Finite Group Databasebeta

← #14917014

Subgroups — #14917014

Order 2816.

2538 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13071786C214yesmaximal, complemented
3#13071637C212yesmaximal, complemented
4#13071628C212yesmaximal, complemented
5#13071588C212yesmaximal, complemented
6#13071521C212yesmaximal, complemented
7#13071442C214yesmaximal, complemented
8#13071364C211yesmaximal, characteristic, complemented
9#13071362C211yesmaximal, characteristic, complemented
10#13071342C211yesmaximal, characteristic, complemented
11#13071318C214yesmaximal, complemented
12#13071242C214yesmaximal, complemented
13#13071008C211yesmaximal, characteristic, complemented
14D11×#382C211yesmaximal, characteristic, complemented
15C11×#2328C211yesmaximal, characteristic, complemented
16C22×#4341C2212yes—
17C2×C11×#127C2211yescharacteristic
18C2×C4×D4×C11C2212yes—
19C2×#66991C2212yes—
20C2×#66991C2212yes—
21C2×#66989C2212yes—
22C2×D4×Dic11C2212yes—
23C2×D4×Dic11C2212yes—
24C2×D4×Dic11C2212yes—
25C2×C4×C22⋊D11C2214yes—
26#10623247C4116yescomplemented
27C2×C4⋊C4×D11C2212yes—
28C2×(C22⋊D11)⋊C4C2214yes—
29C2×C42×D11C2211yescharacteristic
30C2×#66922C2211yescharacteristic
31C11×#390C2212yes—
32C11×#386C2214yes—
33C11×#386C2214yes—
34C11×#382C2211yescharacteristic
35C11×#376C2211yescharacteristic
36#10622834C2212yes—
37#10622833C2214yes—
38#10622833C2214yes—
39#10622823C2214yes—
40#10622823C2214yes—
41C2×C11⋊#95C2214yes—
42#10622590C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622569C2214yes—
46#10622569C2214yes—
47#10622559C2214yes—
48#10622559C2214yes—
49#10622558C2214yes—
50#10622558C2214yes—
51#10622557C2214yes—
52#10622557C2214yes—
53#10622556C2214yes—
54#10622555C2214yes—
55C22⋊C4×Dic11C2214yes—
56C4×(C2×D11)⋊C4C2211yescharacteristic
57C4×(C2×D11)⋊C4C2211yescharacteristic
58#10622549C2211yescharacteristic
59C4×C4⋊Dic11C2212yes—
60#10622545C2211yescharacteristic
61C4×Dic11⋊C4C2211yescharacteristic
62C4×Dic11⋊C4C2211yescharacteristic
63#10622541C2212yes—
64#10622280C2212yes—
65#10622277C2212yes—
66D11×#95C2212yes—
67D11×#95C2212yes—
68#10622267C2214yes—
69#10622266C2214yes—
70#10622264C2212yes—
71#10622263C2212yes—
72#10622263C2212yes—
73#10622263C2212yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×D4×C11C2312yes—
77C22×D4×C11C2312yes—
78C22×D4×C11C2312yes—
79C23×C4×C11C2314yes—
80C22×C22⋊D11C2314yes—
81C23×Dic11C2314yes—
82C23×Dic11C2314yes—
83C2×#4341—48no—
84C2×#4341C2×C4116yescomplemented
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2314yes—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2312yes—
90C11×#127C2×C418yescomplemented
91C4×D4×C11—44no—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103C2×C22⋊Dic11C2314yes—
104#66991C2×C4116yescomplemented
105#66991C2×C4116yescomplemented
106#66989C2×C4116yescomplemented
107D4×Dic11—44no—
108D4×Dic11C2×C4116yescomplemented
109D4×Dic11C2×C4116yescomplemented
110C4×C22⋊D11—48no—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2311yescharacteristic
128C4⋊C4×D11—44no—
129(C22⋊D11)⋊C4—48no—
130C42×D11C2×C418yescomplemented
131#66922C2×C418yescomplemented
132C11×#95C2312yes—
133C11×#95C2312yes—
134C11×#95C2312yes—
135C11×#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2312yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2312yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150#34398—111nomaximal, Sylow
151C24×C11C2414yes—
152C23×D11C2411yescharacteristic
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—44no—
156C2×D4×C11—44no—
157C2×D4×C11C22×C418yes—
158C2×D4×C11C22×C418yes—
159C2×D4×C11C22×C418yes—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11—44no—
163C22×C4×C11C2412yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11C22×C4116yes—
172C22×Dic11—44no—
173C22×Dic11—44no—
174C22×Dic11—44no—
175C22×Dic11—44no—
176C22×Dic11—44no—
177C22×Dic11C22×C4116yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2414yes—
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2411yescharacteristic
184C22×Dic11C2414yes—
185#4341—432no—
186C2×C4×D11—24no—
187C2×C4×D11—28no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—42no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C414yes—
195C2×C4×D11C22×C414yes—
196C2×Dic22—44no—
