Finite Group Databasebeta

← #14723402

Subgroups — #14723402

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077729C211yesmaximal, characteristic, complemented
2C4×#66985C211yesmaximal, characteristic
3#13067480C212yesmaximal, complemented
4#13067473C212yesmaximal, complemented
5#13067452C212yesmaximal, complemented
6#13067445C212yesmaximal, complemented
7#13067369C211yesmaximal, characteristic, complemented
8#13066996C211yesmaximal, characteristic, complemented
9C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10#13066906C211yesmaximal, characteristic, complemented
11C11×#2972C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66985C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C8×D4×C11—21no—
16C8×D4×C11—21no—
17C8×D4×C11C2212yes—
18C8×D4×C11C2212yes—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C2×C11×C22⋊C8—22no—
22#10622828C411yescharacteristic
23#10622631C412yes—
24C4×#4324C2212yes—
25#10622627C412yes—
26C4×#4323C2212yes—
27#10622579C411yescharacteristic
28#10622577C411yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622450—21no—
33#10622448—21no—
34#10622343—22no—
35#10622301C2212yescomplemented
36#10622292C2212yescomplemented
37D4⋊(C11⋊C8)C2212yes—
38D4⋊(C11⋊C8)C2212yes—
39#10622122C2211yescharacteristic, complemented
40#10622122C2211yescharacteristic, complemented
41#10622121C2211yescharacteristic, complemented
42#10622121C2211yescharacteristic, complemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45#10622093C2212yescomplemented
46#10622092C2212yescomplemented
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C2×#4339C2×C411yescharacteristic
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11C2×C412yes—
55C4×D4×C11C2312yes—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×#4324C2×C412yes—
60#66985—24no—
61C2×#4323C2×C412yes—
62C4×C22⋊D11—21no—
63C4×C22⋊D11—21no—
64#66979C2×C411yescharacteristic
65C2×#4318C2×C411yescharacteristic
66C2×#4318C2×C411yescharacteristic
67C22×C11⋊C8—21no—
68C22×C11⋊C8—21no—
69C2×#4313—22no—
70C4×D44C2×C411yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73C42×D11—21no—
74C4×Dic22C2×C411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×C4⋊C8D411yescharacteristic
77C11×C4⋊C8D411yescharacteristic
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2311yescharacteristic
80C11×C22⋊C8—21no—
81C11×C22⋊C8—22no—
82C11×C22⋊C8—22no—
83C11×C22⋊C8D412yes—
84C4×C8×C11—21no—
85C4×C8×C11C2312yes—
86#66896C2×C412yes—
87#66896C2×C412yes—
88(C2×D11)⋊C8—22no—
89#66879—22no—
90Dic11⋊C8—22no—
91#66874C2×C412yes—
92#66873C2×C412yes—
93#66872C2×C412yes—
94#66871C2×C412yes—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2312yes—
97#66867C2×C412yes—
98C4×C11⋊C8—21no—
99C4×C11⋊C8C2311yescharacteristic
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2312yes—
102#17873—111nomaximal, Sylow
103C24×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11M1614yescomplemented
107C2×D4×C11C22×C412yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—81no—
112C22×C4×C11—81no—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—21no—
117#4339—22no—
118#4339—22no—
119C2×D44C22×C411yescharacteristic
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×Dic22C22×C411yescharacteristic
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—82no—
127C2×C8×C11—82no—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C42×C11C22×C411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—21no—
139#4324—24no—
