Finite Group Databasebeta

← #14737778

Subgroups — #14737778

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13068163C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068115C212yesmaximal, complemented
7#13068081C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66985—21no—
15#10623008C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#436—21no—
18C11×#436—21no—
19C11×#436C2212yes—
20C11×#436C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622828—21no—
25#10622727—21no—
26#10622727—21no—
27#10622632C2212yes—
28#10622629—22no—
29#10622628C2212yes—
30#10622622—22no—
31#10622621C2212yes—
32#10622620C2212yes—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622307C2211yescharacteristic, complemented
38#10622306C2211yescharacteristic, complemented
39C4×#4314—21no—
40C4×#4314—21no—
41#10622294C2211yescharacteristic, complemented
42#10622293C2211yescharacteristic, complemented
43#10622124C2212yescomplemented
44#10622123C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622096C2212yescomplemented
48#10622096C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—44no—
55C22×C8×C11—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4324—22no—
66#66985—44no—
67C2×#4323—22no—
68#66983—21no—
69#66983—21no—
70#66979—21no—
71#66977—21no—
72#66977—21no—
73C2×#4318—21no—
74C2×#4318—21no—
75C2×#4314—21no—
76C2×#4314—21no—
77#66928—21no—
78#66927C2311yescharacteristic
79C4×D44—21no—
80C4×D44—21no—
81#66923—21no—
82#66922C2311yescharacteristic
83#66922C2311yescharacteristic
84#66922C2311yescharacteristic
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×C22⋊C8—22no—
90C11×C22⋊C8—22no—
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94C4×C8×C11C2311yescharacteristic
95#66896—22no—
96#66896—22no—
97#66885—21no—
98#66885—21no—
99#66881—21no—
100#66881—21no—
101#66880—21no—
102#66880—21no—
103#66874—22no—
104#66873—22no—
105#66872—22no—
106#66871—22no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)C2312yes—
110C4⋊(C11⋊C8)C2312yes—
111#19279—111nomaximal, Sylow
112C24×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—41no—
126#4339—42no—
127#4339—42no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C11×M16—44no—
136C11×M16—44no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—41no—
140C2×C8×C11—42no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153C22⋊Dic11—41no—
154#4324—44no—
155#4323—44no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166C4×Dic11—41no—
167#4318—42no—
168#4318—42no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171#4314—42no—
172#4314—42no—
173#3167—111no—
174#3077—111no—
175#3036—111no—
176C2×#436D1111yescharacteristic, complemented
177#1699—112no—
178#1697—112no—
179#1691—112no—
180#1685—112no—
181#1567—111no—
182#1550—111no—
183#1547—111no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11#12111yescharacteristic
189C22×D11—41no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—42no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—44no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C22⋊D11—82no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213D44—41no—
214D44—41no—
215D44—41no—
216D44—41no—
217D44—81no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221Dic22—41no—
222Dic22—41no—
223Dic22—81no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—21no—
227C8×C11—42no—
228C8×C11AGL(1,ℤ/8)12yescomplemented
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×AGL(1,ℤ/8)—221no—
232C22×M16—21no—
233#533—111no—
234#532—111no—
235C2×C4×D4C2×D1111yescharacteristic
236#498—111no—
237#492—111no—
238#487—111no—
239#486—111no—
240#478—222no—
241#476—112no—
242#474—112no—
243#465—221no—
244#465—221no—
245#463—222no—
246#461—112no—
247#459—112no—
248C4×SD16—221no—
249C4×SD16—221no—
250#436—21no—
251#436—21no—
252#436C2×D1112yes—
253#436C2×D1112yes—
254#428—221no—
255#423—111no—
256#423—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258#418—221no—
259#417—221no—
260C2×C22⋊C8—21no—
261C2×C4×C8C2×D1111yescharacteristic
262#335—112no—
263#335—112no—
264#333—112no—
265#332—112no—
266#332—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—84no—
274C22×C11#46812yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11#46812yes—
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×#13711yescharacteristic
287C4×C11#57511yescharacteristic
288Dic11—81no—
