Finite Group Databasebeta

← #14770844

Subgroups — #14770844

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622846C211yesmaximal, characteristic
2#13071499C211yesmaximal, characteristic, complemented
3#13069309C212yesmaximal, complemented
4#13069254C212yesmaximal, complemented
5#13068863C212yesmaximal, complemented
6#13068708C211yesmaximal, characteristic, complemented
7#13068643C211yesmaximal, characteristic, complemented
8#13068556C211yesmaximal, characteristic
9#13068441C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#2339C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×#66979C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#391C2212yes—
17C11×#386—22no—
18C11×#381—21no—
19C11×#380C2211yescharacteristic
20C4×C11×C22⋊C4C2211yescharacteristic
21C2×C11×#95—21no—
22#10622846C418yescomplemented
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66871C2212yes—
32#10622557—22no—
33C4×C4⋊Dic11C2212yes—
34#10622541C2212yes—
35C2×#66867C2212yes—
36#10622263—21no—
37#10622261—21no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11C2311yescharacteristic
52C4×D4×C11—24no—
53C4×D4×C11—42no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11C2312yes—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61#66979—22no—
62#66979C2×C414yescomplemented
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C22×C11⋊C8—42no—
70C22×C11⋊C8C2×C414yescomplemented
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C11×#95—21no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95D411yescharacteristic
78C11×#95D411yescharacteristic
79#66899—42no—
80#66899C2×C414yescomplemented
81#66899C2×C414yescomplemented
82#66896—24no—
83#66896C2×C414yes—
84#66896C2×C414yes—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—22no—
89#66871—42no—
90#66867—42no—
91#22564—111nomaximal, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C11×#41—28no—
95C11×#41—44no—
96C11×#41—48no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11C22×C412yes—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11#4114yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—82no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—44no—
129C11×C22⋊C4—81no—
130C42×C11—22no—
131C42×C11—22no—
132C22⋊Dic11—24no—
133C22⋊Dic11—81no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—82no—
141C4×Dic11—24no—
142C4×Dic11—44no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C2×#416—111no—
152#2346—111no—
153#2339D1111yescharacteristic
154#1935—112no—
155#1928—112no—
156#1862—112no—
157#1825—111no—
158#1808—111no—
159#1788—111no—
160#1762—112no—
161#1752—111no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—42no—
176D4×C11—22no—
177D4×C11—24no—
178D4×C11—48no—
179D4×C11#11714yes—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—48no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—88no—
197C2×C4×C11C4×D412yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4112yes—
201C2×C4×C11H(5,𝔽2)12yes—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C11⋊C8—42no—
213C22×#41C2×D1111yescharacteristic
214C23×C8—111no—
215C2×C4×D4C2×D1112yes—
216C2×#117—111no—
217C2×#107—112no—
218#416—118no—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—112no—
222C2×#102—111no—
223C2×#102—111no—
224C2×#102—112no—
225C2×C22⋊C8—111no—
226C2×#97—112no—
227#391C2×D1112yes—
228#389—112no—
229#388—222no—
230#386—22no—
231#382—221no—
232#381—21no—
233#380—111no—
234#380C2×D1111yescharacteristic
235C4×C4⋊C4—112no—
236C4×C22⋊C4C2×D1111yescharacteristic
237#376—221no—
238C2×#95—21no—
239#340—112no—
240#340—112no—
241#340—112no—
242#336—112no—
243C22×C11—22no—
244C22×C11—24no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11C2×C4×D411yescharacteristic
254C22×C11#54612yes—
255C22×C11#57512yes—
256C22×C11#57611yescharacteristic
257C22×C11#57811yescharacteristic
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—82no—
263C4×C11C2×#11711yescharacteristic
264C4×C11#51811yescharacteristic
265C4×C11#55112yes—
266Dic11—42no—
267Dic11—42no—
268Dic11—82no—
269C2×#41—22no—
