Finite Group Databasebeta

← #14788570

Subgroups — #14788570

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622688C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3#13073986C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069710C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic
8#13068950C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C11×#559C211yesmaximal, characteristic
12C11×#559—24no—
13C11×#559—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124C2212yes—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2212yes—
22C22×#4326C2211yescharacteristic
23C22×#4324C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622843—21no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622688—24no—
32C4×#4326—24no—
33#10622597—22no—
34#10622586—21no—
35C2×#66874C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C23×C4×C11—22no—
51C22×Dic22C2311yescharacteristic
52C11×#127—22no—
53C11×#127D414yes—
54C11×#124—28no—
55C11×#124—24no—
56C11×#124—24no—
57C11×#123—216no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C4×D4×C11—28no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4326—22no—
76C2×#4326—22no—
77C2×#4326—22no—
78C2×#4324—24no—
79C2×#4324—24no—
80C2×#4324—42no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×Dic22—22no—
92C4×Dic22—22no—
93#66899—22no—
94#66899—42no—
95#66896—24no—
96#66896—24no—
97#66896—42no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101#66874—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24190—111nomaximal, Sylow
106C24×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—81no—
126C2×D4×C11—81no—
127C2×D4×C11C2×D414yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—28no—
131C22×C4×C11—82no—
132C22×C4×C11—82no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22#4112yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11C2×D412yes—
159C42×C11C2×D412yes—
160#4326—28no—
161#4324—48no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C4⋊Dic11—81no—
168Dic11⋊C4—42no—
169Dic11⋊C4—82no—
170C4×Dic11—42no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8#4112yes—
180C2×#559D1111yescharacteristic
181C2×#460—111no—
182C2×C4×Q16—111no—
183#2582—111no—
184#2042—112no—
185#2015—112no—
186#1984—111no—
187#1957—111no—
188#1877—112no—
189#1862—112no—
190#1803—111no—
191C23×C11—24no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—44no—
204D4×C11—24no—
205D4×C11—24no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—48no—
209D4×C11—84no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—88no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11#13512yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244Dic22—22no—
245Dic22—22no—
246Dic22—41no—
247Dic22—41no—
248C11⋊C8—22no—
249C11⋊C8—41no—
250C11⋊C8—42no—
251C22×Q16—111no—
252C22×SD16—112no—
253#559—24no—
254#559—24no—
255C2×#127C2×D1111yescharacteristic
256C2×#124—21no—
257C2×#124C2×D1112yes—
258C2×#123—22no—
259C2×C4×Q8—111no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C2×D1112yes—
264#460—224no—
265C4×Q16—224no—
266C2×#107—111no—
267C2×C4⋊C8—111no—
268C2×#103—111no—
269C2×#103—111no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×C4×C8—111no—
275#398—222no—
276#391—112no—
277#391—221no—
278#389—112no—
279#389—221no—
280#384—111no—
281#340—112no—
282#336—112no—
283#336—112no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11C2×#12011yescharacteristic
292C22×C11#54811yescharacteristic
293C22×C11#55011yescharacteristic
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57611yescharacteristic
297C22×C11#57711yescharacteristic
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11#45214yes—
304C4×C11#52511yescharacteristic
305C4×C11#53711yescharacteristic
306C4×C11#54611yescharacteristic
307C4×C11#54711yescharacteristic
308Dic11—42no—
309Dic11—82no—
310Dic11—81no—
311C22×Q8—111no—
312C22×Q8C22⋊D1111yescharacteristic
313C22×Q8C22×D1111yescharacteristic
314C22×D4—21no—
315C22×D4—21no—
316C22×D4C22×D1112yes—
317C23×C4—22no—
318C2×Q16—222no—
319C2×Q16—222no—
