Finite Group Databasebeta

← #14684533

Subgroups — #14684533

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×#10622564C212yesmaximal, complemented
2#13066873C212yesmaximal, complemented
3#13066869C211yesmaximal, characteristic, complemented
4#13066861C212yesmaximal, complemented
5#13066861C212yesmaximal, complemented
6#13066861C212yesmaximal, complemented
7#13066857C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9C2×C11×#394C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C11×#394C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622564—28no—
33C25×C11C2312yes—
34C22×D4×C11—42no—
35C22×D4×C11—42no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—41no—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4—42no—
54C2×C11×C22⋊C4C2×C418yes—
55C2×C11×C22⋊C4C2×C418yes—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—42no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—41no—
71C2×C4⋊Dic11—41no—
72C2×C4⋊Dic11—42no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11—41no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11—41no—
78C2×C4×Dic11D414yescomplemented
79C11×#95C2×C414yes—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—41no—
88#14632—111nomaximal, Sylow
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11C22×C414yes—
104C24×C11C2411yescharacteristic
105C2×D4×C11—44no—
106C2×D4×C11—48no—
107C2×D4×C11—44no—
108C2×D4×C11—48no—
109C2×D4×C11—44no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
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×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11C2×D414yes—
162C11×C4⋊C4—44no—
163C11×C22⋊C4—216no—
164C11×C22⋊C4—48no—
165C22⋊Dic11—48no—
166C22⋊Dic11—48no—
167C22⋊Dic11—48no—
168C22⋊Dic11—48no—
169C4⋊Dic11—44no—
170C4⋊Dic11—48no—
171C4⋊Dic11—44no—
172C4×Dic11—44no—
173C2×#394D1111yescharacteristic
174C2×#388—112no—
175#1442—112no—
176#1441—111no—
177#1439—112no—
178#1439—112no—
179#1439—112no—
180#1438—112no—
181C4⋊#95—111no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11H(5,𝔽2)11yescharacteristic
221C23×C11H(5,𝔽2)12yes—
222C23×C11H(5,𝔽2)11yescharacteristic
223C23×C11H(5,𝔽2)12yes—
224C23×C11H(5,𝔽2)11yescharacteristic
225C23×C11H(5,𝔽2)12yes—
226C23×C112−1+411yescharacteristic
227C23×C112−1+412yes—
228D4×C11—416no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C4×D414yes—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
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—
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—
280C2×Dic11—42no—
281C23×D4C2×D1111yescharacteristic
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4C2×D1112yes—
291C22×C22⋊C4C2×D1112yes—
292C22×C42—111no—
293#394Dic1118yescomplemented
294#388—228no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95C2×D1111yescharacteristic
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11#51812yes—
321C22×C11#51811yescharacteristic
322C22×C11#52012yes—
323C22×C11#52011yescharacteristic
324C22×C11#53411yescharacteristic
325C22×C11#53512yes—
326C22×C11#53711yescharacteristic
327C22×C11#53712yes—
328C22×C11#53811yescharacteristic
329C22×C11#53911yescharacteristic
330C22×C11#54012yes—
331C22×C11#54212yes—
332C22×C11#56011yescharacteristic
333C22×C11#56012yes—
334C22×C11#56012yes—
335C22×C11H(3,𝔽4)11yescharacteristic
336C22×C11H(3,𝔽4)11yescharacteristic
337C22×C11#56212yes—
338C22×C11#56212yes—
339C22×C11#56212yes—
340C22×C11#56312yes—
341C22×C11#56311yescharacteristic
342C4×C11—24no—
343C4×C11—44no—
344C4×C11—42no—
345C4×C11—42no—
346Dic11—44no—
347Dic11—82no—
348Dic11—82no—
349Dic11—82no—
350C25C22×D1112yes—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4C2×Dic1114yes—
356C23×C4—112no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—112no—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—441no—
369C2×C4⋊C4—441no—
370C2×C4⋊C4—442no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4—442no—
373C2×C4⋊C4—441no—
374C2×C4⋊C4C2×Dic1114yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
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⋊C4C2×Dic1118yes—
392C2×C22⋊C4C2×Dic1118yes—
393C2×C42—114no—
394C2×C42—441no—
395C2×C42—441no—
396#95—224no—
397#95—224no—
398#95—442no—
399#95—442no—
400#95—441no—
401#95—442no—
402#95—442no—
403#95—442no—
404#95C2×Dic1114yes—
405C2×C11—84no—
406C2×C11#232412yes—
407C2×C11#232511yescharacteristic
408C2×C11#237511yescharacteristic
409C2×C11#237612yes—
410C2×C11#237911yescharacteristic
411C2×C11#281312yes—
412C2×C11#281911yescharacteristic
413C2×C11#282311yescharacteristic
414C2×C11#282811yescharacteristic
415C2×C11#283211yescharacteristic
416C2×C11#283712yes—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24C22×Dic1114yes—
432C24C23×D1111yescharacteristic
433C2×D4—44no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—48no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—114no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
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×C4D4×D1112yes—
485C22×C4#434112yes—
486C22×C4C22×Dic1114yes—
487C22×C4C22×Dic1112yes—
488C22×C4C22×Dic1112yes—
489C22×C4C22×Dic1112yes—
490C4⋊C4—44no—
491C4⋊C4—444no—
492C4⋊C4—448no—
493C4⋊C4—444no—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C42—444no—
501C11#1463211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C2×D4×D1111yescharacteristic
538C23C2×#434111yescharacteristic
539C23#6703711yescharacteristic
540C23#6703712yes—
541C23#6703711yescharacteristic
542C23#6703712yes—
543C23#6704211yescharacteristic
544C23#6704212yes—
545C23#6704311yescharacteristic
546C23#6704312yes—
547C23C23×Dic1111yescharacteristic
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
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×C4D4×Dic1114yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#1062312511yescharacteristic
617C22#1062312611yescharacteristic
618C22#1062312612yes—
619C22#1062312811yescharacteristic
620C22#1062313311yescharacteristic
621C22#1062313412yes—
622C22#1062313611yescharacteristic
623C22#1062313812yes—
624C22#1062313912yes—
625C22#1062314811yescharacteristic
626C22#1062315012yes—
627C22#1062318212yes—
628C22#1062319712yes—
629C22#1062319812yes—
630C22#1062319812yes—
631C22#1062320311yescharacteristic
632C22#1062321411yescharacteristic
633C22#1062321512yes—
634C22C2×D4×Dic1111yescharacteristic
635C22#1062332912yes—
636C22#1062332911yescharacteristic
637C22#1062335811yescharacteristic
638C22#1062335812yes—
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—444no—
644C4—882no—
645C4—882no—
646C4—882no—
647C2—84no—
648C2#1307131112yes—
649C2#1307132111yescharacteristic
650C2#1307175711yescharacteristic
651C2#1307176412yes—
652C2#1307179011yescharacteristic
653C2#1307662312yes—
654C2#1307666011yescharacteristic
655C2#1307668711yescharacteristic
656C2#1307673911yescharacteristic
657C2#1307678711yescharacteristic
658C2#1307683212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14632
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
2. #13066873C2semidirect
3. #13066869C2semidirect
4. #13066861C2semidirect
5. #13066861C2semidirect
6. #13066861C2semidirect
8. #13066845C2semidirect
22. C11×#394C4semidirect
78. C2×C4×Dic11D4semidirect
293. #394Dic11semidirect
501. C11#14632semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
#130668732
#130668692
#130668612
#130668572
#130668452
C2×C11×#3942
#1463211