270C2×#41—24no—
271C2×#41—42no—
272C2×#41C4×D1114yes—
273C22×Q8C22×D1111yescharacteristic
274C22×D4—21no—
275C22×D4C22×D1111yescharacteristic
276C23×C4—21no—
277C23×C4—22no—
278C23×C4C22×D1111yescharacteristic
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—114no—
282C22×C8—112no—
283C22×C8—442no—
284C4×D4—24no—
285C4×D4—42no—
286#117—114no—
287#117—222no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1112yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4C22⋊D1112yes—
298C2×C42—221no—
299C2×C42—222no—
300C2×C42C22×D1112yes—
301#107—442no—
302#103—114no—
303#103—114no—
304#103—442no—
305#102—114no—
306#102—114no—
307#102—224no—
308C22⋊C8—222no—
309#97—442no—
310#95—21no—
311#95—22no—
312#95—22no—
313#95—221no—
314#95—222no—
315#95—222no—
316#95C22⋊D1111yescharacteristic
317#95C22⋊D1111yescharacteristic
318C2×C11—42no—
319C2×C11—44no—
320C2×C11#234211yescharacteristic
321C2×C11#294311yescharacteristic
322C2×C11#295111yescharacteristic
323C2×C11#331512yes—
324C2×C11#331912yes—
325C24—21no—
326C24C2×C22⋊D1111yescharacteristic
327#41—28no—
328#41—44no—
329#41—48no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C2×C4×D1112yes—
334C2×D4—24no—
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C2×C4×D1112yes—
339C2×D4#434114yes—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—82no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4C2×C4×D1112yes—
353C22×C4#433912yes—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C2×C22⋊D1112yes—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C23×D1111yescharacteristic
358C2×C8—112no—
359C2×C8—112no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—444no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—112no—
369C4⋊C4—112no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—882no—
375C22⋊C4—42no—
376C22⋊C4—44no—
377C22⋊C4—81no—
378C22⋊C4—224no—
379C22⋊C4—881no—
380C42—22no—
381C42—22no—
382C42—224no—
383C42—444no—
384C11#2256411yescharacteristic, complemented, Sylow
385C23—22no—
386C23—24no—
387C23—22no—
388C23—22no—
389C23—21no—
390C23—21no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23C4×C22⋊D1112yes—
395C23C22×C22⋊D1111yescharacteristic
396Q8—22no—
397Q8—22no—
398Q8—42no—
399D4—22no—
400D4—24no—
401D4—48no—
402D4#6693014yes—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—48no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—88no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4C4×C22⋊D1112yes—
429C2×C4C22×C4×D1111yescharacteristic
430C2×C4C2×#433911yescharacteristic
431C2×C4C2×#434112yes—
432C2×C4#6703712yes—
433C8—222no—
434C8—222no—
435C8—442no—
436C22—22no—
437C22—24no—
438C22—22no—
439C22—22no—
440C22—42no—
441C22—44no—
442C22—42no—
443C22—44no—
444C22—42no—
445C22—42no—
446C22C2×C4×C22⋊D1111yescharacteristic
447C22#1062333712yes—
448C22#1062335312yes—
449C22#1062336611yescharacteristic
450C22#1062336911yescharacteristic
451C4—22no—
452C4—42no—
453C4—42no—
454C4—42no—
455C4—82no—
456C4—442no—
457C4—442no—
458C4—882no—
459C4C2×#6693011yescharacteristic
460C4#1062301711yescharacteristic
461C4#1062302612yes—
462C2—42no—
463C2—44no—
464C2#1307146111yescharacteristic
465C2#1307741411yescharacteristic
466C2#1307748911yescharacteristic
467C2#1308071212yes—
468C2#1308077212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2339C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2339D11
hypocenterC11#22564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #13071499C2semidirect
3. #13069309C2semidirect
4. #13069254C2semidirect
5. #13068863C2semidirect
6. #13068708C2semidirect
7. #13068643C2semidirect
9. #13068441C2semidirect
10. #13068394C2semidirect
22. #10622846C4semidirect
62. #66979C2×C4semidirect
70. C22×C11⋊C8C2×C4semidirect
80. #66899C2×C4semidirect
81. #66899C2×C4semidirect
384. C11#22564semidirect

Maximal subgroups

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

subgroupindex
C2×#106228462
#130714992
#130693092
#130692542
#130688632
#130687082
#130686432
#130685562
#130684412
#130683942
C11×#23392
#2256411