Finite Group Databasebeta

← #14788523

Subgroups — #14788523

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic
4#13069857C212yesmaximal, complemented
5#13069692C212yesmaximal
6#13069553C211yesmaximal, characteristic, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal, complemented
9#13068869C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999—21no—
16C22×#4324C2212yes—
17C22×#4323C2211yescharacteristic
18#10623115—24no—
19#10623115—24no—
20C2×#66951—22no—
21C2×#66945—21no—
22C2×#66928C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2212yes—
26C11×#396—22no—
27C11×#390C2212yes—
28C11×#389C2212yes—
29C11×#384C2211yescharacteristic
30C11×#380—21no—
31C2×#66896C2211yescharacteristic
32#10622632—24no—
33C4×#4323—24no—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C2×#66873C2211yescharacteristic
38C2×#66873C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22C2312yes—
51C11×C22⋊Q8—44no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66999—28no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—42no—
72C2×#4323—22no—
73C2×#4323—22no—
74C2×#4323—22no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—22no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86#66951—216no—
87#66945—28no—
88#66928—24no—
89#66928—24no—
90C4×D44—22no—
91C4×D44D414yes—
92#66922—22no—
93#66922D414yes—
94C4×Dic22—24no—
95C4×Dic22—24no—
96C11×#95—22no—
97#66896—22no—
98#66874—24no—
99#66874—24no—
100#66874—42no—
101#66873—22no—
102#66873—42no—
103#66871—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24185—111nomaximal, Sylow
107C24×C11—21no—
108C23×D11—21no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11#4112yes—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—22no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44C2×D412yes—
136C2×C4×D11—24no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22C2×D414yes—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—81no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—82no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161#4324—48no—
162#4323—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11C2×D412yes—
170Dic11⋊C4—28no—
171C4×Dic11—28no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8#4112yes—
181C2×#556—111no—
182C2×#461—111no—
183C2×C4×D8—111no—
184#2538D1111yescharacteristic, complemented
185#2042—112no—
186#2012—112no—
187#1984—111no—
188#1956—111no—
189#1880—112no—
190#1863—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207Q8×C11—44no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
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—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—84no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#13512yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243D44—22no—
244D44—22no—
245D44—41no—
246D44—41no—
247C4×D11—48no—
248Dic22—24no—
249Dic22—24no—
250Dic22—42no—
251Dic22—42no—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C11⋊C8—42no—
255C22×SD16—112no—
256C22×D8—111no—
257#556—224no—
258#556—224no—
259C2×C4⋊Q8—111no—
260C2×#126—222no—
261C2×#124—112no—
262C2×C22⋊Q8—21no—
263C2×C22⋊Q8—221no—
264C2×C4×Q8—112no—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×#117—221no—
269#461—224no—
270C4×D8—224no—
271C2×#107—111no—
272C2×C4⋊C8—111no—
273C2×#103—112no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#102—111no—
277C2×#102—111no—
278C2×#102—112no—
279C2×C4×C8—111no—
280#396—22no—
281#390C2×D1112yes—
282#389C2×D1112yes—
283#384C2×D1111yescharacteristic
284#380—21no—
285#340—112no—
286#336—112no—
287#336—112no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C2×#12011yescharacteristic
296C22×C11#54811yescharacteristic
297C22×C11#55011yescharacteristic
298C22×C11C2×#13511yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57811yescharacteristic
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—82no—
313C4×C11—81no—
314C4×C11#44914yes—
315C4×C11#52511yescharacteristic
316C4×C11#53711yescharacteristic
317C4×C11#54611yescharacteristic
318C4×C11#54711yescharacteristic
319Dic11—44no—
320Dic11—42no—
321C22×Q8—112no—
322C22×Q8C22⋊D1111yescharacteristic