140#4323—24no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143C4⋊Dic11C22×C411yescharacteristic
144C4⋊Dic11C22×C411yescharacteristic
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150#4318—22no—
151#4318—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—42no—
156C2×C11⋊C8—81no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159#4313—82no—
160#2989—111no—
161#2972D1111yescharacteristic, complemented
162C4×AGL(1,ℤ/8)—111no—
163#1586—112no—
164#1585—112no—
165#1582—112no—
166#1581—112no—
167#1565—111no—
168#1476—111no—
169C2×D4⋊C8—111no—
170#1451—111no—
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—81no—
174C23×C11—81no—
175C23×C11C4×D411yescharacteristic
176C22×D11—21no—
177D4×C11—22no—
178D4×C11—24no—
179D4×C11C2×M1614yes—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—82no—
187C2×C4×C11—81no—
188C2×C4×C11C4×D411yescharacteristic
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11C2×M1612yes—
192C2×C4×C11#13112yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C22⋊D11—42no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200D44—21no—
201D44—21no—
202C4×D11—41no—
203C4×D11—41no—
204C4×D11—42no—
205C4×D11—81no—
206Dic22—21no—
207Dic22—21no—
208C8×C11—22no—
209C8×C11—22no—
210C8×C11—41no—
211C8×C11—41no—
212C11⋊C8—22no—
213C11⋊C8—22no—
214C11⋊C8—22no—
215C11⋊C8—41no—
216C11⋊C8—42no—
217C2×AGL(1,ℤ/8)—111no—
218C4×#41—111no—
219C2×C4×D4C2×D1111yescharacteristic
220#446—112no—
221#442—112no—
222#440—112no—
223C4×SD16—112no—
224C4×D8—112no—
225#436—112no—
226#435—222no—
227C8×D4—21no—
228C8×D4—21no—
229C8×D4C2×D1112yes—
230C8×D4C2×D1112yes—
231#432—221no—
232#431C2×D1111yescharacteristic
233#431C2×D1111yescharacteristic
234#428—111no—
235#423—221no—
236C2×C4⋊C8—111no—
237#418—111no—
238#417—111no—
239C2×C22⋊C8—22no—
240C4×M16—111no—
241C2×C4×C8—111no—
242#335—112no—
243#334—112no—
244Q8⋊C8—111no—
245Q8⋊C8—111no—
246D4⋊C8—112no—
247D4⋊C8—112no—
248D4⋊C8—111no—
249D4⋊C8—111no—
250#322—112no—
251#322—112no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—24no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—84no—
258C22×C11#43512yes—
259C22×C11C2×C4×D411yescharacteristic
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—42no—
267C4×C11#43512yes—
268C4×C11C22×M1611yescharacteristic
269C4×C11C2×#13111yescharacteristic
270C4×C11#57611yescharacteristic
271C4×C11#57711yescharacteristic
272Dic11—41no—
273Dic11—41no—
274Dic11—41no—
275C2×#41—111no—
276C22×D4C4×D1111yescharacteristic
277C23×C4—21no—
278AGL(1,ℤ/8)—224no—
279C2×SD16—112no—
280C2×D8—112no—
281C2×M16—111no—
282C2×M16—111no—
283C2×M16—222no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—221no—
287C22×C8—221no—
288C4×Q8—111no—
289C4×Q8—111no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—111no—
293C4×D4—111no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4C4×D1112yes—
297C4×D4C22×D1112yes—
298#117—111no—
299#117—221no—
300C2×C4⋊C4C4×D1111yescharacteristic
301C2×C22⋊C4—21no—
302C2×C42—221no—
303C2×C42C22×D1111yescharacteristic
304#107—112no—
305#106—112no—
306C4⋊C8—112no—
307C4⋊C8—222no—
308C4⋊C8—221no—
309C4⋊C8C22⋊D1111yescharacteristic
310C4⋊C8C22⋊D1111yescharacteristic
311C4⋊C8C22×D1111yescharacteristic
312C4⋊C8C22×D1111yescharacteristic
313#103—112no—
314#102—112no—
315#102—112no—
316#102—112no—
317C22⋊C8—21no—
318C22⋊C8—22no—
319C22⋊C8—22no—
320C22⋊C8—222no—
321C22⋊C8C22⋊D1112yes—
322#97—112no—
323#97—222no—
324C4×C8—21no—
325C4×C8—112no—
326C4×C8—111no—
327C4×C8—111no—
