Finite Group Databasebeta

← #14741612

Subgroups — #14741612

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic, complemented
2#13079557C211yesmaximal, characteristic, complemented
3#13079175C211yesmaximal, characteristic, complemented
4#13079158C211yesmaximal, characteristic, complemented
5#13079066C211yesmaximal, characteristic
6#13068243C212yesmaximal, complemented
7#13068236C212yesmaximal, complemented
8#13068206C212yesmaximal, complemented
9#13068202C212yesmaximal, complemented
10C8×#4318C211yesmaximal, characteristic, complemented
11C2×C11×#492C211yesmaximal, characteristic, complemented
12C22×C11×SD16—22no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×#66985—22no—
16#10623008C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#492—22no—
19C11×#492C2212yes—
20C11×#492C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622831—22no—
23#10622727—22no—
24#10622701C2212yescomplemented
25#10622697—22no—
26#10622693—22no—
27#10622692C2212yescomplemented
28#10622692C2212yescomplemented
29#10622691C2212yescomplemented
30#10622689C2212yes—
31#10622689C2212yes—
32#10622688—22no—
33#10622687—22no—
34#10622686C2212yes—
35#10622683C2212yes—
36#10622581—22no—
37#10622577—22no—
38#10622538C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622307C2211yescharacteristic, complemented
41#10622306C2211yescharacteristic, complemented
42C4×#4314—22no—
43#10622294C2211yescharacteristic, complemented
44#10622293C2211yescharacteristic, complemented
45#10622092C2212yescomplemented
46C8×C11⋊C8C2212yescomplemented
47C22×Q8×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C2×#4339—21no—
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—48no—
55C22×C8×C11D412yes—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4324—24no—
68C2×#4324—24no—
69#66985—48no—
70C2×#4323—24no—
71#66983—21no—
72#66983—21no—
73#66979—21no—
74#66977—21no—
75#66977—21no—
76C2×#4318D412yes—
77C2×#4314—22no—
78#66928—21no—
79#66927C2311yescharacteristic
80C4×D44—21no—
81C4×D44—21no—
82#66923—21no—
83#66922C2311yescharacteristic
84#66922C2311yescharacteristic
85#66922C2311yescharacteristic
86C4×Dic22—21no—
87C4×Dic22—21no—
88C4×C8×C11D412yes—
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#66896—24no—
92C22⋊(C11⋊C8)D412yes—
93#66885—22no—
94#66881—22no—
95#66880—22no—
96#66873—24no—
97#66872—24no—
98#66872—24no—
99#66871—24no—
100C4⋊(C11⋊C8)D412yes—
101#66867D412yes—
102C4×C11⋊C8C2312yes—
103C4×C11⋊C8C2312yes—
104#19621—111nomaximal, Sylow
105C24×C11—41no—
106C2×Q8×C11—22no—
107C2×Q8×C11—44no—
108C2×Q8×C11—41no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—44no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—44no—
117C2×D4×C11—82no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—41no—
123#4339—44no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C11×SD16—48no—
132C11×SD16—48no—
133C2×C8×C11—24no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D412yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2411yescharacteristic
144C22⋊Dic11—41no—
145#4324—48no—
146#4324—84no—
147#4323—48no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159#4318SD1618yescomplemented
160C2×C11⋊C8C2×D414yes—
161C2×C11⋊C8C2×D414yes—
162#4314—44no—
163#3227—111no—
164#3208—111no—
165#3167—111no—
166#3165—111no—
167#3151—111no—
168C2×#492D1111yescharacteristic, complemented
169#1715—112no—
170#1714—112no—
171#1706—112no—
172#1705—112no—
173C8×M16—111no—
174C23×C11—42no—
175C23×C11—82no—
176C23×C11—82no—
177C23×C11—82no—
178C23×C11#12711yescharacteristic
179C22×D11—41no—
180Q8×C11—44no—
181Q8×C11—82no—
182D4×C11—44no—
183D4×C11—44no—
184D4×C11—44no—
185D4×C11—82no—
186D4×C11—82no—
187D4×C11—82no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—42no—
191C2×C4×C11—82no—
192C2×C4×C11#12711yescharacteristic
193C2×C4×C11#12711yescharacteristic
194C2×C4×C11#12711yescharacteristic
195C2×C4×C11C2×SD1614yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—42no—
204D44—42no—
205D44—42no—
206C4×D11—82no—
207Dic22—42no—
208Dic22—42no—
209Dic22—42no—
210C8×C11—22no—
211C8×C11AGL(1,ℤ/8)14yescomplemented
212C11⋊C8—24no—
213C11⋊C8C2×SD1618yescomplemented
214C2×AGL(1,ℤ/8)—222no—
215C22×SD16—22no—
216#533—111no—
217#532—111no—
218C2×C4⋊Q8C2×D1111yescharacteristic
219C2×#127C2×D1111yescharacteristic
220#501—222no—
221#500—112no—
222#498—112no—
223#498—112no—
224#498—111no—
225#496—222no—
226#493—112no—
227#492—22no—
228#492—112no—
229#492—112no—
230#492—111no—
231#492C2×D1112yes—
232#492C2×D1112yes—
233#487—111no—
234#486—112no—
235#486—112no—
236#486—111no—
237#481—222no—
238#476—222no—
239#465—222no—
240#460—222no—
241#450—222no—
