Finite Group Databasebeta

← #14684531

Subgroups — #14684531

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2C2×#10622553C212yesmaximal, complemented
3#13066871C212yesmaximal, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066862C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066856C212yesmaximal
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622604C418yescomplemented
32#10622553—28no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—42no—
43C22×D44—42no—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44C2×C414yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C4⋊C4C2×C414yes—
53C2×C42×C11—41no—
54C2×C42×C11—41no—
55C2×C42×C11D414yescomplemented
56C2×(C2×D11)⋊C4—24no—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C418yes—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11—41no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4—42no—
79C11×#95—42no—
80C11×#95—42no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—41no—
87C11⋊#95C2×C414yes—
88#14632—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
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×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
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×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11C22×C414yes—
157C2×D44—44no—
158C2×D44—48no—
159C2×D44—44no—
160C2×D44—48no—
161C2×D44—44no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164C42×C11—44no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171C4⋊Dic11—44no—
172Dic11⋊C4—48no—
173C2×#394—111no—
174C2×#388—112no—
175#1442—112no—
176#1441—111no—
177#1439—112no—
178#1439—112no—
179#1439—112no—
180#1438—112no—
181C4⋊#95D1111yescharacteristic, complemented
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)12yes—
188C23×C11H(5,𝔽2)11yescharacteristic
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C112−1+411yescharacteristic
192C23×C112−1+412yes—
193C22×D11—24no—
194C22×D11—24no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
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—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11C4×D414yes—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280D44—416no—
281C23×D4—111no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C42C2×D1111yescharacteristic
293#394—118no—
294#388—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95C2×D1112yes—
303C2×#95C2×D1112yes—
304C22×C11C2×C4×D411yescharacteristic
305C22×C11#51811yescharacteristic
306C22×C11#51812yes—
307C22×C11#52011yescharacteristic
308C22×C11#52012yes—
309C22×C11#53411yescharacteristic
310C22×C11#53512yes—
311C22×C11#53711yescharacteristic
312C22×C11#53712yes—
313C22×C11#53811yescharacteristic
314C22×C11#53911yescharacteristic
315C22×C11#54012yes—
316C22×C11#54212yes—
317C22×C11#56011yescharacteristic
318C22×C11#56012yes—
319C22×C11#56012yes—
320C22×C11H(3,𝔽4)11yescharacteristic
321C22×C11H(3,𝔽4)11yescharacteristic
322C22×C11#56212yes—
323C22×C11#56212yes—
324C22×C11#56212yes—
325C22×C11#56311yescharacteristic
326C22×C11#56312yes—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C2×D11—82no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—82no—
347Dic11—44no—
348Dic11—82no—
349Dic11—82no—
350C25—112no—
351C22×D4—114no—
352C22×D4—442no—
353C22×D4—441no—
354C22×D4—441no—
355C22×D4—442no—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4C22×D1112yes—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—22no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—442no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4—441no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4C4×D1114yes—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C22⋊C4—442no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C42—41no—
394C2×C42—41no—
395C2×C42D4414yescomplemented
396#95—42no—
397#95—42no—
398#95—114no—
399#95—224no—
400#95—224no—
401#95—441no—
402#95—442no—
403#95—442no—
404#95—442no—
405C2×C11#232412yes—
406C2×C11#232511yescharacteristic
407C2×C11#237511yescharacteristic
408C2×C11#237612yes—
409C2×C11#237911yescharacteristic
410C2×C11#281312yes—
411C2×C11#281911yescharacteristic
412C2×C11#282311yescharacteristic
413C2×C11#282811yescharacteristic
414C2×C11#283211yescharacteristic
415C2×C11#283712yes—
416D11—84no—
417C24—114no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24C23×D1111yescharacteristic
433C2×D4—444no—
434C2×D4—448no—
435C2×D4—444no—
436C2×D4—448no—
437C2×D4—444no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—114no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4C2×D4414yes—
488C22×C4C2×D4412yes—
489C22×C4#433912yes—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C4⋊C4—448no—
493C4⋊C4—444no—
494C22⋊C4—2216no—
495C22⋊C4—448no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C42—44no—
501C11#1463211yescharacteristic, complemented, Sylow
502C23—224no—
503C23—224no—
504C23—224no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23C22×C4×D1111yescharacteristic
538C23C22×D4411yescharacteristic
539C23C2×#433911yescharacteristic
540C23#6703711yescharacteristic
541C23#6703712yes—
542C23#6703711yescharacteristic
543C23#6703711yescharacteristic
544C23#6704011yescharacteristic
545C23#6704012yes—
546C23#6704212yes—
547C23#6704212yes—
548D4—4416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4C4×D4414yes—
601C22—444no—
602C22—444no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22—882no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22—882no—
615C22—882no—
616C22C2×C4×D4411yescharacteristic
617C22#1062301711yescharacteristic
618C22#1062302411yescharacteristic
619C22#1062302511yescharacteristic
620C22#1062303511yescharacteristic
621C22#1062304112yes—
622C22#1062304111yescharacteristic
623C22#1062304611yescharacteristic
624C22#1062305612yes—
625C22#1062307612yes—
626C22#1062309312yes—
627C22#1062310512yes—
628C22#1062311312yes—
629C22#1062315112yes—
630C22#1062315112yes—
631C22#1062317812yes—
632C22#1062317812yes—
633C22#1062321411yescharacteristic
634C22#1062321411yescharacteristic
635C22#1062323112yes—
636C22#1062325111yescharacteristic
637C22#1062326611yescharacteristic
638C22#1062326612yes—
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—82no—
644C4—444no—
645C4—882no—
646C4—882no—
647C2—884no—
648C2#1307131012yes—
649C2#1307131911yescharacteristic
650C2#1307175311yescharacteristic
651C2#1307176112yes—
652C2#1307178811yescharacteristic
653C2#1307662012yes—
654C2#1307666211yescharacteristic
655C2#1307669011yescharacteristic
656C2#1307673511yescharacteristic
657C2#1307678311yescharacteristic
658C2#1307682612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. #13066871C2semidirect
4. #13066869C2semidirect
5. #13066862C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
9. C11×C4⋊#95C2semidirect
31. #10622604C4semidirect
55. C2×C42×C11D4semidirect
181. C4⋊#95D11semidirect
395. C2×C42D44semidirect
501. C11#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106225532
#130668712
#130668692
#130668622
#130668602
#130668582
#130668562
C11×C4⋊#952
#1463211