Finite Group Databasebeta

← #14912773

Subgroups — #14912773

Order 2816.

2638 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2#13071425C214yesmaximal, complemented
3#13071377C214yesmaximal, complemented
4#13071364C211yesmaximal, characteristic, complemented
5#13071362C211yesmaximal, characteristic, complemented
6#13071342C211yesmaximal, characteristic, complemented
7#13071312C212yesmaximal, complemented
8#13071303C212yesmaximal, complemented
9#13071101C214yesmaximal, complemented
10#13071078C212yesmaximal, complemented
11#13071056C214yesmaximal, complemented
12#13071009C211yesmaximal, characteristic, complemented
13C4×D4×Dic11C212yesmaximal, complemented
14#13070955C211yesmaximal, 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—
25C22×C4×Dic11C2214yes—
26#10623247C4116yescomplemented
27C2×#66930C2214yes—
28C2×#66925C2211yescharacteristic
29C2×#66925C2211yescharacteristic
30C2×C42×D11C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C11×#390C2212yes—
33C11×#386C2214yes—
34C11×#386C2214yes—
35C11×#382C2211yescharacteristic
36C11×#376C2211yescharacteristic
37#10622834C2212yes—
38#10622833C2214yes—
39#10622833C2214yes—
40#10622826C2214yes—
41#10622823C2214yes—
42C4×C22⋊Dic11C2214yes—
43#10622600C2212yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46#10622586C2212yes—
47#10622571C2214yes—
48#10622570C2214yes—
49#10622570C2214yes—
50#10622559C2214yes—
51#10622558C2214yes—
52#10622558C2214yes—
53#10622557C2214yes—
54#10622557C2214yes—
55C22⋊C4×Dic11C2214yes—
56C22⋊C4×Dic11C2214yes—
57C22⋊C4×Dic11C2214yes—
58#10622549C2211yescharacteristic
59C4×C4⋊Dic11C2212yes—
60#10622545C2211yescharacteristic
61C42×Dic11C2211yescharacteristic
62C42×Dic11C2211yescharacteristic
63#10622541C2212yes—
64#10622279C2212yes—
65#10622279C2212yes—
66#10622279C2212yes—
67#10622277C2212yes—
68#10622267C2214yes—
69#10622266C2214yes—
70#10622264C2212yes—
71#10622262C2212yes—
72#10622262C2212yes—
73#10622261C2212yes—
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×D11C2311yescharacteristic
88C22×Dic22C2312yes—
89C11×#127C2×C418yes—
90C4×D4×C11—28no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11C2314yes—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103#66991C2×C4116yescomplemented
104#66991C2×C4116yescomplemented
105#66989C2×C4116yescomplemented
106D4×Dic11—28no—
107D4×Dic11C2×C4116yescomplemented
108D4×Dic11C2×C4116yescomplemented
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11—48no—
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132#66930—48no—
133#66925—24no—
134#66925—24no—
135C42×D11C2×C418yescomplemented
136#66922C2×C418yescomplemented
137C11×#95C2312yes—
138C11×#95C2312yes—
139C11×#95C2312yes—
140C11×#95C2312yes—
141C11⋊#95C2312yes—
142C11⋊#95C2312yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151#34086—111nomaximal, Sylow
152C24×C11C2414yes—
153C23×D11C2411yescharacteristic
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—44no—
157C2×D4×C11—44no—
158C2×D4×C11C22×C418yes—
159C2×D4×C11C22×C418yes—
160C2×D4×C11C22×C418yes—
161C22×C4×C11—28no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2412yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—44no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11C22×C4116yes—
173C22×Dic11—28no—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11—44no—
177C22×Dic11—44no—
178C22×Dic11C22×C4116yes—
179C22×Dic11C2414yes—
180C22×Dic11C2412yes—
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2411yescharacteristic
186#4341—432no—
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—42no—
191C2×C4×D11C22×C414yes—
192C2×C4×D11C22×C414yes—
193C2×C4×D11C22×C414yes—
194C2×Dic22—44no—
195C2×Dic22C22×C418yes—
196C11×C4⋊C4—24no—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—44no—
199C11×C22⋊C4—44no—
200C42×C11—22no—
201C42×C11C22×C414yes—
202C42×C11#4114yescomplemented
203C22⋊Dic11—28no—
204C22⋊Dic11—44no—
205C22⋊Dic11—44no—
206C22⋊Dic11C22×C4116yes—
207C22⋊Dic11C22×C4116yes—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—44no—
211C4⋊Dic11—24no—
212C4⋊Dic11C22×C418yes—
213C4⋊Dic11C22×C418yes—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—44no—
