Finite Group Databasebeta

← #14726756

Subgroups — #14726756

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2C2×#10622581C212yesmaximal, complemented
3#13067652C214yesmaximal, complemented
4#13067635C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#2487C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic, complemented
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623086—22no—
14#10623085—24no—
15D4×D44—22no—
16#10623041C2212yes—
17#10623024—21no—
18#10623024C2212yes—
19#10623008—21no—
20C11×#400C2212yescomplemented
21C11×#399C2212yescomplemented
22C11×#389—21no—
23C11×#386—21no—
24C11×#385—21no—
25C11×#380—21no—
26C11×#380C2211yescharacteristic, complemented
27C2×C22⋊(C11⋊C8)C2212yescomplemented
28#10622581—24no—
29#10622581C2218yescomplemented
30C2×#66873—22no—
31C2×#66872—22no—
32#10622166C2212yescomplemented
33#10622163C2212yescomplemented
34#10622089C2218yescomplemented
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C22×C22⋊D11—22no—
41#67037—44no—
42#67037—44no—
43C2×#4341—24no—
44C2×D4×D11—24no—
45C2×#4339—22no—
46C22×D44—21no—
47C22×D44D412yes—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4D411yescharacteristic
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C42×C11D411yescharacteristic
62#66983—22no—
63#66983—22no—
64#66983—22no—
65#66983—22no—
66#66983—22no—
67#66983—22no—
68#66983D414yes—
69#66983C2314yes—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D412yes—
74C22×C11⋊C8—22no—
75#66950—24no—
76#66948—24no—
77#66939—24no—
78#66939—24no—
79#66935—24no—
80#66935—24no—
81#66928—22no—
82#66927—21no—
83C4×D44—22no—
84C4×D44—22no—
85#66922—21no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95C2312yes—
89C22⋊(C11⋊C8)—22no—
90C22⋊(C11⋊C8)C2314yes—
91#66873—28no—
92#66872—28no—
93#18203—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C24×C11C2×D411yescharacteristic
96C23×D11—22no—
97C23×D11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11SD1614yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—24no—
118C2×C22⋊D11—24no—
119C2×C22⋊D11—44no—
120C2×C22⋊D11—44no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125#4341—416no—
126D4×D11—416no—
127#4339—44no—
128#4339—44no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—44no—
134C2×D44—82no—
135C2×D44C2×D414yes—
136C2×C4×D11—24no—
137C2×Dic22—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—82no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—82no—
148C42×C11—21no—
149C42×C11—21no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×D414yes—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—44no—
160#3496—111no—
161C2×#481—112no—
162#2487D1111yescharacteristic, complemented
163#1616—114no—
164#1613—114no—
165#1519—112no—
166#1459—111no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11#12012yes—
174C23×C11C2×SD1612yes—
175C23×C11C2×SD1612yes—
176C23×C11AGL(1,ℤ/8)12yes—
177C23×C11C22×D411yescharacteristic
178C22×D11—24no—
179C22×D11—44no—
180C22×D11—44no—
181C22×D11—82no—
182C22×D11—82no—
183C22×D11—82no—
184C22×D11—82no—
185D4×C11—28no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—81no—
204C2×C4×C11—84no—
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11C22×D412yes—
209C22⋊D11—48no—
210C22⋊D11—44no—
211C22⋊D11—44no—
212C22⋊D11—48no—
213C2×Dic11—24no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216D44—44no—
217D44—44no—
218D44—44no—
219D44—82no—
220D44—82no—
221C4×D11—48no—
222Dic22—44no—
223C11⋊C8—44no—
224C2×H(5,𝔽2)—221no—
225#547—222no—
226#546—224no—
227D42—222no—
228#537—112no—
229#534—112no—
230#534—221no—
231#532—221no—
232C2×#121—112no—
233C2×#121—221no—
234C2×C4×D4C2×D1111yescharacteristic
235C22×C4⋊C4C2×D1111yescharacteristic, complemented
236#481—118no—
237#481—224no—
238C2×#106—222no—
239C2×#102—222no—
240C2×C22⋊C8—112no—
241#400C2×D1112yescomplemented
242#399C2×D1112yescomplemented
243#389—21no—
244#386—21no—
245#385—21no—
246#380—21no—
247#380C2×D1111yescharacteristic, complemented
248#327—118no—
249#324—112no—
250#323—112no—
251C22×C11—21no—
252C22×C11—22no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—81no—
262C22×C11#45014yes—
263C22×C11C2×#12011yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C2×D11—44no—
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—164no—
270C2×D11—164no—
271C4×C11—22no—
272C4×C11—21no—
273C4×C11—22no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—82no—
277C4×C11—82no—
278C4×C11#45812yes—
279Dic11—44no—
