Finite Group Databasebeta

← #14781779

Subgroups — #14781779

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×#66961C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic, complemented
4#13071106C211yesmaximal, characteristic, complemented
5C2×#10622552C211yesmaximal, characteristic, complemented
6#13069934C214yesmaximal, complemented
7#13069927C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C2×C11×#423C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4—22no—
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×#66961—24no—
19C2×#66961—24no—
20C2×#66961—24no—
21C22×D88C2212yes—
22C22×#4314C2212yes—
23C11×#423—24no—
24C2×C11×C4⋊C8C2214yescomplemented
25#10622826—22no—
26#10622746—24no—
27#10622744—24no—
28C2×#66885C2214yes—
29C2×#66885C2212yescomplemented
30C2×#66880C2212yescomplemented
31#10622552—21no—
32#10622552—21no—
33#10622552C2214yes—
34#10622552C2212yescomplemented
35C4×(C2×D11)⋊C4—21no—
36C4×(C2×D11)⋊C4—21no—
37#10622542C2212yescomplemented
38#10622189C2214yescomplemented
39C24×D11—21no—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C23×Dic11—21no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339D414yes—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16D414yes—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11D411yescharacteristic
72C2×C42×C11D411yescharacteristic
73C2×C42×C11C2312yes—
74C2×C22⋊Dic11—21no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—48no—
80#66979—22no—
81#66979—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2312yes—
87C2×C4×Dic11—21no—
88#66961—232no—
89C2×D88—24no—
90C2×D88—24no—
91C2×D88—24no—
92C2×#4314—24no—
93C2×#4314—24no—
94C2×#4314—24no—
95C11×C4⋊C8—28no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98#66885—28no—
99#66885—24no—
100#66880—24no—
101#23546—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C23×D11—24no—
104C23×D11—21no—
105C23×D11—22no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11—42no—
109C23×D11—42no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—42no—
125C2×C22⋊D11—42no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—44no—
130C22×Dic11—42no—
131#4339—28no—
132#4339—28no—
133#4339—44no—
134#4339—44no—
135C2×D44—28no—
136C2×D44—24no—
137C2×D44—28no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44C2×D414yes—
153C2×D44C2×D412yes—
154C2×C4×D11—24no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C2×D412yes—
163C11×M16—28no—
164C11×M16—44no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2×D414yes—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C22⋊Dic11—42no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—44no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—42no—
185C4×Dic11—42no—
186D88—216no—
187#4314—216no—
188C22×AGL(1,ℤ/8)—111no—
189C2×#423D1111yescharacteristic, complemented
190C2×#417—111no—
191C2×#418—111no—
192#2297—111no—
193C2×#390—111no—
194#2055—114no—
195#2054—114no—
196#1736—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11#12112yes—
200C23×C11#12112yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—416no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—44no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—44no—
214C22×D11—48no—
215C22×D11—84no—
216C22×D11—84no—
217C22×D11—88no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—48no—
224C2×C4×C11#12014yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12314yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12414yes—
231C2×C4×C11AGL(1,ℤ/8)14yescomplemented
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C22⋊D11—48no—
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—84no—
248D44—24no—
249D44—22no—
250D44—24no—
251D44—22no—
252D44—42no—
253D44—41no—
254D44—42no—
255D44—41no—
256D44—48no—
257C4×D11—48no—
258Dic22—22no—
259Dic22—22no—
260Dic22—41no—
261Dic22—41no—
262C8×C11—24no—
263C8×C11—42no—
264C22×#41—111no—
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×M16C2×D1111yescharacteristic
272C22×M16C2×D1111yescharacteristic
273C2×#117—111no—
274C22×C4⋊C4—111no—
275C22×C22⋊C4—222no—
276C22×C42C2×D1111yescharacteristic
277#423—24no—
278C2×C4⋊C8C2×D1114yescomplemented
279#418—224no—
280#417—224no—
281C2×#103—112no—
282C2×#102—114no—
283C2×#102—112no—
284#391—112no—
285#390—112no—
286#390—114no—
287#390—221no—
288#390—221no—
289#386—222no—
290C4×C22⋊C4—221no—
291C4×C22⋊C4—221no—
292#340—114no—
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11#39414yes—
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#12111yescharacteristic
300C22×C11C2×#12111yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)12yes—
302C22×C11#57512yes—
303C2×D11—44no—
304C2×D11—42no—
305C2×D11—48no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—816no—
309C2×D11—82no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—84no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11#39414yes—
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C4×C11C2×#12311yescharacteristic
320C4×C11C2×#12411yescharacteristic
321Dic11—42no—
322Dic11—82no—
323Dic11—82no—
324C25—221no—