217Dic11⋊C4—44no—
218C4×Dic11—24no—
219C4×Dic11—28no—
220C4×Dic11—24no—
221C4×Dic11—22no—
222C4×Dic11—44no—
223C4×Dic11—44no—
224C4×Dic11—42no—
225C4×Dic11—42no—
226C4×Dic11C22×C414yes—
227C4×Dic11C22×C414yes—
228C4×Dic11C22×C414yes—
229C4×Dic11#4114yescomplemented
230C2×#532—111no—
231#2337—114no—
232#2333—114no—
233#2331—111no—
234#2331—111no—
235#2328—111no—
236#2328D1111yescharacteristic, complemented
237#2324—112no—
238#2324—112no—
239#2297—114no—
240#2293—112no—
241#2290—114no—
242#2283—111no—
243C42×D4—112no—
244C4×#117—111no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11C23×C418yes—
252C23×C11C2511yescharacteristic
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11C23×C412yes—
258D4×C11—216no—
259D4×C11—48no—
260D4×C11—48no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—416no—
272C2×C4×C11C23×C412yes—
273C2×C4×C11C23×C412yes—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4112yes—
278C22⋊D11—416no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—232no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—416no—
294C2×Dic11C23×C412yes—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C418yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C2×#4114yes—
299C2×Dic11H(5,𝔽2)14yes—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—44no—
303Dic22—48no—
304C22×#41—112no—
305#532—1116no—
306C2×C4⋊Q8—111no—
307C2×#127C2×D1111yescharacteristic
308C2×#124—112no—
309C2×#121—112no—
310C2×#121—112no—
311C2×C4×D4—112no—
312C2×C4×D4—112no—
313C2×C4×D4—112no—
314C2×C4×D4C2×D1112yes—
315C2×#117—114no—
316C2×#117—111no—
317C2×#117—111no—
318C22×C42—111no—
319C22×C42—114no—
320#391—114no—
321#391—114no—
322#390—112no—
323#390—114no—
324#390—114no—
325#390C2×D1112yes—
326#389—112no—
327#389—112no—
328#388—114no—
329#388—114no—
330#388—114no—
331#388—114no—
332#387—114no—
333#387—114no—
334#386—114no—
335#386—114no—
336#386—114no—
337#386—114no—
338#386C2×D1114yes—
339#386C2×D1114yes—
340#385—114no—
341#385—114no—
342#383—112no—
343#382—111no—
344#382C2×D1111yescharacteristic
345#381—112no—
346#380—112no—
347C4×C4⋊C4—112no—
348C4×C4⋊C4—112no—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—112no—
351C4×C4⋊C4—112no—
352C4×C22⋊C4—114no—
353C4×C22⋊C4—114no—
354C4×C22⋊C4—114no—
355C4×C22⋊C4—114no—
356C4×C22⋊C4—112no—
357C4×C22⋊C4—112no—
358C4×C22⋊C4—112no—
359#376—111no—
360#376—112no—
361#376C2×D1111yescharacteristic
362C43—111no—
363C43—111no—
364C22×C11—28no—
365C22×C11—28no—
366C22×C11—28no—
367C22×C11—44no—
368C22×C11—44no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11C24×C411yescharacteristic
372C22×C11C22×#4111yescharacteristic
373C22×C11C22×#4111yescharacteristic
374C22×C11C2×H(5,𝔽2)12yes—
375C22×C11#58512yes—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—24no—
384C4×C11—42no—
385C4×C11—44no—
386C4×C11C4×#4114yes—
387Dic11—22no—
388Dic11—28no—
389Dic11—22no—
390Dic11—24no—
391Dic11—42no—
392Dic11—44no—
393Dic11#51814yes—
394C2×#41—1116no—
395C2×#41—448no—
396C22×Q8—112no—
397C22×D4—114no—
398C22×D4C22×D1112yes—
399C22×D4C22×D1112yes—
400C22×D4C22×D1112yes—
401C23×C4—114no—
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—114no—
406C23×C4C22×D1114yes—
407C4⋊Q8—118no—
408#127C4×D1118yes—
409#124—1116no—
410#121—1116no—
411#121—1116no—
412C4×D4—28no—
413C4×D4—1116no—
414C4×D4—1116no—
415C4×D4—228no—
416#117—224no—
417#117—224no—
418#117—448no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4C22×D1112yes—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—112no—
431C2×C22⋊C4—112no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4C22×D1114yes—
436C2×C22⋊C4C22×D1114yes—
437C2×C22⋊C4C22×D1114yes—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—118no—
443C2×C42—112no—
444C2×C42—111no—
445C2×C42—114no—
446C2×C42—112no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42—448no—
452C2×C42C22×D1111yescharacteristic
453C2×C42C22×D1111yescharacteristic
454C2×C42C22×D1111yescharacteristic
455#95—112no—
456#95—112no—
457#95—114no—
458#95—112no—
459#95—114no—
460#95—114no—
461#95—114no—
462#95—112no—
463#95—114no—
464#95—114no—
