Finite Group Databasebeta

← #14729885

Subgroups — #14729885

Order 2816.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078996C211yesmaximal, characteristic, complemented
2#13078746C211yesmaximal, characteristic, complemented
3#13078715C211yesmaximal, characteristic
4#13067830C214yesmaximal, complemented
5#13067823C214yesmaximal, complemented
6#13067342C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic
9C2×C11×#554C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—22no—
12C11×#554—22no—
13C11×#554C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22#10623001C2211yescharacteristic
23#10622841—21no—
24#10622838—22no—
25#10622831—21no—
26#10622695—22no—
27#10622694C2212yescomplemented
28#10622694C2212yescomplemented
29#10622644C2212yescomplemented
30#10622643—22no—
31#10622633C2212yescomplemented
32#10622632C2212yes—
33#10622631—22no—
34#10622620C2212yes—
35#10622584—21no—
36#10622583—21no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622184C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11D412yes—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8D412yes—
51C11×C4⋊Q8C2312yes—
52C11×#125—24no—
53C11×#125—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—28no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11D412yes—
61C4×Q8×C11C2312yes—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—21no—
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—24no—
93#66899—24no—
94#66899—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66874—22no—
100#66872—22no—
101#66871—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8C2312yes—
108#18530—111nomaximal, Sylow
109C24×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—42no—
113C2×Q8×C11—44no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—24no—
117C2×D4×C11—21no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11—84no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C2×Dic22—21no—
132C2×Dic22—21no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—28no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C2×D412yes—
144C11×C4⋊C4C2×D412yes—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—41no—
155#4326—44no—
156#4324—44no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164#4318—42no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#554D1111yescharacteristic
169#3139—111no—
170#3113—111no—
171#3110—111no—
172#1644—114no—
173#1643—114no—
174#1558—111no—
175#1491—111no—
176#1490—111no—
177C23×C11—24no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11#12011yescharacteristic
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—44no—
185Q8×C11—42no—
186Q8×C11—82no—
187D4×C11—24no—
188D4×C11—22no—
189D4×C11#13714yes—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—44no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—88no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×Dic11—41no—
211C2×Dic11—41no—
212Dic22—42no—
213Dic22—42no—
214C11⋊C8—42no—
215C11⋊C8—42no—
216C11⋊C8—42no—
217#554—22no—
218#554—22no—
219#554—22no—
220#554C2×D1114yes—
221#533—111no—
222C2×C4⋊Q8C2×D1111yescharacteristic
223C2×#125—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—22no—
226C2×C4×Q8C2×D1111yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4C2×D1111yescharacteristic
229C22×C4⋊C4—21no—
230#491—222no—
231#487—112no—
232#487—112no—
233#484—221no—
234#483—221no—
235#475—112no—
236#474—112no—
237#462—112no—
238#461—112no—
239#451—221no—
240#450—221no—
241#441—222no—
242#440—222no—
243#432—111no—
244#432—111no—
245#419—222no—
246C4×M16—111no—
247#333—114no—
248Q8⋊C8—114no—
249D4⋊C8—114no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—24no—
253C22×C11—48no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11#45512yes—
257C22×C11C2×#12011yescharacteristic
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—44no—
266C4×C11C2×#13712yes—
267C4×C11#57512yes—
268Dic11—81no—
269Dic11—81no—
270C22×Q8C22⋊D1111yescharacteristic
271C22×Q8C22⋊D1112yes—
272C22×D4C22⋊D1111yescharacteristic
273C23×C4—22no—
274C23×C4—21no—
275C2×Q16—222no—
276C2×SD16—222no—
277C2×M16—221no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—111no—
281C4⋊Q8—111no—
282C4⋊Q8C22⋊D1112yes—
283C4⋊Q8C22×D1112yes—
284#125—24no—
285#125—24no—
286#125—221no—
287C22⋊Q8—24no—
288C22⋊Q8—28no—
289C22⋊Q8—24no—
290C22⋊Q8—28no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—221no—
296C4×Q8—221no—
297C4×Q8C22⋊D1112yes—
298C4×Q8C22×D1112yes—
299C4×D4—24no—
300C4×D4—24no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4C22⋊D1112yes—
304C4×D4C22×D1112yes—
305#117—221no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4C22⋊D1111yescharacteristic
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C42—21no—
318C2×C42C22×D1111yescharacteristic
319#107—222no—
320#106—222no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323#103—224no—
324#103—224no—
325#103—222no—
326#103—222no—
327#103—222no—
328#102—222no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331#97—221no—
332#97—221no—
333#97—221no—
334C4×C8—112no—
335C2×C11—22no—
336C2×C11—44no—
337C2×C11#300411yescharacteristic
338C2×C11#300511yescharacteristic
339C2×C11C2×#45511yescharacteristic
340C24—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—44no—
345C2×Q8—221no—
346C2×Q8—221no—
347C2×Q8C2×C22⋊D1112yes—
348C2×Q8C2×C22⋊D1114yes—
349C2×D4—24no—
350C2×D4—21no—
351C2×D4C2×C22⋊D1112yes—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—28no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—44no—
360C22×C4—84no—
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364Q16—444no—
365SD16—444no—
366M16—442no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C4⋊C4—28no—
371C4⋊C4—28no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4C2×C22⋊D1112yes—
387C4⋊C4C2×C22⋊D1112yes—
388C22⋊C4—28no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—441no—
392C42—22no—
393C42—22no—
394C42—441no—
395C42C2×C22⋊D1111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C2×C22⋊D1111yescharacteristic
398C42C23×D1111yescharacteristic
399C11#1853011yescharacteristic, complemented, Sylow
400C23—24no—
401C23—22no—
402C23—42no—
403C23—42no—
404C23#6700611yescharacteristic
405Q8—22no—
406Q8—22no—
407Q8—44no—
408Q8—42no—
409Q8—82no—
410Q8—442no—
411Q8—442no—
412D4—24no—
413D4—22no—
414D4#6699514yes—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—88no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4#6700611yescharacteristic
432C2×C4#6700611yescharacteristic
433C2×C4#6700611yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C2×C4C22×C22⋊D1111yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—442no—
438C8—442no—
439C8—442no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—48no—
444C22—42no—
445C22—42no—
446C22#1062285512yes—
447C22C2×#6700611yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—44no—
456C4—881no—
457C4—881no—
458C4C2×#6699512yes—
459C4#1062335312yes—
460C2—22no—
461C2—44no—
462C2#1307785011yescharacteristic
463C2#1307785811yescharacteristic
464C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#554C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11#18530
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13078996C2semidirect
2. #13078746C2semidirect
4. #13067830C2semidirect
5. #13067823C2semidirect
6. #13067342C2semidirect
7. #13067063C2semidirect
27. #10622694C22semidirect
28. #10622694C22semidirect
29. #10622644C22semidirect
31. #10622633C22semidirect
40. #10622184C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
399. C11#18530semidirect

Maximal subgroups

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

subgroupindex
#130789962
#130787462
#130787152
#130678302
#130678232
#130673422
#130670632
#130670592
C2×C11×#5542
#1853011