197C2×Dic22C22×C418yes—
198C11×C4⋊C4—24no—
199C11×C22⋊C4—44no—
200C11×C22⋊C4—44no—
201C11×C22⋊C4—44no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11C22×C414yes—
205C22⋊Dic11—44no—
206C22⋊Dic11—44no—
207C22⋊Dic11—44no—
208C22⋊Dic11C22×C4116yes—
209C22⋊Dic11C22×C4116yes—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11C22×C418yes—
214C4⋊Dic11C22×C418yes—
215Dic11⋊C4—44no—
216Dic11⋊C4—44no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—44no—
220C4×Dic11—22no—
221C4×Dic11—22no—
222C4×Dic11—44no—
223C4×Dic11—44no—
224C4×Dic11C22×C414yes—
225C4×Dic11C22×C414yes—
226C4×Dic11C22×C414yes—
227C2×#532—111no—
228#2379—114no—
229#2361—112no—
230#2361—112no—
231#2357—112no—
232#2349—112no—
233#2339—114no—
234#2331—111no—
235#2331—111no—
236#2328—111no—
237#2328D1111yescharacteristic, complemented
238#2325—114no—
239#2318—114no—
240#2283—111no—
241C2×#382—111no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11C23×C418yes—
249C23×C11C2511yescharacteristic
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—22no—
253C22×D11C23×C412yes—
254C22×D11H(5,𝔽2)14yes—
255D4×C11—216no—
256D4×C11—48no—
257D4×C11—48no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—88no—
270C2×C4×C11C23×C412yes—
271C2×C4×C11C23×C412yes—
272C2×C4×C11C23×C412yes—
273C2×C4×C11H(5,𝔽2)12yes—
274C2×C4×C112−1+412yes—
275C22⋊D11—232no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—416no—
292C2×Dic11—88no—
293C2×Dic11C23×C412yes—
294C2×Dic11C23×C412yes—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C418yes—
297C4×D11—28no—
298C4×D11—28no—
299C4×D11—44no—
300C4×D11—88no—
301Dic22—48no—
302C22×#41—112no—
303#532—1116no—
304C2×C4⋊Q8—111no—
305C2×#127C2×D1111yescharacteristic
306C2×#124—112no—
307C2×#121—112no—
308C2×#121—112no—
309C2×C4×D4—112no—
310C2×C4×D4—112no—
311C2×C4×D4—112no—
312C2×C4×D4—114no—
313C2×C4×D4—114no—
314C2×C4×D4C2×D1112yes—
315C22×C4⋊C4—112no—
316C22×C42—111no—
317#391—114no—
318#391—114no—
319#390—112no—
320#390C2×D1112yes—
321#389—112no—
322#389—112no—
323#388—114no—
324#388—114no—
325#388—114no—
326#388—114no—
327#387—114no—
328#387—114no—
329#386—114no—
330#386—114no—
331#386—114no—
332#386—114no—
333#386C2×D1114yes—
334#386C2×D1114yes—
335#385—114no—
336#385—114no—
337#385—114no—
338#385—114no—
339#383—112no—
340#382—112no—
341#382—111no—
342#382—112no—
343#382—112no—
344#382—112no—
345#382C2×D1111yescharacteristic
346#381—114no—
347#381—112no—
348#380—114no—
349#380—112no—
350C4×C4⋊C4—112no—
351C4×C4⋊C4—112no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C22⋊C4—114no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4—111no—
357#376—111no—
358#376C2×D1111yescharacteristic
359C2×#95—114no—
360C2×#95—112no—
361C2×#95—112no—
362C22×C11—28no—
363C22×C11—28no—
364C22×C11—28no—
365C22×C11—44no—
366C22×C11—44no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11C24×C411yescharacteristic
370C22×C11C2×H(5,𝔽2)11yescharacteristic
371C22×C11C2×H(5,𝔽2)12yes—
372C22×C11C2×2−1+411yescharacteristic
373C22×C11#58512yes—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—24no—
377C2×D11—24no—
378C2×D11#51814yes—
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—42no—
382C4×C11—44no—
383C4×C11—42no—
384C4×C11#52014yes—
385Dic11—28no—
386Dic11—22no—
387Dic11—22no—
388Dic11—22no—
389Dic11—44no—
390Dic11—42no—
391Dic11—42no—
392C2×#41—1116no—
393C2×#41—448no—
394C22×Q8—112no—
395C22×D4—114no—
396C22×D4C22×D1112yes—
397C22×D4C22×D1112yes—
398C22×D4C22×D1112yes—
399C23×C4—114no—
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—114no—
404C23×C4—114no—
405C23×C4C22×D1114yes—
406C4⋊Q8—118no—
407#127C4×D1118yescomplemented
408#124—1116no—
409#121—1116no—
410#121—1116no—
411C4×D4—44no—
412C4×D4—1116no—
413C4×D4—1116no—
414C4×D4—444no—
415C4×D4—448no—
416C4×D4—448no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—114no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—444no—
426C2×C4⋊C4C22×D1112yes—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—112no—
430C2×C22⋊C4—112no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4C22×D1114yes—
435C2×C22⋊C4C22×D1114yes—
436C2×C22⋊C4C22×D1114yes—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—118no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—114no—
