Finite Group Databasebeta

← #14650960

Subgroups — #14650960

Order 2816.

802 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077868C211yesmaximal, characteristic
2#13071446C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic, complemented
4#13067133C211yesmaximal, characteristic, complemented
5#13066523C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1789C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×#67002C412yescomplemented
10C2×D4×Dic11—21no—
11C2×#66983C2211yescharacteristic
12C2×C11×#104—22no—
13C11×#407C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15#10622851—22no—
16#10622845C412yescomplemented
17#10622843—21no—
18#10622840—21no—
19#10622833—22no—
20#10622830—21no—
21#10622825C2211yescharacteristic
22#10622824—21no—
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C11⋊#95—21no—
25#10622820C2211yescharacteristic
26C2×#66870—22no—
27#10622108—21no—
28#10622108—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—44no—
32C2×C11×#41C2×C412yes—
33C2×C11×#41D412yes—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C23×Dic11—22no—
41C22×D44C2×C411yescharacteristic, complemented
42C2×C11×M16—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—21no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11D412yes—
48#67002—44no—
49C2×#4325—22no—
50D4×Dic11—44no—
51C2×#4323—22no—
52#66983—21no—
53#66983—21no—
54#66983—21no—
55#66983—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic, complemented
59C2×C4×Dic11—21no—
60C2×#4318C2×C412yescomplemented
61C11×#104—44no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65#66899—22no—
66#66896—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—21no—
70C11⋊#95D411yescharacteristic
71C11⋊#95D411yescharacteristic
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66870—44no—
75#9365—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C11×#41—24no—
80C11×#41—24no—
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—44no—
84C11×#41—44no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C2×Q8×C11C22⋊C412yes—
88C2×D4×C11—24no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11—44no—
93C2×D4×C11C22⋊C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—44no—
99C22×C4×C11—41no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—42no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C22×Dic11—44no—
115C22×Dic11—44no—
116C22×Dic11—82no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—42no—
120C11×M16—42no—
121C2×C8×C11—41no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—41no—
124C42×C11—42no—
125C22⋊Dic11—42no—
126C22⋊Dic11—44no—
127C22⋊Dic11—42no—
128#4325—44no—
129#4323—44no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—42no—
135C4×Dic11—42no—
136#4318—42no—
137C2×C11⋊C8—22no—
138#3006—111no—
139#2339—111no—
140#1964—111no—
141#1789D1111yescharacteristic, complemented
142#1507—111no—
143#1305—111no—
144#1297—111no—
145C23×C11—24no—
146C23×C11—22no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11C4×D411yescharacteristic
155C23×C11#12011yescharacteristic
156C23×C11#12111yescharacteristic
157C22×D11—41no—
158C22×D11—42no—
159C22×D11—81no—
160C22×D11—81no—
161Q8×C11—22no—
162Q8×C11—22no—
163Q8×C11—42no—
164D4×C11—24no—
165D4×C11—22no—
166D4×C11—44no—
167D4×C11—44no—
168D4×C11#9914yescomplemented
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C22⋊D11—82no—
187C22⋊D11—81no—
188C22⋊D11—81no—
189C2×Dic11—22no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—88no—
201D44—42no—
202D44—81no—
203C8×C11—81no—
204C11⋊C8—42no—
205C22×#41C2×D1111yescharacteristic
206C2×AGL(1,ℤ/8)—112no—
207C2×#121—111no—
208C2×C4×D4—221no—
209#449—222no—
210#448—221no—
211#447—221no—
212C2×#104—22no—
213#417—112no—
214C2×#99—222no—
215#407—111no—
216#407C2×D1111yescharacteristic
217#391—221no—
218#386—222no—
219#381—221no—
220#380—111no—
221C4×C22⋊C4—111no—
222C4×C22⋊C4C2×D1111yescharacteristic
223C2×#95—221no—
224#327—221no—
225#327—221no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—24no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#38611yescharacteristic
242C22×C11#45311yescharacteristic
243C22×C11#45411yescharacteristic
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—162no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11C2×#9912yes—
254Dic11—42no—
255Dic11—81no—
256Dic11—82no—
257Dic11—81no—
