Finite Group Databasebeta

← #14767640

Subgroups — #14767640

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622687C211yesmaximal, characteristic
2#13071342C211yesmaximal, characteristic, complemented
3#13071324C211yesmaximal, characteristic, complemented
4#13069427C211yesmaximal, characteristic, complemented
5#13068968C212yesmaximal, complemented
6#13068962C212yesmaximal, complemented
7#13068961C212yesmaximal, complemented
8#13068948C212yesmaximal, complemented
9#13068751C211yesmaximal, characteristic, complemented
10#13068367C211yesmaximal, characteristic, complemented
11C11×#1957C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×#4324C2212yes—
15C22×#4323C2212yes—
16C2×#66946C2211yescharacteristic
17C2×#66940C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22C11×#384C2211yescharacteristic
23#10622834C2212yes—
24#10622833—22no—
25#10622833—22no—
26C2×#66885C2212yes—
27C2×#66880C2212yes—
28#10622687C418yescomplemented
29#10622603—22no—
30#10622602—22no—
31#10622601C2211yescharacteristic
32#10622587C2211yescharacteristic
33#10622549C2211yescharacteristic
34#10622545C2211yescharacteristic
35C2×#66867C2211yescharacteristic
36#10622188C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C22×D4×C11—22no—
41C22×D4×C11C2312yes—
42C23×Dic11—22no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C11×#127—22no—
48C11×#127C2×C414yescomplemented
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56D4×Dic11—42no—
57D4×Dic11—42no—
58C2×#4324—42no—
59C2×#4324—42no—
60C2×#4324C2×C418yescomplemented
61C2×#4323—42no—
62C2×#4323—42no—
63C2×#4323C2×C418yescomplemented
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66946—42no—
74#66940—42no—
75#66928—22no—
76#66928C2×C414yescomplemented
77C11×#102—42no—
78C11×#102—42no—
79C4×C8×C11—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95D412yes—
83C11⋊#95D412yes—
84#66885—42no—
85#66880—42no—
86#66867C2×C414yescomplemented
87#22279—111nomaximal, Sylow
88C24×C11—22no—
89C23×D11—21no—
90C2×D4×C11—28no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—82no—
97C2×D4×C11—82no—
98C2×D4×C11C22×C414yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—44no—
106C22×Dic11—82no—
107C22×Dic11—82no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C2×D44—21no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44C22×C412yes—
115C2×C4×D11—42no—
116C2×C4×D11—82no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22C22×C412yes—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—82no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129C22⋊Dic11—44no—
130C22⋊Dic11—82no—
131C22⋊Dic11—82no—
132#4324—48no—
133#4323—48no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139Dic11⋊C4—42no—
140C4×Dic11—22no—
141C4×Dic11—22no—
142C4×Dic11—42no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8C22×C414yes—
146C2×#496—111no—
147#2328—111no—
148#2326—111no—
149#1958—111no—
150#1957D1111yescharacteristic, complemented
151#1880—112no—
152#1879—112no—
153#1879—112no—
154#1877—112no—
155#1836—111no—
156#1746—111no—
157C23×C11—24no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C22×D411yescharacteristic
165C22×D11—22no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—42no—
169C22×D11—42no—
170D4×C11—24no—
171D4×C11—24no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—88no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11C4×D414yes—
182C2×C4×C11C23×C411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11H(5,𝔽2)12yes—
185C2×C4×C11H(5,𝔽2)12yes—
186C2×Dic11—22no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—88no—
200D44—24no—
201D44—42no—
202C4×D11—84no—
203Dic22—24no—
204Dic22—42no—
205C8×C11—42no—
206C11⋊C8—24no—
207C22×SD16—112no—
208C22×D8—112no—
209C2×#127C2×D1111yescharacteristic
210C2×#124—111no—
211C2×C4×Q8—111no—
212C2×C4×D4—112no—
213C2×C4×D4—111no—
214#496—118no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#102C2×D1112yes—
218C2×#102C2×D1112yes—
219C2×#97—111no—
220C2×C4×C8C2×D1111yescharacteristic
221#391—111no—
222#390—112no—
223#390—111no—
224#388—222no—
225#386—222no—
226#386—222no—
227#385—222no—
228#384C2×D1111yescharacteristic
229#382—111no—
230#376—111no—
231#340—112no—
232#340—112no—
233#336—112no—
234#336—112no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11#53511yescharacteristic
244C22×C11#53511yescharacteristic
245C22×C11#57612yes—