328C4×C8—221no—
329C4×C8C22×D1112yes—
330C2×C11—22no—
331C2×C11—44no—
332C2×C11C2×#43511yescharacteristic
333C2×C11#294611yescharacteristic
334C2×C11#295611yescharacteristic
335D11—81no—
336C24—21no—
337#41—222no—
338#41—222no—
339C2×Q8—111no—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4—111no—
343C2×D4—221no—
344C2×D4#431314yescomplemented
345C2×D4C2×C4×D1112yes—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—81no—
350C22×C4—81no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4#433911yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357SD16—224no—
358D8—224no—
359M16—222no—
360M16—222no—
361M16—882no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—82no—
365C2×C8—82no—
366C2×C8—112no—
367C2×C8—112no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—442no—
372C2×C8—881no—
373C2×C8C2×C22⋊D1112yes—
374C2×C8C2×C22⋊D1112yes—
375C4⋊C4—21no—
376C4⋊C4—111no—
377C4⋊C4—111no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4C2×C4×D1112yes—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C42—221no—
387C42—221no—
388C42—221no—
389C42C2×C4×D1111yescharacteristic
390C42#433911yescharacteristic
391C42C2×C22⋊D1111yescharacteristic
392C42C23×D1111yescharacteristic
393C11#1787311yescharacteristic, complemented, Sylow
394C23—22no—
395C23—24no—
396C23—81no—
397C23—81no—
398C23—221no—
399C23C4×C22⋊D1111yescharacteristic
400Q8—221no—
401Q8—221no—
402D4—24no—
403D4—22no—
404D4—221no—
405D4—221no—
406D4—442no—
407D4C2×#431314yes—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—881no—
423C2×C4C2×#431312yes—
424C2×C4#6695412yes—
425C2×C4C4×C22⋊D1111yescharacteristic
426C2×C4C4×C22⋊D1111yescharacteristic
427C2×C4C4×C22⋊D1111yescharacteristic
428C2×C4C22×C4×D1111yescharacteristic
429C2×C4C2×#433911yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C8—22no—
432C8—22no—
433C8—41no—
434C8—41no—
435C8—222no—
436C8—222no—
437C8—222no—
438C8—441no—
439C8—442no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—84no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22#1062272412yes—
450C22C2×C4×C22⋊D1111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—441no—
456C4—441no—
457C4—441no—
458C4#1062272412yes—
459C4C22×#431311yescharacteristic
460C4C2×#6695411yescharacteristic
461C4#1062336611yescharacteristic
462C4#1062336711yescharacteristic
463C2—22no—
464C2—44no—
465C2—881no—
466C2C2×#1062272411yescharacteristic
467C2#1307744811yescharacteristic
468C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×C4×D4
prime radicalC2×#66985C4
cosocleC42×C11C24
hypercenter#2972D11
hypocenterC11#17873
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13077729C2semidirect
3. #13067480C2semidirect
4. #13067473C2semidirect
5. #13067452C2semidirect
6. #13067445C2semidirect
7. #13067369C2semidirect
8. #13066996C2semidirect
9. C2×D4⋊(C11⋊C8)C2semidirect
10. #13066906C2semidirect
11. C11×#2972C2semidirect
35. #10622301C22semidirect
36. #10622292C22semidirect
39. #10622122C22semidirect
40. #10622122C22semidirect
41. #10622121C22semidirect
42. #10622121C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
45. #10622093C22semidirect
46. #10622092C22semidirect
106. C2×D4×C11M16semidirect
161. #2972D11semidirect
344. C2×D4#4313semidirect
393. C11#17873semidirect

Maximal subgroups

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

subgroupindex
#130777292
C4×#669852
#130674802
#130674732
#130674522
#130674452
#130673692
#130669962
C2×D4⋊(C11⋊C8)2
#130669062
C11×#29722
#1787311