C25—444no—
255C25—444no—
256C25C22×D1111yescharacteristic
257C23×C4—112no—
258C23×C4—118no—
259C23×C4—114no—
260C23×C4—224no—
261C23×C4—224no—
262C23×C4—444no—
263C23×C4—444no—
264C23×C4C22×D1114yes—
265C23×C4C22×D1112yes—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C22⋊C4—44no—
269C2×C22⋊C4—114no—
270C2×C22⋊C4—118no—
271C2×C22⋊C4—2232no—
272C2×C22⋊C4—224no—
273C2×C22⋊C4—224no—
274C2×C22⋊C4—224no—
275C2×C22⋊C4—228no—
276C2×C22⋊C4—228no—
277C2×C22⋊C4—228no—
278C2×C22⋊C4—228no—
279C2×C22⋊C4—224no—
280C2×C22⋊C4—444no—
281C2×C22⋊C4—444no—
282C2×C22⋊C4—444no—
283C2×C22⋊C4C4×D1114yes—
284#95—44no—
285#95—444no—
286#95—444no—
287#95—444no—
288C2×C11—44no—
289C2×C11C2×#38111yescharacteristic
290C2×C11#230812yes—
291C2×C11#231214yes—
292C2×C11#262214yes—
293C2×C11#262214yes—
294D11—28no—
295D11—44no—
296C24—24no—
297C24—24no—
298C24—24no—
299C24—112no—
300C24—114no—
301C24—118no—
302C24—112no—
303C24—114no—
304C24—1116no—
305C24—2216no—
306C24—2232no—
307C24—224no—
308C24—224no—
309C24—224no—
310C24—224no—
311C24—224no—
312C24—4416no—
313C24—448no—
314C24—4416no—
315C24—448no—
316C24—4416no—
317C24—4416no—
318C24—4416no—
319C24—4416no—
320C24C2×C4×D1112yes—
321C24D4×D1114yes—
322C24C23×D1111yescharacteristic
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—114no—
335C22×C4—2216no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—224no—
339C22×C4—224no—
340C22×C4—224no—
341C22×C4—224no—
342C22×C4—224no—
343C22×C4—224no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—224no—
347C22×C4—4416no—
348C22×C4—448no—
349C22×C4—4416no—
350C22×C4—448no—
351C22×C4C2×C4×D1114yes—
352C22⋊C4—28no—
353C22⋊C4—48no—
354C22⋊C4—2216no—
355C22⋊C4—228no—
356C22⋊C4—4416no—
357C22⋊C4—4416no—
358C22⋊C4—448no—
359C11#1434111yescharacteristic, complemented, Sylow
360C23—24no—
361C23—28no—
362C23—24no—
363C23—28no—
364C23—28no—
365C23—24no—
366C23—44no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—114no—
371C23—118no—
372C23—1116no—
373C23—114no—
374C23—2232no—
375C23—228no—
376C23—228no—
377C23—224no—
378C23—228no—
379C23—228no—
380C23—224no—
381C23—228no—
382C23—228no—
383C23—224no—
384C23—228no—
385C23—224no—
386C23—228no—
387C23—228no—
388C23—224no—
389C23—4432no—
390C23—4464no—
391C23—4464no—
392C23—4464no—
393C23—444no—
394C23—444no—
395C23—444no—
396C23—444no—
397C23C22⋊C4×D1114yes—
398C23C22×C4×D1111yescharacteristic
399C23C2×D4×D1112yes—
400C23#6703714yes—
401C23#41×D1114yes—
402C23#6704214yes—
403C2×C4—24no—
404C2×C4—28no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—224no—
416C2×C4—228no—
417C2×C4—4432no—
418C2×C4—442no—
419C2×C4—444no—
420C2×C4—442no—
421C2×C4—444no—
422C2×C4—444no—
423C2×C4—444no—
424C2×C4—444no—
425C2×C4—444no—
426C2×C4—444no—
427C2×C4—444no—
428C22—28no—
429C22—24no—
430C22—48no—
431C22—48no—
432C22—48no—
433C22—118no—
434C22—228no—
435C22—2216no—
436C22—2216no—
437C22—2216no—
438C22—228no—
439C22—224no—
440C22—4464no—
441C22—448no—
442C22—448no—
443C22—448no—
444C22C2×C22⋊C4×D1111yescharacteristic
445C22D11×#11712yes—
446C22#1062307614yes—
447C22#1062312012yes—
448C22#1062313614yes—
449C22#1062314414yes—
450C22D11×#12314yes—
451C22#1062318412yes—
452C22#1062318814yes—
453C22#1062320914yes—
454C22#1062323514yes—
455C4—44no—
456C4—84no—
457C4—444no—
458C4—884no—
459C2—44no—
460C2—228no—
461C2—444no—
462C2D11×#38111yescharacteristic
463C2#1307119012yes—
464C2#1307121014yes—
465C2#1307438814yes—
466C2#1307439014yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1440D11
hypocenterC11#14341
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. #13066865C2semidirect
4. #13066864C2semidirect
5. #13066863C2semidirect
6. (C2×D11)⋊#95C2semidirect
7. C11×#1440C2semidirect
18. C2×C22⋊C4×D11C4semidirect
19. C2×C11×#95C22semidirect
20. C2×C11⋊#95C22semidirect
21. C2×C11⋊#95C22semidirect
22. C2×C11⋊#95C22semidirect
132. #1440D11semidirect
217. C2×#95C2×D11semidirect
359. C11#14341semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×#106225682
#130668652
#130668642
#130668632
(C2×D11)⋊#952
C11×#14402
#1434111