Finite Group Databasebeta

← #14781775

Subgroups — #14781775

Order 2816.

1674 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10622537C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C2×#10622552C211yesmaximal, characteristic, complemented
6#13069931C214yesmaximal, complemented
7#13069926C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C11×#2297C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#67002—24no—
15C2×#67002—24no—
16C2×#67002—24no—
17C22×#4325C2212yes—
18C22×#4323C2212yes—
19C22×(C2×D11)⋊C4—22no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#391C2212yescomplemented
24C11×#390C2212yescomplemented
25C11×#386—22no—
26C4×C11×C22⋊C4—21no—
27C4×C11×C22⋊C4—21no—
28#10622845—24no—
29C2×#66899C2212yescomplemented
30C2×#66896C2212yescomplemented
31#10622614—24no—
32C2×#66873C2214yes—
33#10622552—21no—
34#10622552—21no—
35#10622552C2214yes—
36#10622537—24no—
37C2×C4⋊(C11⋊C8)C2214yescomplemented
38#10622167C2214yescomplemented
39C24×D11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41D414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—21no—
58C22×D44—22no—
59C22×D44D414yes—
60C22×D44C2312yes—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—21no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2312yes—
73#67002—232no—
74C2×#4325—24no—
75C2×#4325—24no—
76C2×#4325—24no—
77C2×#4323—24no—
78C2×#4323—24no—
79C2×#4323—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—48no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2312yes—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318D414yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2312yes—
95C11×#95—22no—
96C11×#95—22no—
97#66899—24no—
98#66896—24no—
99#66873—28no—
100C4⋊(C11⋊C8)—28no—
101#23546—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11C2×D411yescharacteristic
104C23×D11—24no—
105C23×D11—22no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11—42no—
109C23×D11—42no—
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—24no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—44no—
149C22×Dic11—42no—
150C2×D44—28no—
151C2×D44—24no—
152C2×D44—28no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44—44no—
161C2×D44—44no—
162C2×D44C2×D414yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C22⋊C4—44no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—44no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—42no—
173#4325—216no—
174#4323—216no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—48no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180#4318—28no—
181#4318—44no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D414yes—
188C22×AGL(1,ℤ/8)—111no—
189C2×#423—111no—
190C2×#417—111no—
191C2×#418—111no—
192#2297D1111yescharacteristic, complemented
193C2×#390—111no—
194#2055—114no—
195#2054—114no—
196#1736—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11#12112yes—
205C23×C11#12112yes—
206C23×C11#12112yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—416no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—48no—
215C22×D11—84no—
216C22×D11—84no—
217C22×D11—88no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—48no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—48no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—48no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11#12014yes—
241C2×C4×C11#12112yes—
242C2×C4×C11#12112yes—
243C2×C4×C11#12112yes—
244C2×C4×C11#12314yes—
245C2×C4×C11#12314yes—
246C2×C4×C11#12414yes—
247C2×C4×C11AGL(1,ℤ/8)14yescomplemented
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—84no—
257D44—24no—
258D44—24no—
259D44—42no—
260D44—42no—
261D44—48no—
262C11⋊C8—24no—
263C11⋊C8—42no—
264C22×#41C2×D1111yescharacteristic
265C23×D4—111no—
266C2×AGL(1,ℤ/8)—224no—
267C2×AGL(1,ℤ/8)—224no—
268C2×AGL(1,ℤ/8)—224no—
269C22×SD16—112no—
270C22×D8—112no—
271C22×M16—111no—
272C22×M16—111no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C22⋊C4—222no—
276C22×C42C2×D1111yescharacteristic
277#423—224no—
278C2×C4⋊C8—114no—
279#418—224no—
280#417—224no—
281C2×#103—112no—
282C2×#102—112no—
283C2×#102—114no—
284#391C2×D1112yescomplemented
285#390—114no—
286#390—221no—
287#390—221no—
288#390C2×D1112yescomplemented
289#386—22no—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—21no—
292#340—114no—
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11#39414yes—
303C22×C11C2×#12111yescharacteristic
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×#12111yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11#57512yes—
308C2×D11—44no—
309C2×D11—48no—
310C2×D11—816no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—84no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11#39414yes—
319C4×C11C2×#12011yescharacteristic
320C4×C11C2×#12311yescharacteristic