289Dic11—81no—
290Dic11—81no—
291C2×#41—221no—
292C22×D4D4411yescharacteristic
293C23×C4—21no—
294AGL(1,ℤ/8)—444no—
295C2×SD16—222no—
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—222no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—44no—
302C2×M16—221no—
303C2×M16—221no—
304C22×C8—21no—
305C22×C8C22⋊D1111yescharacteristic
306C22×C8C22⋊D1111yescharacteristic
307C4⋊Q8—111no—
308C4⋊Q8—111no—
309C4⋊Q8—111no—
310#127—111no—
311#125—221no—
312#124—221no—
313C22⋊Q8—221no—
314C22⋊Q8—221no—
315#121—221no—
316#121—221no—
317C4×Q8—221no—
318C4×Q8—221no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4D4412yes—
324C4×D4C22×D1112yes—
325#117—221no—
326C2×C4⋊C4D4411yescharacteristic
327C2×C22⋊C4—21no—
328C2×C42C22×D1111yescharacteristic
329#107—222no—
330#106—221no—
331#106—221no—
332#106—222no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8C22×D1112yes—
339#103—221no—
340#103—221no—
341#103—222no—
342#102—222no—
343#102—222no—
344#102—221no—
345#102—221no—
346#102—222no—
347C22⋊C8—22no—
348C22⋊C8—22no—
349C4×C8C22⋊D1111yescharacteristic
350C4×C8C22⋊D1111yescharacteristic
351C4×C8C22×D1111yescharacteristic
352C4×C8C22×D1111yescharacteristic
353C2×C11—22no—
354C2×C11—82no—
355C2×C11#303611yescharacteristic
356C2×C11C2×#46811yescharacteristic
357C2×C11#306711yescharacteristic
358D11—161no—
359C24—21no—
360#41—442no—
361#41—442no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—441no—
372C2×D4C2×D4412yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—441no—
379C22×C4C2×D4411yescharacteristic
380C22×C4#433911yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382SD16—442no—
383SD16—444no—
384SD16—442no—
385D8—444no—
386M16—44no—
387M16—44no—
388M16—442no—
389M16—442no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—41no—
393C2×C8—42no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8C2×C22⋊D1111yescharacteristic
397C2×C8C2×C22⋊D1111yescharacteristic
398C2×C8C2×C22⋊D1111yescharacteristic
399C2×C8C2×C22⋊D1111yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4C2×D4412yes—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—441no—
416C42C2×D4411yescharacteristic
417C42#433911yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1927911yescharacteristic, complemented, Sylow
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—441no—
426C23#6698311yescharacteristic
427Q8—441no—
428Q8—441no—
429Q8—441no—
430Q8—441no—
431Q8—881no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—441no—
436D4—441no—
437D4—441no—
438D4—441no—
439D4—881no—
440D4—882no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—882no—
453C2×C4#6696112yes—
454C2×C4#6696212yes—
455C2×C4#6698311yescharacteristic
456C2×C4#6698311yescharacteristic
457C2×C4#6698311yescharacteristic
458C2×C4C22×D4411yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—21no—
462C8—21no—
463C8—21no—
464C8—42no—
465C8—442no—
466C8—442no—
467C8#6698512yescomplemented
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22#1062274712yes—
478C22C2×#6698311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—881no—
484C4—881no—
485C4—881no—
486C4#1062274712yes—
487C4C2×#6696111yescharacteristic
488C4C2×#6696211yescharacteristic
489C4C2×#6698511yescharacteristic
490C4#1062335311yescharacteristic
491C2—22no—
492C2—82no—
493C2—1761no—
494C2#1307808011yescharacteristic
495C2C2×#1062274711yescharacteristic
496C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#436C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenterC2×#436D11
hypocenterC11#19279
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. #13079175C2semidirect
2. #13078413C2semidirect
4. #13068163C2semidirect
5. #13068149C2semidirect
6. #13068115C2semidirect
7. #13068081C2semidirect
8. #13067375C2semidirect
9. #13067304C2semidirect
10. #13067291C2semidirect
11. C2×C11×#436C2semidirect
37. #10622307C22semidirect
38. #10622306C22semidirect
41. #10622294C22semidirect
42. #10622293C22semidirect
43. #10622124C22semidirect
44. #10622123C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622096C22semidirect
48. #10622096C22semidirect
176. C2×#436D11semidirect
228. C8×C11AGL(1,ℤ/8)semidirect
420. C11#19279semidirect
467. C8#66985semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130784132
#130780802
#130681632
#130681492
#130681152
#130680812
#130673752
#130673042
#130672912
C2×C11×#4362
#1927911