Finite Group Databasebeta

← #14780593

Subgroups — #14780593

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4314C211yesmaximal, characteristic, complemented
2C2×#10623356C211yesmaximal, characteristic, complemented
3C2×#10623361C211yesmaximal, characteristic
4C2×#10622733C211yesmaximal, characteristic, complemented
5C2×#10622744C211yesmaximal, characteristic, complemented
6#13069621C218yesmaximal, complemented
7#13068333C211yesmaximal, characteristic, complemented
8C2×C11×#408C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14#10623361—24no—
15#10623361—24no—
16#10623356—24no—
17#10623356—24no—
18C2×#67000—21no—
19C2×#66997—21no—
20C2×#66993—21no—
21C2×#66990—22no—
22C2×#66989—21no—
23C2×#66988—22no—
24C2×#66983C2214yes—
25C2×#66979C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×#66977C2214yescomplemented
28C22×#4314—24no—
29C22×#4314—24no—
30C22×#4314—24no—
31C22×#4314C2214yes—
32C11×#408—24no—
33C2×C11×C22⋊C8C2214yescomplemented
34#10622744—24no—
35#10622733—24no—
36C2×#66885C2214yes—
37C2×#66880C2214yescomplemented
38#10622189C2214yescomplemented
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×#41—22no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11D412yes—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
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—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—21no—
66C22×Dic22—22no—
67C22×Dic22D414yescomplemented
68C22×Dic22C2312yes—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2312yes—
76C22×C8×C11C2312yes—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#67000—28no—
81#66997—28no—
82#66993—28no—
83#66990—216no—
84#66989—28no—
85#66988—216no—
86#66983—28no—
87#66983—28no—
88C2×(C2×D11)⋊C4—24no—
89#66979—22no—
90#66979—22no—
91#66979D414yes—
92#66979D414yescomplemented
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2312yes—
95#66977—28no—
96#66977—28no—
97C2×Dic11⋊C4—24no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×#4314—232no—
101C2×#4314—28no—
102C2×#4314—28no—
103C2×#4314—28no—
104C11×C22⋊C8—28no—
105#66885—28no—
106#66880—28no—
107#23388—111nomaximal, Sylow
108C24×C11C2×D412yes—
109C24×C11C2×D411yescharacteristic
110C23×D11—22no—
111C23×D11—24no—
112C23×D11—42no—
113C23×D11—42no—
114C23×D11—84no—
115C11×#41—44no—
116C11×#41—44no—
117C11×#41—44no—
118C11×#41—44no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—216no—
144C2×C22⋊D11—88no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C2×D44—24no—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—42no—
160C2×D44—44no—
161C2×D44—42no—
162C2×D44—44no—
163C2×D44C2×D414yes—
164C2×Dic22—28no—
165C2×Dic22—24no—
166C2×Dic22—28no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—42no—
173C2×Dic22—44no—
174C2×Dic22—42no—
175C2×Dic22—44no—
176C2×Dic22C2×D414yes—
177C11×M16—44no—
178C2×C8×C11—28no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11C2×D414yes—
185C22⋊Dic11—216no—
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188(C2×D11)⋊C4—216no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11C2×D414yes—
192C4⋊Dic11C2×D414yes—
193Dic11⋊C4—216no—
194C4×Dic11—24no—
195C4×Dic11—24no—
196#4314—232no—
197C23×SD16—111no—
198C2×#536—111no—
199C2×#535—111no—
200C2×#419—111no—
201C2×#418—111no—
202C2×#408D1111yescharacteristic, complemented
203#2000—118no—
204#1735—111no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—28no—
210C23×C11#12012yes—
211C23×C11#12012yes—
212C23×C11#12112yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—88no—
220C22×D11—88no—
221C22×D11—88no—
222Q8×C11—44no—
223D4×C11—48no—
224D4×C11—44no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11#12012yes—
233C2×C4×C11#12012yes—
234C2×C4×C11#12014yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12714yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—816no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—44no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254D44—24no—
255D44—24no—
256D44—42no—
257D44—42no—
258D44—48no—
259Dic22—24no—
260Dic22—24no—
261Dic22—42no—
262Dic22—42no—
263Dic22—48no—
264C8×C11—24no—
265C8×C11—42no—
266C22×#41C2×D1111yescharacteristic
267C23×Q8—111no—
268C23×D4—111no—
269C22×SD16—114no—
270C22×SD16—224no—
271C22×SD16—224no—
272C22×SD16—224no—
273C22×M16C2×D1111yescharacteristic
274C23×C8C2×D1111yescharacteristic
275#536—224no—
276#536—224no—
277#535—224no—
278#535—224no—
279C2×C4⋊Q8—221no—
280C2×#127—221no—
281C2×#124—221no—
282C2×#124—221no—
283C2×#123—222no—
284C2×C22⋊Q8—114no—
285C2×#121—114no—
286C2×#120—222no—
287C2×#117—111no—
288C2×#117—111no—
289#419—224no—
290#418—224no—
291C2×#103—114no—
292C2×#102—114no—
293#408—24no—
294C2×C22⋊C8C2×D1114yescomplemented
295#340—114no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11#39214yes—
304C22×C11C2×#12011yescharacteristic
305C22×C11C2×#12011yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11#57714yes—
308C2×D11—44no—
309C2×D11—48no—
310C2×D11—816no—
311C2×D11—84no—
312C2×D11—84no—
313C4×C11—42no—
314C4×C11#39214yes—
315C4×C11C2×#12011yescharacteristic