321C4×C11C2×#12311yescharacteristic
322C4×C11C2×#12411yescharacteristic
323Dic11—82no—
324C25—221no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41D4414yes—
331C22×Q8C22×D1111yescharacteristic
332C22×D4—21no—
333C22×D4—114no—
334C22×D4—112no—
335C22×D4—222no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—221no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—221no—
344C23×C4C22⋊D1112yes—
345C23×C4C22×D1111yescharacteristic
346AGL(1,ℤ/8)—2232no—
347C2×SD16—224no—
348C2×SD16—224no—
349C2×SD16—224no—
350C2×D8—224no—
351C2×D8—224no—
352C2×D8—224no—
353C2×M16—114no—
354C2×M16—222no—
355C2×M16—222no—
356C2×M16—222no—
357C2×M16—222no—
358C2×M16—222no—
359C22×C8—112no—
360C22×C8—112no—
361#117—22no—
362#117—22no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—448no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—21no—
377C2×C42C22⋊D1111yescharacteristic
378C2×C42C22⋊D1111yescharacteristic
379C2×C42C22×D1112yes—
380C4⋊C8—228no—
381#103—224no—
382#102—228no—
383#102—224no—
384#95—22no—
385#95—22no—
386C2×C11—24no—
387C2×C11—82no—
388C2×C11C2×#39411yescharacteristic
389C2×C11#303612yes—
390C2×C11#303811yescharacteristic
391C2×C11#304011yescharacteristic
392C2×C11#305512yes—
393D11—84no—
394C24—21no—
395C24—224no—
396C24—222no—
397C24—444no—
398C24—444no—
399C24—442no—
400C24—442no—
401C24C2×C22⋊D1111yescharacteristic
402#41—28no—
403#41—28no—
404#41—44no—
405#41—44no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C2×D4412yes—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—114no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—224no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—444no—
430C2×D4—444no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4C2×D4412yes—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—222no—
443C22×C4—444no—
444C22×C4—442no—
445C22×C4C2×D4412yes—
446C22×C4#433912yes—
447C22×C4D4×D1112yes—
448C22×C4D4×D1112yes—
449C22×C4#434112yes—
450C22×C4#434112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455SD16—2216no—
456D8—2216no—
457M16—228no—
458M16—444no—
459C2×C8—114no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—442no—
470C22⋊C4—44no—
471C22⋊C4—42no—
472C22⋊C4—44no—
473C22⋊C4—448no—
474C22⋊C4—448no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—42no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—42no—
487C23—42no—
488C23—224no—
489C23—4416no—
490C23—442no—
491C23—442no—
492C23—448no—
493C23—444no—
494C23—444no—
495C23—884no—
496C23—884no—
497C23—888no—
498C23#6698312yes—
499C23#6699112yes—
500C23#6699212yes—
501C23C22×C22⋊D1111yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—48no—
509D4—41no—
510D4—41no—
511D4—224no—
512D4—224no—
513D4—442no—
514D4—442no—
515D4—448no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—48no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—442no—
530C2×C4—444no—
531C2×C4—884no—
532C2×C4#6693514yes—
533C2×C4#6693614yes—
534C2×C4#6693814yes—
535C2×C4#6693914yes—
536C2×C4#6698312yes—
537C2×C4#6699112yes—
538C2×C4#6699212yes—
539C2×C4#6700214yescomplemented
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×#434111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C8—224no—
547C8—442no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—82no—
556C22—82no—
557C22—448no—
558C22—444no—
559C22—8816no—
560C22—882no—
561C22—882no—
562C22—884no—
563C22#1062257414yes—
564C22C2×#6698311yescharacteristic
565C22C2×#6699111yescharacteristic
566C22C2×#6699211yescharacteristic
567C22C2×#6700212yes—
568C22#1062335312yes—
569C4—24no—
570C4—42no—
571C4—42no—
572C4—82no—
573C4—882no—
574C4#1062257414yes—
575C4C2×#6693511yescharacteristic
576C4C2×#6693611yescharacteristic
577C4C2×#6693811yescharacteristic
578C4C2×#6693911yescharacteristic
579C2—24no—
580C2—82no—
581C2—884no—
582C2C2×#1062257411yescharacteristic
583C2#1307807612yes—
584C2#1307809611yescharacteristic
585C2#1307811011yescharacteristic
586C2#1307823712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
hypercenter#2297D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C2×#10622537C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622614C2semidirect
5. C2×#10622552C2semidirect
6. #13069931C2semidirect
7. #13069926C2semidirect
8. #13068337C2semidirect
9. C11×#2297C2semidirect
23. C11×#391C22semidirect
24. C11×#390C22semidirect
29. C2×#66899C22semidirect
30. C2×#66896C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
38. #10622167C22semidirect
192. #2297D11semidirect
247. C2×C4×C11AGL(1,ℤ/8)semidirect
284. #391C2×D11semidirect
288. #390C2×D11semidirect
480. C11#23546semidirect
539. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106225372
C2×#106228452
C2×#106226142
C2×#106225522
#130699312
#130699262
#130683372
C11×#22972
#2354611