Finite Group Databasebeta

← #14644678

Subgroups — #14644678

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66983C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C11×#1434C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×C4×C22⋊D11—21no—
9C2×C4×D44C411yescharacteristic, complemented
10C2×C11×#95—21no—
11C2×C11×#95—21no—
12C2×C11×#95C2212yes—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622553—21no—
17#10622552C411yescharacteristic, complemented
18C4×(C2×D11)⋊C4—21no—
19C4×C4⋊Dic11C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×C4×C11⋊C8—21no—
22#10622162—21no—
23#10622089C418yescomplemented
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C2×C42×C11—42no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37#66983—22no—
38#66983C2×C414yes—
39C4×C22⋊D11—42no—
40C4×C22⋊D11—42no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C22×C11⋊C8—22no—
51C4×D44—42no—
52C11×#95—22no—
53C11×#95—42no—
54C11×#95—42no—
55C11×#95C2×C414yescomplemented
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)C2×C414yescomplemented
61C4×C11⋊C8—42no—
62#8220—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—24no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11D812yes—
84C22×C4×C11SD1612yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4112yes—
89C2×C22⋊D11—24no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—42no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C2×D44—21no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44C4212yes—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—41no—
106C42×C11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109(C2×D11)⋊C4—24no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11C4212yes—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122C4×#121—111no—
123C4×C22⋊C8—111no—
124C2×#327—112no—
125#1434D1111yescharacteristic, complemented
126#1294—112no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11C4×D412yes—
133C23×C11C2×D811yescharacteristic
134C23×C11C2×SD1611yescharacteristic
135C23×C11#13512yes—
136C22×D11—22no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#9912yes—
169C2×C4×C11#10212yes—
170C2×C4×C11#10212yes—
171C2×C4×C11C2×C4211yescharacteristic
172C2×C4×C11#11711yescharacteristic
173C2×C4×C11C4×D412yes—
174C22⋊D11—44no—
175C22⋊D11—44no—
176C2×Dic11—22no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185D44—42no—
186D44—42no—
187C4×D11—84no—
188C11⋊C8—44no—
189C2×#121—111no—
190C2×C4×D4—111no—
191C2×C4×D4—221no—
192C22×C42C2×D1111yescharacteristic
193C2×C22⋊C8—112no—
194C2×C4×C8—221no—
195#390—111no—
196#389—111no—
197#388—221no—
198#386—221no—
199#380—111no—
200C4×C4⋊C4—111no—
201C4×C22⋊C4—221no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95C2×D1112yes—
205#336—221no—
206#327—118no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11C4×C22⋊C411yescharacteristic
216C22×C11C2×#9911yescharacteristic
217C22×C11#41011yescharacteristic
218C22×C11C2×#10211yescharacteristic
219C22×C11#41611yescharacteristic
220C22×C11#42111yescharacteristic
221C22×C11#42111yescharacteristic
222C22×C11C4×D812yes—
223C22×C11C4×SD1612yes—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—41no—
238C4×C11—84no—
239Dic11—42no—
240Dic11—81no—
241Dic11—81no—
242C22×D4—111no—
243C22×D4—221no—
244C23×C4—22no—
245C23×C4—221no—
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22×D1111yescharacteristic
249C22×C8—222no—
250#121—114no—
251#121—222no—
252C4×D4—442no—
253C4×D4—442no—
254C4×D4—442no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C42—42no—
265C2×C42—221no—
266C2×C42C4×D1111yescharacteristic
267C2×C42C4×D1111yescharacteristic
268C2×C42D4411yescharacteristic
269C2×C42D4411yescharacteristic
270C22⋊C8—114no—
271C22⋊C8—222no—
272C4×C8—442no—
273#95—22no—
274#95—42no—
275#95—42no—
276#95—221no—
277#95—221no—
278#95—221no—
279#95C4×D1114yescomplemented
280C2×C11—22no—
281C2×C11—22no—
282C2×C11#151611yescharacteristic
283C2×C11#151711yescharacteristic
284C2×C11#151911yescharacteristic
285C2×C11#152111yescharacteristic
286C2×C11C4×#9911yescharacteristic
287C2×C11#175911yescharacteristic
288C2×C11C4×#10211yescharacteristic
289D11—82no—
290C24—221no—
291C24C2×C22⋊D1111yescharacteristic
292C2×D4—112no—
293C2×D4—224no—
294C2×D4—221no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—442no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4(C2×D11)⋊C411yescharacteristic
321C22×C4(C2×D11)⋊C411yescharacteristic
322C22×C4(C2×D11)⋊C411yescharacteristic
323C22×C4(C2×D11)⋊C411yescharacteristic
324C22×C4#432312yes—
325C22×C4#432512yes—
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4C2×C4×D1112yes—
328C22×C4C2×D4411yescharacteristic
329C22×C4#433912yes—
330C2×C8—224no—
331C2×C8—442no—
332C2×C8—442no—
333C4⋊C4—112no—
334C4⋊C4—221no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C4⋊C4—442no—
338C22⋊C4—224no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C42—22no—
345C42—22no—
346C42—41no—
347C42—41no—
348C42—442no—
349C11#822011yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—222no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23C2×(C2×D11)⋊C411yescharacteristic
362C23C4×C22⋊D1112yes—
363C23C2×#432311yescharacteristic
364C23C2×#432511yescharacteristic
365C23#6700312yes—
366D4—442no—
367D4—442no—
368D4—444no—
369D4—444no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—222no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—884no—
405C2×C4#6687012yes—
406C2×C4#6687312yes—
407C2×C4#6687312yes—
408C2×C4C42×D1111yescharacteristic
409C2×C4#6692511yescharacteristic
410C2×C4C4×D4412yes—
411C8—444no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—442no—
421C22—442no—
422C22—442no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22C4×(C2×D11)⋊C411yescharacteristic
428C22C2×#6687011yescharacteristic
429C22C2×#6687311yescharacteristic
430C22#1062261511yescharacteristic
431C22#1062261811yescharacteristic
432C22#1062261811yescharacteristic
433C22#1062261911yescharacteristic
434C22C4×#432312yes—
435C22C4×#432512yes—
436C4—22no—
437C4—21no—
438C4—21no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—84no—
444C4—442no—
445C4—881no—
446C4—881no—
447C2—22no—
448C2—22no—
449C2—882no—
450C2#1306717011yescharacteristic
451C2#1306717511yescharacteristic
452C2#1306718311yescharacteristic
453C2#1306719111yescharacteristic
454C2C4×#6687011yescharacteristic
455C2#1306842711yescharacteristic
456C2C4×#6687311yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8220
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C11⋊C8)C2semidirect
4. #13066495C2semidirect
5. C11×#1434C2semidirect
9. C2×C4×D44C4semidirect
17. #10622552C4semidirect
19. C4×C4⋊Dic11C4semidirect
20. #10622541C4semidirect
23. #10622089C4semidirect
55. C11×#95C2×C4semidirect
60. C22⋊(C11⋊C8)C2×C4semidirect
125. #1434D11semidirect
279. #95C4×D11semidirect
349. C11#8220semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
C4×C22⋊(C11⋊C8)2
C2×#106220892
#130664952
C11×#14342
#822011