258C2×#41—21no—
259C2×#41—21no—
260C2×#41—44no—
261C2×#41C4×D1112yes—
262C2×#41C22⋊D1112yes—
263C22×Q8D4411yescharacteristic
264C22×D4—21no—
265C22×D4—111no—
266C22×D4—221no—
267C22×D4D4411yescharacteristic
268C23×C4—21no—
269C23×C4—222no—
270C23×C4C22×D1111yescharacteristic
271AGL(1,ℤ/8)—444no—
272C2×SD16—222no—
273C2×D8—222no—
274C2×M16—21no—
275C2×M16—112no—
276#121—221no—
277#121—221no—
278#121—221no—
279#121—221no—
280C4×D4—444no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—221no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—112no—
285C2×C22⋊C4—222no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C42—21no—
289C2×C42—221no—
290#104—44no—
291#103—222no—
292#102—222no—
293#99—444no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298#95—21no—
299#95—111no—
300#95—111no—
301#95—222no—
302#95—222no—
303#95—221no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—41no—
307C2×C11—41no—
308C2×C11—44no—
309C2×C11#188311yescharacteristic
310C2×C11#189811yescharacteristic
311C2×C11#190611yescharacteristic
312D11—161no—
313C24—21no—
314C24—221no—
315C24D4×D1111yescharacteristic
316#41—24no—
317#41—24no—
318#41—42no—
319#41—42no—
320#41—44no—
321#41—44no—
322C2×Q8—21no—
323C2×Q8—42no—
324C2×Q8(C2×D11)⋊C412yes—
325C2×D4—24no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—21no—
329C2×D4—44no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—442no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4(C2×D11)⋊C412yes—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—44no—
343C22×C4—41no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—222no—
348C22×C4—444no—
349C22×C4—444no—
350C22×C4—882no—
351C22×C4C2×C4×D1111yescharacteristic
352C22×C4C2×D4411yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4#434111yescharacteristic
355C22×C4#434111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357SD16—444no—
358D8—444no—
359M16—42no—
360M16—442no—
361C2×C8—41no—
362C2×C8—222no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—442no—
366C22⋊C4—22no—
367C22⋊C4—41no—
368C22⋊C4—442no—
369C22⋊C4—444no—
370C22⋊C4—441no—
371C22⋊C4—441no—
372C22⋊C4—442no—
373C42—42no—
374C42—442no—
375C11#936511yescharacteristic, complemented, Sylow
376C23—24no—
377C23—22no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—41no—
384C23—41no—
385C23—442no—
386C23—441no—
387C23—881no—
388C23—881no—
389C23(C22⋊D11)⋊C411yescharacteristic
390C23#6693511yescharacteristic
391C23#6699211yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395D4—24no—
396D4—22no—
397D4—44no—
398D4—44no—
399D4—442no—
400D4—881no—
401D4—882no—
402D4—881no—
403D4—881no—
404D4#6687014yescomplemented
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—222no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4—888no—
430C2×C4(C22⋊D11)⋊C411yescharacteristic
431C2×C4#6693911yescharacteristic
432C2×C4C2×(C2×D11)⋊C411yescharacteristic
433C2×C4#6699211yescharacteristic
434C8—81no—
435C8—442no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—24no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—44no—
446C22—44no—
447C22—42no—
448C22—42no—
449C22—81no—
450C22—81no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—1762no—
455C22#1062243511yescharacteristic
456C22#1062244011yescharacteristic
457C22#1062257111yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—82no—
463C4—442no—
464C4—882no—
465C4—881no—
466C4—881no—
467C4C2×#6687012yes—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—44no—
473C2—1761no—
474C2#1306899011yescharacteristic
475C2#1306906711yescharacteristic
476C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1789C2
socleC22×C11#386
prime radical#13077868C2
cosocleC23×C4×C11C23
hypercenter#1789D11
hypocenterC11#9365
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13071446C2semidirect
3. #13069452C2semidirect
4. #13067133C2semidirect
5. #13066523C2semidirect
6. #13066502C2semidirect
7. C11×#1789C2semidirect
9. C2×#67002C4semidirect
16. #10622845C4semidirect
41. C22×D44C2×C4semidirect
58. C2×C4⋊Dic11C2×C4semidirect
60. C2×#4318C2×C4semidirect
141. #1789D11semidirect
168. D4×C11#99semidirect
375. C11#9365semidirect
404. D4#66870semidirect

Maximal subgroups

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

subgroupindex
#130778682
#130714462
#130694522
#130671332
#130665232
#130665022
C11×#17892
#936511