323C22×D4—111no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—221no—
327C2×SD16—224no—
328C2×SD16—224no—
329C2×SD16—442no—
330C2×D8—222no—
331C2×D8—222no—
332C2×D8—222no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C4⋊Q8—114no—
337C4⋊Q8—222no—
338#126—2216no—
339#124—224no—
340#124—224no—
341C22⋊Q8—44no—
342C22⋊Q8—228no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—224no—
346C4×Q8—224no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—114no—
350C4×D4—222no—
351#117—228no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C4⋊C4C22⋊D1112yes—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1112yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C42—222no—
370C2×C42C22×D1112yes—
371C2×C42C22×D1111yescharacteristic
372#107—222no—
373C4⋊C8—222no—
374#103—224no—
375#103—224no—
376#103—442no—
377#102—222no—
378#102—222no—
379#102—442no—
380C4×C8—222no—
381#95—22no—
382C2×C11—82no—
383C2×C11#240711yescharacteristic
384C2×C11C2×#44911yescharacteristic
385C2×C11#301311yescharacteristic
386C2×C11#336011yescharacteristic
387C2×C11#336711yescharacteristic
388C2×C11#339311yescharacteristic
389C2×C11#339711yescharacteristic
390D11—82no—
391C24—21no—
392C24—221no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—114no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—112no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4#434312yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4C2×C22⋊D1112yes—
425C22×C4C2×C22⋊D1112yes—
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429SD16—448no—
430D8—228no—
431C2×C8—112no—
432C2×C8—221no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—221no—
440C4⋊C4—22no—
441C4⋊C4—24no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—44no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C4⋊C4—112no—
450C4⋊C4—228no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—221no—
454C22⋊C4—44no—
455C22⋊C4—42no—
456C22⋊C4—82no—
457C22⋊C4—228no—
458C22⋊C4—228no—
459C22⋊C4—224no—
460C42—22no—
461C42—22no—
462C42—228no—
463C42D4×D1112yes—
464C42D4×D1112yes—
465C11#2418511yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—222no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23C22×C22⋊D1111yescharacteristic
481Q8—44no—
482Q8—224no—
483Q8—224no—
484Q8—442no—
485Q8—442no—
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4—222no—
491D4—222no—
492D4—441no—
493D4—441no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—448no—
516C2×C4#6698512yes—
517C2×C4#6699012yes—
518C2×C4#6699012yes—
519C2×C4#6700312yes—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×#434311yescharacteristic
523C2×C4#6704011yescharacteristic
524C2×C4#41×D1111yescharacteristic
525C2×C4#6704211yescharacteristic
526C8—222no—
527C8—441no—
528C8—442no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22C2×#6698511yescharacteristic
544C22C2×#6699011yescharacteristic
545C22#1062334811yescharacteristic
546C22C2×#6700311yescharacteristic
547C22#1062336511yescharacteristic
548C22#1062336711yescharacteristic
549C22#1062336911yescharacteristic
550C4—22no—
551C4—42no—
552C4—42no—
553C4—82no—
554C4—81no—
555C4—442no—
556C4—444no—
557C4#1062265014yes—
558C4#1062315811yescharacteristic
559C4#1062316011yescharacteristic
560C4#1062316111yescharacteristic
561C4#1062316211yescharacteristic
562C2—82no—
563C2—882no—
564C2#1307196311yescharacteristic
565C2C2×#1062265011yescharacteristic
566C2#1307792811yescharacteristic
567C2#1308126511yescharacteristic
568C2#1308133411yescharacteristic
569C2#1308160011yescharacteristic
570C2#1308163211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2538D11
hypocenterC11#24185
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. C2×#10622632C2semidirect
4. #13069857C2semidirect
6. #13069553C2semidirect
7. #13069417C2semidirect
8. #13068974C2semidirect
9. #13068869C2semidirect
10. #13068613C2semidirect
11. C11×#2538C2semidirect
184. #2538D11semidirect
465. C11#24185semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106226322
C2×C4×#43232
#130698572
#130696922
#130695532
#130694172
#130689742
#130688692
#130686132
C11×#25382
#2418511