Finite Group Databasebeta

← #14651750

Subgroups — #14651750

Order 2816.

812 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077061C211yesmaximal, characteristic, complemented
2#13071931C211yesmaximal, characteristic
3#13066942C212yesmaximal, complemented
4#13066525C212yesmaximal, complemented
5C11×#1785C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C2×#66990C411yescharacteristic
8C2×#66990C411yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C22×#4318—21no—
11C2×C11×#101—21no—
12C2×C11×#100—21no—
13C11×#407C2212yes—
14#10622847—24no—
15#10622844—21no—
16#10622836—21no—
17#10622833C411yescharacteristic
18#10622833C411yescharacteristic
19#10622826—21no—
20#10622826—21no—
21#10622824C2211yescharacteristic
22#10622820—21no—
23#10622820C2212yes—
24#10622106—24no—
25C24×D11C2×C411yescharacteristic
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—42no—
29C2×C11×#41—42no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—21no—
38C22×C22⋊D11—21no—
39C23×Dic11C2×C411yescharacteristic
40C2×C11×M16—22no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11C2×C411yescharacteristic
44C2×C22⋊Dic11C2×C411yescharacteristic
45#66990—42no—
46#66990—42no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53C2×#4318—22no—
54C2×#4318—22no—
55C2×#4318—42no—
56C2×#4318—42no—
57C22×C11⋊C8—22no—
58C11×#101—42no—
59C11×#100—42no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)—24no—
67C22⋊(C11⋊C8)—22no—
68C22⋊(C11⋊C8)D414yescomplemented
69#9511—111nomaximal, Sylow
70C24×C11C22⋊C411yescharacteristic
71C24×C11C22⋊C411yescharacteristic
72C24×C11C22×C411yescharacteristic
73C23×D11—21no—
74C23×D11—22no—
75C23×D11—42no—
76C23×D11—41no—
77C23×D11—41no—
78C23×D11—81no—
79C11×#41—44no—
80C11×#41—44no—
81C11×#41—48no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11#4112yes—
110C2×C22⋊D11—42no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—81no—
115C2×C22⋊D11—81no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11—81no—
121C11×M16—42no—
122C11×M16—42no—
123C2×C8×C11—42no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—81no—
127C22⋊Dic11—81no—
128(C2×D11)⋊C4—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—41no—
133#4318—44no—
134#4318—42no—
135#4318—42no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—44no—
138#2879—111no—
139#2404—111no—
140#1785D1111yescharacteristic, complemented
141#1462—112no—
142#1306—112no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11#9912yes—
157C23×C11C2×C22⋊C411yescharacteristic
158C23×C11C4×D412yes—
159C22×D11—22no—
160C22×D11—24no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—42no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—84no—
169C22×D11—84no—
170C22×D11—82no—
171C22×D11—82no—
172Q8×C11—44no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—44no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11#9912yes—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12112yes—
195C2×C4×C11#12311yescharacteristic
196C22⋊D11—84no—
197C22⋊D11—84no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—82no—
208C8×C11—82no—
209C11⋊C8—44no—
210C22×#41C2×D1111yescharacteristic
211C22×M16—221no—
212C2×#120—111no—
213C2×#120—111no—
214C22×C22⋊C4—111no—
215C2×#101—21no—
216C2×#100—21no—
217#408—224no—
218#407—112no—
219#407—221no—
220#407C2×D1112yes—
221#393—221no—
222#392—221no—
223#386—111no—
224#386—111no—
225#386—221no—
226#386—221no—
227#381—111no—
228#323—224no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#38611yescharacteristic
247C22×C11C2×#9911yescharacteristic
248C22×C11C2×#9911yescharacteristic
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—84no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—84no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—41no—
263Dic11—81no—
264Dic11—81no—
265Dic11—81no—
266C25—111no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—42no—
270C2×#41—42no—
271C22×Q8C22⋊D1111yescharacteristic
272C22×D4—221no—
273C22×D4—221no—
274C22×D4C4×D1111yescharacteristic
275C22×D4C4×D1111yescharacteristic
276C22×D4C22⋊D1111yescharacteristic
277C23×C4—111no—
278C23×C4D4411yescharacteristic
279C23×C4D4411yescharacteristic
280C23×C4C22×D1111yescharacteristic
281C2×M16—22no—
282C2×M16—222no—
283C2×M16—222no—
284C2×M16—442no—
285C2×M16—442no—
286C22×C8—222no—
287#120—442no—
288#120—442no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299#101—42no—
300#100—42no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303C22⋊C8—114no—
304C22⋊C8—224no—
305C22⋊C8—222no—
306#95—221no—
307#95—221no—
308#95—221no—
309#95—221no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—42no—
313C2×C11—42no—
314C2×C11—81no—
315C2×C11#189111yescharacteristic
316C2×C11#189811yescharacteristic
317C2×C11#191411yescharacteristic
318D11—82no—
319C24—221no—
320C24—222no—
321C24—441no—
322C24—441no—
323C24—442no—
324C24—881no—
325C24(C2×D11)⋊C411yescharacteristic
326C24(C2×D11)⋊C411yescharacteristic
327C24C2×C4×D1111yescharacteristic
328#41—44no—
329#41—44no—
330#41—48no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—41no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—881no—
348C2×D4—881no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—881no—
364C22×C4(C2×D11)⋊C411yescharacteristic
365C22×C4(C2×D11)⋊C411yescharacteristic
366C22×C4C2×D4411yescharacteristic
367C22×C4D4×D1112yes—
368C22×C4#434112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370M16—42no—
371M16—42no—
372M16—444no—
373M16—442no—
374M16—442no—
375C2×C8—42no—
376C2×C8—224no—
377C2×C8—444no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—442no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—881no—
386C22⋊C4—881no—
387C11#951111yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—222no—
402C23—224no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—442no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—882no—
411C23—882no—
412C23—884no—
413C23—884no—
414C23#6687012yes—
415C23(C22⋊D11)⋊C412yes—
416C23C2×(C2×D11)⋊C411yescharacteristic
417Q8—44no—
418D4—44no—
419D4—44no—
420D4—44no—
421D4—884no—
422D4—884no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4#6687012yes—
450C2×C4#6693511yescharacteristic
451C2×C4#6693911yescharacteristic
452C2×C4#6699212yes—
453C8—82no—
454C8—444no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—81no—
471C22—81no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—881no—
476C22—881no—
477C22—884no—
478C22—884no—
479C22—881no—
480C22—881no—
481C22C2×#6687011yescharacteristic
482C22C2×#6687011yescharacteristic
483C22#1062257111yescharacteristic
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—41no—
489C4—881no—
490C4—881no—
491C4—881no—
492C2—21no—
493C2—21no—
494C2—42no—
495C2—42no—
496C2—81no—
497C2—882no—
498C2#1306903211yescharacteristic
499C2#1306906711yescharacteristic
500C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1785C2
socleC22×C11#386
prime radical#13071931C2
cosocleC23×C4×C11C23
hypercenter#1785D11
hypocenterC11#9511
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
1. #13077061C2semidirect
3. #13066942C2semidirect
4. #13066525C2semidirect
5. C11×#1785C2semidirect
68. C22⋊(C11⋊C8)D4semidirect
140. #1785D11semidirect
387. C11#9511semidirect

Maximal subgroups

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

subgroupindex
#130770612
#130719312
#130669422
#130665252
C11×#17852
#951111