246C22×C11#57712yes—
247C2×D11—42no—
248C2×D11—44no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—82no—
252C4×C11—24no—
253C4×C11—81no—
254C4×C11—81no—
255C4×C11#51812yes—
256C4×C11#54012yes—
257Dic11—42no—
258Dic11—41no—
259Dic11—41no—
260Dic11—42no—
261Dic11—82no—
262C22×Q8—111no—
263C22×D4—22no—
264C22×D4—111no—
265C22×D4C22×D1112yes—
266C23×C4—221no—
267C23×C4—222no—
268C2×SD16—118no—
269C2×SD16—442no—
270C2×SD16—442no—
271C2×D8—118no—
272C2×D8—442no—
273C2×D8—442no—
274C22×C8—112no—
275C22×C8C22×D1112yes—
276#127—22no—
277#127C4×D1114yescomplemented
278#124—114no—
279#124—222no—
280C4×Q8—442no—
281C4×D4—442no—
282C4×D4—442no—
283C4×D4—442no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4C22×D1111yescharacteristic
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—222no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—221no—
298C2×C42C22×D1111yescharacteristic
299#103—442no—
300#102—42no—
301#102—42no—
302#102—442no—
303#97—114no—
304C4×C8—22no—
305#95—112no—
306#95—112no—
307#95—222no—
308#95—222no—
309C2×C11—84no—
310C2×C11#232811yescharacteristic
311C2×C11#294612yes—
312C2×C11#322011yescharacteristic
313C2×C11#322111yescharacteristic
314C2×C11#322412yes—
315D11—82no—
316C24—22no—
317C24—221no—
318C2×Q8—112no—
319C2×Q8—221no—
320C2×Q8—222no—
321C2×Q8—222no—
322C2×D4—28no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—82no—
329C2×D4—82no—
330C2×D4—112no—
331C2×D4—221no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4C2×C4×D1114yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—112no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—221no—
341C22×C4—222no—
342C22×C4—442no—
343C22×C4—444no—
344C22×C4—882no—
345C22×C4—882no—
346C22×C4—882no—
347C22×C4D4×D1112yes—
348C22×C4C23×D1111yescharacteristic
349SD16—448no—
350D8—448no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—114no—
355C2×C8—222no—
356C2×C8—222no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—82no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4—442no—
363C22⋊C4—228no—
364C22⋊C4—442no—
365C22⋊C4—444no—
366C22⋊C4—882no—
367C22⋊C4—882no—
368C22⋊C4—882no—
369C42—222no—
370C42—222no—
371C42—442no—
372C42C2×C4×D1112yes—
373C42#434112yes—
374C11#2227911yescharacteristic, complemented, Sylow
375C23—24no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—222no—
383C23—441no—
384C23—442no—
385C23—442no—
386C23—441no—
387C23C2×D4×D1111yescharacteristic
388Q8—224no—
389Q8—442no—
390D4—24no—
391D4—24no—
392D4—42no—
393D4—42no—
394D4—88no—
395D4—224no—
396D4—442no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—884no—
417C2×C4—888no—
418C2×C4(C22⋊D11)⋊C414yes—
419C2×C4C22×C4×D1111yescharacteristic
420C2×C4C2×#434111yescharacteristic
421C2×C4#6703712yes—
422C2×C4#6704212yes—
423C8—42no—
424C8—224no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—82no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—444no—
433C22—442no—
434C22—881no—
435C22—881no—
436C22—882no—
437C22C2×(C22⋊D11)⋊C411yescharacteristic
438C22#1062320511yescharacteristic
439C22#1062324611yescharacteristic
440C22#1062328812yes—
441C22#1062329312yes—
442C4—24no—
443C4—81no—
444C4—81no—
445C4—441no—
446C4—441no—
447C4—442no—
448C4—442no—
449C4—882no—
450C4#1062307612yes—
451C4#1062315012yes—
452C2—84no—
453C2—882no—
454C2#1307134011yescharacteristic
455C2#1307744212yes—
456C2#1307965911yescharacteristic
457C2#1307967011yescharacteristic
458C2#1307971312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1957C2
socleC23×C11C22×D4
prime radicalC2×#10622687C2
cosocleC22×C4×C11C24
hypercenter#1957D11
hypocenterC11#22279
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13071342C2semidirect
3. #13071324C2semidirect
4. #13069427C2semidirect
5. #13068968C2semidirect
6. #13068962C2semidirect
7. #13068961C2semidirect
8. #13068948C2semidirect
9. #13068751C2semidirect
10. #13068367C2semidirect
11. C11×#1957C2semidirect
28. #10622687C4semidirect
48. C11×#127C2×C4semidirect
60. C2×#4324C2×C4semidirect
63. C2×#4323C2×C4semidirect
76. #66928C2×C4semidirect
86. #66867C2×C4semidirect
150. #1957D11semidirect
277. #127C4×D11semidirect
374. C11#22279semidirect

Maximal subgroups

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

subgroupindex
C2×#106226872
#130713422
#130713242
#130694272
#130689682
#130689622
#130689612
#130689482
#130687512
#130683672
C11×#19572
#2227911