Finite Group Databasebeta

← #14737257

Subgroups — #14737257

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic, complemented
3#13079068C211yesmaximal, characteristic, complemented
4#13068095C212yesmaximal, complemented
5#13068081C212yesmaximal, complemented
6#13067971C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067266C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#2935C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#532C2211yescharacteristic
14C2×#66961—21no—
15C2×#66961—21no—
16#10623008C2211yescharacteristic
17C2×#66927C2211yescharacteristic
18C11×#436C2212yescomplemented
19C11×#435—22no—
20C8×D4×C11C2212yescomplemented
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#408—21no—
23C4×C11×M16C2211yescharacteristic
24#10622701—21no—
25#10622700—21no—
26#10622686—21no—
27#10622685—21no—
28#10622651—22no—
29#10622649—22no—
30#10622628C2212yes—
31#10622628C2212yes—
32#10622628C2212yescomplemented
33#10622620C2212yescomplemented
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622325—22no—
37#10622308C2212yes—
38#10622306C2212yes—
39#10622123C2212yes—
40#10622123C2212yes—
41#10622123C2211yescharacteristic, complemented
42#10622123C2211yescharacteristic, complemented
43#10622120C2211yescharacteristic, complemented
44#10622120C2211yescharacteristic, complemented
45#10622096C2212yescomplemented
46#10622095C2212yescomplemented
47C2×C11×#41—21no—
48C2×#4339—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C11×#131—44no—
53C2×C11×M16—22no—
54C2×C11×M16D411yescharacteristic
55C2×C11×M16D411yescharacteristic
56C22×C8×C11—21no—
57C22×C8×C11—22no—
58C11×C4⋊Q8D411yescharacteristic
59C11×#127D411yescharacteristic
60C11×#124—21no—
61C11×#121—21no—
62C11×#121D412yes—
63C4×D4×C11—21no—
64C4×D4×C11C2312yes—
65C2×C42×C11C2311yescharacteristic
66C2×#4323—22no—
67C2×#4323—22no—
68C2×#4323—22no—
69#66983—21no—
70#66983—21no—
71C22×C11⋊C8—21no—
72#66961—44no—
73#66961—44no—
74C2×D88—22no—
75C2×D88—22no—
76C2×#4314—22no—
77C2×#4314—22no—
78#66928—21no—
79#66927—21no—
80#66927—21no—
81#66927—21no—
82#66927C2312yes—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2311yescharacteristic
89C11×C4⋊C8C2311yescharacteristic
90C11×C22⋊C8—22no—
91C11×C22⋊C8—22no—
92C11×#97D412yes—
93C4×C8×C11C2312yes—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96#66873—22no—
97#66873—22no—
98#66873—22no—
99#66871—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4×C11⋊C8—21no—
105#19230—111nomaximal, Sylow
106C23×D11—41no—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C2×D412yes—
114C22×C4×C11—22no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—41no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—22no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44—81no—
133C2×D44—81no—
134C2×D44—82no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×M16—22no—
138C11×M16—44no—
139C11×M16D814yescomplemented
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—44no—
143C2×C8×C11—42no—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154#4323—82no—
155#4323—82no—
156#4323—82no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—81no—
165D88—44no—
166D88—44no—
167#4314—44no—
168#4314—44no—
169#3245—111no—
170#3205—111no—
171#3151—111no—
172#2935D1111yescharacteristic, complemented
173#1687—112no—
174#1685—112no—
175#1667—112no—
176#1665—112no—
177#1565—111no—
178#1540—111no—
179C2×#331—111no—
180C23×C11—22no—
181C23×C11#12111yescharacteristic
182C22×D11—41no—
183C22×D11—42no—
184C22×D11—82no—
185C22×D11—82no—
186C22×D11—82no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—44no—
191D4×C11—42no—
192D4×C11—81no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11C2×D812yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C22⋊D11—82no—
208C2×Dic11—41no—
209D44—42no—
210D44—41no—
211D44—42no—
212D44—41no—
213D44—41no—
214D44—42no—
215D44—42no—
216D44—41no—
217D44—81no—
218D44—82no—
219D44—82no—
220D44—82no—
221D44—82no—
222C4×D11—82no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—22no—
226C8×C11—41no—
227C8×C11—41no—
228C8×C11C2×D814yes—
229C11⋊C8—42no—
230C11⋊C8—41no—
231C11⋊C8—41no—
232C2×AGL(1,ℤ/8)—221no—
233C2×AGL(1,ℤ/8)—221no—
234C2×#131—21no—
235#532—111no—
236#532C2×D1111yescharacteristic
237C2×#127—111no—
238#496—222no—
239#493—112no—
240#493—221no—
241#492—112no—
242#486—221no—
243#474—112no—
244#474—221no—
245#466—222no—
246#459—112no—
247#459—112no—
248#459—112no—
249#459—221no—
250#447—222no—
251#436C2×D1112yescomplemented
252#435—22no—
253C8×D4C2×D1112yescomplemented
254#431—111no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8C2×D1111yescharacteristic
257#408—21no—
258C4×M16C2×D1111yescharacteristic
259#335—112no—
260#334—112no—
261#332—111no—
262#332—111no—
263#331—112no—
264#331—112no—
265#331—111no—
266#331—111no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11#45912yes—
273C22×C11C2×#12111yescharacteristic
274C2×D11—82no—
275C2×D11—81no—
276C2×D11—82no—
