Finite Group Databasebeta

← #14737339

Subgroups — #14737339

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13079557C211yesmaximal, characteristic, complemented
3#13077563C211yesmaximal, characteristic, complemented
4#13068097C212yesmaximal, complemented
5#13068085C212yesmaximal, complemented
6#13067973C212yesmaximal, complemented
7#13067961C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067265C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3151C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×AGL(1,ℤ/8)—21no—
14C11×#532C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#496—22no—
18C11×#493C2212yes—
19C11×#492C2212yes—
20C4×C11×M16C2211yescharacteristic
21#10622831—22no—
22#10622735—21no—
23#10622732—21no—
24#10622707C2212yescomplemented
25#10622689—21no—
26#10622688C2212yes—
27#10622688C2212yes—
28#10622688C2212yescomplemented
29#10622683—21no—
30#10622654—22no—
31#10622632—21no—
32#10622621—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622314—22no—
37#10622292C2212yescomplemented
38C8×Dic22C2212yescomplemented
39#10622185C2211yescharacteristic, complemented
40#10622185C2211yescharacteristic, complemented
41#10622182C2212yes—
42#10622182C2212yes—
43#10622182C2211yescharacteristic, complemented
44#10622182C2211yescharacteristic, complemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C11×AGL(1,ℤ/8)—44no—
52C11×AGL(1,ℤ/8)—44no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C2×C11×M16D411yescharacteristic
58C2×C11×M16D411yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#127—21no—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127C2312yes—
64C11×#127C2311yescharacteristic
65C11×#124—21no—
66C11×#121—21no—
67C11×#121—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4324—22no—
72C2×#4324—22no—
73C2×#4324—22no—
74#66979—21no—
75#66977—21no—
76#66977D412yes—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66923—21no—
80#66922D411yescharacteristic
81#66922D411yescharacteristic
82C4×Dic22—21no—
83C4×Dic22C2312yes—
84C11×#97D412yes—
85C4×C8×C11C2312yes—
86#66896—22no—
87#66896—22no—
88#66896—22no—
89C22⋊(C11⋊C8)—21no—
90#66879—22no—
91Dic11⋊C8—22no—
92Dic11⋊C8—22no—
93C8×Dic11—22no—
94#66874—22no—
95#66872—22no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4×C11⋊C8—21no—
104#19238—111nomaximal, Sylow
105C24×C11—41no—
106C11×#41—42no—
107C11×#41—42no—
108C2×Q8×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—81no—
122C2×D4×C11—81no—
123C2×D4×C11—82no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C2×Dic22—21no—
129C2×Dic22C2×D412yes—
130C11×SD16—44no—
131C11×SD16—44no—
132C11×D8—44no—
133C11×D8—44no—
134C11×M16—22no—
135C11×M16SD1614yescomplemented
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—22no—
147#4324—82no—
148#4324—82no—
149#4324—82no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11C2×D412yes—
154Dic11⋊C4—22no—
155Dic11⋊C4—22no—
156C4×Dic11—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—42no—
163C2×C11⋊C8—81no—
164#3246—111no—
165#3208—111no—
166#3151D1111yescharacteristic
167#2962—111no—
168#1688—112no—
169#1686—112no—
170#1668—112no—
171#1666—112no—
172#1565—111no—
173#1540—111no—
174C2×#331—111no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—82no—
178C23×C11—82no—
179C23×C11—82no—
180C23×C11#12111yescharacteristic
181Q8×C11—41no—
182Q8×C11—41no—
183D4×C11—41no—
184D4×C11—42no—
185D4×C11—41no—
186D4×C11—42no—
187D4×C11—41no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—41no—
191D4×C11—81no—
192D4×C11—82no—
193D4×C11—82no—
194D4×C11—82no—
195D4×C11—82no—
196D4×C11—82no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—82no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11AGL(1,ℤ/8)12yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212Dic22—22no—
213Dic22—22no—
214Dic22—81no—
215C8×C11—22no—
216C8×C11C2×SD1614yes—
217C11⋊C8—41no—
218C11⋊C8—41no—
219C11⋊C8—42no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C2×AGL(1,ℤ/8)—21no—
223C2×AGL(1,ℤ/8)—21no—
224#533—111no—
225#532C2×D1111yescharacteristic
226C2×#127C2×D1111yescharacteristic
227#496—22no—
228#493C2×D1112yes—
229#492—221no—
230#492C2×D1112yes—
231#486—221no—
232#476—221no—
233#475—112no—
234#465—222no—
235#461—221no—
236#460—112no—
237#460—112no—
238#460—112no—
239#450—222no—
240#446—112no—
241#446—222no—
242C8×Q8—112no—
243#431—111no—
244#424—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—111no—
247#405—221no—
248C4×M16C2×D1111yescharacteristic
249#335—112no—
250#334—112no—
251#332—111no—
252#332—111no—
253#331—112no—
254#331—112no—
255#331—111no—
256#331—111no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—81no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—81no—
