Finite Group Databasebeta

← #14726495

Subgroups — #14726495

Order 2816.

1242 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078552C212yesmaximal, complemented
2#13071875C211yesmaximal, characteristic, complemented
3#13067653C212yesmaximal, complemented
4#13067636C212yesmaximal, complemented
5#13067619C212yesmaximal, complemented
6#13067602C212yesmaximal, complemented
7#13067132C212yesmaximal, complemented
8#13066954C211yesmaximal, characteristic, complemented
9C11×#3496C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)—21no—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66979C2211yescharacteristic, complemented
22#10622835—21no—
23#10622828—22no—
24C4×C22⋊Dic11—21no—
25C4×C22⋊Dic11C2211yescharacteristic, complemented
26#10622820C2212yescomplemented
27#10622648—24no—
28#10622647C2214yescomplemented
29#10622646C2214yescomplemented
30#10622599C2211yescharacteristic, complemented
31#10622596C2211yescharacteristic, complemented
32#10622577—22no—
33#10622566C2211yescharacteristic, complemented
34#10622565—21no—
35#10622562C2211yescharacteristic, complemented
36C4×Dic11⋊C4—21no—
37#10622175C2214yescomplemented
38#10622175C2214yescomplemented
39#10622166C2212yescomplemented
40#10622163C2212yescomplemented
41C11×H(5,𝔽2)—44no—
42C11×H(5,𝔽2)—44no—
43C2×C11×#41—24no—
44C2×C11×#41—22no—
45C22×D4×C11—24no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D412yes—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C11×C4⋊Q8—21no—
54C11×#127—21no—
55C11×#124—22no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—24no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—22no—
66C11×#121D414yes—
67C11×#121C2314yes—
68C11×#120—24no—
69C11×#120—24no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4C2311yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66979—22no—
87#66979—22no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95#66896—24no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95C2311yescharacteristic
102C11⋊#95C2311yescharacteristic
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105#66872—24no—
106#66871—24no—
107#18173—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C11×#41—44no—
113C11×#41—416no—
114C11×#41—44no—
115C2×Q8×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—44no—
127C2×D4×C11—416no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—82no—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C42×C11—21no—
164C42×C11—21no—
165C22⋊Dic11—42no—
166C22⋊Dic11—42no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171Dic11⋊C4—42no—
172Dic11⋊C4—42no—
173C4×Dic11—42no—
174C4×Dic11—41no—
175C4×Dic11—41no—
176#4318—44no—
177C2×C11⋊C8—24no—
178#3496D1111yescharacteristic
179#3094—112no—
180#2395—111no—
181#1616—112no—
182#1613—112no—
183#1610—112no—
184#1607—112no—
185#1507—112no—
186#1465—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—24no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—82no—
199C23×C11—82no—
200C23×C11—82no—
201C23×C11—82no—
202C23×C11#12012yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—44no—
206D4×C11—28no—
207D4×C11—44no—
208D4×C11—44no—
209D4×C11—48no—
210D4×C11—48no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—44no—
214D4×C11—82no—
215D4×C11—82no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—48no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—81no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D412yes—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C11⋊C8—44no—
249C2×H(5,𝔽2)—21no—
250#547—22no—
251#546—24no—
252D42—22no—
253#537C2×D1112yes—
254#534—21no—
255#534C2×D1112yes—
256#532—21no—
257C2×#121—21no—
258C2×#121C2×D1112yes—
259C2×C4×D4C2×D1111yescharacteristic
260C2×#117—111no—
261#482—224no—
262#481—114no—
263#480—114no—
264#428—222no—
265#418—222no—
266#407—112no—
267#400—111no—
268#399—111no—
269#398—111no—
270#397—111no—
271#397—221no—
272#394—221no—
273C4×C4⋊C4—221no—
274C4×C22⋊C4—111no—
275C4×C22⋊C4—221no—
276#327—114no—
277#327—114no—
278#324—112no—
279#323—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—164no—
296C22×C11—164no—
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C11—22no—
301C4×C11—21no—
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—41no—
305C4×C11—41no—
306C4×C11#45812yes—