325C2×#41—114no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C22×Q8—111no—
332C22×D4—114no—
333C22×D4—111no—
334C22×D4—112no—
335C22×D4—221no—
336C22×D4—221no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—222no—
341C22×D4—222no—
342C23×C4—221no—
343C23×C4—221no—
344C23×C4D4412yes—
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—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16C22⋊D1114yes—
359C22×C8C22×D1112yes—
360C22×C8C22×D1112yes—
361#117—222no—
362#117—222no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—221no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—448no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—221no—
377C2×C42D4411yescharacteristic
378C2×C42D4411yescharacteristic
379C2×C42C22×D1112yes—
380C4⋊C8—28no—
381#103—224no—
382#102—224no—
383#102—228no—
384#95—222no—
385#95—222no—
386C2×C11—24no—
387C2×C11C2×#39411yescharacteristic
388C2×C11#303612yes—
389C2×C11#303811yescharacteristic
390C2×C11#304011yescharacteristic
391C2×C11#305512yes—
392D11—82no—
393D11—84no—
394C24—224no—
395C24—221no—
396C24—222no—
397C24—444no—
398C24—444no—
399C24—442no—
400C24—442no—
401C24C2×D4411yescharacteristic
402#41—228no—
403#41—228no—
404#41—444no—
405#41—444no—
406C2×Q8—112no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×D4—112no—
413C2×D4—114no—
414C2×D4—224no—
415C2×D4—228no—
416C2×D4—224no—
417C2×D4—228no—
418C2×D4—222no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—222no—
425C2×D4—221no—
426C2×D4—221no—
427C2×D4—222no—
428C2×D4—442no—
429C2×D4—442no—
430C2×D4—444no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—444no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—42no—
437C22×C4—221no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—444no—
444C22×C4—442no—
445C22×C4C2×D4412yes—
446C22×C4C2×D4412yes—
447C22×C4C2×D4411yescharacteristic
448C22×C4#433912yes—
449C22×C4D4×D1112yes—
450C22×C4D4×D1112yes—
451C22×C4#434312yes—
452C22×C4#434312yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C23×D1111yescharacteristic
455SD16—2216no—
456D8—2216no—
457M16—28no—
458M16—44no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8C2×C22⋊D1114yes—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—442no—
470C22⋊C4—448no—
471C22⋊C4—444no—
472C22⋊C4—442no—
473C22⋊C4—448no—
474C22⋊C4—444no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—442no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—222no—
484C23—224no—
485C23—4416no—
486C23—444no—
487C23—442no—
488C23—442no—
489C23—444no—
490C23—441no—
491C23—442no—
492C23—441no—
493C23—442no—
494C23—448no—
495C23—884no—
496C23—884no—
497C23—888no—
498C23#6694812yes—
499C23#6694812yes—
500C23#6698312yes—
501C23C22×D4411yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506D4—224no—
507D4—222no—
508D4—222no—
509D4—224no—
510D4—448no—
511D4—442no—
512D4—441no—
513D4—442no—
514D4—441no—
515D4—448no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—222no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—448no—
526C2×C4—444no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—884no—
532C2×C4#6694714yes—
533C2×C4#6694714yes—
534C2×C4#6694812yes—
535C2×C4#6694812yes—
536C2×C4#6696114yescomplemented
537C2×C4#6698312yes—
538C2×C4#6699014yes—
539C2×C4#6700014yes—
540C2×C4C2×#433911yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434311yescharacteristic
544C2×C4C2×#434311yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—24no—
547C8—42no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—448no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—444no—
557C22—8816no—
558C22—882no—
559C22—882no—
560C22—882no—
561C22—884no—
562C22—882no—
563C22#1062260414yes—
564C22C2×#6694811yescharacteristic
565C22C2×#6694811yescharacteristic
566C22C2×#6696112yes—
567C22#1062327912yes—
568C22C2×#6698311yescharacteristic
569C4—24no—
570C4—42no—
571C4—442no—
572C4—882no—
573C4—882no—
574C4#1062260414yes—
575C4C2×#6694711yescharacteristic
576C4C2×#6694711yescharacteristic
577C4C2×#6699011yescharacteristic
578C4C2×#6700011yescharacteristic
579C2—24no—
580C2—884no—
581C2—882no—
582C2C2×#1062260411yescharacteristic
583C2#1307808212yes—
584C2#1307809711yescharacteristic
585C2#1307811111yescharacteristic
586C2#1307823512yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#423C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
hypercenterC2×#423D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
2. C2×#10622746C2semidirect
3. C2×#10622744C2semidirect
4. #13071106C2semidirect
5. C2×#10622552C2semidirect
6. #13069934C2semidirect
7. #13069927C2semidirect
8. #13068336C2semidirect
9. C2×C11×#423C2semidirect
24. C2×C11×C4⋊C8C22semidirect
29. C2×#66885C22semidirect
30. C2×#66880C22semidirect
34. #10622552C22semidirect
37. #10622542C22semidirect
38. #10622189C22semidirect
189. C2×#423D11semidirect
231. C2×C4×C11AGL(1,ℤ/8)semidirect
278. C2×C4⋊C8C2×D11semidirect
480. C11#23546semidirect
536. C2×C4#66961semidirect

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106227462
C2×#106227442
#130711062
C2×#106225522
#130699342
#130699272
#130683362
C2×C11×#4232
#2354611