263C22×C11—82no—
264C22×C11—81no—
265C22×C11—164no—
266C22×C11#46012yes—
267C22×C11C2×#12111yescharacteristic
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—81no—
272C4×C11#46012yes—
273C4×C11C22×SD1611yescharacteristic
274C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C4×C11#57611yescharacteristic
276C4×C11#57711yescharacteristic
277Dic11—42no—
278Dic11—42no—
279C2×#41—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283AGL(1,ℤ/8)—44no—
284AGL(1,ℤ/8)—44no—
285C2×SD16—22no—
286C2×SD16—22no—
287C2×SD16—222no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—22no—
291C2×D8—22no—
292C2×M16C22⋊D1111yescharacteristic
293C2×M16C22⋊D1111yescharacteristic
294C22×C8—221no—
295C22×C8—221no—
296C4⋊Q8—111no—
297C4⋊Q8—111no—
298C4⋊Q8C22×D1111yescharacteristic
299#127—21no—
300#127—21no—
301#127—21no—
302#127C22×D1112yes—
303#127C22×D1111yescharacteristic
304#125—221no—
305#124—21no—
306C22⋊Q8—112no—
307C22⋊Q8—221no—
308#121—21no—
309#121—21no—
310C4×Q8—112no—
311C4×Q8—221no—
312C4×D4—21no—
313C4×D4—21no—
314#117—221no—
315C2×C42C22×D1111yescharacteristic
316#106—222no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—112no—
320C4⋊C8—111no—
321C4⋊C8—111no—
322C4⋊C8—222no—
323C4⋊C8—222no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326#103—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330C22⋊C8—221no—
331#97—222no—
332#97C22⋊D1112yes—
333C4×C8—222no—
334C4×C8—221no—
335C4×C8C22×D1112yes—
336C2×C11—22no—
337C2×C11—161no—
338C2×C11—162no—
339C2×C11C2×#46011yescharacteristic
340C2×C11#306211yescharacteristic
341C2×C11#306811yescharacteristic
342C24—41no—
343#41—42no—
344#41—42no—
345C2×Q8—21no—
346C2×Q8—112no—
347C2×Q8—221no—
348C2×D4—21no—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—22no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—81no—
361C2×D4—81no—
362C2×D4—82no—
363C22×C4—41no—
364C22×C4D4×D1111yescharacteristic
365C22×C4#434111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367SD16—44no—
368SD16—44no—
369SD16—882no—
370SD16—882no—
371SD16—882no—
372D8—44no—
373D8—44no—
374M16—22no—
375M16#432414yescomplemented
376C2×C8—221no—
377C2×C8—221no—
378C2×C8—222no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—442no—
382C2×C8—881no—
383C2×C8C2×C22⋊D1112yes—
384C2×C8C2×C22⋊D1112yes—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—112no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—222no—
396C42—222no—
397C42D4×D1111yescharacteristic
398C42#434111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1923811yescharacteristic, complemented, Sylow
402C23—41no—
403C23—42no—
404C23—82no—
405C23—82no—
406C23—82no—
407C23#6699111yescharacteristic
408Q8—41no—
409Q8—41no—
410Q8—222no—
411Q8—222no—
412Q8—881no—
413D4—41no—
414D4—42no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—42no—
419D4—41no—
420D4—42no—
421D4—81no—
422D4—82no—
423D4—82no—
424D4—82no—
425D4—82no—
426D4—82no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4#6698512yes—
435C2×C4C2×#432412yes—
436C2×C4#6699111yescharacteristic
437C2×C4#6699111yescharacteristic
438C2×C4#6699111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—22no—
443C8—442no—
444C8—441no—
445C8—441no—
446C8—441no—
447C8—441no—
448C8C2×#432414yes—
449C22—21no—
450C22—21no—
451C22—82no—
452C22—81no—
453C22—81no—
454C22—82no—
455C22—82no—
456C22—81no—
457C22—164no—
458C22#1062268812yes—
459C22C2×#6699111yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—81no—
464C4—442no—
465C4—442no—
466C4#1062268812yes—
467C4#1062330511yescharacteristic
468C4#1062330611yescharacteristic
469C4C2×#6698511yescharacteristic
470C4C22×#432411yescharacteristic
471C2—22no—
472C2—162no—
473C2—161no—
474C2C2×#1062268811yescharacteristic
475C2#1307829011yescharacteristic
476C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3151C2
socleC22×C11C2×#121
hypercenter#3151D11
hypocenterC11#19238
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13079557C2semidirect
3. #13077563C2semidirect
4. #13068097C2semidirect
5. #13068085C2semidirect
6. #13067973C2semidirect
7. #13067961C2semidirect
8. #13067368C2semidirect
9. #13067265C2semidirect
10. C2×#10622182C2semidirect
24. #10622707C22semidirect
28. #10622688C22semidirect
37. #10622292C22semidirect
38. C8×Dic22C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
43. #10622182C22semidirect
44. #10622182C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
135. C11×M16SD16semidirect
375. M16#4324semidirect
401. C11#19238semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795572
#130775632
#130680972
#130680852
#130679732
#130679612
#130673682
#130672652
C2×#106221822
C11×#31512
#1923811