Finite Group Databasebeta

← #14788829

Subgroups — #14788829

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622688C212yesmaximal, complemented
2C2×#10622831C212yesmaximal, complemented
3C4×#66977C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069704C212yesmaximal, complemented
6#13069544C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068547C212yesmaximal, complemented
9C22×C11×#127C211yesmaximal, characteristic
10C23×D4×C11—21no—
11C23×D4×C11—21no—
12C23×D4×C11C2212yes—
13C2×C11×#127—28no—
14C2×C11×#127—21no—
15C2×C11×#127—21no—
16C2×C11×#127C2212yes—
17C2×C11×#127C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×#4324C2214yescomplemented
20C2×#66977C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic, complemented
22#10622831—28no—
23C2×#66896C2214yescomplemented
24C2×#66896C2214yescomplemented
25C2×#66896C2214yescomplemented
26#10622825C2211yescharacteristic
27#10622823—21no—
28C4×C22⋊Dic11—21no—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622688—28no—
31C4×C4⋊Dic11C2211yescharacteristic, complemented
32#10622546—21no—
33C4×Dic11⋊C4—21no—
34#10622542C2211yescharacteristic, complemented
35#10622541C2211yescharacteristic, complemented
36C2×C4⋊(C11⋊C8)C2212yescomplemented
37#10622162C2212yescomplemented
38C25×C11—22no—
39C22×D4×C11—28no—
40C22×D4×C11—28no—
41C22×D4×C11—28no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—44no—
50C22×D4×C11—44no—
51C22×D4×C11—44no—
52C22×D4×C11—44no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×Dic22C2311yescharacteristic
59C11×#127—28no—
60C11×#127—28no—
61C11×#127—28no—
62C11×#127—24no—
63C11×#127D418yes—
64C2×C42×C11—24no—
65C2×C42×C11D411yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×#4324—28no—
72C2×#4324—28no—
73C2×#4324—44no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77#66977—22no—
78#66977D414yescomplemented
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8C2314yes—
85C4×Dic22—24no—
86#66896—28no—
87#66896—28no—
88#66896—44no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C22⋊(C11⋊C8)—24no—
95C4⋊(C11⋊C8)—24no—
96#24211—111nomaximal, Sylow
97C24×C11—28no—
98C24×C11—24no—
99C24×C11—44no—
100C24×C11—44no—
101C24×C11—44no—
102C24×C11—44no—
103C24×C11—44no—
104C24×C11—44no—
105C24×C11C2×D411yescharacteristic
106C2×D4×C11—28no—
107C2×D4×C11—28no—
108C2×D4×C11—28no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—416no—
117C2×D4×C11—416no—
118C2×D4×C11—432no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—432no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11C2×D418yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11SD1614yescomplemented
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×Dic22—22no—
152C2×Dic22—21no—
153C2×Dic22—22no—
154C2×Dic22C2×D412yescomplemented
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11C2×D414yes—
159C22⋊Dic11—24no—
160C22⋊Dic11—42no—
161#4324—416no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11C2×D412yescomplemented
166Dic11⋊C4—24no—
167Dic11⋊C4—42no—
168Dic11⋊C4—42no—
169C4×Dic11—42no—
170C4×Dic11—42no—
171C2×C11⋊C8—24no—
172C2×C11⋊C8—24no—
173C2×C11⋊C8—24no—
174C22×#127D1111yescharacteristic
175C2×#460—112no—
176C2×#450—112no—
177C4×C22⋊Q8—111no—
178#2041—112no—
179#2014—112no—
180#1982—112no—
181#1797—111no—
182#1786—112no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—28no—
188C23×C11—416no—
189C23×C11—416no—
190C23×C11—416no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—88no—
198C23×C11—88no—
199C23×C11—88no—
200C23×C11—88no—
201C23×C11#12112yes—
202C23×C11C2×SD1612yes—
203C23×C11AGL(1,ℤ/8)12yes—
204C23×C11C22×D411yescharacteristic
205D4×C11—28no—
206D4×C11—28no—
207D4×C11—416no—
208D4×C11—416no—
209D4×C11—416no—
210D4×C11—416no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—416no—
214C2×C4×C11—28no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—28no—
226C2×C4×C11#12012yes—
227C2×C4×C11#12012yes—
228C2×C4×C11#12112yes—
229C2×C4×C11C2×SD1612yes—
230C2×C4×C11C2×SD1612yes—
231C2×C4×C11AGL(1,ℤ/8)12yes—
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C2×Dic11—22no—
238C2×Dic11—22no—
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—
248C2×Dic11—41no—
249Dic22—24no—
250Dic22—42no—
251C11⋊C8—44no—
252C23×D4—21no—
253C23×D4—21no—
254C23×D4C2×D1112yes—
255C22×SD16—114no—
256C2×#127—28no—
257C2×#127—21no—
258C2×#127—21no—
259C2×#127C2×D1112yes—
260C2×#127C2×D1112yes—
261C2×C22⋊Q8—111no—
262C2×C4×Q8—111no—
263C22×C42C2×D1111yescharacteristic
264#460—228no—
265#450—228no—
266C2×C4⋊C8—112no—
267C2×#102—114no—
268C2×#102—114no—
269C2×#102—114no—
270C2×C22⋊C8—112no—
271#391—111no—
272#389—111no—
273#387—221no—
274#385—221no—
275#380—111no—
276C4×C4⋊C4—111no—
277C4×C4⋊C4—221no—
278C4×C22⋊C4—221no—
279#336—112no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—48no—
287C22×C11—48no—
288C22×C11—48no—
289C22×C11—832no—
290C22×C11—84no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11#46014yescomplemented
295C22×C11C2×#12011yescharacteristic
296C22×C11C2×#12111yescharacteristic