316C4×C11C2×#12111yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12711yescharacteristic
319Dic11—44no—
320Dic11—44no—
321Dic11—44no—
322C25—221no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C22×Q8—114no—
330C22×Q8—112no—
331C22×Q8—221no—
332C22×Q8—222no—
333C22×Q8—222no—
334C22×Q8—222no—
335C22×Q8—222no—
336C22×Q8—222no—
337C22×Q8D4411yescharacteristic
338C22×D4—114no—
339C22×D4—112no—
340C22×D4—224no—
341C22×D4—221no—
342C22×D4—222no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4D4412yes—
348C22×D4D4411yescharacteristic
349C23×C4—221no—
350C23×C4C22×D1112yes—
351C23×C4C22×D1111yescharacteristic
352C2×SD16—228no—
353C2×SD16—228no—
354C2×SD16—2232no—
355C2×SD16—228no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8C22⋊D1114yescomplemented
362C22×C8C22×D1112yes—
363C22×C8C22×D1112yes—
364C4⋊Q8—228no—
365#127—228no—
366#124—228no—
367#124—228no—
368#123—2216no—
369C22⋊Q8—228no—
370C22⋊Q8—228no—
371#121—228no—
372#121—228no—
373#120—2216no—
374#117—114no—
375#117—114no—
376#117—222no—
377#117—222no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—224no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C42—221no—
386C2×C42—221no—
387#103—228no—
388#102—228no—
389C22⋊C8—28no—
390C2×C11—24no—
391C2×C11—82no—
392C2×C11C2×#39211yescharacteristic
393C2×C11#300912yes—
394C2×C11#301012yes—
395C2×C11#305712yes—
396D11—84no—
397C24—222no—
398C24—224no—
399C24—442no—
400C24—442no—
401C24—884no—
402C24C2×D4412yes—
403C24C2×D4411yescharacteristic
404#41—44no—
405#41—44no—
406#41—44no—
407#41—44no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—114no—
412C2×Q8—224no—
413C2×Q8—222no—
414C2×Q8—228no—
415C2×Q8—228no—
416C2×Q8—222no—
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—442no—
421C2×Q8—444no—
422C2×Q8—442no—
423C2×Q8—444no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—114no—
431C2×D4—2216no—
432C2×D4—224no—
433C2×D4—228no—
434C2×D4—228no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—442no—
441C2×D4—444no—
442C2×D4—442no—
443C2×D4—444no—
444C2×D4—888no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4C2×D4412yes—
458C22×C4C2×D4411yescharacteristic
459C22×C4#433912yes—
460C22×C4D4×D1112yes—
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4D4×D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C23×D1111yescharacteristic
466SD16—2232no—
467M16—44no—
468C2×C8—28no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8C2×C22⋊D1114yes—
475C4⋊C4—114no—
476C4⋊C4—114no—
477C4⋊C4—2216no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C22⋊C4—2216no—
481C22⋊C4—2216no—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C42—224no—
485C42—224no—
486C11#2338811yescharacteristic, complemented, Sylow
487C23—24no—
488C23—22no—
489C23—22no—
490C23—28no—
491C23—22no—
492C23—224no—
493C23—442no—
494C23—448no—
495C23—442no—
496C23—448no—
497C23—888no—
498C23—888no—
499C23—888no—
500C23#6693512yes—
501C23#6693512yes—
502C23#6698312yes—
503C23C22×D4411yescharacteristic
504Q8—44no—
505Q8—224no—
506Q8—224no—
507Q8—442no—
508Q8—442no—
509Q8—448no—
510D4—48no—
511D4—44no—
512D4—224no—
513D4—224no—
514D4—442no—
515D4—442no—
516D4—448no—
517D4—8816no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—442no—
529C2×C4—444no—
530C2×C4—444no—
531C2×C4—442no—
532C2×C4—448no—
533C2×C4#6693512yes—
534C2×C4#6693512yes—
535C2×C4#6693714yes—
536C2×C4#6693714yes—
537C2×C4#6698312yes—
538C2×C4#6699014yes—
539C2×C4#6699314yes—
540C2×C4C2×#433911yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—24no—
547C8—42no—
548C22—24no—
549C22—24no—
550C22—24no—
551C22—44no—
552C22—44no—
553C22—42no—
554C22—44no—
555C22—448no—
556C22—444no—
557C22—8816no—
558C22—884no—
559C22—884no—
560C22#1062257314yes—
561C22C2×#6693511yescharacteristic
562C22C2×#6693511yescharacteristic
563C22#1062328214yes—
564C22C2×#6698311yescharacteristic
565C4—42no—
566C4—444no—
567C4—444no—
568C4—444no—
569C4#1062257314yes—
570C4C2×#6693711yescharacteristic
571C4C2×#6693711yescharacteristic
572C4C2×#6699011yescharacteristic
573C4C2×#6699311yescharacteristic
574C2—24no—
575C2—82no—
576C2—884no—
577C2C2×#1062257311yescharacteristic
578C2#1307789512yes—
579C2#1307790412yes—
580C2#1307825512yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
hypercenterC2×#408D11
hypocenterC11#23388
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C23×#4314C2semidirect
2. C2×#10623356C2semidirect
4. C2×#10622733C2semidirect
5. C2×#10622744C2semidirect
6. #13069621C2semidirect
7. #13068333C2semidirect
8. C2×C11×#408C2semidirect
27. C2×#66977C22semidirect
33. C2×C11×C22⋊C8C22semidirect
37. C2×#66880C22semidirect
38. #10622189C22semidirect
67. C22×Dic22D4semidirect
74. C22×C8×C11D4semidirect
92. #66979D4semidirect
202. C2×#408D11semidirect
294. C2×C22⋊C8C2×D11semidirect
361. C22×C8C22⋊D11semidirect
486. C11#23388semidirect

Maximal subgroups

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

subgroupindex
C23×#43142
C2×#106233562
C2×#106233612
C2×#106227332
C2×#106227442
#130696212
#130683332
C2×C11×#4082
#2338811