Finite Group Databasebeta

← #14729969

Subgroups — #14729969

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079158C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic, complemented
3#13078715C211yesmaximal, characteristic, complemented
4#13067900C214yesmaximal, complemented
5#13067851C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067059C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic, complemented
9C2×C11×#547C211yesmaximal, characteristic
10C22×C11×#41—21no—
11C11×#547—22no—
12C11×#547—22no—
13C11×#547—22no—
14C11×#547C2214yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×#121—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22#10623001C2211yescharacteristic
23#10622831—21no—
24#10622831—21no—
25#10622693—22no—
26#10622692C2212yescomplemented
27#10622691C2212yescomplemented
28#10622632C2212yescomplemented
29#10622632C2212yescomplemented
30#10622631—22no—
31#10622631—22no—
32#10622620C2212yescomplemented
33#10622620C2212yescomplemented
34#10622583—21no—
35#10622583—21no—
36#10622577—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yescomplemented
41D4⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—48no—
46C22×Q8×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D412yes—
56C11×C4⋊Q8C2312yes—
57C11×#123—28no—
58C11×#123—28no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C11×#121—24no—
62C11×#121—24no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11D412yes—
68C4×D4×C11D412yes—
69C4×D4×C11C2312yes—
70C4×D4×C11C2312yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4324—22no—
83C2×#4324—22no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87C2×#4318—21no—
88#66923—21no—
89#66922C2311yescharacteristic
90#66922C2311yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93#66896—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66874—22no—
98#66874—22no—
99#66872—24no—
100#66871—24no—
101#66871—22no—
102#66871—22no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106#66867—21no—
107#66867—21no—
108C4×C11⋊C8C2312yes—
109#18539—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11—21no—
112C11×#41—416no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—44no—
118C2×D4×C11—24no—
119C2×D4×C11—28no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—48no—
124C2×D4×C11C2×D412yes—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—28no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—44no—
135C22×C4×C11—44no—
136C22×C4×C11—48no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C2×Dic22—21no—
141C2×Dic22—21no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C2×D414yes—
149C11×C4⋊C4C2×D412yes—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160C22⋊Dic11—41no—
161#4324—44no—
162#4324—44no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169C4×Dic11—41no—
170#4318—24no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×#547D1111yescharacteristic
175#3165—111no—
176#3110—111no—
177#3110—111no—
178#1654—114no—
179#1647—114no—
180#1556—111no—
181#1490—111no—
182#1490—111no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11#12011yescharacteristic
192Q8×C11—44no—
193Q8×C11—44no—
194D4×C11—24no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—42no—
199D4×C11—416no—
200D4×C11AGL(1,ℤ/8)14yes—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11—416no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×Dic11—41no—
222C2×Dic11—41no—
223Dic22—42no—
224Dic22—42no—
225C11⋊C8—24no—
226C11⋊C8—42no—
227C11⋊C8—42no—
228C22×#41—21no—
229#547—22no—
230#547—22no—
231#547—22no—
232#547C2×D1114yes—
233#533—111no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#123—22no—
236C2×C22⋊Q8—21no—
237C2×#121—21no—
238C2×C4×D4C2×D1111yescharacteristic
239C2×C4×D4C2×D1111yescharacteristic
240C22×C4⋊C4—21no—
241#501—222no—
242#500—112no—
243#498—112no—
244#484—221no—
245#484—221no—
246#474—112no—
247#474—112no—
248#461—112no—
249#461—112no—
250#450—221no—
251#450—221no—
252#440—222no—
253#440—222no—
254#432—111no—
255#432—111no—
256#428—222no—
257C4×M16—111no—
258#332—114no—
259D4⋊C8—114no—
