Finite Group Databasebeta

← #14649508

Subgroups — #14649508

Order 2816.

1348 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
1#13076898C211yesmaximal, characteristic
2#13068526C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal, complemented
4#13066495C212yesmaximal, complemented
5C22×C11×#95C211yesmaximal, characteristic, complemented
6C24×C4×C11—21no—
7C24×C4×C11C2211yescharacteristic
8C2×#67006—21no—
9C2×#66983C412yescomplemented
10C2×#66983C2211yescharacteristic
11C2×C11×#95—21no—
12C2×C11×#95—24no—
13C2×C11×#95C2212yes—
14#10622826—21no—
15#10622826—22no—
16#10622825C412yescomplemented
17#10622825C2211yescharacteristic
18C2×C22⋊(C11⋊C8)—22no—
19C2×C22⋊(C11⋊C8)C2212yes—
20#10622089—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—24no—
23C23×C4×C11—28no—
24C23×C4×C11—22no—
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—44no—
28C23×C4×C11—44no—
29C23×C4×C11—42no—
30C23×C4×C11—42no—
31C23×C4×C11C2×C412yes—
32C23×C4×C11D412yes—
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C22×D44C2×C411yescharacteristic, complemented
38#67006—42no—
39#67006—42no—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—21no—
42#66983—22no—
43#66983—22no—
44#66983—44no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic, complemented
48C2×C4⋊Dic11C2×C412yescomplemented
49C22×C11⋊C8—22no—
50C11×#95—24no—
51C11×#95—22no—
52C11×#95D414yescomplemented
53C11⋊#95—22no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—44no—
58#9147—111nomaximal, Sylow
59C24×C11—24no—
60C24×C11—24no—
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—21no—
64C24×C11—21no—
65C24×C11C22⋊C412yes—
66C24×C11D812yes—
67C24×C11SD1612yes—
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C22×C4×C11—216no—
71C22×C4×C11—28no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—21no—
75C22×C4×C11—24no—
76C22×C4×C11—21no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—48no—
84C22×C4×C11—48no—
85C22×C4×C11—48no—
86C22×C4×C11—416no—
87C22×C4×C11—416no—
88C22×C4×C11—44no—
89C22×C4×C11—48no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C22⋊C412yes—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11#4112yes—
97C2×C22⋊D11—44no—
98C2×C22⋊D11—44no—
99C2×C22⋊D11—44no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C2×D44—22no—
109C2×D44—42no—
110C22⋊Dic11—44no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—22no—
116C4⋊Dic11—42no—
117C2×C11⋊C8—44no—
118C2×C11⋊C8—42no—
119#2847—111no—
120C22×#95D1111yescharacteristic, complemented
121#1779—111no—
122C2×#327—112no—
123#1294—112no—
124C23×C11—24no—
125C23×C11—24no—
126C23×C11—28no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—28no—
130C23×C11—28no—
131C23×C11—28no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—22no—
142C23×C11#9914yes—
143C23×C11#10214yes—
144C23×C11#10414yes—
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11C2×D811yescharacteristic
149C23×C11C2×SD1611yescharacteristic
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C23×C11#13711yescharacteristic
152C22×D11—41no—
153C22×D11—42no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—42no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—28no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—48no—
166C2×C4×C11—48no—
167C2×C4×C11—432no—
168C2×C4×C11—44no—
169C2×C4×C11—48no—
170C2×C4×C11—48no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—44no—
174C2×C4×C11C4×D412yes—
175C2×C4×C11#12112yes—
176C22⋊D11—88no—
177C22⋊D11—81no—
178C22⋊D11—81no—
179C22⋊D11—81no—
180C22⋊D11—81no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187D44—82no—
188C11⋊C8—82no—
189C24×C4—21no—
190C24×C4C2×D1111yescharacteristic
191C2×#121—111no—
192C2×#121—112no—
193C2×#120—221no—
194C2×C22⋊C8—112no—
195C2×C22⋊C8—222no—
196#386—222no—
197#386—221no—
198#380—111no—
199#380—112no—
200C2×#95—21no—
201C2×#95—24no—
202C2×#95C2×D1112yes—
203#327—224no—
204C22×C11—28no—
205C22×C11—28no—
206C22×C11—28no—
207C22×C11—28no—
208C22×C11—24no—
209C22×C11—21no—
210C22×C11—24no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—24no—
214C22×C11—21no—
215C22×C11—22no—
216C22×C11—24no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—24no—
220C22×C11—24no—
221C22×C11—22no—
222C22×C11#32718yescomplemented
223C22×C11#38611yescharacteristic
224C22×C11C2×#9912yes—
225C22×C11C2×#10211yescharacteristic
226C22×C11#41711yescharacteristic
227C22×C11C2×#10412yes—
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#48011yescharacteristic
231C22×C11#48111yescharacteristic