280H(5,𝔽2)—444no—
281H(5,𝔽2)—444no—
282C2×#41—224no—
283C2×#41—222no—
284C22×D4—112no—
285C22×D4—221no—
286C22×D4—224no—
287C22×D4—222no—
288C22×D4—222no—
289C22×D4C22⋊D1111yescharacteristic
290C23×C4—21no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C22×C8—222no—
294C4⋊Q8—221no—
295#127—221no—
296#124—222no—
297#123—224no—
298#123—224no—
299C22⋊Q8—224no—
300#121—114no—
301#121—114no—
302#121—224no—
303#121—222no—
304#121—222no—
305#121—222no—
306#121—222no—
307#121—222no—
308#121—222no—
309#120—224no—
310#120—224no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—222no—
314C4×D4—222no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C22×D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4C22⋊D1111yescharacteristic
329C2×C22⋊C4C22×D1111yescharacteristic
330C2×C42C22⋊D1111yescharacteristic
331#106—228no—
332#102—228no—
333C22⋊C8—114no—
334C22⋊C8—222no—
335#95—22no—
336#95—22no—
337#95C22×D1112yes—
338C2×C11—21no—
339C2×C11—24no—
340C2×C11—21no—
341C2×C11—42no—
342C2×C11C2×#45011yescharacteristic
343C2×C11#302111yescharacteristic
344C2×C11C2×#45811yescharacteristic
345D11—84no—
346C24—222no—
347C24—222no—
348C24C2×C22⋊D1111yescharacteristic
349C24C2×C22⋊D1111yescharacteristic
350#41—444no—
351#41—4416no—
352#41—444no—
353C2×Q8—222no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—114no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—224no—
361C2×D4—224no—
362C2×D4—224no—
363C2×D4—222no—
364C2×D4—444no—
365C2×D4—4416no—
366C2×D4—444no—
367C2×D4—444no—
368C2×D4—444no—
369C2×D4—444no—
370C2×D4—882no—
371C2×D4#432514yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—82no—
380C22×C4—224no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4D4×D1112yes—
384C22×C4D4×D1112yes—
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C23×D1111yescharacteristic
390C2×C8—224no—
391C2×C8—444no—
392C4⋊C4—22no—
393C4⋊C4—24no—
394C4⋊C4—42no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—82no—
398C4⋊C4—114no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—42no—
405C22⋊C4—82no—
406C22⋊C4—224no—
407C22⋊C4—224no—
408C22⋊C4—224no—
409C22⋊C4—224no—
410C42—21no—
411C42—21no—
412C11#1820311yescharacteristic, complemented, Sylow
413C23—21no—
414C23—21no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—224no—
420C23—444no—
421C23—444no—
422C23—882no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6699012yes—
427C23C2×#432512yes—
428C23C2×#432512yes—
429C23#6700212yes—
430C23C22×C22⋊D1111yescharacteristic
431Q8—444no—
432D4—28no—
433D4—444no—
434D4—444no—
435D4—448no—
436D4—444no—
437D4—444no—
438D4—448no—
439D4—444no—
440D4—882no—
441D4—882no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—81no—
460C2×C4—84no—
461C2×C4—224no—
462C2×C4—448no—
463C2×C4—444no—
464C2×C4—444no—
465C2×C4#6699011yescharacteristic
466C2×C4#6699011yescharacteristic
467C2×C4C2×#432512yes—
468C2×C4C2×D4×D1112yes—
469C8—444no—
470C22—21no—
471C22—22no—
472C22—21no—
473C22—22no—
474C22—22no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—81no—
481C22—444no—
482C22—444no—
483C22—444no—
484C22—1764no—
485C22—1764no—
486C22#1062265914yes—
487C22C2×#6699011yescharacteristic
488C22C22×#432511yescharacteristic
489C22C2×#6700211yescharacteristic
490C4—22no—
491C4—22no—
492C4—21no—
493C4—41no—
494C4—41no—
495C4—82no—
496C4—82no—
497C4—444no—
498C4#1062266612yes—
499C2—21no—
500C2—21no—
501C2—24no—
502C2—42no—
503C2—884no—
504C2C2×#1062265911yescharacteristic
505C2#1307798711yescharacteristic
506C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2487C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2487D11
hypocenterC11#18203
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. C2×#10622581C2semidirect
3. #13067652C2semidirect
4. #13067635C2semidirect
5. #13067183C2semidirect
6. #13066934C2semidirect
7. C11×#2487C2semidirect
10. C22×C11×C4⋊C4C22semidirect
20. C11×#400C22semidirect
21. C11×#399C22semidirect
26. C11×#380C22semidirect
27. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622581C22semidirect
32. #10622166C22semidirect
33. #10622163C22semidirect
34. #10622089C22semidirect
162. #2487D11semidirect
235. C22×C4⋊C4C2×D11semidirect
241. #400C2×D11semidirect
242. #399C2×D11semidirect
247. #380C2×D11semidirect
412. C11#18203semidirect

Maximal subgroups

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

subgroupindex
#130823802
C2×#106225812
#130676522
#130676352
#130671832
#130669342
C11×#24872
#1820311