Finite Group Databasebeta

← #14680293

Subgroups — #14680293

Order 2816.

2782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C2×#10622570C214yesmaximal, complemented
3C2×#10622263C211yesmaximal, characteristic, complemented
4C2×#10622261C211yesmaximal, characteristic, complemented
5#13066857C211yesmaximal, characteristic, complemented
6#13066856C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C214yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C23×C22⋊D11C2212yes—
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C22×C11×C22⋊C4C2214yes—
15C22×C22⋊Dic11C2214yes—
16C2×#66993—24no—
17C2×#66993—24no—
18C2×#66993C418yescomplemented
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2214yes—
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30#10622570—216no—
31#10622263—24no—
32#10622261—24no—
33C25×C11C2312yes—
34C24×D11C2312yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—44no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—24no—
43C22×C22⋊D11—24no—
44C22×C22⋊D11—24no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11—28no—
47C22×C22⋊D11—28no—
48C22×C22⋊D11—44no—
49C22×C22⋊D11—44no—
50C22×C22⋊D11C2×C418yes—
51C22×C22⋊D11C2×C418yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—44no—
59C22×D44C2×C414yes—
60C2×C11×C22⋊C4—28no—
61C2×C11×C22⋊C4—44no—
62C2×C11×C22⋊C4—44no—
63C2×C22⋊Dic11—28no—
64C2×C22⋊Dic11—44no—
65C2×C22⋊Dic11—44no—
66#66993—232no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4—44no—
71C2×(C2×D11)⋊C4—44no—
72C2×(C2×D11)⋊C4—44no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—28no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11C2×C414yes—
78C2×C4×Dic11D414yes—
79C2×C4×Dic11D414yes—
80C2×C4×Dic11D418yescomplemented
81C11×#95—22no—
82C11×#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87#14272—111nomaximal, Sylow
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11C22×C414yes—
97C24×C11C2411yescharacteristic
98C23×D11—24no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11—24no—
105C23×D11—24no—
106C23×D11C22×C414yes—
107C2×D4×C11—28no—
108C2×D4×C11—48no—
109C2×D4×C11—48no—
110C2×D4×C11—48no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C2×C22⋊D11—216no—
126C2×C22⋊D11—216no—
127C2×C22⋊D11—232no—
128C2×C22⋊D11—416no—
129C2×C22⋊D11—48no—
130C2×C22⋊D11—416no—
131C2×C22⋊D11—48no—
132C2×C22⋊D11—416no—
133C2×C22⋊D11—48no—
134C2×C22⋊D11—48no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11C22×C412yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×D414yes—
154C22×Dic11#4114yes—
155C2×D44—28no—
156C2×D44—48no—
157C2×D44—48no—
158C2×D44—48no—
159C11×C22⋊C4—416no—
160C22⋊Dic11—416no—
161(C2×D11)⋊C4—416no—
162(C2×D11)⋊C4—416no—
163Dic11⋊C4—48no—
164C4×Dic11—216no—
165C4×Dic11C22⋊C4116yescomplemented
166C22×#127—111no—
167C2×#390—114no—
168C2×#382—111no—
169C2×#376—111no—
170#1438—111no—
171#1438—111no—
172#1438—111no—
173#1438—114no—
174#1438D1111yescharacteristic, complemented
175C23×C11—24no—
176C23×C11—28no—
177C23×C11—28no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—44no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—42no—
186C23×C11—44no—
187C23×C11—42no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11C23×C411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C22×D412yes—
200C23×C11C2×#4112yes—
201C23×C11H(5,𝔽2)12yes—
202C23×C11H(5,𝔽2)14yes—
203C23×C11H(5,𝔽2)12yes—
204C22×D11—24no—
205C22×D11—28no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—28no—