277C2×D11—81no—
278C2×D11—82no—
279C2×D11—81no—
280C2×D11—164no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—42no—
285C4×C11#45912yes—
286C4×C11C22×D811yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—81no—
291C2×#41—21no—
292C2×#41—221no—
293C22×D4—221no—
294C22×D4—221no—
295C22×D4—221no—
296AGL(1,ℤ/8)—444no—
297AGL(1,ℤ/8)—444no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—222no—
301C2×D8—222no—
302C2×D8—222no—
303C2×D8—222no—
304C2×D8—222no—
305#131—44no—
306C2×M16—22no—
307C2×M16C22⋊D1111yescharacteristic
308C2×M16C22⋊D1111yescharacteristic
309C22×C8—21no—
310C22×C8—22no—
311C22×C8—221no—
312C4⋊Q8—111no—
313C4⋊Q8D4411yescharacteristic
314#127—112no—
315#127—111no—
316#127—221no—
317#127—221no—
318#127—221no—
319#127D4411yescharacteristic
320#124—21no—
321#124—221no—
322#121—21no—
323#121—221no—
324#121—221no—
325#121D4412yes—
326C4×D4—21no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4C22×D1112yes—
330C2×C42C22×D1111yescharacteristic
331#107—222no—
332C4⋊C8—21no—
333C4⋊C8—112no—
334C4⋊C8—111no—
335C4⋊C8—111no—
336C4⋊C8—221no—
337C4⋊C8C22×D1111yescharacteristic
338C4⋊C8C22×D1111yescharacteristic
339#102—222no—
340#102—222no—
341#102—222no—
342#102—222no—
343C22⋊C8—22no—
344C22⋊C8—22no—
345C22⋊C8—221no—
346#97C22⋊D1112yes—
347C4×C8—221no—
348C4×C8C22×D1112yes—
349C2×C11—22no—
350C2×C11—82no—
351C2×C11C2×#45911yescharacteristic
352C2×C11#306211yescharacteristic
353C2×C11#306811yescharacteristic
354D11—161no—
355D11—162no—
356C24—441no—
357#41—42no—
358#41—42no—
359#41—442no—
360#41—442no—
361C2×Q8—21no—
362C2×Q8—221no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—221no—
369C2×D4—222no—
370C2×D4—221no—
371C2×D4—222no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—881no—
379C2×D4—881no—
380C2×D4—882no—
381C2×D4C2×D4412yes—
382C22×C4—22no—
383C22×C4—441no—
384C22×C4C2×D4411yescharacteristic
385C22×C4#433911yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—444no—
388SD16—444no—
389D8—444no—
390D8—444no—
391D8—882no—
392D8—882no—
393D8—882no—
394M16—22no—
395M16—44no—
396M16#432314yescomplemented
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—42no—
400C2×C8—44no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—222no—
404C2×C8—881no—
405C2×C8C2×C22⋊D1112yes—
406C2×C8C2×C22⋊D1112yes—
407C4⋊C4—21no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4C2×D4412yes—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42C2×D4411yescharacteristic
416C42#433911yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1923011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—441no—
422C23—442no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6698311yescharacteristic
427Q8—42no—
428Q8—441no—
429Q8—441no—
430D4—22no—
431D4—22no—
432D4—44no—
433D4—42no—
434D4—81no—
435D4—442no—
436D4—441no—
437D4—441no—
438D4—442no—
439D4—441no—
440D4—442no—
441D4—441no—
442D4—442no—
443D4—882no—
444D4—881no—
445D4—882no—
446D4—882no—
447D4—882no—
448D4—882no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—441no—
456C2×C4—882no—
457C2×C4#6698311yescharacteristic
458C2×C4#6698311yescharacteristic
459C2×C4#6698311yescharacteristic
460C2×C4C2×#432312yes—
461C2×C4#6700212yes—
462C2×C4C22×D4411yescharacteristic
463C2×C4C2×#433911yescharacteristic
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—22no—
466C8—41no—
467C8—41no—
468C8—441no—
469C8—442no—
470C8—441no—
471C8C2×#432314yes—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—881no—
478C22—882no—
479C22—882no—
480C22—881no—
481C22—882no—
482C22—881no—
483C22—1764no—
484C22#1062262812yes—
485C22C2×#6698311yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—881no—
491C4#1062262812yes—
492C4#1062328211yescharacteristic
493C4#1062328311yescharacteristic
494C4C22×#432311yescharacteristic
495C4C2×#6700211yescharacteristic
496C2—22no—
497C2—82no—
498C2—1762no—
499C2—1761no—
500C2C2×#1062262811yescharacteristic
501C2#1307829611yescharacteristic
502C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
hypercenter#2935D11
hypocenterC11#19230
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079531C2semidirect
3. #13079068C2semidirect
4. #13068095C2semidirect
5. #13068081C2semidirect
6. #13067971C2semidirect
7. #13067957C2semidirect
8. #13067368C2semidirect
9. #13067266C2semidirect
10. C2×#10622123C2semidirect
11. C11×#2935C2semidirect
18. C11×#436C22semidirect
20. C8×D4×C11C22semidirect
32. #10622628C22semidirect
33. #10622620C22semidirect
41. #10622123C22semidirect
42. #10622123C22semidirect
43. #10622120C22semidirect
44. #10622120C22semidirect
45. #10622096C22semidirect
46. #10622095C22semidirect
139. C11×M16D8semidirect
172. #2935D11semidirect
251. #436C2×D11semidirect
253. C8×D4C2×D11semidirect
396. M16#4323semidirect
419. C11#19230semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130795312
#130790682
#130680952
#130680812
#130679712
#130679572
#130673682
#130672662
C2×#106221232
C11×#29352
#1923011