Finite Group Databasebeta

← #14684614

Subgroups — #14684614

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2#13066884C211yesmaximal, characteristic, complemented
3#13066874C212yesmaximal, complemented
4#13066864C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066856C212yesmaximal
8#13066854C212yesmaximal, complemented
9C11×#1436C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32C24×D11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×D44—42no—
42C22×D44—42no—
43C22×D44—41no—
44C22×D44—41no—
45C22×D44C2×C414yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C42×C11—42no—
50C2×C42×C11—41no—
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×(C2×D11)⋊C4—42no—
54C2×(C2×D11)⋊C4—42no—
55C2×(C2×D11)⋊C4—42no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×(C2×D11)⋊C4C2×C418yes—
69C2×Dic11⋊C4—42no—
70C2×Dic11⋊C4—42no—
71C2×Dic11⋊C4—42no—
72C11×#95—24no—
73C11×#95—42no—
74C11×#95—41no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95—41no—
81C11⋊#95—41no—
82C11⋊#95C2×C414yes—
83#14641—111nomaximal, Sylow
84C24×C11C2411yescharacteristic
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11C22×C414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11#4114yes—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C22×C414yes—
150C2×D44—44no—
151C2×D44—48no—
152C2×D44—48no—
153C2×D44—44no—
154C2×D44—44no—
155C11×C4⋊C4—44no—
156C42×C11—44no—
157(C2×D11)⋊C4—48no—
158(C2×D11)⋊C4—48no—
159(C2×D11)⋊C4—48no—
160(C2×D11)⋊C4—48no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163Dic11⋊C4—48no—
164C2×#394—111no—
165#1445—111no—
166#1442—112no—
167#1440—112no—
168#1439—112no—
169#1439—112no—
170#1438—112no—
171#1437—112no—
172#1436D1111yescharacteristic, complemented
173C23×C11C23×C411yescharacteristic
174C23×C11C2×#4112yes—
175C23×C11H(5,𝔽2)11yescharacteristic
176C23×C11H(5,𝔽2)12yes—
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)12yes—
179C23×C11H(5,𝔽2)12yes—
180C23×C11H(5,𝔽2)12yes—
181C23×C112−1+412yes—
182C22×D11—24no—
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267D44—416no—
268C23×D4—111no—
269C22×C4⋊C4—112no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C42C2×D1111yescharacteristic
278#394—118no—
279C2×#95—111no—
280C2×#95—112no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—111no—
285C2×#95—112no—
286C2×#95—111no—
287C2×#95C2×D1112yes—
288C2×#95C2×D1112yes—
289C2×#95C2×D1111yescharacteristic
290C22×C11C4×#4111yescharacteristic
291C22×C11#51811yescharacteristic
292C22×C11#51811yescharacteristic
293C22×C11#51812yes—
294C22×C11#52012yes—
295C22×C11#53812yes—
296C22×C11#53812yes—
297C22×C11#53912yes—
298C22×C11#54012yes—
299C22×C11#54012yes—
300C22×C11#54212yes—
301C22×C11#56012yes—
302C22×C11#56012yes—
303C22×C11#56012yes—
304C22×C11#56011yescharacteristic
305C22×C11H(3,𝔽4)11yescharacteristic
306C22×C11H(3,𝔽4)11yescharacteristic
307C22×C11#56212yes—
308C22×C11#56212yes—
309C22×C11#56212yes—
310C22×C11#56311yescharacteristic
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—82no—
331Dic11—44no—
332Dic11—82no—
333Dic11—82no—
334C25—112no—
335C22×D4—114no—
336C22×D4—442no—
337C22×D4—441no—
338C22×D4—441no—
339C22×D4—442no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1112yes—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—442no—
351C2×C4⋊C4—442no—
352C2×C4⋊C4—442no—
353C2×C4⋊C4C4×D1114yes—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—224no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—442no—
359C2×C22⋊C4—442no—
360C2×C22⋊C4—442no—
361C2×C22⋊C4—442no—
362C2×C22⋊C4—442no—
363C2×C22⋊C4—442no—
364C2×C22⋊C4—442no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4—442no—
368C2×C22⋊C4—442no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—442no—
371C2×C22⋊C4—442no—
372C2×C42—42no—
373C2×C42—41no—
374#95—24no—
375#95—42no—
376#95—41no—
377#95—114no—
378#95—441no—
379#95—441no—
380#95—442no—
381#95—442no—
382#95—442no—
383#95—442no—
384#95—442no—
385C2×C11#233311yescharacteristic
386C2×C11#233512yes—
387C2×C11#237511yescharacteristic
388C2×C11#237712yes—
389C2×C11#237911yescharacteristic
390C2×C11#282412yes—
391C2×C11#282812yes—
392C2×C11#282912yes—
393C2×C11#283712yes—
394D11—84no—
395C24—114no—
396C24—222no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—222no—
401C24—222no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24C23×D1111yescharacteristic
411C2×D4—444no—
412C2×D4—448no—
413C2×D4—444no—
414C2×D4—448no—
415C2×D4—444no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—114no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4C2×C4×D1112yes—
463C22×C4C2×C4×D1112yes—
464C22×C4C2×C4×D1112yes—
465C22×C4#433914yes—
466C4⋊C4—44no—
467C4⋊C4—448no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4—448no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C42—44no—
475C11#1464111yescharacteristic, complemented, Sylow
476C23—224no—
477C23—224no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—224no—
482C23—224no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23C22×C4×D1111yescharacteristic
512C23C2×#433912yes—
513C23#6703711yescharacteristic
514C23#6703711yescharacteristic
515C23#6703712yes—
516C23#6704012yes—
517C23#6704212yes—
518C23#6704212yes—
519C23#6704212yes—
520D4—4416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C22—444no—
572C22—444no—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—444no—
578C22—882no—
579C22—882no—
580C22—882no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22—882no—
585C22—882no—
586C22C4×#433911yescharacteristic
587C22#1062301711yescharacteristic
588C22#1062304612yes—
589C22#1062305211yescharacteristic
590C22#1062306612yes—
591C22#1062307612yes—
592C22#1062309112yes—
593C22#1062309112yes—
594C22#1062309312yes—
595C22#1062310512yes—
596C22#1062311312yes—
597C22#1062312511yescharacteristic
598C22#1062315112yes—
599C22#1062317812yes—
600C22#1062317812yes—
601C22#1062319711yescharacteristic
602C22#1062319712yes—
603C22#1062321411yescharacteristic
604C22#1062323112yes—
605C22#1062324212yes—
606C22#1062326611yescharacteristic
607C4—42no—
608C4—42no—
609C4—42no—
610C4—44no—
611C4—82no—
612C4—444no—
613C4—882no—
614C4—882no—
615C2—884no—
616C2#1307138111yescharacteristic
617C2#1307140012yes—
618C2#1307175411yescharacteristic
619C2#1307177112yes—
620C2#1307178811yescharacteristic
621C2#1307669612yes—
622C2#1307673312yes—
623C2#1307674612yes—
624C2#1307682612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. #13066884C2semidirect
3. #13066874C2semidirect
4. #13066864C2semidirect
5. #13066860C2semidirect
6. #13066860C2semidirect
8. #13066854C2semidirect
9. C11×#1436C2semidirect
31. #10622604C4semidirect
172. #1436D11semidirect
475. C11#14641semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
#130668842
#130668742
#130668642
#130668602
#130668562
#130668542
C11×#14362
#1464111