465#95C22×D1112yes—
466#95C22×D1112yes—
467#95C22×D1112yes—
468#95C22×D1112yes—
469C2×C11—48no—
470C2×C11C2×C4×#4111yescharacteristic
471C2×C11C2×#51811yescharacteristic
472C2×C11#342811yescharacteristic
473C2×C11#346012yes—
474C2×C11#346012yes—
475D11—42no—
476C24—111no—
477C24C23×D1114yes—
478#41—4432no—
479C2×Q8—118no—
480C2×Q8—444no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—1116no—
486C2×D4—444no—
487C2×D4—444no—
488C2×D4C2×C4×D1118yes—
489C2×D4C2×C4×D1118yes—
490C2×D4C2×C4×D1118yes—
491C22×C4—28no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—111no—
495C22×C4—1116no—
496C22×C4—111no—
497C22×C4—112no—
498C22×C4—111no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—112no—
505C22×C4—224no—
506C22×C4—228no—
507C22×C4—228no—
508C22×C4—228no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—442no—
512C22×C4—444no—
513C22×C4—444no—
514C22×C4C23×D1114yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1112yes—
519C22×C4C23×D1111yescharacteristic
520C4⋊C4—24no—
521C4⋊C4—118no—
522C4⋊C4—118no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—444no—
527C4⋊C4—444no—
528C22⋊C4—28no—
529C22⋊C4—44no—
530C22⋊C4—44no—
531C22⋊C4—1116no—
532C22⋊C4—1116no—
533C22⋊C4—224no—
534C22⋊C4—228no—
535C22⋊C4—224no—
536C22⋊C4—444no—
537C22⋊C4—444no—
538C22⋊C4—444no—
539C42—22no—
540C42—114no—
541C42—114no—
542C42—114no—
543C42—114no—
544C42—224no—
545C42—228no—
546C42—224no—
547C42—222no—
548C42—444no—
549C42—444no—
550C42—442no—
551C42—442no—
552C42C2×C4×D1114yes—
553C42#434114yescomplemented
554C11#3408611yescharacteristic, complemented, Sylow
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—112no—
562C23—221no—
563C23—221no—
564C23—222no—
565C23—222no—
566C23C22×C4×D1118yes—
567C23C24×D1111yescharacteristic
568Q8—448no—
569D4—216no—
570D4—48no—
571D4—48no—
572D4—4416no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—416no—
584C2×C4—112no—
585C2×C4—114no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—118no—
589C2×C4—114no—
590C2×C4—228no—
591C2×C4—2232no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—228no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—444no—
607C2×C4—4416no—
608C2×C4C22×C4×D1112yes—
609C2×C4C22×C4×D1112yes—
610C2×C4C22×C4×D1112yes—
611C2×C4C2×#434114yes—
612C2×C4C2×#434112yes—
613C2×C4#41×D1112yes—
614C22—28no—
615C22—28no—
616C22—28no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—222no—
622C22—222no—
623C22—222no—
624C22—442no—
625C22—442no—
626C22C23×C4×D1111yescharacteristic
627C22C22×#434111yescharacteristic
628C22C2×#41×D1111yescharacteristic
629C22D11×H(5,𝔽2)12yes—
630C22#1062345512yes—
631C4—24no—
632C4—22no—
633C4—22no—
634C4—44no—
635C4—42no—
636C4—114no—
637C4—224no—
638C4—222no—
639C4—228no—
640C4—222no—
641C4—442no—
642C4—444no—
643C4C4×#434114yes—
644C2—48no—
645C2—442no—
646C2C2×C4×#434111yescharacteristic
647C2D11×#51811yescharacteristic
648C2#1308181411yescharacteristic
649C2#1308202912yes—
650C2#1308203112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2328C2
socle, cosocleC23×C11C25
prime radicalC2×#10623247C2
hypercenter#2328D11
hypocenterC11#34086
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13071425C2semidirect
3. #13071377C2semidirect
4. #13071364C2semidirect
5. #13071362C2semidirect
6. #13071342C2semidirect
7. #13071312C2semidirect
8. #13071303C2semidirect
9. #13071101C2semidirect
10. #13071078C2semidirect
11. #13071056C2semidirect
12. #13071009C2semidirect
13. C4×D4×Dic11C2semidirect
14. #13070955C2semidirect
15. C11×#2328C2semidirect
26. #10623247C4semidirect
84. C2×#4341C2×C4semidirect
103. #66991C2×C4semidirect
104. #66991C2×C4semidirect
105. #66989C2×C4semidirect
107. D4×Dic11C2×C4semidirect
108. D4×Dic11C2×C4semidirect
135. C42×D11C2×C4semidirect
136. #66922C2×C4semidirect
202. C42×C11#41semidirect
229. C4×Dic11#41semidirect
236. #2328D11semidirect
553. C42#4341semidirect
554. C11#34086semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
#130714252
#130713772
#130713642
#130713622
#130713422
#130713122
#130713032
#130711012
#130710782
#130710562
#130710092
C4×D4×Dic112
#130709552
C11×#23282
#3408611