Finite Group Databasebeta

← #14729996

Subgroups — #14729996

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079158C211yesmaximal, characteristic, complemented
2#13078746C211yesmaximal, characteristic, complemented
3#13078715C211yesmaximal, characteristic
4#13067886C214yesmaximal, complemented
5#13067872C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic
9C2×C11×#556C211yesmaximal, characteristic
10C11×#556—22no—
11C11×#556—22no—
12C11×#556—22no—
13C11×#556C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22#10623001C2211yescharacteristic
23#10622841—21no—
24#10622831—21no—
25#10622693—22no—
26#10622692C2212yescomplemented
27#10622691C2212yescomplemented
28#10622644C2212yescomplemented
29#10622643—22no—
30#10622633C2212yescomplemented
31#10622632C2212yes—
32#10622631—22no—
33#10622620C2212yes—
34#10622584—21no—
35#10622583—21no—
36#10622577—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8D412yes—
50C11×C4⋊Q8C2312yes—
51C11×#126—28no—
52C11×#126—28no—
53C11×#124—24no—
54C11×#124—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11D412yes—
62C4×Q8×C11C2312yes—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D412yes—
66C4×D4×C11C2312yes—
67C11×#117—24no—
68C11×#117—24no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326—22no—
82C2×#4324—22no—
83#66979—21no—
84#66977—21no—
85#66977—21no—
86C2×#4318—21no—
87#66923—21no—
88#66922C2311yescharacteristic
89#66922C2311yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92#66899—22no—
93#66896—22no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#66874—22no—
97#66874—22no—
98#66872—24no—
99#66872—22no—
100#66871—24no—
101#66871—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108#18542—111nomaximal, Sylow
109C24×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—42no—
114C2×Q8×C11—44no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×Dic22—21no—
130C2×Dic22—21no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C2×D414yes—
140C11×C4⋊C4C2×D412yes—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—28no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11—28no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2411yescharacteristic
153C22⋊Dic11—41no—
154#4326—44no—
155#4324—44no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163#4318—24no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×#556D1111yescharacteristic
168#3165—111no—
169#3113—111no—
170#3110—111no—
171#1652—114no—
172#1650—114no—
173#1556—111no—
174#1491—111no—
175#1490—111no—
176C23×C11—22no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11#12011yescharacteristic
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—42no—
184Q8×C11—44no—
185Q8×C11—44no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×Dic11—41no—
209C2×Dic11—41no—
210Dic22—42no—
211Dic22—42no—
212C11⋊C8—24no—
213C11⋊C8—42no—
214C11⋊C8—42no—
215#556—22no—
216#556—22no—
217#556—22no—
218#556C2×D1114yes—
219#533—111no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#126—22no—
222C2×#124—21no—
223C2×C22⋊Q8—21no—
224C2×C4×Q8—21no—
225C2×C4×Q8C2×D1111yescharacteristic
226C2×C4×D4C2×D1111yescharacteristic
227C2×#117—21no—
228#501—222no—
229#500—112no—
230#498—112no—
231#484—221no—
232#483—221no—
233#475—112no—
234#474—112no—
235#462—112no—
236#461—112no—
237#451—221no—
238#450—221no—
239#441—222no—
240#440—222no—
241#432—111no—
242#432—111no—
243#428—222no—
244C4×M16—111no—
245#332—114no—
246Q8⋊C8—114no—
247D4⋊C8—114no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—84no—
254C22×C11#45612yes—
255C22×C11C2×#12011yescharacteristic
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—44no—
263C4×C11—42no—
264C4×C11#57512yes—
265C4×C11#57512yes—
266Dic11—81no—
267Dic11—81no—
268C22×Q8—21no—
269C22×Q8C22⋊D1111yescharacteristic
270C22×D4C22⋊D1111yescharacteristic
271C23×C4—21no—
272C2×Q16—222no—
273C2×SD16—222no—
274C2×M16—221no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—111no—
278C4⋊Q8—111no—
279C4⋊Q8C22⋊D1112yes—
280C4⋊Q8C22×D1112yes—
281#126—28no—
282#126—28no—
283#125—221no—
284#124—24no—
285#124—24no—
286C22⋊Q8—24no—
287C22⋊Q8—24no—
288C22⋊Q8—221no—
289C22⋊Q8—221no—
290C4×Q8—24no—
291C4×Q8—24no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—221no—
295C4×Q8—221no—
296C4×Q8C22⋊D1112yes—
297C4×Q8C22×D1112yes—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4C22⋊D1112yes—
301C4×D4C22×D1112yes—
302#117—24no—
303#117—24no—
304#117—221no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22⋊D1112yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—21no—
314C2×C42—22no—
315C2×C42—21no—
316C2×C42C22×D1111yescharacteristic
317#107—224no—
318#107—222no—
319#106—224no—
320#106—222no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323#103—222no—
324#103—222no—
325#103—222no—
326#102—222no—
327C22⋊C8—221no—
328C22⋊C8—221no—
329#97—221no—
330#97—221no—
331#97—221no—
332C4×C8—112no—
333C2×C11—22no—
334C2×C11—82no—
335C2×C11#300511yescharacteristic
336C2×C11#300511yescharacteristic
337C2×C11C2×#45611yescharacteristic
338C24—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—42no—
343C2×Q8—44no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8C2×C22⋊D1112yes—
347C2×D4—21no—
348C2×D4—42no—
349C2×D4C2×C22⋊D1112yes—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—44no—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360Q16—444no—
361SD16—444no—
362M16—224no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—222no—
366C4⋊C4—28no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4C2×C22⋊D1112yes—
381C4⋊C4C2×C22⋊D1112yes—
382C4⋊C4C2×C22⋊D1114yes—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—441no—
388C42—28no—
389C42—22no—
390C42—22no—
391C42—441no—
392C42C2×C22⋊D1111yescharacteristic
393C42C2×C22⋊D1111yescharacteristic
394C42C2×C22⋊D1111yescharacteristic
395C42C23×D1111yescharacteristic
396C11#1854211yescharacteristic, complemented, Sylow
397C23—22no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23#6700611yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—42no—
405Q8—44no—
406Q8—44no—
407Q8—442no—
408Q8—442no—
409D4—22no—
410D4—22no—
411D4—42no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4#6700611yescharacteristic
428C2×C4#6700611yescharacteristic
429C2×C4#6700611yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C8—224no—
434C8—442no—
435C8—442no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22#1062285912yes—
443C22C2×#6700611yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—42no—
452C4—881no—
453C4—881no—
454C4#1062335312yes—
455C4#1062335312yes—
456C2—22no—
457C2—82no—
458C2#1307785811yescharacteristic
459C2#1307785811yescharacteristic
460C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#556C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×#556D11
hypocenterC11#18542
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13079158C2semidirect
2. #13078746C2semidirect
4. #13067886C2semidirect
5. #13067872C2semidirect
6. #13067333C2semidirect
7. #13067063C2semidirect
26. #10622692C22semidirect
27. #10622691C22semidirect
28. #10622644C22semidirect
30. #10622633C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
396. C11#18542semidirect

Maximal subgroups

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

subgroupindex
#130791582
#130787462
#130787152
#130678862
#130678722
#130673332
#130670632
#130670592
C2×C11×#5562
#1854211