Finite Group Databasebeta

← #14780590

Subgroups — #14780590

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×#4325C211yesmaximal, characteristic, complemented
2C2×#10623347C211yesmaximal, characteristic, complemented
3C2×#10623056C211yesmaximal, characteristic
4C2×#10622744C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic, complemented
6#13069618C218yesmaximal, complemented
7#13068332C211yesmaximal, characteristic, complemented
8C2×C11×#419C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623347—24no—
15#10623347—24no—
16C2×#67000—21no—
17C2×#66999C2214yescomplemented
18C2×#66997—21no—
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325—24no—
22C22×#4325C2214yes—
23C2×#66982—22no—
24C2×#66979C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26#10623056—24no—
27#10623056—24no—
28C2×#66948C2214yes—
29C2×#66935—22no—
30C2×#66928—21no—
31C2×#66927—21no—
32C11×#419—24no—
33C2×C11×#103C2214yescomplemented
34#10622744—24no—
35#10622742—24no—
36C2×#66885C2214yes—
37C2×(C2×D11)⋊C8C2214yescomplemented
38#10622167C2214yescomplemented
39C24×D11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11D414yescomplemented
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11D412yes—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—22no—
61C22×D44—21no—
62C22×D44—22no—
63C22×D44—24no—
64C22×D44D411yescharacteristic
65C22×D44D414yes—
66C22×D44C2312yes—
67C22×C4×D11C2312yes—
68C22×Dic22D411yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C22×C8×C11C2312yes—
73C11×#117—22no—
74C11×#117D414yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—21no—
79#67000—28no—
80#66999—28no—
81#66999—28no—
82#66997—28no—
83C2×#4325—232no—
84C2×#4325—28no—
85C2×#4325—28no—
86C2×#4325—28no—
87#66982—216no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90#66979—22no—
91#66979D414yescomplemented
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—24no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8D414yescomplemented
98C22×C11⋊C8C2312yes—
99#66948—28no—
100#66948—28no—
101#66935—216no—
102#66928—28no—
103#66927—28no—
104C11×#103—28no—
105#66885—28no—
106(C2×D11)⋊C8—28no—
107#23388—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—22no—
110C23×D11—24no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—84no—
114C23×D11C2×D412yes—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11—44no—
126C2×Q8×C11—44no—
127C2×Q8×C11C2×D414yes—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—24no—
143C2×C22⋊D11—24no—
144C22×Dic11—22no—
145C22×Dic11C2×D412yes—
146#4339—44no—
147#4339—44no—
148#4339—44no—
149#4339—44no—
150C2×D44—216no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—22no—
154C2×D44—28no—
155C2×D44—22no—
156C2×D44—28no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—44no—
165C2×D44—44no—
166C2×D44—88no—
167C2×D44C2×D414yes—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C11×M16—44no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C2×D414yes—
183C11×C22⋊C4—24no—
184C42×C11—24no—
185C22⋊Dic11—24no—
186#4325—232no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—216no—
189C4⋊Dic11—22no—
190C4⋊Dic11C2×D414yes—
191Dic11⋊C4—216no—
192C4×Dic11—24no—
193C2×C11⋊C8—28no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yes—
197C23×SD16—111no—
198C2×#536—111no—
199C2×#535—111no—
200C2×#419D1111yescharacteristic, complemented
201C2×#418—111no—
202C2×#408—111no—
203#2000—118no—
204#1735—111no—
205C23×C11—24no—
206C23×C11#12012yes—
207C23×C11#12012yes—
208C23×C11#12112yes—
209C23×C11C22×D411yescharacteristic
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—28no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—88no—
220C22×D11—88no—
221C22×D11—88no—
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—48no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11—48no—
233C2×C4×C11#12014yes—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12714yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—44no—
252D44—24no—
253D44—24no—
254D44—42no—
255D44—42no—
256D44—48no—
257D44—44no—
258D44—816no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263Dic22—44no—
264C8×C11—42no—
265C11⋊C8—24no—
266C22×#41—111no—
267C23×Q8C2×D1111yescharacteristic
268C23×D4—111no—
269C22×SD16—114no—
270C22×SD16—224no—
271C22×SD16—224no—
272C22×SD16—224no—
273C22×M16C2×D1111yescharacteristic
274C23×C8—111no—
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×#117C2×D1111yescharacteristic
289#419—24no—
290#418—224no—
291C2×#103C2×D1114yescomplemented
292C2×#102—114no—
293#408—224no—
294C2×C22⋊C8—114no—
295#340—114no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11#39214yes—
300C22×C11C2×#12011yescharacteristic
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×#12111yescharacteristic
303C22×C11#57714yes—
304C2×D11—42no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—48no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—816no—