209C22×D11—44no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—42no—
217C22×D11—44no—
218C22×D11—42no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—44no—
225D4×C11—416no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—28no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11C2×C22⋊C414yes—
240C22⋊D11—432no—
241C22⋊D11—432no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—28no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252C2×Dic11—44no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11C2×C22⋊C414yes—
257C2×Dic11C2×C22⋊C414yes—
258C2×Dic11C4×D418yes—
259C2×Dic11#12118yes—
260C2×Dic11#12414yes—
261C2×Dic11#12714yes—
262D44—416no—
263C23×D4—112no—
264C23×D4—112no—
265C23×D4—111no—
266C23×D4C2×D1111yescharacteristic
267C2×#127—118no—
268C2×#127—224no—
269C2×#127—224no—
270C22×C4⋊C4—112no—
271C22×C22⋊C4—114no—
272C22×C22⋊C4—114no—
273C22×C22⋊C4—114no—
274C22×C22⋊C4C2×D1114yes—
275C22×C42—111no—
276C22×C42—112no—
277#390—2216no—
278#382—224no—
279#376—224no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—112no—
283C2×#95—111no—
284C2×#95C2×D1111yescharacteristic
285C2×#95C2×D1111yescharacteristic
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—48no—
289C22×C11—48no—
290C22×C11—44no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11—84no—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11C2×C4×D412yes—
297C22×C11#51812yes—
298C22×C11#51812yes—
299C22×C11C2×#12112yes—
300C22×C11C2×#12411yescharacteristic
301C22×C11C2×#12711yescharacteristic
302C22×C11#53511yescharacteristic
303C22×C11#53512yes—
304C22×C11#53512yes—
305C22×C11#53514yes—
306C22×C11#53512yes—
307C22×C11#53514yes—
308C22×C11#53511yescharacteristic
309C22×C11#54014yes—
310C22×C11#54014yes—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—48no—
314C2×D11—48no—
315C2×D11—44no—
316C2×D11—84no—
317C2×D11—84no—
318C2×D11—84no—
319C2×D11—84no—
320C4×C11—24no—
321C4×C11—44no—
322C4×C11—82no—
323Dic11—24no—
324Dic11—44no—
325Dic11—82no—
326Dic11#39018yes—
327C25—112no—
328C25C22×D1112yes—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—44no—
332C22×D4—118no—
333C22×D4—118no—
334C22×D4—114no—
335C22×D4—224no—
336C22×D4—224no—
337C22×D4—224no—
338C22×D4—224no—
339C22×D4—228no—
340C22×D4—228no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—444no—
344C22×D4—444no—
345C22×D4—444no—
346C22×D4C4×D1114yes—
347C23×C4—111no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4C22×D1112yes—
352C23×C4C22×D1112yes—
353C23×C4C22×D1111yescharacteristic
354#127—2232no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—228no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—228no—
361C2×C22⋊C4—228no—
362C2×C22⋊C4—228no—
363C2×C22⋊C4—444no—
364C2×C22⋊C4—444no—
365C2×C22⋊C4—444no—
366C2×C22⋊C4—444no—
367C2×C22⋊C4—444no—
368C2×C22⋊C4—444no—
369C2×C42—114no—
370C2×C42—114no—
371C2×C42—114no—
372C2×C42—118no—
373C2×C42—224no—
374C2×C42—224no—
375#95—22no—
376#95—22no—
377#95—224no—
378#95—224no—
379#95—222no—
380#95—222no—
381C2×C11—84no—
382C2×C11C2×#39011yescharacteristic
383C2×C11#230911yescharacteristic
384C2×C11#230911yescharacteristic
385C2×C11#232814yes—
386C2×C11#261912yes—
387C2×C11#261912yes—
388C2×C11#264112yes—
389C2×C11#265712yes—
390D11—84no—
391C24—24no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—114no—
400C24—224no—
401C24—222no—
402C24—222no—
403C24—224no—
404C24—224no—
405C24—224no—
406C24—224no—
407C24—224no—
408C24C2×C4×D1114yes—