307Dic11—42no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311H(5,𝔽2)—44no—
312H(5,𝔽2)—44no—
313C2×#41—24no—
314C2×#41—22no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4C22⋊D1111yescharacteristic
320C22×D4C22⋊D1112yes—
321C23×C4C22⋊D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C2×M16—222no—
324C4⋊Q8—21no—
325#127—21no—
326#124—22no—
327#123—24no—
328#123—24no—
329C22⋊Q8—24no—
330#121—22no—
331#121—22no—
332#121—24no—
333#121—22no—
334#121—22no—
335#121—22no—
336#121—22no—
337#121C22⋊D1114yes—
338#121C22×D1114yes—
339#120—24no—
340#120—24no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345#117—222no—
346#117—222no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22⋊D1112yes—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4C22⋊D1111yescharacteristic
361C2×C22⋊C4C22×D1111yescharacteristic
362C2×C42—221no—
363C2×C42—221no—
364C2×C42C22⋊D1111yescharacteristic
365#107—224no—
366#106—224no—
367#102—224no—
368#102—224no—
369C22⋊C8—114no—
370C22⋊C8—222no—
371#95—111no—
372#95—111no—
373#95—221no—
374#95—221no—
375#95—221no—
376#95—221no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—42no—
380C2×C11—42no—
381C2×C11—84no—
382C2×C11#300311yescharacteristic
383C2×C11#301811yescharacteristic
384C2×C11C2×#45811yescharacteristic
385C24—22no—
386C24—22no—
387C24C2×C22⋊D1111yescharacteristic
388C24C2×C22⋊D1111yescharacteristic
389#41—44no—
390#41—416no—
391#41—44no—
392C2×Q8—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—44no—
404C2×D4—416no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—82no—
410C2×D4C2×C22⋊D1114yes—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1112yes—
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1112yes—
428C22×C4C23×D1111yescharacteristic
429M16—444no—
430C2×C8—224no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—442no—
438C4⋊C4—442no—
439C4⋊C4C2×C22⋊D1114yes—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—442no—
447C22⋊C4—442no—
448C22⋊C4—442no—
449C22⋊C4—442no—
450C42—21no—
451C42—21no—
452C42—442no—
453C42—441no—
454C42—441no—
455C11#1817311yescharacteristic, complemented, Sylow
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—24no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—44no—
466C23—44no—
467C23—82no—
468C23—82no—
469C23—82no—
470C23—82no—
471C23#6698512yes—
472C23#6700612yes—
473C23C22×C22⋊D1111yescharacteristic
474Q8—44no—
475D4—28no—
476D4—44no—
477D4—44no—
478D4—48no—
479D4—48no—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—82no—
484D4—82no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—48no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—81no—
501C2×C4—222no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4#6698512yes—
514C2×C4#6700611yescharacteristic
515C2×C4#6700611yescharacteristic
516C2×C4C22×C22⋊D1112yes—
517C8—444no—
518C22—21no—
519C22—21no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—42no—
525C22—41no—
526C22—41no—
527C22—44no—
528C22—44no—
529C22—44no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—164no—
534C22—164no—
535C22C2×#6698511yescharacteristic
536C22C2×#6698511yescharacteristic
537C22C2×#6700611yescharacteristic
538C4—22no—
539C4—22no—
540C4—21no—
541C4—44no—
542C4—41no—
543C4—41no—
544C4—442no—
545C4—881no—
546C4—881no—
547C4—881no—
548C4#1062285612yes—
549C2—21no—
550C2—21no—
551C2—42no—
552C2—42no—
553C2—84no—
554C2#1307784311yescharacteristic
555C2#1307796511yescharacteristic
556C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18173
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13078552C2semidirect
2. #13071875C2semidirect
3. #13067653C2semidirect
4. #13067636C2semidirect
5. #13067619C2semidirect
6. #13067602C2semidirect
7. #13067132C2semidirect
8. #13066954C2semidirect
21. C2×#66979C22semidirect
25. C4×C22⋊Dic11C22semidirect
26. #10622820C22semidirect
28. #10622647C22semidirect
29. #10622646C22semidirect
30. #10622599C22semidirect
31. #10622596C22semidirect
33. #10622566C22semidirect
35. #10622562C22semidirect
37. #10622175C22semidirect
38. #10622175C22semidirect
39. #10622166C22semidirect
40. #10622163C22semidirect
455. C11#18173semidirect

Maximal subgroups

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

subgroupindex
#130785522
#130718752
#130676532
#130676362
#130676192
#130676022
#130671322
#130669542
C11×#34962
#1817311