311C2×D11—84no—
312C2×D11—84no—
313C4×C11—44no—
314C4×C11—44no—
315C4×C11#39214yes—
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12111yescharacteristic
319C4×C11C2×#12711yescharacteristic
320Dic11—42no—
321Dic11—44no—
322C25—221no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—111no—
336C22×Q8D4414yescomplemented
337C22×Q8C22×D1112yes—
338C22×D4—112no—
339C22×D4—114no—
340C22×D4—111no—
341C22×D4—112no—
342C22×D4—224no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4—221no—
348C22×D4—222no—
349C23×C4—21no—
350C23×C4—112no—
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—114no—
360C22×C8—112no—
361C22×C8—222no—
362C22×C8—222no—
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—22no—
375#117—114no—
376#117—222no—
377#117C22⋊D1114yes—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4C22×D1112yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—221no—
385C2×C42—21no—
386C2×C42—221no—
387#103—28no—
388#102—228no—
389C22⋊C8—228no—
390C2×C11—24no—
391C2×C11C2×#39211yescharacteristic
392C2×C11#300912yes—
393C2×C11#301012yes—
394C2×C11#305712yes—
395D11—82no—
396D11—84no—
397C24—112no—
398C24—222no—
399C24—224no—
400C24—442no—
401C24—442no—
402C24—884no—
403C24D4×D1111yescharacteristic
404#41—444no—
405#41—444no—
406#41—444no—
407#41—444no—
408C2×Q8—24no—
409C2×Q8—22no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—42no—
417C2×Q8—44no—
418C2×Q8—42no—
419C2×Q8—44no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8C2×D4414yes—
424C2×D4—114no—
425C2×D4—2216no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—228no—
430C2×D4—222no—
431C2×D4—228no—
432C2×D4—222no—
433C2×D4—224no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—442no—
441C2×D4—442no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—888no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—112no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4C2×D4412yes—
459C22×C4#433912yes—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4D4×D1112yes—
464C22×C4C2×C22⋊D1112yes—
465C22×C4C23×D1111yescharacteristic
466SD16—2232no—
467M16—44no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—114no—
472C2×C8—228no—
473C2×C8—222no—
474C2×C8—222no—
475C4⋊C4—22no—
476C4⋊C4—114no—
477C4⋊C4—2216no—
478C4⋊C4—222no—
479C4⋊C4C2×C22⋊D1114yes—
480C22⋊C4—24no—
481C22⋊C4—2216no—
482C22⋊C4—2216no—
483C22⋊C4—224no—
484C42—24no—
485C42—224no—
486C11#2338811yescharacteristic, complemented, Sylow
487C23—24no—
488C23—222no—
489C23—222no—
490C23—228no—
491C23—224no—
492C23—222no—
493C23—442no—
494C23—442no—
495C23—448no—
496C23—448no—
497C23—888no—
498C23—888no—
499C23—888no—
500C23#6693512yes—
501C23#6693712yes—
502C23#6699012yes—
503C23C2×D4×D1111yescharacteristic
504Q8—24no—
505Q8—24no—
506Q8—42no—
507Q8—42no—
508Q8—48no—
509Q8—444no—
510D4—224no—
511D4—224no—
512D4—448no—
513D4—442no—
514D4—442no—
515D4—448no—
516D4—444no—
517D4—8816no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—48no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—444no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4#6693514yes—
534C2×C4#6693512yes—
535C2×C4#6693714yes—
536C2×C4#6693712yes—
537C2×C4#6698314yes—
538C2×C4#6699012yes—
539C2×C4#6699314yes—
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—42no—
547C8—224no—
548C22—24no—
549C22—24no—
550C22—24no—
551C22—444no—
552C22—448no—
553C22—444no—
554C22—442no—
555C22—444no—
556C22—444no—
557C22—8816no—
558C22—884no—
559C22—884no—
560C22#1062257314yes—
561C22C2×#6693511yescharacteristic
562C22C2×#6693711yescharacteristic
563C22#1062330914yes—
564C22C2×#6699011yescharacteristic
565C4—44no—
566C4—44no—
567C4—444no—
568C4—442no—
569C4#1062257314yes—
570C4C2×#6693511yescharacteristic
571C4C2×#6693711yescharacteristic
572C4C2×#6698311yescharacteristic
573C4C2×#6699311yescharacteristic
574C2—24no—
575C2—882no—
576C2—884no—
577C2C2×#1062257311yescharacteristic
578C2#1307789212yes—
579C2#1307790312yes—
580C2#1307825812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
hypercenterC2×#419D11
hypocenterC11#23388
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C23×#4325C2semidirect
2. C2×#10623347C2semidirect
4. C2×#10622744C2semidirect
5. C2×#10622742C2semidirect
6. #13069618C2semidirect
7. #13068332C2semidirect
8. C2×C11×#419C2semidirect
17. C2×#66999C22semidirect
33. C2×C11×#103C22semidirect
37. C2×(C2×D11)⋊C8C22semidirect
38. #10622167C22semidirect
46. C22×Q8×C11D4semidirect
91. #66979D4semidirect
97. C22×C11⋊C8D4semidirect
200. C2×#419D11semidirect
291. C2×#103C2×D11semidirect
336. C22×Q8D44semidirect
486. C11#23388semidirect

Maximal subgroups

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

subgroupindex
C23×#43252
C2×#106233472
C2×#106230562
C2×#106227442
C2×#106227422
#130696182
#130683322
C2×C11×#4192
#2338811