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—82no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—48no—
240C4×C11—42no—
241Dic11—81no—
242Dic11—82no—
243C25C22⋊D1111yescharacteristic
244C22×D4—111no—
245C22×D4—222no—
246C22×D4—221no—
247C23×C4—24no—
248C23×C4—28no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4C4×D1112yes—
257C23×C4D4412yes—
258C23×C4C22⋊D1111yescharacteristic
259C23×C4C22×D1111yescharacteristic
260C22×C8—222no—
261#121—222no—
262#121—222no—
263#121—444no—
264#120—442no—
265#120—442no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C22⋊C4—222no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—221no—
272C22⋊C8—222no—
273C22⋊C8—222no—
274C22⋊C8—444no—
275#95—24no—
276#95—22no—
277#95—222no—
278#95—221no—
279#95C22⋊D1114yescomplemented
280C2×C11—21no—
281C2×C11—28no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11C2×#32712yes—
286C2×C11#150412yes—
287C2×C11#187411yescharacteristic
288C2×C11#189611yescharacteristic
289C2×C11#189811yescharacteristic
290D11—161no—
291C24—24no—
292C24—24no—
293C24—21no—
294C24—21no—
295C24—21no—
296C24—21no—
297C24—221no—
298C24(C2×D11)⋊C412yes—
299C24#432312yes—
300C24#432512yes—
301C24C2×C22⋊D1111yescharacteristic
302C2×D4—222no—
303C2×D4—442no—
304C2×D4—444no—
305C2×D4—444no—
306C2×D4—444no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—441no—
313C22×C4—216no—
314C22×C4—28no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—48no—
327C22×C4—48no—
328C22×C4—48no—
329C22×C4—416no—
330C22×C4—44no—
331C22×C4—416no—
332C22×C4—48no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—222no—
336C22×C4—221no—
337C22×C4(C2×D11)⋊C412yes—
338C22×C4C2×C4×D1111yescharacteristic
339C22×C4C2×D4411yescharacteristic
340C22×C4#433912yes—
341C22×C4C2×C22⋊D1112yes—
342C2×C8—444no—
343C2×C8—442no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C22⋊C4—444no—
347C22⋊C4—444no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—442no—
351C11#914711yescharacteristic, complemented, Sylow
352C23—24no—
353C23—24no—
354C23—28no—
355C23—24no—
356C23—24no—
357C23—28no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—28no—
369C23—28no—
370C23—442no—
371C23—442no—
372C23—441no—
373C23—441no—
374C23—441no—
375C23#6686914yes—
376C23#6687014yes—
377C23#6687314yes—
378C23C2×(C2×D11)⋊C411yescharacteristic
379C23#6698211yescharacteristic
380C23C2×#432311yescharacteristic
381C23#6698511yescharacteristic
382C23C2×#432511yescharacteristic
383C23#6699511yescharacteristic
384C23#6700611yescharacteristic
385D4—882no—
386D4—881no—
387D4—881no—
388D4—881no—
389D4—881no—
390D4—888no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—28no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—48no—
400C2×C4—48no—
401C2×C4—432no—
402C2×C4—44no—
403C2×C4—48no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4C4×C22⋊D1112yes—
415C2×C4#6698312yes—
416C8—882no—
417C22—28no—
418C22—28no—
419C22—28no—
420C22—28no—
421C22—21no—
422C22—24no—
423C22—21no—
424C22—21no—
425C22—24no—
426C22—21no—
427C22—22no—
428C22—24no—
429C22—22no—
430C22—22no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—24no—
435C22—881no—
436C22—881no—
437C22—882no—
438C22—882no—
439C22—881no—
440C22#1062208918yescomplemented
441C22C2×#6686912yes—
442C22C2×#6687012yes—
443C22C2×#6687311yescharacteristic
444C22#1062257911yescharacteristic
445C22#1062258011yescharacteristic
446C22#1062258111yescharacteristic
447C22#1062282611yescharacteristic
448C22#1062283011yescharacteristic
449C22#1062284011yescharacteristic
450C4—22no—
451C4—22no—
452C4—48no—
453C4—42no—
454C4—882no—
455C4—881no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—28no—
461C2—1761no—
462C2C2×#1062208912yes—
463C2#1306711812yes—
464C2#1306893311yescharacteristic
465C2#1306905911yescharacteristic
466C2#1306906911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radical#13076898C2
cosocleC23×C4×C11C23
hypercenterC22×#95D11
hypocenterC11#9147
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. #13068526C2semidirect
3. C2×#10622089C2semidirect
4. #13066495C2semidirect
5. C22×C11×#95C2semidirect
9. C2×#66983C4semidirect
16. #10622825C4semidirect
37. C22×D44C2×C4semidirect
47. C2×C4⋊Dic11C2×C4semidirect
48. C2×C4⋊Dic11C2×C4semidirect
52. C11×#95D4semidirect
120. C22×#95D11semidirect
222. C22×C11#327semidirect
279. #95C22⋊D11semidirect
351. C11#9147semidirect
440. C22#10622089semidirect

Maximal subgroups

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

subgroupindex
#130768982
#130685262
C2×#106220892
#130664952
C22×C11×#952
#914711