409C24C23×D1111yescharacteristic
410C2×D4—28no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—2216no—
415C2×D4—2216no—
416C2×D4—2232no—
417C2×D4—228no—
418C2×D4—448no—
419C2×D4—448no—
420C2×D4—448no—
421C2×D4—448no—
422C2×D4—4416no—
423C2×D4—448no—
424C2×D4—4416no—
425C2×D4—448no—
426C2×D4—4416no—
427C2×D4—448no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—224no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—222no—
458C22×C4C2×C4×D1112yes—
459C22×C4D4×D1114yes—
460C22×C4D4×D1112yes—
461C22×C4D4×D1112yes—
462C4⋊C4—448no—
463C22⋊C4—416no—
464C22⋊C4—4416no—
465C22⋊C4—4416no—
466C22⋊C4—4416no—
467C42—1116no—
468C42—2216no—
469C11#1427211yescharacteristic, complemented, Sylow
470C23—24no—
471C23—24no—
472C23—24no—
473C23—28no—
474C23—28no—
475C23—42no—
476C23—42no—
477C23—44no—
478C23—44no—
479C23—44no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—42no—
490C23—42no—
491C23—224no—
492C23—224no—
493C23—224no—
494C23—228no—
495C23—228no—
496C23—442no—
497C23—442no—
498C23—444no—
499C23—444no—
500C23—444no—
501C23—444no—
502C23—444no—
503C23—444no—
504C23—444no—
505C23—444no—
506C23—444no—
507C23—444no—
508C23—444no—
509C23—444no—
510C23—442no—
511C23—442no—
512C23C22×C4×D1111yescharacteristic
513C23C2×D4×D1111yescharacteristic
514C23C2×D4×D1112yes—
515C23C2×D4×D1111yescharacteristic
516C23#6703712yes—
517C23#6703714yes—
518C23#41×D1112yes—
519C23#6704212yes—
520D4—416no—
521D4—4416no—
522D4—4432no—
523D4—4432no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—28no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—118no—
540C2×C4—118no—
541C2×C4—114no—
542C2×C4—114no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—442no—
550C2×C4—444no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4—442no—
555C2×C4—444no—
556C2×C4—442no—
557C2×C4C22⋊C4×D1114yes—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—48no—
562C22—48no—
563C22—84no—
564C22—84no—
565C22—84no—
566C22—84no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22—448no—
571C22—448no—
572C22—884no—
573C22—884no—
574C22—884no—
575C22—884no—
576C22C2×C22⋊C4×D1111yescharacteristic
577C22#1062301712yes—
578C22C4×D4×D1112yes—
579C22#1062307612yes—
580C22#1062312312yes—
581C22#1062312314yes—
582C22#1062312312yes—
583C22D11×#12112yes—
584C22#1062313812yes—
585C22#1062313814yes—
586C22#1062314614yes—
587C22#1062319414yes—
588C22D11×#12411yescharacteristic
589C22#1062320511yescharacteristic
590C22D11×#12711yescharacteristic
591C22#1062324611yescharacteristic
592C4—24no—
593C4—44no—
594C4—82no—
595C4—118no—
596C4—224no—
597C4—444no—
598C4—882no—
599C2—84no—
600C2—884no—
601C2D11×#39011yescharacteristic
602C2#1307119511yescharacteristic
603C2#1307119711yescharacteristic
604C2#1307133714yes—
605C2#1307436512yes—
606C2#1307436812yes—
607C2#1307455812yes—
608C2#1307472112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66993C2
hypercenter#1438D11
hypocenterC11#14272
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622263C2semidirect
4. C2×#10622261C2semidirect
5. #13066857C2semidirect
6. #13066856C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. C11×#1438C2semidirect
18. C2×#66993C4semidirect
80. C2×C4×Dic11D4semidirect
165. C4×Dic11C22⋊C4semidirect
174. #1438D11semidirect
469. C11#14272semidirect

Maximal subgroups

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

subgroupindex
C22×#669932
C2×#106225702
C2×#106222632
C2×#106222612
#130668572
#130668562
#130668552
C11×#14382
#1427211