Finite Group Databasebeta

← #14810431

Subgroups — #14810431

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic, complemented
2C2×#10622668C212yesmaximal, complemented
3#13069757C212yesmaximal, complemented
4#13069752C212yesmaximal, complemented
5#13069588C212yesmaximal, complemented
6#13068934C212yesmaximal
7#13068924C212yesmaximal, complemented
8#13068378C211yesmaximal, characteristic, complemented
9C11×#2850C211yesmaximal, characteristic
10C23×Dic22—21no—
11C2×C11×#124C2211yescharacteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11—21no—
16C22×C4⋊Dic11C2212yes—
17C2×#66922—21no—
18C2×#66922—21no—
19C2×#66922—28no—
20C2×#66922C2212yes—
21C2×#66922C2212yes—
22C11×#391C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#386—21no—
27C11×#386—21no—
28C11×#382C2211yescharacteristic
29C2×#66899C2214yes—
30C2×#66896C2214yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622668—28no—
33C2×#66867C2212yes—
34#10622167C2214yes—
35#10622167C2214yes—
36#10622162C2212yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—22no—
44C22×Dic22—28no—
45C22×Dic22—22no—
46C22×Dic22—22no—
47C22×Dic22—44no—
48C22×Dic22—44no—
49C11×#124—24no—
50C11×C22⋊Q8—24no—
51C11×#121—24no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—24no—
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C4⋊Dic11—28no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—28no—
71C2×C4⋊Dic11C2314yes—
72C22×C11⋊C8C2314yes—
73#66922—28no—
74#66922—28no—
75#66922—24no—
76#66922—28no—
77#66922D418yescomplemented
78C11×#95—21no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—21no—
82#66899—28no—
83#66896—28no—
84C22⋊(C11⋊C8)—24no—
85#66867—24no—
86#25908—111nomaximal, Sylow
87C24×C11—21no—
88C24×C11C2×D411yescharacteristic
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4114yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—28no—
117C22×Dic11—24no—
118C22×Dic11—44no—
119C22×Dic11—44no—
120C2×Dic22—28no—
121C2×Dic22—28no—
122C2×Dic22—432no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11C2×D414yes—
140C4⋊Dic11—28no—
141C4⋊Dic11—28no—
142C4⋊Dic11—28no—
143C4⋊Dic11—24no—
144C4⋊Dic11C2×D418yes—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—24no—
148C22×C4⋊Q8—111no—
149C2×#489—112no—
150#2850D1111yescharacteristic
151#2024—112no—
152#2023—112no—
153#1993—112no—
154#1874—112no—
155#1872—112no—
156#1749—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11#12412yes—
169C23×C11AGL(1,ℤ/8)12yes—
170C23×C11#13712yes—
171C23×C11C22×D411yescharacteristic
172Q8×C11—44no—
173D4×C11—44no—
174D4×C11—84no—
175C2×C4×C11—28no—
176C2×C4×C11—28no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
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—28no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#12012yes—
198C2×C4×C11#12012yes—
199C2×C4×C11#12412yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11C2×#4112yes—
204C2×C4×C112−1+412yes—
205C2×Dic11—28no—
206C2×Dic11—416no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209Dic22—416no—
210Dic22—416no—
211C11⋊C8—44no—
212C23×Q8—221no—
213C2×C4⋊Q8—112no—
214C2×C4⋊Q8—112no—
215C2×C4⋊Q8—228no—
216C2×C4⋊Q8—221no—
217C2×C4⋊Q8—221no—
218C2×#124C2×D1111yescharacteristic
219C2×C22⋊Q8C2×D1111yescharacteristic
220C2×#121C2×D1111yescharacteristic
221C22×C4⋊C4—112no—
222C22×C4⋊C4—221no—
223C22×C42C2×D1111yescharacteristic
224#489—228no—
225C2×#103—114no—
226C2×#102—114no—
227C2×C22⋊C8—112no—
228C2×#97—112no—
229#391C2×D1111yescharacteristic
230#390C2×D1111yescharacteristic
231#388—21no—
232#388—21no—
233#386—21no—
234#386—21no—
235#382C2×D1111yescharacteristic
236#340—114no—
237#340—114no—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11#48914yescomplemented
253C22×C11C2×#12011yescharacteristic
254C22×C11C2×#12411yescharacteristic
255C22×C11#53611yescharacteristic