260D4⋊C8—114no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—48no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—84no—
271C22×C11#45612yes—
272C22×C11C2×#12011yescharacteristic
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—44no—
279C4×C11—42no—
280C4×C11C2×AGL(1,ℤ/8)12yes—
281C4×C11#57512yes—
282Dic11—81no—
283Dic11—81no—
284C2×#41—24no—
285C2×#41—24no—
286C2×#41—48no—
287C22×Q8—21no—
288C22×D4—22no—
289C22×D4C22⋊D1111yescharacteristic
290C22×D4C22⋊D1111yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C2×SD16—222no—
295C2×SD16—222no—
296C2×M16—221no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—111no—
300C4⋊Q8—111no—
301C4⋊Q8C22⋊D1112yes—
302C4⋊Q8C22×D1112yes—
303#125—221no—
304#123—28no—
305#123—28no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310#121—24no—
311#121—24no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4C22⋊D1112yes—
319C4×D4C22⋊D1112yes—
320C4×D4C22×D1112yes—
321C4×D4C22×D1112yes—
322#117—221no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22⋊D1112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42C22×D1111yescharacteristic
334#107—224no—
335#107—222no—
336#107—222no—
337#106—224no—
338C4⋊C8—112no—
339C4⋊C8—112no—
340#103—222no—
341#103—222no—
342#102—222no—
343#102—222no—
344C22⋊C8—221no—
345C22⋊C8—221no—
346#97—221no—
347#97—221no—
348#97—221no—
349C4×C8—112no—
350C2×C11—22no—
351C2×C11—44no—
352C2×C11—82no—
353C2×C11#300311yescharacteristic
354C2×C11#300511yescharacteristic
355C2×C11C2×#45611yescharacteristic
356C24—21no—
357C24—21no—
358#41—416no—
359#41—48no—
360#41—48no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—44no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×D4—24no—
367C2×D4—28no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—42no—
371C2×D4—48no—
372C2×D4C2×C22⋊D1112yes—
373C2×D4C2×C22⋊D1112yes—
374C22×C4—28no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—44no—
383C22×C4—44no—
384C22×C4—48no—
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388SD16—444no—
389SD16—444no—
390M16—224no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—28no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×C22⋊D1112yes—
407C4⋊C4C2×C22⋊D1112yes—
408C4⋊C4C2×C22⋊D1114yes—
409C22⋊C4—28no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—441no—
415C42—441no—
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1853911yescharacteristic, complemented, Sylow
421C23—24no—
422C23—22no—
423C23—22no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23#6700611yescharacteristic
430Q8—44no—
431Q8—44no—
432Q8—442no—
433Q8—442no—
434D4—24no—
435D4—22no—
436D4—22no—
437D4—22no—
438D4—42no—
439D4—416no—
440D4#6698514yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—416no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4#6700611yescharacteristic
458C2×C4#6700611yescharacteristic
459C2×C4#6700611yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—224no—
464C8—442no—
465C8—442no—
466C22—21no—
467C22—21no—
468C22—24no—
469C22—48no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—84no—
476C22#1062285912yes—
477C22C2×#6700611yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—44no—
484C4—42no—
485C4—881no—
486C4—881no—
487C4C2×#6698512yes—
488C4#1062335312yes—
489C2—22no—
490C2—44no—
491C2—82no—
492C2#1307784311yescharacteristic
493C2#1307785811yescharacteristic
494C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC22×C11C2×#120
hypercenterC2×#547D11
hypocenterC11#18539
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13079158C2semidirect
2. #13078715C2semidirect
3. #13078715C2semidirect
4. #13067900C2semidirect
5. #13067851C2semidirect
6. #13067333C2semidirect
7. #13067059C2semidirect
8. #13067059C2semidirect
26. #10622692C22semidirect
27. #10622691C22semidirect
28. #10622632C22semidirect
29. #10622632C22semidirect
32. #10622620C22semidirect
33. #10622620C22semidirect
40. #10622185C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
420. C11#18539semidirect

Maximal subgroups

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

subgroupindex
#130791582
#130787152
#130679002
#130678512
#130673332
#130670592
C2×C11×#5472
#1853911