320C2×Q16—222no—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—111no—
327#127—22no—
328#127C22⋊D1114yes—
329#124—28no—
330#124—24no—
331#124—24no—
332#123—216no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—222no—
337C4×Q8—222no—
338C4×Q8C22⋊D1114yes—
339C4×D4—28no—
340C4×D4—24no—
341C4×D4—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4C22⋊D1111yescharacteristic
350C2×C4⋊C4C22⋊D1112yes—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C42—21no—
356C2×C42—221no—
357C2×C42C22×D1112yes—
358C2×C42C22×D1111yescharacteristic
359#107—222no—
360C4⋊C8—222no—
361#103—222no—
362#103—222no—
363#103—442no—
364#102—224no—
365#102—224no—
366#102—442no—
367C4×C8—222no—
368#95—222no—
369#95—222no—
370#95—222no—
371C2×C11—84no—
372C2×C11#240711yescharacteristic
373C2×C11C2×#45211yescharacteristic
374C2×C11#301211yescharacteristic
375C2×C11#336511yescharacteristic
376C2×C11#337511yescharacteristic
377C2×C11#339611yescharacteristic
378C2×C11#340011yescharacteristic
379C24—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—221no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8C2×C22⋊D1112yes—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4C2×C22⋊D1114yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—28no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4C2×C22⋊D1112yes—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420Q16—228no—
421SD16—448no—
422C2×C8—112no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—222no—
426C2×C8—221no—
427C2×C8—222no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—222no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—221no—
438C4⋊C4—221no—
439C4⋊C4—442no—
440C4⋊C4—442no—
441C4⋊C4—882no—
442C4⋊C4—881no—
443C4⋊C4C2×C22⋊D1112yes—
444C22⋊C4—28no—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C42—24no—
448C42—22no—
449C42—22no—
450C42—442no—
451C42C2×C22⋊D1112yes—
452C42C2×C22⋊D1112yes—
453C11#2419011yescharacteristic, complemented, Sylow
454C23—24no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22×C22⋊D1111yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—41no—
465Q8—41no—
466Q8—44no—
467Q8—222no—
468Q8—222no—
469Q8—441no—
470Q8—441no—
471D4—24no—
472D4—24no—
473D4—42no—
474D4—48no—
475D4—42no—
476D4—84no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—88no—
492C2×C4—222no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4#6700312yes—
502C2×C4#6700412yes—
503C2×C4#6700612yes—
504C2×C4#6700612yes—
505C2×C4#41×D1111yescharacteristic
506C2×C4#41×D1111yescharacteristic
507C2×C4#6704211yescharacteristic
508C2×C4#6704311yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C2×C4C22×C22⋊D1111yescharacteristic
511C8—222no—
512C8—442no—
513C8—441no—
514C22—44no—
515C22—44no—
516C22—44no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22C2×#6700311yescharacteristic
522C22C2×#6700411yescharacteristic
523C22#1062336211yescharacteristic
524C22#1062336511yescharacteristic
525C22#1062336611yescharacteristic
526C22#1062336711yescharacteristic
527C22C2×#6700611yescharacteristic
528C4—22no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—442no—
534C4—882no—
535C4—881no—
536C4#1062285214yes—
537C4#1062335511yescharacteristic
538C4#1062335911yescharacteristic
539C4#1062336011yescharacteristic
540C4#1062336411yescharacteristic
541C2—84no—
542C2#1307195511yescharacteristic
543C2C2×#1062285211yescharacteristic
544C2#1307792011yescharacteristic
545C2#1308130811yescharacteristic
546C2#1308142611yescharacteristic
547C2#1308162411yescharacteristic
548C2#1308166911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11#24190
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
3. #13073986C2semidirect
4. #13069852C2semidirect
5. #13069710C2semidirect
6. #13069553C2semidirect
8. #13068950C2semidirect
9. #13068863C2semidirect
10. #13068621C2semidirect
453. C11#24190semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
C2×C4×#43262
#130739862
#130698522
#130697102
#130695532
#130694232
#130689502
#130688632
#130686212
C2×C11×#5592
#2419011