444C2×C42—114no—
445C2×C42C22×D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448#95—114no—
449#95—112no—
450#95—114no—
451#95—112no—
452#95—112no—
453#95—114no—
454#95—114no—
455#95—112no—
456#95—112no—
457#95—112no—
458#95—112no—
459#95—112no—
460#95—114no—
461#95—114no—
462#95C22×D1112yes—
463#95C22×D1112yes—
464#95C22×D1112yes—
465#95C22×D1112yes—
466C2×C11—48no—
467C2×C11C2×#51811yescharacteristic
468C2×C11C2×#52011yescharacteristic
469C2×C11#342811yescharacteristic
470C2×C11#355812yes—
471C2×C11#355912yes—
472D11—24no—
473C24—111no—
474C24C23×D1114yes—
475#41—4432no—
476C2×Q8—118no—
477C2×Q8—444no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—1116no—
483C2×D4—228no—
484C2×D4—228no—
485C2×D4C2×C4×D1118yes—
486C2×D4C2×C4×D1118yes—
487C2×D4C2×C4×D1118yes—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—114no—
495C22×C4—1116no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—114no—
502C22×C4—224no—
503C22×C4—228no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—442no—
507C22×C4—444no—
508C22×C4—444no—
509C22×C4—444no—
510C22×C4—444no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—444no—
514C22×C4C23×D1112yes—
515C22×C4C23×D1114yes—
516C22×C4C23×D1112yes—
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520C4⋊C4—24no—
521C4⋊C4—118no—
522C4⋊C4—118no—
523C4⋊C4—224no—
524C4⋊C4—444no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C22⋊C4—44no—
530C22⋊C4—44no—
531C22⋊C4—44no—
532C22⋊C4—1116no—
533C22⋊C4—1116no—
534C22⋊C4—224no—
535C22⋊C4—224no—
536C22⋊C4—444no—
537C22⋊C4—444no—
538C22⋊C4—444no—
539C42—22no—
540C42—22no—
541C42—114no—
542C42—114no—
543C42—114no—
544C42—222no—
545C42—222no—
546C42—444no—
547C42—444no—
548C42C2×C4×D1114yes—
549C11#3439811yescharacteristic, complemented, Sylow
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—112no—
557C23—114no—
558C23—221no—
559C23—221no—
560C23—222no—
561C23C22×C4×D1118yes—
562C23C24×D1111yescharacteristic
563Q8—448no—
564D4—216no—
565D4—48no—
566D4—48no—
567D4—2232no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—88no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—118no—
584C2×C4—228no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—228no—
592C2×C4—222no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—444no—
602C2×C4—4416no—
603C2×C4—888no—
604C2×C4—888no—
605C2×C4C22×C4×D1112yes—
606C2×C4C22×C4×D1112yes—
607C2×C4C22×C4×D1112yes—
608C2×C4#6703712yes—
609C2×C4#6704312yes—
610C22—28no—
611C22—28no—
612C22—28no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—114no—
618C22—224no—
619C22—222no—
620C22—222no—
621C22—224no—
622C22C23×C4×D1111yescharacteristic
623C22C2×#6703711yescharacteristic
624C22C2×#6704311yescharacteristic
625C22D11×H(5,𝔽2)12yes—
626C22#1062345512yes—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—42no—
631C4—44no—
632C4—222no—
633C4—228no—
634C4—222no—
635C4—222no—
636C4—442no—
637C4—442no—
638C4—444no—
639C4#1062307714yes—
640C2—48no—
641C2—224no—
642C2D11×#51811yescharacteristic
643C2C2×#1062307711yescharacteristic
644C2#1308181411yescharacteristic
645C2#1308313412yes—
646C2#1308314612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2328C2
socle, cosocleC23×C11C25
prime radicalC2×#10623247C2
hypercenter#2328D11
hypocenterC11#34398
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13071786C2semidirect
3. #13071637C2semidirect
4. #13071628C2semidirect
5. #13071588C2semidirect
6. #13071521C2semidirect
7. #13071442C2semidirect
8. #13071364C2semidirect
9. #13071362C2semidirect
10. #13071342C2semidirect
11. #13071318C2semidirect
12. #13071242C2semidirect
13. #13071008C2semidirect
14. D11×#382C2semidirect
15. C11×#2328C2semidirect
26. #10623247C4semidirect
84. C2×#4341C2×C4semidirect
90. C11×#127C2×C4semidirect
104. #66991C2×C4semidirect
105. #66991C2×C4semidirect
106. #66989C2×C4semidirect
108. D4×Dic11C2×C4semidirect
109. D4×Dic11C2×C4semidirect
130. C42×D11C2×C4semidirect
131. #66922C2×C4semidirect
237. #2328D11semidirect
407. #127C4×D11semidirect
549. C11#34398semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130717862
#130716372
#130716282
#130715882
#130715212
#130714422
#130713642
#130713622
#130713422
#130713182
#130712422
#130710082
D11×#3822
C11×#23282
#3439811