242C4×SD16—222no—
243#431—111no—
244#428—222no—
245C4×M16—111no—
246C2×C4×C8C2×D1111yescharacteristic
247#322—112no—
248C82—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—164no—
255C22×C11#49212yes—
256C22×C11C2×#12711yescharacteristic
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—82no—
263C4×C11#49212yes—
264C4×C11C22×SD1612yes—
265C4×C11C2×AGL(1,ℤ/8)12yes—
266C4×C11#57712yes—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270C2×#41—221no—
271C22×Q8—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275AGL(1,ℤ/8)—448no—
276C2×SD16—24no—
277C2×SD16—24no—
278C2×SD16—48no—
279C2×SD16—224no—
280C2×SD16—224no—
281C2×SD16—222no—
282C2×D8—224no—
283C2×M16—112no—
284C22×C8C22⋊D1112yes—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—111no—
289C4⋊Q8—111no—
290C4⋊Q8—111no—
291C4⋊Q8C22×D1112yes—
292#127—21no—
293#127—21no—
294#127—21no—
295#127—111no—
296#127C22×D1112yes—
297#125—221no—
298#124—221no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301#121—221no—
302#121—221no—
303C4×Q8—221no—
304C4×Q8—221no—
305C4×D4—221no—
306C4×D4—221no—
307#117—221no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C42C22×D1111yescharacteristic
311#107—224no—
312#106—224no—
313#106—224no—
314#106—222no—
315C4⋊C8—112no—
316#103—222no—
317#102—224no—
318#102—224no—
319#102—222no—
320C22⋊C8—112no—
321#97—112no—
322C4×C8—112no—
323C4×C8—112no—
324C4×C8C22⋊D1112yes—
325C4×C8C22×D1111yescharacteristic
326C4×C8C22×D1111yescharacteristic
327C2×C11—22no—
328C2×C11—162no—
329C2×C11C2×#49211yescharacteristic
330C2×C11#315111yescharacteristic
331C2×C11#315411yescharacteristic
332D11—161no—
333C24—41no—
334#41—444no—
335C2×Q8—22no—
336C2×Q8—44no—
337C2×Q8—41no—
338C2×Q8—221no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—44no—
345C2×D4—44no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—82no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—441no—
354C22×C4—41no—
355C22×C4—441no—
356C22×C4D4×D1111yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359SD16—48no—
360SD16—48no—
361SD16—448no—
362SD16—444no—
363SD16—884no—
364D8—448no—
365M16—118no—
366C2×C8—24no—
367C2×C8—114no—
368C2×C8—114no—
369C2×C8C2×C22⋊D1112yes—
370C2×C8C2×C22⋊D1112yes—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C42—441no—
387C42D4×D1111yescharacteristic
388C42D4×D1111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1962111yescharacteristic, complemented, Sylow
392C23—42no—
393C23—82no—
394C23—82no—
395C23—82no—
396C23—441no—
397C23#6699311yescharacteristic
398Q8—44no—
399Q8—82no—
400Q8—442no—
401Q8—442no—
402Q8—442no—
403D4—44no—
404D4—44no—
405D4—44no—
406D4—82no—
407D4—82no—
408D4—82no—
409D4—442no—
410D4—442no—
411D4—442no—
412D4—882no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—82no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—882no—
421C2×C4SD16×D1114yes—
422C2×C4#6699311yescharacteristic
423C2×C4#6699311yescharacteristic
424C2×C4#6699311yescharacteristic
425C2×C4C2×D4×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4C22×C22⋊D1111yescharacteristic
428C8—22no—
429C8—118no—
430C8—224no—
431C8#6698514yescomplemented
432C22—21no—
433C22—21no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—164no—
438C22—881no—
439C22—881no—
440C22—881no—
441C22#1062278812yes—
442C22C2×#6699311yescharacteristic
443C4—21no—
444C4—21no—
445C4—82no—
446C4—881no—
447C4—881no—
448C4—881no—
449C4#1062278812yes—
450C4C2×SD16×D1112yes—
451C4#1062329312yes—
452C4C2×#6698512yes—
453C2—22no—
454C2—162no—
455C2—1761no—
456C2C2×#1062278811yescharacteristic
457C2#1307906611yescharacteristic
458C2#1307908611yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC22×C11C2×#127
prime radical#13079066C2
hypercenterC2×#492D11
hypocenterC11#19621
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13079744C2semidirect
2. #13079557C2semidirect
3. #13079175C2semidirect
4. #13079158C2semidirect
6. #13068243C2semidirect
7. #13068236C2semidirect
8. #13068206C2semidirect
9. #13068202C2semidirect
10. C8×#4318C2semidirect
11. C2×C11×#492C2semidirect
24. #10622701C22semidirect
27. #10622692C22semidirect
28. #10622692C22semidirect
29. #10622691C22semidirect
40. #10622307C22semidirect
41. #10622306C22semidirect
43. #10622294C22semidirect
44. #10622293C22semidirect
45. #10622092C22semidirect
46. C8×C11⋊C8C22semidirect
159. #4318SD16semidirect
168. C2×#492D11semidirect
211. C8×C11AGL(1,ℤ/8)semidirect
213. C11⋊C8C2×SD16semidirect
391. C11#19621semidirect
431. C8#66985semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130795572
#130791752
#130791582
#130790662
#130682432
#130682362
#130682062
#130682022
C8×#43182
C2×C11×#4922
#1962111