297C22×C11#53511yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11#45014yescomplemented
307C4×C11D4212yes—
308C4×C11#54612yes—
309Dic11—42no—
310Dic11—42no—
311Dic11—81no—
312Dic11—81no—
313C25—22no—
314C22×Q8—111no—
315C22×D4—28no—
316C22×D4—28no—
317C22×D4—28no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4—44no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4C22×D1114yes—
331C23×C4C22⋊D1111yescharacteristic
332C23×C4C22⋊D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C2×SD16—228no—
335C2×SD16—228no—
336C2×SD16—444no—
337C22×C8—114no—
338#127—28no—
339#127—28no—
340#127—28no—
341#127—24no—
342#127C22⋊D1118yes—
343C22⋊Q8—114no—
344C22⋊Q8—222no—
345C4×Q8—224no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C42—24no—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42C22⋊D1111yescharacteristic
358C2×C42C22⋊D1111yescharacteristic
359C2×C42C22×D1111yescharacteristic
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—224no—
362#102—228no—
363#102—228no—
364#102—444no—
365C22⋊C8—224no—
366#95—221no—
367#95—221no—
368#95—221no—
369#95—221no—
370#95—221no—
371C2×C11—24no—
372C2×C11—88no—
373C2×C11#240811yescharacteristic
374C2×C11C2×#45011yescharacteristic
375C2×C11#300311yescharacteristic
376C2×C11C2×#46011yescharacteristic
377C2×C11#303811yescharacteristic
378C2×C11#320811yescharacteristic
379C2×C11#321711yescharacteristic
380C24—28no—
381C24—24no—
382C24—44no—
383C24—44no—
384C24—44no—
385C24—44no—
386C24—44no—
387C24—44no—
388C24C2×C22⋊D1111yescharacteristic
389C2×Q8—112no—
390C2×Q8—221no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—416no—
404C2×D4—416no—
405C2×D4—432no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—432no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4C2×C22⋊D1118yes—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4#432414yescomplemented
430C22×C4D4×D1112yes—
431C22×C4#434112yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438SD16—4416no—
439C2×C8—224no—
440C2×C8—224no—
441C2×C8—224no—
442C4⋊C4—112no—
443C4⋊C4—224no—
444C4⋊C4—221no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—442no—
448C4⋊C4—442no—
449C22⋊C4—224no—
450C22⋊C4—442no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—442no—
455C42—442no—
456C42C2×C22⋊D1114yes—
457C11#2421111yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—28no—
463C23—416no—
464C23—416no—
465C23—416no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23—88no—
473C23—88no—
474C23—88no—
475C23—88no—
476C23#6698512yes—
477C23C2×#432412yes—
478C23#6699112yes—
479C23C22×C22⋊D1111yescharacteristic
480Q8—224no—
481Q8—442no—
482D4—28no—
483D4—28no—
484D4—416no—
485D4—416no—
486D4—416no—
487D4—416no—
488D4—44no—
489D4—44no—
490D4—416no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—222no—
504C2×C4—222no—
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—441no—
514C2×C4—441no—
515C2×C4#6698512yes—
516C2×C4#6698512yes—
517C2×C4C2×#432412yes—
518C2×C4C2×#432412yes—
519C2×C4#6699112yes—
520C2×C4#6700612yes—
521C2×C4#6700612yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4#6703712yes—
525C2×C4C22×C22⋊D1112yes—
526C8—444no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—48no—
534C22—48no—
535C22—48no—
536C22—832no—
537C22—84no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22#1062268814yescomplemented
542C22C2×#6698511yescharacteristic
543C22C2×#6698511yescharacteristic
544C22C2×#6698511yescharacteristic
545C22C22×#432411yescharacteristic
546C22C2×#6699111yescharacteristic
547C22#1062333611yescharacteristic
548C22C2×#6700611yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—22no—
553C4—442no—
554C4—442no—
555C4—881no—
556C4—881no—
557C4#1062283114yescomplemented
558C4D4×C22⋊D1112yes—
559C4#1062333712yes—
560C2—24no—
561C2—88no—
562C2#1307196611yescharacteristic
563C2C2×#1062283111yescharacteristic
564C2#1307784311yescharacteristic
565C2C2×#1062268811yescharacteristic
566C2#1307809211yescharacteristic
567C2#1307955711yescharacteristic
568C2#1307963411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#127C2
socleC23×C11C22×D4
hypercenterC22×#127D11
hypocenterC11#24211
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C2×#10622688C2semidirect
2. C2×#10622831C2semidirect
3. C4×#66977C2semidirect
4. #13069847C2semidirect
5. #13069704C2semidirect
6. #13069544C2semidirect
7. #13068596C2semidirect
8. #13068547C2semidirect
19. C22×#4324C22semidirect
21. C2×C4×Dic22C22semidirect
23. C2×#66896C22semidirect
24. C2×#66896C22semidirect
25. C2×#66896C22semidirect
31. C4×C4⋊Dic11C22semidirect
34. #10622542C22semidirect
35. #10622541C22semidirect
36. C2×C4⋊(C11⋊C8)C22semidirect
37. #10622162C22semidirect
78. #66977D4semidirect
138. C22×C4×C11SD16semidirect
154. C2×Dic22C2×D4semidirect
165. C4⋊Dic11C2×D4semidirect
294. C22×C11#460semidirect
306. C4×C11#450semidirect
429. C22×C4#4324semidirect
457. C11#24211semidirect
541. C22#10622688semidirect
557. C4#10622831semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
C2×#106228312
C4×#669772
#130698472
#130697042
#130695442
#130685962
#130685472
C22×C11×#1272
#2421111