256C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—81no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11#54814yes—
269Dic11—48no—
270C22×Q8—228no—
271C22×Q8—222no—
272C22×Q8—222no—
273C22×Q8—444no—
274C22×Q8—444no—
275C22×Q8C22×D1111yescharacteristic
276C22×D4—21no—
277C22×D4C22×D1111yescharacteristic
278C23×C4—222no—
279C23×C4C22⋊D1111yescharacteristic
280C23×C4C22⋊D1111yescharacteristic
281C23×C4C22×D1111yescharacteristic
282C22×C8—114no—
283C4⋊Q8—118no—
284C4⋊Q8—228no—
285C4⋊Q8—228no—
286C4⋊Q8—228no—
287C4⋊Q8—224no—
288#124—24no—
289C22⋊Q8—24no—
290#121—24no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—114no—
293C2×C4⋊C4—228no—
294C2×C4⋊C4—228no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C42—24no—
307C2×C42C22⋊D1111yescharacteristic
308C2×C42C22⋊D1111yescharacteristic
309C2×C42C22×D1111yescharacteristic
310C2×C42C22×D1111yescharacteristic
311#103—228no—
312#102—228no—
313C22⋊C8—224no—
314#97—224no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319C2×C11—24no—
320C2×C11—161no—
321C2×C11#243611yescharacteristic
322C2×C11#300311yescharacteristic
323C2×C11#300411yescharacteristic
324C2×C11C2×#48911yescharacteristic
325C2×C11#314111yescharacteristic
326C2×C11#323811yescharacteristic
327C2×C11#323911yescharacteristic
328C24—21no—
329C24C2×C22⋊D1111yescharacteristic
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—228no—
334C2×Q8—228no—
335C2×Q8—4432no—
336C2×Q8—444no—
337C2×Q8—444no—
338C2×Q8—444no—
339C2×Q8—444no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—42no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—228no—
358C22×C4—224no—
359C22×C4—444no—
360C22×C4—444no—
361C22×C4#434114yes—
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368C2×C8—224no—
369C2×C8—224no—
370C2×C8—224no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—118no—
375C4⋊C4—228no—
376C4⋊C4—228no—
377C4⋊C4—228no—
378C4⋊C4—224no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42D4×D1114yes—
389C11#2590811yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23#6698912yes—
402C23#6700212yes—
403C23#6700412yes—
404C23C22×C22⋊D1111yescharacteristic
405Q8—44no—
406Q8—4416no—
407Q8—4416no—
408D4—44no—
409D4—84no—
410C2×C4—28no—
411C2×C4—28no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—28no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—228no—
433C2×C4—4416no—
434C2×C4—444no—
435C2×C4—444no—
436C2×C4#6698912yes—
437C2×C4#6699012yes—
438C2×C4#6699012yes—
439C2×C4#6700212yes—
440C2×C4#6700412yes—
441C2×C4C2×D4×D1112yes—
442C2×C4C2×#434112yes—
443C2×C4#6704312yes—
444C8—444no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22#1062266814yescomplemented
459C22C2×#6698911yescharacteristic
460C22C2×#6699011yescharacteristic
461C22C2×#6700211yescharacteristic
462C22C2×#6700211yescharacteristic
463C22C2×#6700411yescharacteristic
464C22C2×#6700411yescharacteristic
465C22#1062335611yescharacteristic
466C4—22no—
467C4—22no—
468C4—22no—
469C4—22no—
470C4—22no—
471C4—81no—
472C4—81no—
473C4—81no—
474C4—448no—
475C4#1062312914yes—
476C2—24no—
477C2—161no—
478C2#1307227511yescharacteristic
479C2#1307784211yescharacteristic
480C2#1307784911yescharacteristic
481C2C2×#1062266811yescharacteristic
482C2#1307900911yescharacteristic
483C2#1307983411yescharacteristic
484C2#1307984311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2850C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2850D11
hypocenterC11#25908
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
2. C2×#10622668C2semidirect
3. #13069757C2semidirect
4. #13069752C2semidirect
5. #13069588C2semidirect
7. #13068924C2semidirect
8. #13068378C2semidirect
77. #66922D4semidirect
252. C22×C11#489semidirect
389. C11#25908semidirect
458. C22#10622668semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
C2×#106226682
#130697572
#130697522
#130695882
#130689342
#130689242
#130683782
C11×#28502
#2590811